Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 30.0% → 39.5%

Time: 1.3min

Alternatives: 49

Speedup: 2.6×

• 88.4% 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: 30.0% 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: 39.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot y2 - j \cdot y3\\ t_2 := a \cdot b - c \cdot i\\ t_3 := y \cdot k - t \cdot j\\ t_4 := y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot t\_1\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ t_5 := c \cdot y4 - a \cdot y5\\ t_6 := y3 \cdot \left(y \cdot t\_5 + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ t_7 := c \cdot y0 - a \cdot y1\\ \mathbf{if}\;y4 \leq -1.85 \cdot 10^{+205}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;y4 \leq -4.6 \cdot 10^{+131}:\\ \;\;\;\;x \cdot \left(\left(y \cdot t\_2 + y2 \cdot t\_7\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq -1.4 \cdot 10^{+41}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;y4 \leq -2.8 \cdot 10^{-94}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y4 \leq -1.6 \cdot 10^{-140}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;y4 \leq 5.5 \cdot 10^{-191}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot t\_3 + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 9.4 \cdot 10^{-117}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot \left(c \cdot i - a \cdot b\right) - y3 \cdot t\_7\right)\right)\\ \mathbf{elif}\;y4 \leq 1.38 \cdot 10^{-18}:\\ \;\;\;\;t\_1 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(\left(k \cdot \left(i \cdot y5 - b \cdot y4\right) + x \cdot t\_2\right) + y3 \cdot t\_5\right)\\ \mathbf{elif}\;y4 \leq 9.5 \cdot 10^{+187}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot t\_3 - c \cdot \left(x \cdot y - z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* k y2) (* j y3)))
        (t_2 (- (* a b) (* c i)))
        (t_3 (- (* y k) (* t j)))
        (t_4
         (*
          y4
          (+
           (+ (* b (- (* t j) (* y k))) (* y1 t_1))
           (* c (- (* y y3) (* t y2))))))
        (t_5 (- (* c y4) (* a y5)))
        (t_6
         (*
          y3
          (+
           (* y t_5)
           (+ (* j (- (* y0 y5) (* y1 y4))) (* z (- (* a y1) (* c y0)))))))
        (t_7 (- (* c y0) (* a y1))))
   (if (<= y4 -1.85e+205)
     (* j (* y4 (- (* t b) (* y1 y3))))
     (if (<= y4 -4.6e+131)
       (* x (+ (+ (* y t_2) (* y2 t_7)) (* j (- (* i y1) (* b y0)))))
       (if (<= y4 -1.4e+41)
         t_6
         (if (<= y4 -2.8e-94)
           t_4
           (if (<= y4 -1.6e-140)
             t_6
             (if (<= y4 5.5e-191)
               (*
                y5
                (+
                 (* a (- (* t y2) (* y y3)))
                 (+ (* i t_3) (* y0 (- (* j y3) (* k y2))))))
               (if (<= y4 9.4e-117)
                 (*
                  z
                  (+
                   (* k (- (* b y0) (* i y1)))
                   (- (* t (- (* c i) (* a b))) (* y3 t_7))))
                 (if (<= y4 1.38e-18)
                   (+
                    (* t_1 (- (* y1 y4) (* y0 y5)))
                    (*
                     y
                     (+ (+ (* k (- (* i y5) (* b y4))) (* x t_2)) (* y3 t_5))))
                   (if (<= y4 9.5e+187)
                     (*
                      i
                      (+
                       (* y1 (- (* x j) (* z k)))
                       (- (* y5 t_3) (* c (- (* x y) (* z t))))))
                     t_4)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (k * y2) - (j * y3);
	double t_2 = (a * b) - (c * i);
	double t_3 = (y * k) - (t * j);
	double t_4 = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_1)) + (c * ((y * y3) - (t * y2))));
	double t_5 = (c * y4) - (a * y5);
	double t_6 = y3 * ((y * t_5) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	double t_7 = (c * y0) - (a * y1);
	double tmp;
	if (y4 <= -1.85e+205) {
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	} else if (y4 <= -4.6e+131) {
		tmp = x * (((y * t_2) + (y2 * t_7)) + (j * ((i * y1) - (b * y0))));
	} else if (y4 <= -1.4e+41) {
		tmp = t_6;
	} else if (y4 <= -2.8e-94) {
		tmp = t_4;
	} else if (y4 <= -1.6e-140) {
		tmp = t_6;
	} else if (y4 <= 5.5e-191) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * t_3) + (y0 * ((j * y3) - (k * y2)))));
	} else if (y4 <= 9.4e-117) {
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) - (y3 * t_7)));
	} else if (y4 <= 1.38e-18) {
		tmp = (t_1 * ((y1 * y4) - (y0 * y5))) + (y * (((k * ((i * y5) - (b * y4))) + (x * t_2)) + (y3 * t_5)));
	} else if (y4 <= 9.5e+187) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * t_3) - (c * ((x * y) - (z * t)))));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_1 = (k * y2) - (j * y3)
    t_2 = (a * b) - (c * i)
    t_3 = (y * k) - (t * j)
    t_4 = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_1)) + (c * ((y * y3) - (t * y2))))
    t_5 = (c * y4) - (a * y5)
    t_6 = y3 * ((y * t_5) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))))
    t_7 = (c * y0) - (a * y1)
    if (y4 <= (-1.85d+205)) then
        tmp = j * (y4 * ((t * b) - (y1 * y3)))
    else if (y4 <= (-4.6d+131)) then
        tmp = x * (((y * t_2) + (y2 * t_7)) + (j * ((i * y1) - (b * y0))))
    else if (y4 <= (-1.4d+41)) then
        tmp = t_6
    else if (y4 <= (-2.8d-94)) then
        tmp = t_4
    else if (y4 <= (-1.6d-140)) then
        tmp = t_6
    else if (y4 <= 5.5d-191) then
        tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * t_3) + (y0 * ((j * y3) - (k * y2)))))
    else if (y4 <= 9.4d-117) then
        tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) - (y3 * t_7)))
    else if (y4 <= 1.38d-18) then
        tmp = (t_1 * ((y1 * y4) - (y0 * y5))) + (y * (((k * ((i * y5) - (b * y4))) + (x * t_2)) + (y3 * t_5)))
    else if (y4 <= 9.5d+187) then
        tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * t_3) - (c * ((x * y) - (z * t)))))
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (k * y2) - (j * y3);
	double t_2 = (a * b) - (c * i);
	double t_3 = (y * k) - (t * j);
	double t_4 = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_1)) + (c * ((y * y3) - (t * y2))));
	double t_5 = (c * y4) - (a * y5);
	double t_6 = y3 * ((y * t_5) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	double t_7 = (c * y0) - (a * y1);
	double tmp;
	if (y4 <= -1.85e+205) {
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	} else if (y4 <= -4.6e+131) {
		tmp = x * (((y * t_2) + (y2 * t_7)) + (j * ((i * y1) - (b * y0))));
	} else if (y4 <= -1.4e+41) {
		tmp = t_6;
	} else if (y4 <= -2.8e-94) {
		tmp = t_4;
	} else if (y4 <= -1.6e-140) {
		tmp = t_6;
	} else if (y4 <= 5.5e-191) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * t_3) + (y0 * ((j * y3) - (k * y2)))));
	} else if (y4 <= 9.4e-117) {
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) - (y3 * t_7)));
	} else if (y4 <= 1.38e-18) {
		tmp = (t_1 * ((y1 * y4) - (y0 * y5))) + (y * (((k * ((i * y5) - (b * y4))) + (x * t_2)) + (y3 * t_5)));
	} else if (y4 <= 9.5e+187) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * t_3) - (c * ((x * y) - (z * t)))));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (k * y2) - (j * y3)
	t_2 = (a * b) - (c * i)
	t_3 = (y * k) - (t * j)
	t_4 = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_1)) + (c * ((y * y3) - (t * y2))))
	t_5 = (c * y4) - (a * y5)
	t_6 = y3 * ((y * t_5) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))))
	t_7 = (c * y0) - (a * y1)
	tmp = 0
	if y4 <= -1.85e+205:
		tmp = j * (y4 * ((t * b) - (y1 * y3)))
	elif y4 <= -4.6e+131:
		tmp = x * (((y * t_2) + (y2 * t_7)) + (j * ((i * y1) - (b * y0))))
	elif y4 <= -1.4e+41:
		tmp = t_6
	elif y4 <= -2.8e-94:
		tmp = t_4
	elif y4 <= -1.6e-140:
		tmp = t_6
	elif y4 <= 5.5e-191:
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * t_3) + (y0 * ((j * y3) - (k * y2)))))
	elif y4 <= 9.4e-117:
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) - (y3 * t_7)))
	elif y4 <= 1.38e-18:
		tmp = (t_1 * ((y1 * y4) - (y0 * y5))) + (y * (((k * ((i * y5) - (b * y4))) + (x * t_2)) + (y3 * t_5)))
	elif y4 <= 9.5e+187:
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * t_3) - (c * ((x * y) - (z * t)))))
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(k * y2) - Float64(j * y3))
	t_2 = Float64(Float64(a * b) - Float64(c * i))
	t_3 = Float64(Float64(y * k) - Float64(t * j))
	t_4 = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * t_1)) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))))
	t_5 = Float64(Float64(c * y4) - Float64(a * y5))
	t_6 = Float64(y3 * Float64(Float64(y * t_5) + Float64(Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(z * Float64(Float64(a * y1) - Float64(c * y0))))))
	t_7 = Float64(Float64(c * y0) - Float64(a * y1))
	tmp = 0.0
	if (y4 <= -1.85e+205)
		tmp = Float64(j * Float64(y4 * Float64(Float64(t * b) - Float64(y1 * y3))));
	elseif (y4 <= -4.6e+131)
		tmp = Float64(x * Float64(Float64(Float64(y * t_2) + Float64(y2 * t_7)) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (y4 <= -1.4e+41)
		tmp = t_6;
	elseif (y4 <= -2.8e-94)
		tmp = t_4;
	elseif (y4 <= -1.6e-140)
		tmp = t_6;
	elseif (y4 <= 5.5e-191)
		tmp = Float64(y5 * Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(Float64(i * t_3) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))))));
	elseif (y4 <= 9.4e-117)
		tmp = Float64(z * Float64(Float64(k * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(Float64(t * Float64(Float64(c * i) - Float64(a * b))) - Float64(y3 * t_7))));
	elseif (y4 <= 1.38e-18)
		tmp = Float64(Float64(t_1 * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(y * Float64(Float64(Float64(k * Float64(Float64(i * y5) - Float64(b * y4))) + Float64(x * t_2)) + Float64(y3 * t_5))));
	elseif (y4 <= 9.5e+187)
		tmp = Float64(i * Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) + Float64(Float64(y5 * t_3) - Float64(c * Float64(Float64(x * y) - Float64(z * t))))));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (k * y2) - (j * y3);
	t_2 = (a * b) - (c * i);
	t_3 = (y * k) - (t * j);
	t_4 = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_1)) + (c * ((y * y3) - (t * y2))));
	t_5 = (c * y4) - (a * y5);
	t_6 = y3 * ((y * t_5) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	t_7 = (c * y0) - (a * y1);
	tmp = 0.0;
	if (y4 <= -1.85e+205)
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	elseif (y4 <= -4.6e+131)
		tmp = x * (((y * t_2) + (y2 * t_7)) + (j * ((i * y1) - (b * y0))));
	elseif (y4 <= -1.4e+41)
		tmp = t_6;
	elseif (y4 <= -2.8e-94)
		tmp = t_4;
	elseif (y4 <= -1.6e-140)
		tmp = t_6;
	elseif (y4 <= 5.5e-191)
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * t_3) + (y0 * ((j * y3) - (k * y2)))));
	elseif (y4 <= 9.4e-117)
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) - (y3 * t_7)));
	elseif (y4 <= 1.38e-18)
		tmp = (t_1 * ((y1 * y4) - (y0 * y5))) + (y * (((k * ((i * y5) - (b * y4))) + (x * t_2)) + (y3 * t_5)));
	elseif (y4 <= 9.5e+187)
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * t_3) - (c * ((x * y) - (z * t)))));
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y * k), $MachinePrecision] - N[(t * j), $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 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(y3 * N[(N[(y * t$95$5), $MachinePrecision] + N[(N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -1.85e+205], N[(j * N[(y4 * N[(N[(t * b), $MachinePrecision] - N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -4.6e+131], N[(x * N[(N[(N[(y * t$95$2), $MachinePrecision] + N[(y2 * t$95$7), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -1.4e+41], t$95$6, If[LessEqual[y4, -2.8e-94], t$95$4, If[LessEqual[y4, -1.6e-140], t$95$6, If[LessEqual[y4, 5.5e-191], N[(y5 * N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(i * t$95$3), $MachinePrecision] + N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 9.4e-117], N[(z * N[(N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y3 * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 1.38e-18], N[(N[(t$95$1 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(N[(k * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(y3 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 9.5e+187], N[(i * N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y5 * t$95$3), $MachinePrecision] - N[(c * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y4 < -1.8499999999999999e205

   1. Initial program 20.0%

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

   3. Taylor expanded in y4 around inf 67.1%

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

   4. Taylor expanded in j around -inf 80.0%

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

      1. mul-1-neg 80.0%

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

      2. *-commutative 80.0%

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

      3. distribute-rgt-neg-in 80.0%

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

      4. +-commutative 80.0%

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

      5. mul-1-neg 80.0%

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

      6. unsub-neg 80.0%

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

      7. *-commutative 80.0%

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

   6. Simplified 80.0%

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

   if -1.8499999999999999e205 < y4 < -4.59999999999999983e131

   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%

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

   5. Taylor expanded in x around inf 62.2%

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

   if -4.59999999999999983e131 < y4 < -1.4e41 or -2.7999999999999998e-94 < y4 < -1.6000000000000001e-140

   1. Initial program 21.2%

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

   3. Taylor expanded in y3 around -inf 69.7%

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

   if -1.4e41 < y4 < -2.7999999999999998e-94 or 9.4999999999999996e187 < y4

   1. Initial program 27.0%

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

   3. Taylor expanded in y4 around inf 70.2%

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

   if -1.6000000000000001e-140 < y4 < 5.5000000000000001e-191

   1. Initial program 33.7%

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

   3. Taylor expanded in y5 around -inf 59.0%

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

   if 5.5000000000000001e-191 < y4 < 9.40000000000000017e-117

   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%

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

   5. Taylor expanded in z around -inf 75.4%

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

   if 9.40000000000000017e-117 < y4 < 1.38e-18

   1. Initial program 55.0%

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

   3. Taylor expanded in y around inf 75.0%

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

   if 1.38e-18 < y4 < 9.4999999999999996e187

   1. Initial program 29.4%

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

   3. Simplified 29.4%

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

   5. Taylor expanded in i around -inf 54.4%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -1.85 \cdot 10^{+205}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;y4 \leq -4.6 \cdot 10^{+131}:\\ \;\;\;\;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}\;y4 \leq -1.4 \cdot 10^{+41}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;y4 \leq -2.8 \cdot 10^{-94}:\\ \;\;\;\;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}\;y4 \leq -1.6 \cdot 10^{-140}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 5.5 \cdot 10^{-191}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 9.4 \cdot 10^{-117}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot \left(c \cdot i - a \cdot b\right) - y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 1.38 \cdot 10^{-18}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(\left(k \cdot \left(i \cdot y5 - b \cdot y4\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq 9.5 \cdot 10^{+187}:\\ \;\;\;\;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{else}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 54.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (((((((a * b) - (c * i)) * ((x * y) - (z * t))) + (((b * y0) - (i * y1)) * ((z * k) - (x * j)))) + (((c * y0) - (a * y1)) * ((x * y2) - (z * y3)))) + (((t * j) - (y * k)) * ((b * y4) - (i * y5)))) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4)))) + (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5)))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))))
	return tmp

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 88.3%

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

   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%

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

   3. Taylor expanded in y3 around -inf 45.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.5%

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

Alternative 3: 42.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot y5 - y1 \cdot y4\\ t_2 := y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot t\_1 + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ t_3 := x \cdot y - z \cdot t\\ t_4 := b \cdot \left(\left(a \cdot t\_3 + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ t_5 := y1 \cdot y4 - y0 \cdot y5\\ t_6 := k \cdot \left(\left(y \cdot \left(i \cdot y5 - b \cdot y4\right) + y2 \cdot t\_5\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{if}\;b \leq -3.3 \cdot 10^{+124}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{+79}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot t\_5 + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-68}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) - c \cdot t\_3\right)\right)\\ \mathbf{elif}\;b \leq -1.25 \cdot 10^{-200}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-233}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-282}:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot t\_1 + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{-262}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-204}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 2.55 \cdot 10^{-26}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{+145}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y0 y5) (* y1 y4)))
        (t_2
         (*
          y3
          (+
           (* y (- (* c y4) (* a y5)))
           (+ (* j t_1) (* z (- (* a y1) (* c y0)))))))
        (t_3 (- (* x y) (* z t)))
        (t_4
         (*
          b
          (+
           (+ (* a t_3) (* y4 (- (* t j) (* y k))))
           (* y0 (- (* z k) (* x j))))))
        (t_5 (- (* y1 y4) (* y0 y5)))
        (t_6
         (*
          k
          (+
           (+ (* y (- (* i y5) (* b y4))) (* y2 t_5))
           (* z (- (* b y0) (* i y1)))))))
   (if (<= b -3.3e+124)
     t_4
     (if (<= b -1.35e+79)
       (*
        y2
        (+
         (+ (* k t_5) (* x (- (* c y0) (* a y1))))
         (* t (- (* a y5) (* c y4)))))
       (if (<= b -6.2e-68)
         (*
          i
          (+
           (* y1 (- (* x j) (* z k)))
           (- (* y5 (- (* y k) (* t j))) (* c t_3))))
         (if (<= b -1.25e-200)
           t_2
           (if (<= b -2.8e-233)
             t_6
             (if (<= b 4.5e-282)
               (*
                j
                (+
                 (+ (* y3 t_1) (* t (- (* b y4) (* i y5))))
                 (* x (- (* i y1) (* b y0)))))
               (if (<= b 2.15e-262)
                 (* y4 (* j (- (* t b) (* y1 y3))))
                 (if (<= b 3.2e-204)
                   t_2
                   (if (<= b 2.55e-26)
                     t_6
                     (if (<= b 4.6e+145) t_2 t_4))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y0 * y5) - (y1 * y4);
	double t_2 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_1) + (z * ((a * y1) - (c * y0)))));
	double t_3 = (x * y) - (z * t);
	double t_4 = b * (((a * t_3) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double t_5 = (y1 * y4) - (y0 * y5);
	double t_6 = k * (((y * ((i * y5) - (b * y4))) + (y2 * t_5)) + (z * ((b * y0) - (i * y1))));
	double tmp;
	if (b <= -3.3e+124) {
		tmp = t_4;
	} else if (b <= -1.35e+79) {
		tmp = y2 * (((k * t_5) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else if (b <= -6.2e-68) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * t_3)));
	} else if (b <= -1.25e-200) {
		tmp = t_2;
	} else if (b <= -2.8e-233) {
		tmp = t_6;
	} else if (b <= 4.5e-282) {
		tmp = j * (((y3 * t_1) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))));
	} else if (b <= 2.15e-262) {
		tmp = y4 * (j * ((t * b) - (y1 * y3)));
	} else if (b <= 3.2e-204) {
		tmp = t_2;
	} else if (b <= 2.55e-26) {
		tmp = t_6;
	} else if (b <= 4.6e+145) {
		tmp = t_2;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = (y0 * y5) - (y1 * y4)
    t_2 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_1) + (z * ((a * y1) - (c * y0)))))
    t_3 = (x * y) - (z * t)
    t_4 = b * (((a * t_3) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    t_5 = (y1 * y4) - (y0 * y5)
    t_6 = k * (((y * ((i * y5) - (b * y4))) + (y2 * t_5)) + (z * ((b * y0) - (i * y1))))
    if (b <= (-3.3d+124)) then
        tmp = t_4
    else if (b <= (-1.35d+79)) then
        tmp = y2 * (((k * t_5) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
    else if (b <= (-6.2d-68)) then
        tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * t_3)))
    else if (b <= (-1.25d-200)) then
        tmp = t_2
    else if (b <= (-2.8d-233)) then
        tmp = t_6
    else if (b <= 4.5d-282) then
        tmp = j * (((y3 * t_1) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))))
    else if (b <= 2.15d-262) then
        tmp = y4 * (j * ((t * b) - (y1 * y3)))
    else if (b <= 3.2d-204) then
        tmp = t_2
    else if (b <= 2.55d-26) then
        tmp = t_6
    else if (b <= 4.6d+145) then
        tmp = t_2
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y0 * y5) - (y1 * y4);
	double t_2 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_1) + (z * ((a * y1) - (c * y0)))));
	double t_3 = (x * y) - (z * t);
	double t_4 = b * (((a * t_3) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double t_5 = (y1 * y4) - (y0 * y5);
	double t_6 = k * (((y * ((i * y5) - (b * y4))) + (y2 * t_5)) + (z * ((b * y0) - (i * y1))));
	double tmp;
	if (b <= -3.3e+124) {
		tmp = t_4;
	} else if (b <= -1.35e+79) {
		tmp = y2 * (((k * t_5) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else if (b <= -6.2e-68) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * t_3)));
	} else if (b <= -1.25e-200) {
		tmp = t_2;
	} else if (b <= -2.8e-233) {
		tmp = t_6;
	} else if (b <= 4.5e-282) {
		tmp = j * (((y3 * t_1) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))));
	} else if (b <= 2.15e-262) {
		tmp = y4 * (j * ((t * b) - (y1 * y3)));
	} else if (b <= 3.2e-204) {
		tmp = t_2;
	} else if (b <= 2.55e-26) {
		tmp = t_6;
	} else if (b <= 4.6e+145) {
		tmp = t_2;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y0 * y5) - (y1 * y4)
	t_2 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_1) + (z * ((a * y1) - (c * y0)))))
	t_3 = (x * y) - (z * t)
	t_4 = b * (((a * t_3) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	t_5 = (y1 * y4) - (y0 * y5)
	t_6 = k * (((y * ((i * y5) - (b * y4))) + (y2 * t_5)) + (z * ((b * y0) - (i * y1))))
	tmp = 0
	if b <= -3.3e+124:
		tmp = t_4
	elif b <= -1.35e+79:
		tmp = y2 * (((k * t_5) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
	elif b <= -6.2e-68:
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * t_3)))
	elif b <= -1.25e-200:
		tmp = t_2
	elif b <= -2.8e-233:
		tmp = t_6
	elif b <= 4.5e-282:
		tmp = j * (((y3 * t_1) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))))
	elif b <= 2.15e-262:
		tmp = y4 * (j * ((t * b) - (y1 * y3)))
	elif b <= 3.2e-204:
		tmp = t_2
	elif b <= 2.55e-26:
		tmp = t_6
	elif b <= 4.6e+145:
		tmp = t_2
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y0 * y5) - Float64(y1 * y4))
	t_2 = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(j * t_1) + Float64(z * Float64(Float64(a * y1) - Float64(c * y0))))))
	t_3 = Float64(Float64(x * y) - Float64(z * t))
	t_4 = Float64(b * Float64(Float64(Float64(a * t_3) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))))
	t_5 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_6 = Float64(k * Float64(Float64(Float64(y * Float64(Float64(i * y5) - Float64(b * y4))) + Float64(y2 * t_5)) + Float64(z * Float64(Float64(b * y0) - Float64(i * y1)))))
	tmp = 0.0
	if (b <= -3.3e+124)
		tmp = t_4;
	elseif (b <= -1.35e+79)
		tmp = Float64(y2 * Float64(Float64(Float64(k * t_5) + Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (b <= -6.2e-68)
		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 * t_3))));
	elseif (b <= -1.25e-200)
		tmp = t_2;
	elseif (b <= -2.8e-233)
		tmp = t_6;
	elseif (b <= 4.5e-282)
		tmp = Float64(j * Float64(Float64(Float64(y3 * t_1) + Float64(t * Float64(Float64(b * y4) - Float64(i * y5)))) + Float64(x * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (b <= 2.15e-262)
		tmp = Float64(y4 * Float64(j * Float64(Float64(t * b) - Float64(y1 * y3))));
	elseif (b <= 3.2e-204)
		tmp = t_2;
	elseif (b <= 2.55e-26)
		tmp = t_6;
	elseif (b <= 4.6e+145)
		tmp = t_2;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y0 * y5) - (y1 * y4);
	t_2 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_1) + (z * ((a * y1) - (c * y0)))));
	t_3 = (x * y) - (z * t);
	t_4 = b * (((a * t_3) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	t_5 = (y1 * y4) - (y0 * y5);
	t_6 = k * (((y * ((i * y5) - (b * y4))) + (y2 * t_5)) + (z * ((b * y0) - (i * y1))));
	tmp = 0.0;
	if (b <= -3.3e+124)
		tmp = t_4;
	elseif (b <= -1.35e+79)
		tmp = y2 * (((k * t_5) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	elseif (b <= -6.2e-68)
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * t_3)));
	elseif (b <= -1.25e-200)
		tmp = t_2;
	elseif (b <= -2.8e-233)
		tmp = t_6;
	elseif (b <= 4.5e-282)
		tmp = j * (((y3 * t_1) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))));
	elseif (b <= 2.15e-262)
		tmp = y4 * (j * ((t * b) - (y1 * y3)));
	elseif (b <= 3.2e-204)
		tmp = t_2;
	elseif (b <= 2.55e-26)
		tmp = t_6;
	elseif (b <= 4.6e+145)
		tmp = t_2;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * t$95$1), $MachinePrecision] + N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(b * N[(N[(N[(a * t$95$3), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(k * N[(N[(N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$5), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.3e+124], t$95$4, If[LessEqual[b, -1.35e+79], N[(y2 * N[(N[(N[(k * t$95$5), $MachinePrecision] + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -6.2e-68], 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 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.25e-200], t$95$2, If[LessEqual[b, -2.8e-233], t$95$6, If[LessEqual[b, 4.5e-282], N[(j * N[(N[(N[(y3 * t$95$1), $MachinePrecision] + N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.15e-262], N[(y4 * N[(j * N[(N[(t * b), $MachinePrecision] - N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.2e-204], t$95$2, If[LessEqual[b, 2.55e-26], t$95$6, If[LessEqual[b, 4.6e+145], t$95$2, t$95$4]]]]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -3.30000000000000015e124 or 4.6e145 < b

   1. Initial program 21.0%

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

   3. Simplified 22.4%

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

   5. Taylor expanded in b around inf 66.9%

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

   if -3.30000000000000015e124 < b < -1.35e79

   1. Initial program 11.9%

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

   3. Taylor expanded in y2 around inf 67.3%

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

   if -1.35e79 < b < -6.1999999999999999e-68

   1. Initial program 36.1%

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

   3. Simplified 36.1%

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

   5. Taylor expanded in i around -inf 53.6%

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

   if -6.1999999999999999e-68 < b < -1.24999999999999998e-200 or 2.1500000000000001e-262 < b < 3.2e-204 or 2.54999999999999995e-26 < b < 4.6e145

   1. Initial program 34.9%

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

   3. Taylor expanded in y3 around -inf 63.1%

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

   if -1.24999999999999998e-200 < b < -2.8000000000000001e-233 or 3.2e-204 < b < 2.54999999999999995e-26

   1. Initial program 41.5%

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

   3. Taylor expanded in k around inf 64.8%

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

   if -2.8000000000000001e-233 < b < 4.50000000000000008e-282

   1. Initial program 36.0%

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

   3. Taylor expanded in j around inf 53.0%

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

   if 4.50000000000000008e-282 < b < 2.1500000000000001e-262

   1. Initial program 0.0%

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

   3. Taylor expanded in y4 around inf 66.7%

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

   4. Taylor expanded in j around inf 67.8%

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

      1. +-commutative 67.8%

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

      2. mul-1-neg 67.8%

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

      3. unsub-neg 67.8%

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

      4. *-commutative 67.8%

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

   6. Simplified 67.8%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.3 \cdot 10^{+124}:\\ \;\;\;\;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}\;b \leq -1.35 \cdot 10^{+79}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-68}:\\ \;\;\;\;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}\;b \leq -1.25 \cdot 10^{-200}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-233}:\\ \;\;\;\;k \cdot \left(\left(y \cdot \left(i \cdot y5 - b \cdot y4\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-282}:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{-262}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-204}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;b \leq 2.55 \cdot 10^{-26}:\\ \;\;\;\;k \cdot \left(\left(y \cdot \left(i \cdot y5 - b \cdot y4\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{+145}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;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)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 37.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot y5 - y1 \cdot y4\\ t_2 := z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot \left(c \cdot i - a \cdot b\right) - y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ t_3 := x \cdot y - z \cdot t\\ t_4 := y \cdot y3 - t \cdot y2\\ t_5 := t \cdot y2 - y \cdot y3\\ t_6 := t \cdot j - y \cdot k\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+216}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0 - k \cdot \frac{y \cdot y4}{z}\right)\right)\\ \mathbf{elif}\;y \leq -1 \cdot 10^{+93}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot t\_1 + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{+33}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot t\_4\right)\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-145}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-204}:\\ \;\;\;\;y5 \cdot \left(a \cdot t\_5 + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-247}:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot t\_1 + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-227}:\\ \;\;\;\;b \cdot \left(\left(a \cdot t\_3 + y4 \cdot t\_6\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-73}:\\ \;\;\;\;a \cdot \left(\left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right) + b \cdot t\_3\right) + y5 \cdot t\_5\right)\\ \mathbf{elif}\;y \leq 1.72 \cdot 10^{+159}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot t\_6 + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot t\_4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y0 y5) (* y1 y4)))
        (t_2
         (*
          z
          (+
           (* k (- (* b y0) (* i y1)))
           (- (* t (- (* c i) (* a b))) (* y3 (- (* c y0) (* a y1)))))))
        (t_3 (- (* x y) (* z t)))
        (t_4 (- (* y y3) (* t y2)))
        (t_5 (- (* t y2) (* y y3)))
        (t_6 (- (* t j) (* y k))))
   (if (<= y -3.8e+216)
     (* b (* z (- (* k y0) (* k (/ (* y y4) z)))))
     (if (<= y -1e+93)
       (*
        y3
        (+
         (* y (- (* c y4) (* a y5)))
         (+ (* j t_1) (* z (- (* a y1) (* c y0))))))
       (if (<= y -3.6e+33)
         (*
          c
          (+
           (+ (* i (- (* z t) (* x y))) (* y0 (- (* x y2) (* z y3))))
           (* y4 t_4)))
         (if (<= y -7e-145)
           t_2
           (if (<= y -6e-204)
             (*
              y5
              (+
               (* a t_5)
               (+ (* i (- (* y k) (* t j))) (* y0 (- (* j y3) (* k y2))))))
             (if (<= y 3e-247)
               (*
                j
                (+
                 (+ (* y3 t_1) (* t (- (* b y4) (* i y5))))
                 (* x (- (* i y1) (* b y0)))))
               (if (<= y 1.65e-227)
                 (* b (+ (+ (* a t_3) (* y4 t_6)) (* y0 (- (* z k) (* x j)))))
                 (if (<= y 1.7e-73)
                   (*
                    a
                    (+ (+ (* y1 (- (* z y3) (* x y2))) (* b t_3)) (* y5 t_5)))
                   (if (<= y 1.72e+159)
                     t_2
                     (*
                      y4
                      (+
                       (+ (* b t_6) (* y1 (- (* k y2) (* j y3))))
                       (* c t_4))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y0 * y5) - (y1 * y4);
	double t_2 = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) - (y3 * ((c * y0) - (a * y1)))));
	double t_3 = (x * y) - (z * t);
	double t_4 = (y * y3) - (t * y2);
	double t_5 = (t * y2) - (y * y3);
	double t_6 = (t * j) - (y * k);
	double tmp;
	if (y <= -3.8e+216) {
		tmp = b * (z * ((k * y0) - (k * ((y * y4) / z))));
	} else if (y <= -1e+93) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_1) + (z * ((a * y1) - (c * y0)))));
	} else if (y <= -3.6e+33) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * t_4));
	} else if (y <= -7e-145) {
		tmp = t_2;
	} else if (y <= -6e-204) {
		tmp = y5 * ((a * t_5) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	} else if (y <= 3e-247) {
		tmp = j * (((y3 * t_1) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))));
	} else if (y <= 1.65e-227) {
		tmp = b * (((a * t_3) + (y4 * t_6)) + (y0 * ((z * k) - (x * j))));
	} else if (y <= 1.7e-73) {
		tmp = a * (((y1 * ((z * y3) - (x * y2))) + (b * t_3)) + (y5 * t_5));
	} else if (y <= 1.72e+159) {
		tmp = t_2;
	} else {
		tmp = y4 * (((b * t_6) + (y1 * ((k * y2) - (j * y3)))) + (c * t_4));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = (y0 * y5) - (y1 * y4)
    t_2 = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) - (y3 * ((c * y0) - (a * y1)))))
    t_3 = (x * y) - (z * t)
    t_4 = (y * y3) - (t * y2)
    t_5 = (t * y2) - (y * y3)
    t_6 = (t * j) - (y * k)
    if (y <= (-3.8d+216)) then
        tmp = b * (z * ((k * y0) - (k * ((y * y4) / z))))
    else if (y <= (-1d+93)) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_1) + (z * ((a * y1) - (c * y0)))))
    else if (y <= (-3.6d+33)) then
        tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * t_4))
    else if (y <= (-7d-145)) then
        tmp = t_2
    else if (y <= (-6d-204)) then
        tmp = y5 * ((a * t_5) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))))
    else if (y <= 3d-247) then
        tmp = j * (((y3 * t_1) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))))
    else if (y <= 1.65d-227) then
        tmp = b * (((a * t_3) + (y4 * t_6)) + (y0 * ((z * k) - (x * j))))
    else if (y <= 1.7d-73) then
        tmp = a * (((y1 * ((z * y3) - (x * y2))) + (b * t_3)) + (y5 * t_5))
    else if (y <= 1.72d+159) then
        tmp = t_2
    else
        tmp = y4 * (((b * t_6) + (y1 * ((k * y2) - (j * y3)))) + (c * t_4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y0 * y5) - (y1 * y4);
	double t_2 = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) - (y3 * ((c * y0) - (a * y1)))));
	double t_3 = (x * y) - (z * t);
	double t_4 = (y * y3) - (t * y2);
	double t_5 = (t * y2) - (y * y3);
	double t_6 = (t * j) - (y * k);
	double tmp;
	if (y <= -3.8e+216) {
		tmp = b * (z * ((k * y0) - (k * ((y * y4) / z))));
	} else if (y <= -1e+93) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_1) + (z * ((a * y1) - (c * y0)))));
	} else if (y <= -3.6e+33) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * t_4));
	} else if (y <= -7e-145) {
		tmp = t_2;
	} else if (y <= -6e-204) {
		tmp = y5 * ((a * t_5) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	} else if (y <= 3e-247) {
		tmp = j * (((y3 * t_1) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))));
	} else if (y <= 1.65e-227) {
		tmp = b * (((a * t_3) + (y4 * t_6)) + (y0 * ((z * k) - (x * j))));
	} else if (y <= 1.7e-73) {
		tmp = a * (((y1 * ((z * y3) - (x * y2))) + (b * t_3)) + (y5 * t_5));
	} else if (y <= 1.72e+159) {
		tmp = t_2;
	} else {
		tmp = y4 * (((b * t_6) + (y1 * ((k * y2) - (j * y3)))) + (c * t_4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y0 * y5) - (y1 * y4)
	t_2 = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) - (y3 * ((c * y0) - (a * y1)))))
	t_3 = (x * y) - (z * t)
	t_4 = (y * y3) - (t * y2)
	t_5 = (t * y2) - (y * y3)
	t_6 = (t * j) - (y * k)
	tmp = 0
	if y <= -3.8e+216:
		tmp = b * (z * ((k * y0) - (k * ((y * y4) / z))))
	elif y <= -1e+93:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_1) + (z * ((a * y1) - (c * y0)))))
	elif y <= -3.6e+33:
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * t_4))
	elif y <= -7e-145:
		tmp = t_2
	elif y <= -6e-204:
		tmp = y5 * ((a * t_5) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))))
	elif y <= 3e-247:
		tmp = j * (((y3 * t_1) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))))
	elif y <= 1.65e-227:
		tmp = b * (((a * t_3) + (y4 * t_6)) + (y0 * ((z * k) - (x * j))))
	elif y <= 1.7e-73:
		tmp = a * (((y1 * ((z * y3) - (x * y2))) + (b * t_3)) + (y5 * t_5))
	elif y <= 1.72e+159:
		tmp = t_2
	else:
		tmp = y4 * (((b * t_6) + (y1 * ((k * y2) - (j * y3)))) + (c * t_4))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y0 * y5) - Float64(y1 * y4))
	t_2 = Float64(z * Float64(Float64(k * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(Float64(t * Float64(Float64(c * i) - Float64(a * b))) - Float64(y3 * Float64(Float64(c * y0) - Float64(a * y1))))))
	t_3 = Float64(Float64(x * y) - Float64(z * t))
	t_4 = Float64(Float64(y * y3) - Float64(t * y2))
	t_5 = Float64(Float64(t * y2) - Float64(y * y3))
	t_6 = Float64(Float64(t * j) - Float64(y * k))
	tmp = 0.0
	if (y <= -3.8e+216)
		tmp = Float64(b * Float64(z * Float64(Float64(k * y0) - Float64(k * Float64(Float64(y * y4) / z)))));
	elseif (y <= -1e+93)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(j * t_1) + Float64(z * Float64(Float64(a * y1) - Float64(c * y0))))));
	elseif (y <= -3.6e+33)
		tmp = Float64(c * Float64(Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3)))) + Float64(y4 * t_4)));
	elseif (y <= -7e-145)
		tmp = t_2;
	elseif (y <= -6e-204)
		tmp = Float64(y5 * Float64(Float64(a * t_5) + Float64(Float64(i * Float64(Float64(y * k) - Float64(t * j))) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))))));
	elseif (y <= 3e-247)
		tmp = Float64(j * Float64(Float64(Float64(y3 * t_1) + Float64(t * Float64(Float64(b * y4) - Float64(i * y5)))) + Float64(x * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (y <= 1.65e-227)
		tmp = Float64(b * Float64(Float64(Float64(a * t_3) + Float64(y4 * t_6)) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (y <= 1.7e-73)
		tmp = Float64(a * Float64(Float64(Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))) + Float64(b * t_3)) + Float64(y5 * t_5)));
	elseif (y <= 1.72e+159)
		tmp = t_2;
	else
		tmp = Float64(y4 * Float64(Float64(Float64(b * t_6) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * t_4)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y0 * y5) - (y1 * y4);
	t_2 = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) - (y3 * ((c * y0) - (a * y1)))));
	t_3 = (x * y) - (z * t);
	t_4 = (y * y3) - (t * y2);
	t_5 = (t * y2) - (y * y3);
	t_6 = (t * j) - (y * k);
	tmp = 0.0;
	if (y <= -3.8e+216)
		tmp = b * (z * ((k * y0) - (k * ((y * y4) / z))));
	elseif (y <= -1e+93)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_1) + (z * ((a * y1) - (c * y0)))));
	elseif (y <= -3.6e+33)
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * t_4));
	elseif (y <= -7e-145)
		tmp = t_2;
	elseif (y <= -6e-204)
		tmp = y5 * ((a * t_5) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	elseif (y <= 3e-247)
		tmp = j * (((y3 * t_1) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))));
	elseif (y <= 1.65e-227)
		tmp = b * (((a * t_3) + (y4 * t_6)) + (y0 * ((z * k) - (x * j))));
	elseif (y <= 1.7e-73)
		tmp = a * (((y1 * ((z * y3) - (x * y2))) + (b * t_3)) + (y5 * t_5));
	elseif (y <= 1.72e+159)
		tmp = t_2;
	else
		tmp = y4 * (((b * t_6) + (y1 * ((k * y2) - (j * y3)))) + (c * t_4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y3 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.8e+216], N[(b * N[(z * N[(N[(k * y0), $MachinePrecision] - N[(k * N[(N[(y * y4), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1e+93], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * t$95$1), $MachinePrecision] + N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.6e+33], N[(c * N[(N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7e-145], t$95$2, If[LessEqual[y, -6e-204], N[(y5 * N[(N[(a * t$95$5), $MachinePrecision] + N[(N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3e-247], N[(j * N[(N[(N[(y3 * t$95$1), $MachinePrecision] + N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e-227], N[(b * N[(N[(N[(a * t$95$3), $MachinePrecision] + N[(y4 * t$95$6), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e-73], N[(a * N[(N[(N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(y5 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.72e+159], t$95$2, N[(y4 * N[(N[(N[(b * t$95$6), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y < -3.80000000000000014e216

   1. Initial program 13.6%

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

   3. Simplified 13.6%

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

   5. Taylor expanded in b around inf 54.5%

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

   6. Taylor expanded in k around -inf 68.6%

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

      1. associate-*r* 68.6%

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

      2. neg-mul-1 68.6%

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

   8. Simplified 68.6%

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

   9. Taylor expanded in z around inf 64.0%

      \[\leadsto b \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \frac{k \cdot \left(y \cdot y4\right)}{z} + k \cdot y0\right)\right)} \]
   10. Step-by-step derivation

       1. +-commutative 64.0%

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

       2. mul-1-neg 64.0%

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

       3. unsub-neg 64.0%

          \[\leadsto b \cdot \left(z \cdot \color{blue}{\left(k \cdot y0 - \frac{k \cdot \left(y \cdot y4\right)}{z}\right)}\right) \]

       4. *-commutative 64.0%

          \[\leadsto b \cdot \left(z \cdot \left(\color{blue}{y0 \cdot k} - \frac{k \cdot \left(y \cdot y4\right)}{z}\right)\right) \]

       5. associate-/l* 68.6%

          \[\leadsto b \cdot \left(z \cdot \left(y0 \cdot k - \color{blue}{k \cdot \frac{y \cdot y4}{z}}\right)\right) \]

   11. Simplified 68.6%

       \[\leadsto b \cdot \color{blue}{\left(z \cdot \left(y0 \cdot k - k \cdot \frac{y \cdot y4}{z}\right)\right)} \]

   if -3.80000000000000014e216 < y < -1.00000000000000004e93

   1. Initial program 38.7%

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

   3. Taylor expanded in y3 around -inf 54.3%

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

   if -1.00000000000000004e93 < y < -3.6000000000000003e33

   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 47.1%

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

   5. Taylor expanded in c around inf 70.7%

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

   if -3.6000000000000003e33 < y < -6.99999999999999994e-145 or 1.7000000000000001e-73 < y < 1.72e159

   1. Initial program 31.5%

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

   3. Simplified 31.5%

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

   5. Taylor expanded in z around -inf 61.3%

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

   if -6.99999999999999994e-145 < y < -5.9999999999999997e-204

   1. Initial program 42.2%

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

   3. Taylor expanded in y5 around -inf 58.7%

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

   if -5.9999999999999997e-204 < y < 2.9999999999999997e-247

   1. Initial program 32.2%

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

   3. Taylor expanded in j around inf 52.3%

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

   if 2.9999999999999997e-247 < y < 1.65e-227

   1. Initial program 33.3%

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

   3. Simplified 33.3%

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

   5. Taylor expanded in b around inf 78.1%

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

   if 1.65e-227 < y < 1.7000000000000001e-73

   1. Initial program 34.8%

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

   3. Simplified 34.8%

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

   5. Taylor expanded in a around inf 69.7%

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

   if 1.72e159 < y

   1. Initial program 20.5%

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

   3. Taylor expanded in y4 around inf 52.9%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+216}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0 - k \cdot \frac{y \cdot y4}{z}\right)\right)\\ \mathbf{elif}\;y \leq -1 \cdot 10^{+93}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{+33}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-145}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot \left(c \cdot i - a \cdot b\right) - y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-204}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-247}:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-227}:\\ \;\;\;\;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}\;y \leq 1.7 \cdot 10^{-73}:\\ \;\;\;\;a \cdot \left(\left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right) + b \cdot \left(x \cdot y - z \cdot t\right)\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 1.72 \cdot 10^{+159}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot \left(c \cdot i - a \cdot b\right) - y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 39.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ t_2 := y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ t_3 := y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;y4 \leq -2.9 \cdot 10^{+205}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq -8.2 \cdot 10^{+130}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq -1.38 \cdot 10^{+38}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y4 \leq -6.2 \cdot 10^{-91}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y4 \leq -4.2 \cdot 10^{-142}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y4 \leq 7.5 \cdot 10^{-11}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 3.7 \cdot 10^{+58} \lor \neg \left(y4 \leq 2.3 \cdot 10^{+149}\right):\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* y4 (- (* t b) (* y1 y3)))))
        (t_2
         (*
          y3
          (+
           (* y (- (* c y4) (* a y5)))
           (+ (* j (- (* y0 y5) (* y1 y4))) (* z (- (* a y1) (* c y0)))))))
        (t_3
         (*
          y4
          (+
           (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
           (* c (- (* y y3) (* t y2)))))))
   (if (<= y4 -2.9e+205)
     t_1
     (if (<= y4 -8.2e+130)
       (*
        x
        (+
         (+ (* y (- (* a b) (* c i))) (* y2 (- (* c y0) (* a y1))))
         (* j (- (* i y1) (* b y0)))))
       (if (<= y4 -1.38e+38)
         t_2
         (if (<= y4 -6.2e-91)
           t_3
           (if (<= y4 -4.2e-142)
             t_2
             (if (<= y4 7.5e-11)
               (*
                y5
                (+
                 (* a (- (* t y2) (* y y3)))
                 (+ (* i (- (* y k) (* t j))) (* y0 (- (* j y3) (* k y2))))))
               (if (or (<= y4 3.7e+58) (not (<= y4 2.3e+149))) t_3 t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (y4 * ((t * b) - (y1 * y3)));
	double t_2 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	double t_3 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double tmp;
	if (y4 <= -2.9e+205) {
		tmp = t_1;
	} else if (y4 <= -8.2e+130) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	} else if (y4 <= -1.38e+38) {
		tmp = t_2;
	} else if (y4 <= -6.2e-91) {
		tmp = t_3;
	} else if (y4 <= -4.2e-142) {
		tmp = t_2;
	} else if (y4 <= 7.5e-11) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	} else if ((y4 <= 3.7e+58) || !(y4 <= 2.3e+149)) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * (y4 * ((t * b) - (y1 * y3)))
    t_2 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))))
    t_3 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    if (y4 <= (-2.9d+205)) then
        tmp = t_1
    else if (y4 <= (-8.2d+130)) then
        tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
    else if (y4 <= (-1.38d+38)) then
        tmp = t_2
    else if (y4 <= (-6.2d-91)) then
        tmp = t_3
    else if (y4 <= (-4.2d-142)) then
        tmp = t_2
    else if (y4 <= 7.5d-11) then
        tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))))
    else if ((y4 <= 3.7d+58) .or. (.not. (y4 <= 2.3d+149))) then
        tmp = t_3
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (y4 * ((t * b) - (y1 * y3)));
	double t_2 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	double t_3 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double tmp;
	if (y4 <= -2.9e+205) {
		tmp = t_1;
	} else if (y4 <= -8.2e+130) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	} else if (y4 <= -1.38e+38) {
		tmp = t_2;
	} else if (y4 <= -6.2e-91) {
		tmp = t_3;
	} else if (y4 <= -4.2e-142) {
		tmp = t_2;
	} else if (y4 <= 7.5e-11) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	} else if ((y4 <= 3.7e+58) || !(y4 <= 2.3e+149)) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = j * (y4 * ((t * b) - (y1 * y3)))
	t_2 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))))
	t_3 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	tmp = 0
	if y4 <= -2.9e+205:
		tmp = t_1
	elif y4 <= -8.2e+130:
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
	elif y4 <= -1.38e+38:
		tmp = t_2
	elif y4 <= -6.2e-91:
		tmp = t_3
	elif y4 <= -4.2e-142:
		tmp = t_2
	elif y4 <= 7.5e-11:
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))))
	elif (y4 <= 3.7e+58) or not (y4 <= 2.3e+149):
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(j * Float64(y4 * Float64(Float64(t * b) - Float64(y1 * y3))))
	t_2 = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(z * Float64(Float64(a * y1) - Float64(c * y0))))))
	t_3 = 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 (y4 <= -2.9e+205)
		tmp = t_1;
	elseif (y4 <= -8.2e+130)
		tmp = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (y4 <= -1.38e+38)
		tmp = t_2;
	elseif (y4 <= -6.2e-91)
		tmp = t_3;
	elseif (y4 <= -4.2e-142)
		tmp = t_2;
	elseif (y4 <= 7.5e-11)
		tmp = Float64(y5 * Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(Float64(i * Float64(Float64(y * k) - Float64(t * j))) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))))));
	elseif ((y4 <= 3.7e+58) || !(y4 <= 2.3e+149))
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = j * (y4 * ((t * b) - (y1 * y3)));
	t_2 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	t_3 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	tmp = 0.0;
	if (y4 <= -2.9e+205)
		tmp = t_1;
	elseif (y4 <= -8.2e+130)
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	elseif (y4 <= -1.38e+38)
		tmp = t_2;
	elseif (y4 <= -6.2e-91)
		tmp = t_3;
	elseif (y4 <= -4.2e-142)
		tmp = t_2;
	elseif (y4 <= 7.5e-11)
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	elseif ((y4 <= 3.7e+58) || ~((y4 <= 2.3e+149)))
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(j * N[(y4 * N[(N[(t * b), $MachinePrecision] - N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = 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 * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = 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[y4, -2.9e+205], t$95$1, If[LessEqual[y4, -8.2e+130], 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[y4, -1.38e+38], t$95$2, If[LessEqual[y4, -6.2e-91], t$95$3, If[LessEqual[y4, -4.2e-142], t$95$2, If[LessEqual[y4, 7.5e-11], N[(y5 * N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y4, 3.7e+58], N[Not[LessEqual[y4, 2.3e+149]], $MachinePrecision]], t$95$3, t$95$1]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y4 < -2.9000000000000001e205 or 3.7000000000000002e58 < y4 < 2.2999999999999998e149

   1. Initial program 23.7%

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

   3. Taylor expanded in y4 around inf 36.5%

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

   4. Taylor expanded in j around -inf 62.2%

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

      1. mul-1-neg 62.2%

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

      2. *-commutative 62.2%

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

      3. distribute-rgt-neg-in 62.2%

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

      4. +-commutative 62.2%

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

      5. mul-1-neg 62.2%

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

      6. unsub-neg 62.2%

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

      7. *-commutative 62.2%

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

   6. Simplified 62.2%

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

   if -2.9000000000000001e205 < y4 < -8.19999999999999955e130

   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%

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

   5. Taylor expanded in x around inf 62.2%

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

   if -8.19999999999999955e130 < y4 < -1.3799999999999999e38 or -6.19999999999999962e-91 < y4 < -4.1999999999999999e-142

   1. Initial program 21.2%

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

   3. Taylor expanded in y3 around -inf 69.7%

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

   if -1.3799999999999999e38 < y4 < -6.19999999999999962e-91 or 7.5e-11 < y4 < 3.7000000000000002e58 or 2.2999999999999998e149 < y4

   1. Initial program 29.3%

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

   3. Taylor expanded in y4 around inf 65.5%

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

   if -4.1999999999999999e-142 < y4 < 7.5e-11

   1. Initial program 39.1%

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

   3. Taylor expanded in y5 around -inf 54.3%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -2.9 \cdot 10^{+205}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;y4 \leq -8.2 \cdot 10^{+130}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq -1.38 \cdot 10^{+38}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;y4 \leq -6.2 \cdot 10^{-91}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq -4.2 \cdot 10^{-142}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 7.5 \cdot 10^{-11}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 3.7 \cdot 10^{+58} \lor \neg \left(y4 \leq 2.3 \cdot 10^{+149}\right):\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 42.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ t_2 := k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ t_3 := x \cdot y - z \cdot t\\ t_4 := b \cdot \left(\left(a \cdot t\_3 + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ t_5 := c \cdot y0 - a \cdot y1\\ \mathbf{if}\;b \leq -9.8 \cdot 10^{+122}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{+83}:\\ \;\;\;\;y2 \cdot \left(\left(t\_2 + x \cdot t\_5\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq -8.1 \cdot 10^{-69}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) - c \cdot t\_3\right)\right)\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{-201}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.12 \cdot 10^{-299}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot \left(c \cdot i - a \cdot b\right) - y3 \cdot t\_5\right)\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-203}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-99}:\\ \;\;\;\;y2 \cdot t\_2\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{+145}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          y3
          (+
           (* y (- (* c y4) (* a y5)))
           (+ (* j (- (* y0 y5) (* y1 y4))) (* z (- (* a y1) (* c y0)))))))
        (t_2 (* k (- (* y1 y4) (* y0 y5))))
        (t_3 (- (* x y) (* z t)))
        (t_4
         (*
          b
          (+
           (+ (* a t_3) (* y4 (- (* t j) (* y k))))
           (* y0 (- (* z k) (* x j))))))
        (t_5 (- (* c y0) (* a y1))))
   (if (<= b -9.8e+122)
     t_4
     (if (<= b -2.5e+83)
       (* y2 (+ (+ t_2 (* x t_5)) (* t (- (* a y5) (* c y4)))))
       (if (<= b -8.1e-69)
         (*
          i
          (+
           (* y1 (- (* x j) (* z k)))
           (- (* y5 (- (* y k) (* t j))) (* c t_3))))
         (if (<= b -8.5e-201)
           t_1
           (if (<= b -1.12e-299)
             (*
              z
              (+
               (* k (- (* b y0) (* i y1)))
               (- (* t (- (* c i) (* a b))) (* y3 t_5))))
             (if (<= b 1.15e-203)
               t_1
               (if (<= b 2.5e-99)
                 (* y2 t_2)
                 (if (<= b 4.3e+145) t_1 t_4))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	double t_2 = k * ((y1 * y4) - (y0 * y5));
	double t_3 = (x * y) - (z * t);
	double t_4 = b * (((a * t_3) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double t_5 = (c * y0) - (a * y1);
	double tmp;
	if (b <= -9.8e+122) {
		tmp = t_4;
	} else if (b <= -2.5e+83) {
		tmp = y2 * ((t_2 + (x * t_5)) + (t * ((a * y5) - (c * y4))));
	} else if (b <= -8.1e-69) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * t_3)));
	} else if (b <= -8.5e-201) {
		tmp = t_1;
	} else if (b <= -1.12e-299) {
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) - (y3 * t_5)));
	} else if (b <= 1.15e-203) {
		tmp = t_1;
	} else if (b <= 2.5e-99) {
		tmp = y2 * t_2;
	} else if (b <= 4.3e+145) {
		tmp = t_1;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))))
    t_2 = k * ((y1 * y4) - (y0 * y5))
    t_3 = (x * y) - (z * t)
    t_4 = b * (((a * t_3) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    t_5 = (c * y0) - (a * y1)
    if (b <= (-9.8d+122)) then
        tmp = t_4
    else if (b <= (-2.5d+83)) then
        tmp = y2 * ((t_2 + (x * t_5)) + (t * ((a * y5) - (c * y4))))
    else if (b <= (-8.1d-69)) then
        tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * t_3)))
    else if (b <= (-8.5d-201)) then
        tmp = t_1
    else if (b <= (-1.12d-299)) then
        tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) - (y3 * t_5)))
    else if (b <= 1.15d-203) then
        tmp = t_1
    else if (b <= 2.5d-99) then
        tmp = y2 * t_2
    else if (b <= 4.3d+145) then
        tmp = t_1
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	double t_2 = k * ((y1 * y4) - (y0 * y5));
	double t_3 = (x * y) - (z * t);
	double t_4 = b * (((a * t_3) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double t_5 = (c * y0) - (a * y1);
	double tmp;
	if (b <= -9.8e+122) {
		tmp = t_4;
	} else if (b <= -2.5e+83) {
		tmp = y2 * ((t_2 + (x * t_5)) + (t * ((a * y5) - (c * y4))));
	} else if (b <= -8.1e-69) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * t_3)));
	} else if (b <= -8.5e-201) {
		tmp = t_1;
	} else if (b <= -1.12e-299) {
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) - (y3 * t_5)));
	} else if (b <= 1.15e-203) {
		tmp = t_1;
	} else if (b <= 2.5e-99) {
		tmp = y2 * t_2;
	} else if (b <= 4.3e+145) {
		tmp = t_1;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))))
	t_2 = k * ((y1 * y4) - (y0 * y5))
	t_3 = (x * y) - (z * t)
	t_4 = b * (((a * t_3) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	t_5 = (c * y0) - (a * y1)
	tmp = 0
	if b <= -9.8e+122:
		tmp = t_4
	elif b <= -2.5e+83:
		tmp = y2 * ((t_2 + (x * t_5)) + (t * ((a * y5) - (c * y4))))
	elif b <= -8.1e-69:
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * t_3)))
	elif b <= -8.5e-201:
		tmp = t_1
	elif b <= -1.12e-299:
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) - (y3 * t_5)))
	elif b <= 1.15e-203:
		tmp = t_1
	elif b <= 2.5e-99:
		tmp = y2 * t_2
	elif b <= 4.3e+145:
		tmp = t_1
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(z * Float64(Float64(a * y1) - Float64(c * y0))))))
	t_2 = Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))
	t_3 = Float64(Float64(x * y) - Float64(z * t))
	t_4 = Float64(b * Float64(Float64(Float64(a * t_3) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))))
	t_5 = Float64(Float64(c * y0) - Float64(a * y1))
	tmp = 0.0
	if (b <= -9.8e+122)
		tmp = t_4;
	elseif (b <= -2.5e+83)
		tmp = Float64(y2 * Float64(Float64(t_2 + Float64(x * t_5)) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (b <= -8.1e-69)
		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 * t_3))));
	elseif (b <= -8.5e-201)
		tmp = t_1;
	elseif (b <= -1.12e-299)
		tmp = Float64(z * Float64(Float64(k * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(Float64(t * Float64(Float64(c * i) - Float64(a * b))) - Float64(y3 * t_5))));
	elseif (b <= 1.15e-203)
		tmp = t_1;
	elseif (b <= 2.5e-99)
		tmp = Float64(y2 * t_2);
	elseif (b <= 4.3e+145)
		tmp = t_1;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	t_2 = k * ((y1 * y4) - (y0 * y5));
	t_3 = (x * y) - (z * t);
	t_4 = b * (((a * t_3) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	t_5 = (c * y0) - (a * y1);
	tmp = 0.0;
	if (b <= -9.8e+122)
		tmp = t_4;
	elseif (b <= -2.5e+83)
		tmp = y2 * ((t_2 + (x * t_5)) + (t * ((a * y5) - (c * y4))));
	elseif (b <= -8.1e-69)
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * t_3)));
	elseif (b <= -8.5e-201)
		tmp = t_1;
	elseif (b <= -1.12e-299)
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) - (y3 * t_5)));
	elseif (b <= 1.15e-203)
		tmp = t_1;
	elseif (b <= 2.5e-99)
		tmp = y2 * t_2;
	elseif (b <= 4.3e+145)
		tmp = t_1;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(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 * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(b * N[(N[(N[(a * t$95$3), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9.8e+122], t$95$4, If[LessEqual[b, -2.5e+83], N[(y2 * N[(N[(t$95$2 + N[(x * t$95$5), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -8.1e-69], 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 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -8.5e-201], t$95$1, If[LessEqual[b, -1.12e-299], N[(z * N[(N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y3 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.15e-203], t$95$1, If[LessEqual[b, 2.5e-99], N[(y2 * t$95$2), $MachinePrecision], If[LessEqual[b, 4.3e+145], t$95$1, t$95$4]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -9.7999999999999995e122 or 4.29999999999999998e145 < b

   1. Initial program 21.0%

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

   3. Simplified 22.4%

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

   5. Taylor expanded in b around inf 66.9%

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

   if -9.7999999999999995e122 < b < -2.50000000000000014e83

   1. Initial program 11.9%

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

   3. Taylor expanded in y2 around inf 67.3%

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

   if -2.50000000000000014e83 < b < -8.10000000000000027e-69

   1. Initial program 36.1%

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

   3. Simplified 36.1%

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

   5. Taylor expanded in i around -inf 53.6%

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

   if -8.10000000000000027e-69 < b < -8.5000000000000007e-201 or -1.11999999999999998e-299 < b < 1.14999999999999996e-203 or 2.49999999999999985e-99 < b < 4.29999999999999998e145

   1. Initial program 34.6%

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

   3. Taylor expanded in y3 around -inf 59.6%

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

   if -8.5000000000000007e-201 < b < -1.11999999999999998e-299

   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 43.3%

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

   5. Taylor expanded in z around -inf 50.7%

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

   if 1.14999999999999996e-203 < b < 2.49999999999999985e-99

   1. Initial program 32.4%

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

   3. Taylor expanded in y2 around inf 53.0%

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

   4. Taylor expanded in k around inf 63.9%

      \[\leadsto y2 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.8 \cdot 10^{+122}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{+83}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq -8.1 \cdot 10^{-69}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) - c \cdot \left(x \cdot y - z \cdot t\right)\right)\right)\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{-201}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;b \leq -1.12 \cdot 10^{-299}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot \left(c \cdot i - a \cdot b\right) - y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-203}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-99}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{+145}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 42.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ t_2 := x \cdot y - z \cdot t\\ t_3 := b \cdot \left(\left(a \cdot t\_2 + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ t_4 := y1 \cdot y4 - y0 \cdot y5\\ t_5 := k \cdot t\_4\\ \mathbf{if}\;b \leq -8.8 \cdot 10^{+122}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{+81}:\\ \;\;\;\;y2 \cdot \left(\left(t\_5 + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq -5.9 \cdot 10^{-68}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) - c \cdot t\_2\right)\right)\\ \mathbf{elif}\;b \leq -7 \cdot 10^{-201}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{-230}:\\ \;\;\;\;k \cdot \left(y2 \cdot t\_4\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-205}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-99}:\\ \;\;\;\;y2 \cdot t\_5\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+144}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          y3
          (+
           (* y (- (* c y4) (* a y5)))
           (+ (* j (- (* y0 y5) (* y1 y4))) (* z (- (* a y1) (* c y0)))))))
        (t_2 (- (* x y) (* z t)))
        (t_3
         (*
          b
          (+
           (+ (* a t_2) (* y4 (- (* t j) (* y k))))
           (* y0 (- (* z k) (* x j))))))
        (t_4 (- (* y1 y4) (* y0 y5)))
        (t_5 (* k t_4)))
   (if (<= b -8.8e+122)
     t_3
     (if (<= b -1.6e+81)
       (*
        y2
        (+ (+ t_5 (* x (- (* c y0) (* a y1)))) (* t (- (* a y5) (* c y4)))))
       (if (<= b -5.9e-68)
         (*
          i
          (+
           (* y1 (- (* x j) (* z k)))
           (- (* y5 (- (* y k) (* t j))) (* c t_2))))
         (if (<= b -7e-201)
           t_1
           (if (<= b -4.8e-230)
             (* k (* y2 t_4))
             (if (<= b 7.5e-205)
               t_1
               (if (<= b 2.7e-99)
                 (* y2 t_5)
                 (if (<= b 1.2e+144) t_1 t_3))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	double t_2 = (x * y) - (z * t);
	double t_3 = b * (((a * t_2) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double t_4 = (y1 * y4) - (y0 * y5);
	double t_5 = k * t_4;
	double tmp;
	if (b <= -8.8e+122) {
		tmp = t_3;
	} else if (b <= -1.6e+81) {
		tmp = y2 * ((t_5 + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else if (b <= -5.9e-68) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * t_2)));
	} else if (b <= -7e-201) {
		tmp = t_1;
	} else if (b <= -4.8e-230) {
		tmp = k * (y2 * t_4);
	} else if (b <= 7.5e-205) {
		tmp = t_1;
	} else if (b <= 2.7e-99) {
		tmp = y2 * t_5;
	} else if (b <= 1.2e+144) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))))
    t_2 = (x * y) - (z * t)
    t_3 = b * (((a * t_2) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    t_4 = (y1 * y4) - (y0 * y5)
    t_5 = k * t_4
    if (b <= (-8.8d+122)) then
        tmp = t_3
    else if (b <= (-1.6d+81)) then
        tmp = y2 * ((t_5 + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
    else if (b <= (-5.9d-68)) then
        tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * t_2)))
    else if (b <= (-7d-201)) then
        tmp = t_1
    else if (b <= (-4.8d-230)) then
        tmp = k * (y2 * t_4)
    else if (b <= 7.5d-205) then
        tmp = t_1
    else if (b <= 2.7d-99) then
        tmp = y2 * t_5
    else if (b <= 1.2d+144) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	double t_2 = (x * y) - (z * t);
	double t_3 = b * (((a * t_2) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double t_4 = (y1 * y4) - (y0 * y5);
	double t_5 = k * t_4;
	double tmp;
	if (b <= -8.8e+122) {
		tmp = t_3;
	} else if (b <= -1.6e+81) {
		tmp = y2 * ((t_5 + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else if (b <= -5.9e-68) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * t_2)));
	} else if (b <= -7e-201) {
		tmp = t_1;
	} else if (b <= -4.8e-230) {
		tmp = k * (y2 * t_4);
	} else if (b <= 7.5e-205) {
		tmp = t_1;
	} else if (b <= 2.7e-99) {
		tmp = y2 * t_5;
	} else if (b <= 1.2e+144) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))))
	t_2 = (x * y) - (z * t)
	t_3 = b * (((a * t_2) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	t_4 = (y1 * y4) - (y0 * y5)
	t_5 = k * t_4
	tmp = 0
	if b <= -8.8e+122:
		tmp = t_3
	elif b <= -1.6e+81:
		tmp = y2 * ((t_5 + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
	elif b <= -5.9e-68:
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * t_2)))
	elif b <= -7e-201:
		tmp = t_1
	elif b <= -4.8e-230:
		tmp = k * (y2 * t_4)
	elif b <= 7.5e-205:
		tmp = t_1
	elif b <= 2.7e-99:
		tmp = y2 * t_5
	elif b <= 1.2e+144:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(z * Float64(Float64(a * y1) - Float64(c * y0))))))
	t_2 = Float64(Float64(x * y) - Float64(z * t))
	t_3 = Float64(b * Float64(Float64(Float64(a * t_2) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))))
	t_4 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_5 = Float64(k * t_4)
	tmp = 0.0
	if (b <= -8.8e+122)
		tmp = t_3;
	elseif (b <= -1.6e+81)
		tmp = Float64(y2 * Float64(Float64(t_5 + Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (b <= -5.9e-68)
		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 * t_2))));
	elseif (b <= -7e-201)
		tmp = t_1;
	elseif (b <= -4.8e-230)
		tmp = Float64(k * Float64(y2 * t_4));
	elseif (b <= 7.5e-205)
		tmp = t_1;
	elseif (b <= 2.7e-99)
		tmp = Float64(y2 * t_5);
	elseif (b <= 1.2e+144)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	t_2 = (x * y) - (z * t);
	t_3 = b * (((a * t_2) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	t_4 = (y1 * y4) - (y0 * y5);
	t_5 = k * t_4;
	tmp = 0.0;
	if (b <= -8.8e+122)
		tmp = t_3;
	elseif (b <= -1.6e+81)
		tmp = y2 * ((t_5 + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	elseif (b <= -5.9e-68)
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * t_2)));
	elseif (b <= -7e-201)
		tmp = t_1;
	elseif (b <= -4.8e-230)
		tmp = k * (y2 * t_4);
	elseif (b <= 7.5e-205)
		tmp = t_1;
	elseif (b <= 2.7e-99)
		tmp = y2 * t_5;
	elseif (b <= 1.2e+144)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(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 * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(N[(a * t$95$2), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(k * t$95$4), $MachinePrecision]}, If[LessEqual[b, -8.8e+122], t$95$3, If[LessEqual[b, -1.6e+81], N[(y2 * N[(N[(t$95$5 + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -5.9e-68], 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 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -7e-201], t$95$1, If[LessEqual[b, -4.8e-230], N[(k * N[(y2 * t$95$4), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.5e-205], t$95$1, If[LessEqual[b, 2.7e-99], N[(y2 * t$95$5), $MachinePrecision], If[LessEqual[b, 1.2e+144], t$95$1, t$95$3]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -8.7999999999999997e122 or 1.2e144 < b

   1. Initial program 21.0%

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

   3. Simplified 22.4%

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

   5. Taylor expanded in b around inf 66.9%

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

   if -8.7999999999999997e122 < b < -1.6e81

   1. Initial program 11.9%

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

   3. Taylor expanded in y2 around inf 67.3%

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

   if -1.6e81 < b < -5.9e-68

   1. Initial program 36.1%

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

   3. Simplified 36.1%

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

   5. Taylor expanded in i around -inf 53.6%

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

   if -5.9e-68 < b < -7.00000000000000016e-201 or -4.8000000000000004e-230 < b < 7.4999999999999996e-205 or 2.7e-99 < b < 1.2e144

   1. Initial program 35.8%

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

   3. Taylor expanded in y3 around -inf 56.1%

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

   if -7.00000000000000016e-201 < b < -4.8000000000000004e-230

   1. Initial program 49.7%

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

   3. Taylor expanded in y2 around inf 63.2%

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

   4. Taylor expanded in k around inf 64.1%

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

   if 7.4999999999999996e-205 < b < 2.7e-99

   1. Initial program 32.4%

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

   3. Taylor expanded in y2 around inf 53.0%

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

   4. Taylor expanded in k around inf 63.9%

      \[\leadsto y2 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.8 \cdot 10^{+122}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{+81}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq -5.9 \cdot 10^{-68}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) - c \cdot \left(x \cdot y - z \cdot t\right)\right)\right)\\ \mathbf{elif}\;b \leq -7 \cdot 10^{-201}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{-230}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-205}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-99}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+144}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 31.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(y0 \cdot \left(b \cdot k - c \cdot y3\right)\right)\\ t_2 := y2 \cdot \left(a \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ t_3 := t \cdot j - y \cdot k\\ t_4 := a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{if}\;y0 \leq -3.1 \cdot 10^{+72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y0 \leq -4.6 \cdot 10^{-53}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;y0 \leq -1.8 \cdot 10^{-130}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y0 \leq -6.4 \cdot 10^{-199}:\\ \;\;\;\;b \cdot \left(y4 \cdot t\_3\right)\\ \mathbf{elif}\;y0 \leq -7 \cdot 10^{-206}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;y0 \leq -6.9 \cdot 10^{-243}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y0 \leq 4 \cdot 10^{-285}:\\ \;\;\;\;y4 \cdot \left(b \cdot t\_3\right)\\ \mathbf{elif}\;y0 \leq 2.45 \cdot 10^{-216}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;y0 \leq 3.9 \cdot 10^{-41}:\\ \;\;\;\;i \cdot \left(x \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;y0 \leq 6.5 \cdot 10^{-18}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y0 \leq 5 \cdot 10^{+168}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* z (* y0 (- (* b k) (* c y3)))))
        (t_2 (* y2 (* a (- (* t y5) (* x y1)))))
        (t_3 (- (* t j) (* y k)))
        (t_4 (* a (* y3 (- (* z y1) (* y y5))))))
   (if (<= y0 -3.1e+72)
     t_1
     (if (<= y0 -4.6e-53)
       (* y4 (* k (- (* y1 y2) (* y b))))
       (if (<= y0 -1.8e-130)
         t_4
         (if (<= y0 -6.4e-199)
           (* b (* y4 t_3))
           (if (<= y0 -7e-206)
             (* a (* y (* x b)))
             (if (<= y0 -6.9e-243)
               t_2
               (if (<= y0 4e-285)
                 (* y4 (* b t_3))
                 (if (<= y0 2.45e-216)
                   (* y2 (* y4 (- (* k y1) (* t c))))
                   (if (<= y0 3.9e-41)
                     (* i (* x (- (* j y1) (* y c))))
                     (if (<= y0 6.5e-18)
                       t_4
                       (if (<= y0 5e+168) 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 = z * (y0 * ((b * k) - (c * y3)));
	double t_2 = y2 * (a * ((t * y5) - (x * y1)));
	double t_3 = (t * j) - (y * k);
	double t_4 = a * (y3 * ((z * y1) - (y * y5)));
	double tmp;
	if (y0 <= -3.1e+72) {
		tmp = t_1;
	} else if (y0 <= -4.6e-53) {
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	} else if (y0 <= -1.8e-130) {
		tmp = t_4;
	} else if (y0 <= -6.4e-199) {
		tmp = b * (y4 * t_3);
	} else if (y0 <= -7e-206) {
		tmp = a * (y * (x * b));
	} else if (y0 <= -6.9e-243) {
		tmp = t_2;
	} else if (y0 <= 4e-285) {
		tmp = y4 * (b * t_3);
	} else if (y0 <= 2.45e-216) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (y0 <= 3.9e-41) {
		tmp = i * (x * ((j * y1) - (y * c)));
	} else if (y0 <= 6.5e-18) {
		tmp = t_4;
	} else if (y0 <= 5e+168) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = z * (y0 * ((b * k) - (c * y3)))
    t_2 = y2 * (a * ((t * y5) - (x * y1)))
    t_3 = (t * j) - (y * k)
    t_4 = a * (y3 * ((z * y1) - (y * y5)))
    if (y0 <= (-3.1d+72)) then
        tmp = t_1
    else if (y0 <= (-4.6d-53)) then
        tmp = y4 * (k * ((y1 * y2) - (y * b)))
    else if (y0 <= (-1.8d-130)) then
        tmp = t_4
    else if (y0 <= (-6.4d-199)) then
        tmp = b * (y4 * t_3)
    else if (y0 <= (-7d-206)) then
        tmp = a * (y * (x * b))
    else if (y0 <= (-6.9d-243)) then
        tmp = t_2
    else if (y0 <= 4d-285) then
        tmp = y4 * (b * t_3)
    else if (y0 <= 2.45d-216) then
        tmp = y2 * (y4 * ((k * y1) - (t * c)))
    else if (y0 <= 3.9d-41) then
        tmp = i * (x * ((j * y1) - (y * c)))
    else if (y0 <= 6.5d-18) then
        tmp = t_4
    else if (y0 <= 5d+168) 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 = z * (y0 * ((b * k) - (c * y3)));
	double t_2 = y2 * (a * ((t * y5) - (x * y1)));
	double t_3 = (t * j) - (y * k);
	double t_4 = a * (y3 * ((z * y1) - (y * y5)));
	double tmp;
	if (y0 <= -3.1e+72) {
		tmp = t_1;
	} else if (y0 <= -4.6e-53) {
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	} else if (y0 <= -1.8e-130) {
		tmp = t_4;
	} else if (y0 <= -6.4e-199) {
		tmp = b * (y4 * t_3);
	} else if (y0 <= -7e-206) {
		tmp = a * (y * (x * b));
	} else if (y0 <= -6.9e-243) {
		tmp = t_2;
	} else if (y0 <= 4e-285) {
		tmp = y4 * (b * t_3);
	} else if (y0 <= 2.45e-216) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (y0 <= 3.9e-41) {
		tmp = i * (x * ((j * y1) - (y * c)));
	} else if (y0 <= 6.5e-18) {
		tmp = t_4;
	} else if (y0 <= 5e+168) {
		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 = z * (y0 * ((b * k) - (c * y3)))
	t_2 = y2 * (a * ((t * y5) - (x * y1)))
	t_3 = (t * j) - (y * k)
	t_4 = a * (y3 * ((z * y1) - (y * y5)))
	tmp = 0
	if y0 <= -3.1e+72:
		tmp = t_1
	elif y0 <= -4.6e-53:
		tmp = y4 * (k * ((y1 * y2) - (y * b)))
	elif y0 <= -1.8e-130:
		tmp = t_4
	elif y0 <= -6.4e-199:
		tmp = b * (y4 * t_3)
	elif y0 <= -7e-206:
		tmp = a * (y * (x * b))
	elif y0 <= -6.9e-243:
		tmp = t_2
	elif y0 <= 4e-285:
		tmp = y4 * (b * t_3)
	elif y0 <= 2.45e-216:
		tmp = y2 * (y4 * ((k * y1) - (t * c)))
	elif y0 <= 3.9e-41:
		tmp = i * (x * ((j * y1) - (y * c)))
	elif y0 <= 6.5e-18:
		tmp = t_4
	elif y0 <= 5e+168:
		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(z * Float64(y0 * Float64(Float64(b * k) - Float64(c * y3))))
	t_2 = Float64(y2 * Float64(a * Float64(Float64(t * y5) - Float64(x * y1))))
	t_3 = Float64(Float64(t * j) - Float64(y * k))
	t_4 = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))))
	tmp = 0.0
	if (y0 <= -3.1e+72)
		tmp = t_1;
	elseif (y0 <= -4.6e-53)
		tmp = Float64(y4 * Float64(k * Float64(Float64(y1 * y2) - Float64(y * b))));
	elseif (y0 <= -1.8e-130)
		tmp = t_4;
	elseif (y0 <= -6.4e-199)
		tmp = Float64(b * Float64(y4 * t_3));
	elseif (y0 <= -7e-206)
		tmp = Float64(a * Float64(y * Float64(x * b)));
	elseif (y0 <= -6.9e-243)
		tmp = t_2;
	elseif (y0 <= 4e-285)
		tmp = Float64(y4 * Float64(b * t_3));
	elseif (y0 <= 2.45e-216)
		tmp = Float64(y2 * Float64(y4 * Float64(Float64(k * y1) - Float64(t * c))));
	elseif (y0 <= 3.9e-41)
		tmp = Float64(i * Float64(x * Float64(Float64(j * y1) - Float64(y * c))));
	elseif (y0 <= 6.5e-18)
		tmp = t_4;
	elseif (y0 <= 5e+168)
		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 = z * (y0 * ((b * k) - (c * y3)));
	t_2 = y2 * (a * ((t * y5) - (x * y1)));
	t_3 = (t * j) - (y * k);
	t_4 = a * (y3 * ((z * y1) - (y * y5)));
	tmp = 0.0;
	if (y0 <= -3.1e+72)
		tmp = t_1;
	elseif (y0 <= -4.6e-53)
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	elseif (y0 <= -1.8e-130)
		tmp = t_4;
	elseif (y0 <= -6.4e-199)
		tmp = b * (y4 * t_3);
	elseif (y0 <= -7e-206)
		tmp = a * (y * (x * b));
	elseif (y0 <= -6.9e-243)
		tmp = t_2;
	elseif (y0 <= 4e-285)
		tmp = y4 * (b * t_3);
	elseif (y0 <= 2.45e-216)
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	elseif (y0 <= 3.9e-41)
		tmp = i * (x * ((j * y1) - (y * c)));
	elseif (y0 <= 6.5e-18)
		tmp = t_4;
	elseif (y0 <= 5e+168)
		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[(z * N[(y0 * N[(N[(b * k), $MachinePrecision] - N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y2 * N[(a * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -3.1e+72], t$95$1, If[LessEqual[y0, -4.6e-53], N[(y4 * N[(k * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1.8e-130], t$95$4, If[LessEqual[y0, -6.4e-199], N[(b * N[(y4 * t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -7e-206], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -6.9e-243], t$95$2, If[LessEqual[y0, 4e-285], N[(y4 * N[(b * t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 2.45e-216], N[(y2 * N[(y4 * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 3.9e-41], N[(i * N[(x * N[(N[(j * y1), $MachinePrecision] - N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 6.5e-18], t$95$4, If[LessEqual[y0, 5e+168], t$95$2, t$95$1]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y0 < -3.09999999999999988e72 or 4.99999999999999967e168 < y0

   1. Initial program 24.6%

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

   3. Simplified 25.8%

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

   5. Taylor expanded in z around -inf 50.3%

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

   6. Taylor expanded in y0 around inf 57.5%

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

   if -3.09999999999999988e72 < y0 < -4.6000000000000003e-53

   1. Initial program 33.3%

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

   3. Taylor expanded in y4 around inf 57.2%

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

   4. Taylor expanded in k around inf 58.3%

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

      1. +-commutative 58.3%

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

      2. mul-1-neg 58.3%

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

      3. unsub-neg 58.3%

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

      4. *-commutative 58.3%

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

   6. Simplified 58.3%

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

   if -4.6000000000000003e-53 < y0 < -1.8000000000000001e-130 or 3.89999999999999991e-41 < y0 < 6.50000000000000008e-18

   1. Initial program 29.0%

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

   3. Simplified 29.0%

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

   5. Taylor expanded in a around inf 58.3%

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

   6. Taylor expanded in y3 around inf 75.1%

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

   if -1.8000000000000001e-130 < y0 < -6.3999999999999999e-199

   1. Initial program 40.7%

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

   3. Simplified 40.7%

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

   5. Taylor expanded in b around inf 34.1%

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

   6. Taylor expanded in y4 around inf 47.8%

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

   if -6.3999999999999999e-199 < y0 < -6.99999999999999979e-206

   1. Initial program 50.0%

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

   3. Simplified 50.0%

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

   5. Taylor expanded in a around inf 51.7%

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

   6. Taylor expanded in y around inf 52.8%

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

   7. Taylor expanded in b around inf 51.1%

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

      1. *-commutative 51.1%

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

   9. Simplified 51.1%

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

   10. Taylor expanded in a around 0 51.1%

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

       1. associate-*r* 52.8%

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

   12. Simplified 52.8%

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

   if -6.99999999999999979e-206 < y0 < -6.89999999999999975e-243 or 6.50000000000000008e-18 < y0 < 4.99999999999999967e168

   1. Initial program 34.3%

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

   3. Taylor expanded in y2 around inf 41.6%

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

   4. Taylor expanded in a around -inf 48.9%

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

      1. mul-1-neg 48.9%

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

   6. Simplified 48.9%

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

   if -6.89999999999999975e-243 < y0 < 4.0000000000000003e-285

   1. Initial program 41.7%

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

   3. Taylor expanded in y4 around inf 58.4%

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

   4. Taylor expanded in b around inf 67.0%

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

   if 4.0000000000000003e-285 < y0 < 2.4500000000000001e-216

   1. Initial program 37.8%

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

   3. Taylor expanded in y2 around inf 57.6%

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

   4. Taylor expanded in y4 around inf 58.9%

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

   if 2.4500000000000001e-216 < y0 < 3.89999999999999991e-41

   1. Initial program 31.2%

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

   3. Simplified 31.2%

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

   5. Taylor expanded in i around -inf 47.4%

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

   6. Taylor expanded in x around inf 44.7%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right)\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -3.1 \cdot 10^{+72}:\\ \;\;\;\;z \cdot \left(y0 \cdot \left(b \cdot k - c \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq -4.6 \cdot 10^{-53}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;y0 \leq -1.8 \cdot 10^{-130}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq -6.4 \cdot 10^{-199}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y0 \leq -7 \cdot 10^{-206}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;y0 \leq -6.9 \cdot 10^{-243}:\\ \;\;\;\;y2 \cdot \left(a \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;y0 \leq 4 \cdot 10^{-285}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y0 \leq 2.45 \cdot 10^{-216}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;y0 \leq 3.9 \cdot 10^{-41}:\\ \;\;\;\;i \cdot \left(x \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;y0 \leq 6.5 \cdot 10^{-18}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 5 \cdot 10^{+168}:\\ \;\;\;\;y2 \cdot \left(a \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y0 \cdot \left(b \cdot k - c \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 29.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ t_2 := y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right)\right)\\ t_3 := b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{if}\;y0 \leq -7.8 \cdot 10^{+207}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;y0 \leq -1.7 \cdot 10^{+145}:\\ \;\;\;\;\left(y3 \cdot y4\right) \cdot \left(y \cdot c - j \cdot y1\right)\\ \mathbf{elif}\;y0 \leq -1.2 \cdot 10^{+73}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y0 \leq -1.1 \cdot 10^{-51}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;y0 \leq -3.7 \cdot 10^{-131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y0 \leq 1.75 \cdot 10^{-283}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y0 \leq 8 \cdot 10^{-136}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;y0 \leq 3.45 \cdot 10^{-41}:\\ \;\;\;\;i \cdot \left(y \cdot \left(c \cdot \left(-x\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 2.3 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y0 \leq 2.7 \cdot 10^{+92}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y0 \leq 3.8 \cdot 10^{+196}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y3 (- (* z y1) (* y y5)))))
        (t_2 (* y4 (* b (- (* t j) (* y k)))))
        (t_3 (* b (* y0 (- (* z k) (* x j))))))
   (if (<= y0 -7.8e+207)
     (* x (* y2 (- (* c y0) (* a y1))))
     (if (<= y0 -1.7e+145)
       (* (* y3 y4) (- (* y c) (* j y1)))
       (if (<= y0 -1.2e+73)
         t_3
         (if (<= y0 -1.1e-51)
           (* y4 (* k (- (* y1 y2) (* y b))))
           (if (<= y0 -3.7e-131)
             t_1
             (if (<= y0 1.75e-283)
               t_2
               (if (<= y0 8e-136)
                 (* y2 (* y4 (- (* k y1) (* t c))))
                 (if (<= y0 3.45e-41)
                   (* i (* y (* c (- x))))
                   (if (<= y0 2.3e-15)
                     t_1
                     (if (<= y0 2.7e+92)
                       t_2
                       (if (<= y0 3.8e+196)
                         (* a (* y5 (- (* t y2) (* y y3))))
                         t_3)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y3 * ((z * y1) - (y * y5)));
	double t_2 = y4 * (b * ((t * j) - (y * k)));
	double t_3 = b * (y0 * ((z * k) - (x * j)));
	double tmp;
	if (y0 <= -7.8e+207) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (y0 <= -1.7e+145) {
		tmp = (y3 * y4) * ((y * c) - (j * y1));
	} else if (y0 <= -1.2e+73) {
		tmp = t_3;
	} else if (y0 <= -1.1e-51) {
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	} else if (y0 <= -3.7e-131) {
		tmp = t_1;
	} else if (y0 <= 1.75e-283) {
		tmp = t_2;
	} else if (y0 <= 8e-136) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (y0 <= 3.45e-41) {
		tmp = i * (y * (c * -x));
	} else if (y0 <= 2.3e-15) {
		tmp = t_1;
	} else if (y0 <= 2.7e+92) {
		tmp = t_2;
	} else if (y0 <= 3.8e+196) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a * (y3 * ((z * y1) - (y * y5)))
    t_2 = y4 * (b * ((t * j) - (y * k)))
    t_3 = b * (y0 * ((z * k) - (x * j)))
    if (y0 <= (-7.8d+207)) then
        tmp = x * (y2 * ((c * y0) - (a * y1)))
    else if (y0 <= (-1.7d+145)) then
        tmp = (y3 * y4) * ((y * c) - (j * y1))
    else if (y0 <= (-1.2d+73)) then
        tmp = t_3
    else if (y0 <= (-1.1d-51)) then
        tmp = y4 * (k * ((y1 * y2) - (y * b)))
    else if (y0 <= (-3.7d-131)) then
        tmp = t_1
    else if (y0 <= 1.75d-283) then
        tmp = t_2
    else if (y0 <= 8d-136) then
        tmp = y2 * (y4 * ((k * y1) - (t * c)))
    else if (y0 <= 3.45d-41) then
        tmp = i * (y * (c * -x))
    else if (y0 <= 2.3d-15) then
        tmp = t_1
    else if (y0 <= 2.7d+92) then
        tmp = t_2
    else if (y0 <= 3.8d+196) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y3 * ((z * y1) - (y * y5)));
	double t_2 = y4 * (b * ((t * j) - (y * k)));
	double t_3 = b * (y0 * ((z * k) - (x * j)));
	double tmp;
	if (y0 <= -7.8e+207) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (y0 <= -1.7e+145) {
		tmp = (y3 * y4) * ((y * c) - (j * y1));
	} else if (y0 <= -1.2e+73) {
		tmp = t_3;
	} else if (y0 <= -1.1e-51) {
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	} else if (y0 <= -3.7e-131) {
		tmp = t_1;
	} else if (y0 <= 1.75e-283) {
		tmp = t_2;
	} else if (y0 <= 8e-136) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (y0 <= 3.45e-41) {
		tmp = i * (y * (c * -x));
	} else if (y0 <= 2.3e-15) {
		tmp = t_1;
	} else if (y0 <= 2.7e+92) {
		tmp = t_2;
	} else if (y0 <= 3.8e+196) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y3 * ((z * y1) - (y * y5)))
	t_2 = y4 * (b * ((t * j) - (y * k)))
	t_3 = b * (y0 * ((z * k) - (x * j)))
	tmp = 0
	if y0 <= -7.8e+207:
		tmp = x * (y2 * ((c * y0) - (a * y1)))
	elif y0 <= -1.7e+145:
		tmp = (y3 * y4) * ((y * c) - (j * y1))
	elif y0 <= -1.2e+73:
		tmp = t_3
	elif y0 <= -1.1e-51:
		tmp = y4 * (k * ((y1 * y2) - (y * b)))
	elif y0 <= -3.7e-131:
		tmp = t_1
	elif y0 <= 1.75e-283:
		tmp = t_2
	elif y0 <= 8e-136:
		tmp = y2 * (y4 * ((k * y1) - (t * c)))
	elif y0 <= 3.45e-41:
		tmp = i * (y * (c * -x))
	elif y0 <= 2.3e-15:
		tmp = t_1
	elif y0 <= 2.7e+92:
		tmp = t_2
	elif y0 <= 3.8e+196:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))))
	t_2 = Float64(y4 * Float64(b * Float64(Float64(t * j) - Float64(y * k))))
	t_3 = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))))
	tmp = 0.0
	if (y0 <= -7.8e+207)
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (y0 <= -1.7e+145)
		tmp = Float64(Float64(y3 * y4) * Float64(Float64(y * c) - Float64(j * y1)));
	elseif (y0 <= -1.2e+73)
		tmp = t_3;
	elseif (y0 <= -1.1e-51)
		tmp = Float64(y4 * Float64(k * Float64(Float64(y1 * y2) - Float64(y * b))));
	elseif (y0 <= -3.7e-131)
		tmp = t_1;
	elseif (y0 <= 1.75e-283)
		tmp = t_2;
	elseif (y0 <= 8e-136)
		tmp = Float64(y2 * Float64(y4 * Float64(Float64(k * y1) - Float64(t * c))));
	elseif (y0 <= 3.45e-41)
		tmp = Float64(i * Float64(y * Float64(c * Float64(-x))));
	elseif (y0 <= 2.3e-15)
		tmp = t_1;
	elseif (y0 <= 2.7e+92)
		tmp = t_2;
	elseif (y0 <= 3.8e+196)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y3 * ((z * y1) - (y * y5)));
	t_2 = y4 * (b * ((t * j) - (y * k)));
	t_3 = b * (y0 * ((z * k) - (x * j)));
	tmp = 0.0;
	if (y0 <= -7.8e+207)
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	elseif (y0 <= -1.7e+145)
		tmp = (y3 * y4) * ((y * c) - (j * y1));
	elseif (y0 <= -1.2e+73)
		tmp = t_3;
	elseif (y0 <= -1.1e-51)
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	elseif (y0 <= -3.7e-131)
		tmp = t_1;
	elseif (y0 <= 1.75e-283)
		tmp = t_2;
	elseif (y0 <= 8e-136)
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	elseif (y0 <= 3.45e-41)
		tmp = i * (y * (c * -x));
	elseif (y0 <= 2.3e-15)
		tmp = t_1;
	elseif (y0 <= 2.7e+92)
		tmp = t_2;
	elseif (y0 <= 3.8e+196)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y4 * N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -7.8e+207], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1.7e+145], N[(N[(y3 * y4), $MachinePrecision] * N[(N[(y * c), $MachinePrecision] - N[(j * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1.2e+73], t$95$3, If[LessEqual[y0, -1.1e-51], N[(y4 * N[(k * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -3.7e-131], t$95$1, If[LessEqual[y0, 1.75e-283], t$95$2, If[LessEqual[y0, 8e-136], N[(y2 * N[(y4 * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 3.45e-41], N[(i * N[(y * N[(c * (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 2.3e-15], t$95$1, If[LessEqual[y0, 2.7e+92], t$95$2, If[LessEqual[y0, 3.8e+196], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y0 < -7.79999999999999945e207

   1. Initial program 33.6%

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

   3. Taylor expanded in y2 around inf 48.0%

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

   4. Taylor expanded in x around inf 53.2%

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

   if -7.79999999999999945e207 < y0 < -1.7e145

   1. Initial program 11.4%

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

   3. Taylor expanded in y4 around inf 41.5%

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

   4. Taylor expanded in y3 around inf 70.8%

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

      1. associate-*r* 70.8%

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

      2. neg-mul-1 70.8%

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

      3. associate-*r* 70.8%

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

      4. neg-mul-1 70.8%

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

      5. cancel-sign-sub 70.8%

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

      6. +-commutative 70.8%

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

      7. fma-undefine 70.8%

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

      8. fma-neg 70.8%

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

      9. *-commutative 70.8%

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

   6. Simplified 70.8%

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

   if -1.7e145 < y0 < -1.20000000000000001e73 or 3.8000000000000001e196 < y0

   1. Initial program 29.5%

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

   3. Simplified 31.8%

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

   5. Taylor expanded in b around inf 41.5%

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

   6. Taylor expanded in y0 around inf 52.8%

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

   if -1.20000000000000001e73 < y0 < -1.1e-51

   1. Initial program 33.3%

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

   3. Taylor expanded in y4 around inf 57.2%

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

   4. Taylor expanded in k around inf 58.3%

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

      1. +-commutative 58.3%

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

      2. mul-1-neg 58.3%

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

      3. unsub-neg 58.3%

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

      4. *-commutative 58.3%

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

   6. Simplified 58.3%

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

   if -1.1e-51 < y0 < -3.7000000000000002e-131 or 3.4499999999999999e-41 < y0 < 2.2999999999999999e-15

   1. Initial program 28.1%

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

   3. Simplified 28.1%

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

   5. Taylor expanded in a around inf 59.6%

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

   6. Taylor expanded in y3 around inf 72.7%

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

   if -3.7000000000000002e-131 < y0 < 1.7499999999999999e-283 or 2.2999999999999999e-15 < y0 < 2.6999999999999999e92

   1. Initial program 38.2%

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

   3. Taylor expanded in y4 around inf 44.2%

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

   4. Taylor expanded in b around inf 42.6%

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

   if 1.7499999999999999e-283 < y0 < 8.00000000000000001e-136

   1. Initial program 35.2%

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

   3. Taylor expanded in y2 around inf 43.9%

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

   4. Taylor expanded in y4 around inf 44.6%

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

   if 8.00000000000000001e-136 < y0 < 3.4499999999999999e-41

   1. Initial program 29.4%

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

   3. Simplified 29.4%

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

   5. Taylor expanded in i around -inf 53.7%

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

   6. Taylor expanded in x around inf 42.1%

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

   7. Taylor expanded in c around inf 47.9%

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

      1. associate-*r* 47.9%

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

   9. Simplified 47.9%

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

   if 2.6999999999999999e92 < y0 < 3.8000000000000001e196

   1. Initial program 22.2%

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

   3. Simplified 22.2%

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

   5. Taylor expanded in a around inf 52.2%

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

   6. Taylor expanded in y5 around inf 52.9%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -7.8 \cdot 10^{+207}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;y0 \leq -1.7 \cdot 10^{+145}:\\ \;\;\;\;\left(y3 \cdot y4\right) \cdot \left(y \cdot c - j \cdot y1\right)\\ \mathbf{elif}\;y0 \leq -1.2 \cdot 10^{+73}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -1.1 \cdot 10^{-51}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;y0 \leq -3.7 \cdot 10^{-131}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 1.75 \cdot 10^{-283}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y0 \leq 8 \cdot 10^{-136}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;y0 \leq 3.45 \cdot 10^{-41}:\\ \;\;\;\;i \cdot \left(y \cdot \left(c \cdot \left(-x\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 2.3 \cdot 10^{-15}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 2.7 \cdot 10^{+92}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y0 \leq 3.8 \cdot 10^{+196}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 42.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ t_2 := y1 \cdot y4 - y0 \cdot y5\\ t_3 := x \cdot y - z \cdot t\\ t_4 := b \cdot \left(\left(a \cdot t\_3 + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ t_5 := x \cdot j - z \cdot k\\ \mathbf{if}\;b \leq -1 \cdot 10^{+123}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;b \leq -7 \cdot 10^{+77}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot t\_2 + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq -8.4 \cdot 10^{-78}:\\ \;\;\;\;i \cdot \left(y1 \cdot t\_5 + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) - c \cdot t\_3\right)\right)\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-279}:\\ \;\;\;\;y1 \cdot \left(\left(a \cdot \left(z \cdot y3 - x \cdot y2\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + i \cdot t\_5\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-203}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-40}:\\ \;\;\;\;k \cdot \left(\left(y \cdot \left(i \cdot y5 - b \cdot y4\right) + y2 \cdot t\_2\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+143}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          y3
          (+
           (* y (- (* c y4) (* a y5)))
           (+ (* j (- (* y0 y5) (* y1 y4))) (* z (- (* a y1) (* c y0)))))))
        (t_2 (- (* y1 y4) (* y0 y5)))
        (t_3 (- (* x y) (* z t)))
        (t_4
         (*
          b
          (+
           (+ (* a t_3) (* y4 (- (* t j) (* y k))))
           (* y0 (- (* z k) (* x j))))))
        (t_5 (- (* x j) (* z k))))
   (if (<= b -1e+123)
     t_4
     (if (<= b -7e+77)
       (*
        y2
        (+
         (+ (* k t_2) (* x (- (* c y0) (* a y1))))
         (* t (- (* a y5) (* c y4)))))
       (if (<= b -8.4e-78)
         (* i (+ (* y1 t_5) (- (* y5 (- (* y k) (* t j))) (* c t_3))))
         (if (<= b -2.3e-279)
           (*
            y1
            (+
             (+ (* a (- (* z y3) (* x y2))) (* y4 (- (* k y2) (* j y3))))
             (* i t_5)))
           (if (<= b 1.5e-203)
             t_1
             (if (<= b 4.4e-40)
               (*
                k
                (+
                 (+ (* y (- (* i y5) (* b y4))) (* y2 t_2))
                 (* z (- (* b y0) (* i y1)))))
               (if (<= b 2.8e+143) t_1 t_4)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	double t_2 = (y1 * y4) - (y0 * y5);
	double t_3 = (x * y) - (z * t);
	double t_4 = b * (((a * t_3) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double t_5 = (x * j) - (z * k);
	double tmp;
	if (b <= -1e+123) {
		tmp = t_4;
	} else if (b <= -7e+77) {
		tmp = y2 * (((k * t_2) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else if (b <= -8.4e-78) {
		tmp = i * ((y1 * t_5) + ((y5 * ((y * k) - (t * j))) - (c * t_3)));
	} else if (b <= -2.3e-279) {
		tmp = y1 * (((a * ((z * y3) - (x * y2))) + (y4 * ((k * y2) - (j * y3)))) + (i * t_5));
	} else if (b <= 1.5e-203) {
		tmp = t_1;
	} else if (b <= 4.4e-40) {
		tmp = k * (((y * ((i * y5) - (b * y4))) + (y2 * t_2)) + (z * ((b * y0) - (i * y1))));
	} else if (b <= 2.8e+143) {
		tmp = t_1;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))))
    t_2 = (y1 * y4) - (y0 * y5)
    t_3 = (x * y) - (z * t)
    t_4 = b * (((a * t_3) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    t_5 = (x * j) - (z * k)
    if (b <= (-1d+123)) then
        tmp = t_4
    else if (b <= (-7d+77)) then
        tmp = y2 * (((k * t_2) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
    else if (b <= (-8.4d-78)) then
        tmp = i * ((y1 * t_5) + ((y5 * ((y * k) - (t * j))) - (c * t_3)))
    else if (b <= (-2.3d-279)) then
        tmp = y1 * (((a * ((z * y3) - (x * y2))) + (y4 * ((k * y2) - (j * y3)))) + (i * t_5))
    else if (b <= 1.5d-203) then
        tmp = t_1
    else if (b <= 4.4d-40) then
        tmp = k * (((y * ((i * y5) - (b * y4))) + (y2 * t_2)) + (z * ((b * y0) - (i * y1))))
    else if (b <= 2.8d+143) then
        tmp = t_1
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	double t_2 = (y1 * y4) - (y0 * y5);
	double t_3 = (x * y) - (z * t);
	double t_4 = b * (((a * t_3) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double t_5 = (x * j) - (z * k);
	double tmp;
	if (b <= -1e+123) {
		tmp = t_4;
	} else if (b <= -7e+77) {
		tmp = y2 * (((k * t_2) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else if (b <= -8.4e-78) {
		tmp = i * ((y1 * t_5) + ((y5 * ((y * k) - (t * j))) - (c * t_3)));
	} else if (b <= -2.3e-279) {
		tmp = y1 * (((a * ((z * y3) - (x * y2))) + (y4 * ((k * y2) - (j * y3)))) + (i * t_5));
	} else if (b <= 1.5e-203) {
		tmp = t_1;
	} else if (b <= 4.4e-40) {
		tmp = k * (((y * ((i * y5) - (b * y4))) + (y2 * t_2)) + (z * ((b * y0) - (i * y1))));
	} else if (b <= 2.8e+143) {
		tmp = t_1;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))))
	t_2 = (y1 * y4) - (y0 * y5)
	t_3 = (x * y) - (z * t)
	t_4 = b * (((a * t_3) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	t_5 = (x * j) - (z * k)
	tmp = 0
	if b <= -1e+123:
		tmp = t_4
	elif b <= -7e+77:
		tmp = y2 * (((k * t_2) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
	elif b <= -8.4e-78:
		tmp = i * ((y1 * t_5) + ((y5 * ((y * k) - (t * j))) - (c * t_3)))
	elif b <= -2.3e-279:
		tmp = y1 * (((a * ((z * y3) - (x * y2))) + (y4 * ((k * y2) - (j * y3)))) + (i * t_5))
	elif b <= 1.5e-203:
		tmp = t_1
	elif b <= 4.4e-40:
		tmp = k * (((y * ((i * y5) - (b * y4))) + (y2 * t_2)) + (z * ((b * y0) - (i * y1))))
	elif b <= 2.8e+143:
		tmp = t_1
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(z * Float64(Float64(a * y1) - Float64(c * y0))))))
	t_2 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_3 = Float64(Float64(x * y) - Float64(z * t))
	t_4 = Float64(b * Float64(Float64(Float64(a * t_3) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))))
	t_5 = Float64(Float64(x * j) - Float64(z * k))
	tmp = 0.0
	if (b <= -1e+123)
		tmp = t_4;
	elseif (b <= -7e+77)
		tmp = Float64(y2 * Float64(Float64(Float64(k * t_2) + Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (b <= -8.4e-78)
		tmp = Float64(i * Float64(Float64(y1 * t_5) + Float64(Float64(y5 * Float64(Float64(y * k) - Float64(t * j))) - Float64(c * t_3))));
	elseif (b <= -2.3e-279)
		tmp = Float64(y1 * Float64(Float64(Float64(a * Float64(Float64(z * y3) - Float64(x * y2))) + Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(i * t_5)));
	elseif (b <= 1.5e-203)
		tmp = t_1;
	elseif (b <= 4.4e-40)
		tmp = Float64(k * Float64(Float64(Float64(y * Float64(Float64(i * y5) - Float64(b * y4))) + Float64(y2 * t_2)) + Float64(z * Float64(Float64(b * y0) - Float64(i * y1)))));
	elseif (b <= 2.8e+143)
		tmp = t_1;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	t_2 = (y1 * y4) - (y0 * y5);
	t_3 = (x * y) - (z * t);
	t_4 = b * (((a * t_3) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	t_5 = (x * j) - (z * k);
	tmp = 0.0;
	if (b <= -1e+123)
		tmp = t_4;
	elseif (b <= -7e+77)
		tmp = y2 * (((k * t_2) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	elseif (b <= -8.4e-78)
		tmp = i * ((y1 * t_5) + ((y5 * ((y * k) - (t * j))) - (c * t_3)));
	elseif (b <= -2.3e-279)
		tmp = y1 * (((a * ((z * y3) - (x * y2))) + (y4 * ((k * y2) - (j * y3)))) + (i * t_5));
	elseif (b <= 1.5e-203)
		tmp = t_1;
	elseif (b <= 4.4e-40)
		tmp = k * (((y * ((i * y5) - (b * y4))) + (y2 * t_2)) + (z * ((b * y0) - (i * y1))));
	elseif (b <= 2.8e+143)
		tmp = t_1;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(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 * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(b * N[(N[(N[(a * t$95$3), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1e+123], t$95$4, If[LessEqual[b, -7e+77], N[(y2 * N[(N[(N[(k * t$95$2), $MachinePrecision] + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -8.4e-78], N[(i * N[(N[(y1 * t$95$5), $MachinePrecision] + N[(N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.3e-279], N[(y1 * N[(N[(N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.5e-203], t$95$1, If[LessEqual[b, 4.4e-40], N[(k * N[(N[(N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.8e+143], t$95$1, t$95$4]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -9.99999999999999978e122 or 2.79999999999999998e143 < b

   1. Initial program 21.0%

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

   3. Simplified 22.4%

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

   5. Taylor expanded in b around inf 66.9%

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

   if -9.99999999999999978e122 < b < -7.0000000000000003e77

   1. Initial program 11.9%

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

   3. Taylor expanded in y2 around inf 67.3%

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

   if -7.0000000000000003e77 < b < -8.4000000000000002e-78

   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%

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

   5. Taylor expanded in i around -inf 50.8%

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

   if -8.4000000000000002e-78 < b < -2.29999999999999995e-279

   1. Initial program 46.1%

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

   3. Taylor expanded in y1 around inf 64.6%

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

   if -2.29999999999999995e-279 < b < 1.5000000000000001e-203 or 4.40000000000000018e-40 < b < 2.79999999999999998e143

   1. Initial program 29.6%

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

   3. Taylor expanded in y3 around -inf 56.5%

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

   if 1.5000000000000001e-203 < b < 4.40000000000000018e-40

   1. Initial program 37.4%

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

   3. Taylor expanded in k around inf 60.6%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+123}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -7 \cdot 10^{+77}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq -8.4 \cdot 10^{-78}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) - c \cdot \left(x \cdot y - z \cdot t\right)\right)\right)\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-279}:\\ \;\;\;\;y1 \cdot \left(\left(a \cdot \left(z \cdot y3 - x \cdot y2\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-203}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-40}:\\ \;\;\;\;k \cdot \left(\left(y \cdot \left(i \cdot y5 - b \cdot y4\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+143}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 32.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y0 \cdot y3\right) \cdot \left(j \cdot y5 - z \cdot c\right)\\ \mathbf{if}\;k \leq -70000000:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;k \leq -4.8 \cdot 10^{-95}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;k \leq -1.05 \cdot 10^{-248}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq 2.06 \cdot 10^{-305}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq 2.8 \cdot 10^{-294}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 8.2 \cdot 10^{-211}:\\ \;\;\;\;\left(z \cdot y3\right) \cdot \left(a \cdot y1 - c \cdot y0\right)\\ \mathbf{elif}\;k \leq 1.1 \cdot 10^{-167}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq 9.5 \cdot 10^{-75}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;k \leq 2.9 \cdot 10^{+21}:\\ \;\;\;\;\left(y3 \cdot y4\right) \cdot \left(y \cdot c - j \cdot y1\right)\\ \mathbf{elif}\;k \leq 2.1 \cdot 10^{+167}:\\ \;\;\;\;y2 \cdot \left(y0 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* y0 y3) (- (* j y5) (* z c)))))
   (if (<= k -70000000.0)
     (* y4 (* k (- (* y1 y2) (* y b))))
     (if (<= k -4.8e-95)
       (* i (* y5 (- (* y k) (* t j))))
       (if (<= k -1.05e-248)
         (* a (* y5 (- (* t y2) (* y y3))))
         (if (<= k 2.06e-305)
           t_1
           (if (<= k 2.8e-294)
             (* a (* y (- (* x b) (* y3 y5))))
             (if (<= k 8.2e-211)
               (* (* z y3) (- (* a y1) (* c y0)))
               (if (<= k 1.1e-167)
                 t_1
                 (if (<= k 9.5e-75)
                   (* c (* i (- (* z t) (* x y))))
                   (if (<= k 2.9e+21)
                     (* (* y3 y4) (- (* y c) (* j y1)))
                     (if (<= k 2.1e+167)
                       (* y2 (* y0 (- (* x c) (* k y5))))
                       (* b (* k (- (* z y0) (* y y4))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y0 * y3) * ((j * y5) - (z * c));
	double tmp;
	if (k <= -70000000.0) {
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	} else if (k <= -4.8e-95) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (k <= -1.05e-248) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (k <= 2.06e-305) {
		tmp = t_1;
	} else if (k <= 2.8e-294) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (k <= 8.2e-211) {
		tmp = (z * y3) * ((a * y1) - (c * y0));
	} else if (k <= 1.1e-167) {
		tmp = t_1;
	} else if (k <= 9.5e-75) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (k <= 2.9e+21) {
		tmp = (y3 * y4) * ((y * c) - (j * y1));
	} else if (k <= 2.1e+167) {
		tmp = y2 * (y0 * ((x * c) - (k * y5)));
	} else {
		tmp = b * (k * ((z * y0) - (y * y4)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y0 * y3) * ((j * y5) - (z * c))
    if (k <= (-70000000.0d0)) then
        tmp = y4 * (k * ((y1 * y2) - (y * b)))
    else if (k <= (-4.8d-95)) then
        tmp = i * (y5 * ((y * k) - (t * j)))
    else if (k <= (-1.05d-248)) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else if (k <= 2.06d-305) then
        tmp = t_1
    else if (k <= 2.8d-294) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (k <= 8.2d-211) then
        tmp = (z * y3) * ((a * y1) - (c * y0))
    else if (k <= 1.1d-167) then
        tmp = t_1
    else if (k <= 9.5d-75) then
        tmp = c * (i * ((z * t) - (x * y)))
    else if (k <= 2.9d+21) then
        tmp = (y3 * y4) * ((y * c) - (j * y1))
    else if (k <= 2.1d+167) then
        tmp = y2 * (y0 * ((x * c) - (k * y5)))
    else
        tmp = b * (k * ((z * y0) - (y * y4)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y0 * y3) * ((j * y5) - (z * c));
	double tmp;
	if (k <= -70000000.0) {
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	} else if (k <= -4.8e-95) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (k <= -1.05e-248) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (k <= 2.06e-305) {
		tmp = t_1;
	} else if (k <= 2.8e-294) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (k <= 8.2e-211) {
		tmp = (z * y3) * ((a * y1) - (c * y0));
	} else if (k <= 1.1e-167) {
		tmp = t_1;
	} else if (k <= 9.5e-75) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (k <= 2.9e+21) {
		tmp = (y3 * y4) * ((y * c) - (j * y1));
	} else if (k <= 2.1e+167) {
		tmp = y2 * (y0 * ((x * c) - (k * y5)));
	} else {
		tmp = b * (k * ((z * y0) - (y * y4)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y0 * y3) * ((j * y5) - (z * c))
	tmp = 0
	if k <= -70000000.0:
		tmp = y4 * (k * ((y1 * y2) - (y * b)))
	elif k <= -4.8e-95:
		tmp = i * (y5 * ((y * k) - (t * j)))
	elif k <= -1.05e-248:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	elif k <= 2.06e-305:
		tmp = t_1
	elif k <= 2.8e-294:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif k <= 8.2e-211:
		tmp = (z * y3) * ((a * y1) - (c * y0))
	elif k <= 1.1e-167:
		tmp = t_1
	elif k <= 9.5e-75:
		tmp = c * (i * ((z * t) - (x * y)))
	elif k <= 2.9e+21:
		tmp = (y3 * y4) * ((y * c) - (j * y1))
	elif k <= 2.1e+167:
		tmp = y2 * (y0 * ((x * c) - (k * y5)))
	else:
		tmp = b * (k * ((z * y0) - (y * y4)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y0 * y3) * Float64(Float64(j * y5) - Float64(z * c)))
	tmp = 0.0
	if (k <= -70000000.0)
		tmp = Float64(y4 * Float64(k * Float64(Float64(y1 * y2) - Float64(y * b))));
	elseif (k <= -4.8e-95)
		tmp = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))));
	elseif (k <= -1.05e-248)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (k <= 2.06e-305)
		tmp = t_1;
	elseif (k <= 2.8e-294)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (k <= 8.2e-211)
		tmp = Float64(Float64(z * y3) * Float64(Float64(a * y1) - Float64(c * y0)));
	elseif (k <= 1.1e-167)
		tmp = t_1;
	elseif (k <= 9.5e-75)
		tmp = Float64(c * Float64(i * Float64(Float64(z * t) - Float64(x * y))));
	elseif (k <= 2.9e+21)
		tmp = Float64(Float64(y3 * y4) * Float64(Float64(y * c) - Float64(j * y1)));
	elseif (k <= 2.1e+167)
		tmp = Float64(y2 * Float64(y0 * Float64(Float64(x * c) - Float64(k * y5))));
	else
		tmp = Float64(b * Float64(k * Float64(Float64(z * y0) - Float64(y * y4))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y0 * y3) * ((j * y5) - (z * c));
	tmp = 0.0;
	if (k <= -70000000.0)
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	elseif (k <= -4.8e-95)
		tmp = i * (y5 * ((y * k) - (t * j)));
	elseif (k <= -1.05e-248)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	elseif (k <= 2.06e-305)
		tmp = t_1;
	elseif (k <= 2.8e-294)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (k <= 8.2e-211)
		tmp = (z * y3) * ((a * y1) - (c * y0));
	elseif (k <= 1.1e-167)
		tmp = t_1;
	elseif (k <= 9.5e-75)
		tmp = c * (i * ((z * t) - (x * y)));
	elseif (k <= 2.9e+21)
		tmp = (y3 * y4) * ((y * c) - (j * y1));
	elseif (k <= 2.1e+167)
		tmp = y2 * (y0 * ((x * c) - (k * y5)));
	else
		tmp = b * (k * ((z * y0) - (y * y4)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y0 * y3), $MachinePrecision] * N[(N[(j * y5), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -70000000.0], N[(y4 * N[(k * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -4.8e-95], N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -1.05e-248], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.06e-305], t$95$1, If[LessEqual[k, 2.8e-294], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 8.2e-211], N[(N[(z * y3), $MachinePrecision] * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.1e-167], t$95$1, If[LessEqual[k, 9.5e-75], N[(c * N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.9e+21], N[(N[(y3 * y4), $MachinePrecision] * N[(N[(y * c), $MachinePrecision] - N[(j * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.1e+167], N[(y2 * N[(y0 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if k < -7e7

   1. Initial program 24.5%

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

   3. Taylor expanded in y4 around inf 46.4%

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

   4. Taylor expanded in k around inf 50.8%

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

      1. +-commutative 50.8%

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

      2. mul-1-neg 50.8%

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

      3. unsub-neg 50.8%

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

      4. *-commutative 50.8%

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

   6. Simplified 50.8%

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

   if -7e7 < k < -4.8e-95

   1. Initial program 47.5%

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

   3. Simplified 47.5%

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

   5. Taylor expanded in i around -inf 57.7%

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

   6. Taylor expanded in y5 around inf 43.6%

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

   if -4.8e-95 < k < -1.05e-248

   1. Initial program 47.5%

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

   3. Simplified 47.5%

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

   5. Taylor expanded in a around inf 50.7%

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

   6. Taylor expanded in y5 around inf 39.1%

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

   if -1.05e-248 < k < 2.0600000000000001e-305 or 8.2000000000000005e-211 < k < 1.1e-167

   1. Initial program 21.9%

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

   3. Taylor expanded in y3 around -inf 53.6%

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

   4. Taylor expanded in y0 around inf 53.9%

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

      1. associate-*r* 63.9%

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

      2. +-commutative 63.9%

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

      3. mul-1-neg 63.9%

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

      4. unsub-neg 63.9%

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

      5. *-commutative 63.9%

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

      6. *-commutative 63.9%

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

   6. Simplified 63.9%

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

   if 2.0600000000000001e-305 < k < 2.79999999999999991e-294

   1. Initial program 50.0%

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

   3. Simplified 50.0%

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

   5. Taylor expanded in a around inf 76.3%

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

   6. Taylor expanded in y around inf 76.3%

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

   if 2.79999999999999991e-294 < k < 8.2000000000000005e-211

   1. Initial program 40.0%

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

   3. Simplified 40.0%

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

   5. Taylor expanded in z around -inf 60.8%

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

   6. Taylor expanded in y3 around inf 48.0%

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

      1. associate-*r* 54.1%

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

      2. neg-mul-1 54.1%

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

      3. +-commutative 54.1%

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

      4. sub-neg 54.1%

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

   8. Simplified 54.1%

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

   if 1.1e-167 < k < 9.4999999999999991e-75

   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%

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

   5. Taylor expanded in i around -inf 53.2%

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

   6. Taylor expanded in c around inf 53.4%

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

   if 9.4999999999999991e-75 < k < 2.9e21

   1. Initial program 18.2%

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

   3. Taylor expanded in y4 around inf 36.4%

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

   4. Taylor expanded in y3 around inf 65.1%

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

      1. associate-*r* 59.9%

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

      2. neg-mul-1 59.9%

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

      3. associate-*r* 59.9%

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

      4. neg-mul-1 59.9%

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

      5. cancel-sign-sub 59.9%

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

      6. +-commutative 59.9%

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

      7. fma-undefine 59.9%

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

      8. fma-neg 59.9%

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

      9. *-commutative 59.9%

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

   6. Simplified 59.9%

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

   if 2.9e21 < k < 2.0999999999999999e167

   1. Initial program 35.7%

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

   3. Taylor expanded in y2 around inf 50.3%

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

   4. Taylor expanded in y0 around inf 68.4%

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

   if 2.0999999999999999e167 < k

   1. Initial program 14.8%

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

   3. Simplified 14.8%

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

   5. Taylor expanded in b around inf 44.6%

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

   6. Taylor expanded in k around -inf 71.0%

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

      1. associate-*r* 71.0%

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

      2. neg-mul-1 71.0%

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

   8. Simplified 71.0%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -70000000:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;k \leq -4.8 \cdot 10^{-95}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;k \leq -1.05 \cdot 10^{-248}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq 2.06 \cdot 10^{-305}:\\ \;\;\;\;\left(y0 \cdot y3\right) \cdot \left(j \cdot y5 - z \cdot c\right)\\ \mathbf{elif}\;k \leq 2.8 \cdot 10^{-294}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 8.2 \cdot 10^{-211}:\\ \;\;\;\;\left(z \cdot y3\right) \cdot \left(a \cdot y1 - c \cdot y0\right)\\ \mathbf{elif}\;k \leq 1.1 \cdot 10^{-167}:\\ \;\;\;\;\left(y0 \cdot y3\right) \cdot \left(j \cdot y5 - z \cdot c\right)\\ \mathbf{elif}\;k \leq 9.5 \cdot 10^{-75}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;k \leq 2.9 \cdot 10^{+21}:\\ \;\;\;\;\left(y3 \cdot y4\right) \cdot \left(y \cdot c - j \cdot y1\right)\\ \mathbf{elif}\;k \leq 2.1 \cdot 10^{+167}:\\ \;\;\;\;y2 \cdot \left(y0 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 32.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot y0 - y \cdot y4\\ t_2 := a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{if}\;k \leq -25000000:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;k \leq -4.8 \cdot 10^{-95}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;k \leq -3.2 \cdot 10^{-242}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq 3.9 \cdot 10^{-305}:\\ \;\;\;\;\left(y0 \cdot y3\right) \cdot \left(j \cdot y5 - z \cdot c\right)\\ \mathbf{elif}\;k \leq 2.8 \cdot 10^{-294}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 6 \cdot 10^{-155}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;k \leq 4.5 \cdot 10^{-151}:\\ \;\;\;\;\left(b \cdot k\right) \cdot t\_1\\ \mathbf{elif}\;k \leq 2 \cdot 10^{-53}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;k \leq 4.5 \cdot 10^{+19}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;k \leq 1.6 \cdot 10^{+172}:\\ \;\;\;\;y2 \cdot \left(y0 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(k \cdot t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* z y0) (* y y4))) (t_2 (* a (* y1 (- (* z y3) (* x y2))))))
   (if (<= k -25000000.0)
     (* y4 (* k (- (* y1 y2) (* y b))))
     (if (<= k -4.8e-95)
       (* i (* y5 (- (* y k) (* t j))))
       (if (<= k -3.2e-242)
         (* a (* y5 (- (* t y2) (* y y3))))
         (if (<= k 3.9e-305)
           (* (* y0 y3) (- (* j y5) (* z c)))
           (if (<= k 2.8e-294)
             (* a (* y (- (* x b) (* y3 y5))))
             (if (<= k 6e-155)
               t_2
               (if (<= k 4.5e-151)
                 (* (* b k) t_1)
                 (if (<= k 2e-53)
                   (* x (* y2 (- (* c y0) (* a y1))))
                   (if (<= k 4.5e+19)
                     t_2
                     (if (<= k 1.6e+172)
                       (* y2 (* y0 (- (* x c) (* k y5))))
                       (* b (* k 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 * y0) - (y * y4);
	double t_2 = a * (y1 * ((z * y3) - (x * y2)));
	double tmp;
	if (k <= -25000000.0) {
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	} else if (k <= -4.8e-95) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (k <= -3.2e-242) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (k <= 3.9e-305) {
		tmp = (y0 * y3) * ((j * y5) - (z * c));
	} else if (k <= 2.8e-294) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (k <= 6e-155) {
		tmp = t_2;
	} else if (k <= 4.5e-151) {
		tmp = (b * k) * t_1;
	} else if (k <= 2e-53) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (k <= 4.5e+19) {
		tmp = t_2;
	} else if (k <= 1.6e+172) {
		tmp = y2 * (y0 * ((x * c) - (k * y5)));
	} else {
		tmp = b * (k * 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 = (z * y0) - (y * y4)
    t_2 = a * (y1 * ((z * y3) - (x * y2)))
    if (k <= (-25000000.0d0)) then
        tmp = y4 * (k * ((y1 * y2) - (y * b)))
    else if (k <= (-4.8d-95)) then
        tmp = i * (y5 * ((y * k) - (t * j)))
    else if (k <= (-3.2d-242)) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else if (k <= 3.9d-305) then
        tmp = (y0 * y3) * ((j * y5) - (z * c))
    else if (k <= 2.8d-294) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (k <= 6d-155) then
        tmp = t_2
    else if (k <= 4.5d-151) then
        tmp = (b * k) * t_1
    else if (k <= 2d-53) then
        tmp = x * (y2 * ((c * y0) - (a * y1)))
    else if (k <= 4.5d+19) then
        tmp = t_2
    else if (k <= 1.6d+172) then
        tmp = y2 * (y0 * ((x * c) - (k * y5)))
    else
        tmp = b * (k * 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 = (z * y0) - (y * y4);
	double t_2 = a * (y1 * ((z * y3) - (x * y2)));
	double tmp;
	if (k <= -25000000.0) {
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	} else if (k <= -4.8e-95) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (k <= -3.2e-242) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (k <= 3.9e-305) {
		tmp = (y0 * y3) * ((j * y5) - (z * c));
	} else if (k <= 2.8e-294) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (k <= 6e-155) {
		tmp = t_2;
	} else if (k <= 4.5e-151) {
		tmp = (b * k) * t_1;
	} else if (k <= 2e-53) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (k <= 4.5e+19) {
		tmp = t_2;
	} else if (k <= 1.6e+172) {
		tmp = y2 * (y0 * ((x * c) - (k * y5)));
	} else {
		tmp = b * (k * 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 * y0) - (y * y4)
	t_2 = a * (y1 * ((z * y3) - (x * y2)))
	tmp = 0
	if k <= -25000000.0:
		tmp = y4 * (k * ((y1 * y2) - (y * b)))
	elif k <= -4.8e-95:
		tmp = i * (y5 * ((y * k) - (t * j)))
	elif k <= -3.2e-242:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	elif k <= 3.9e-305:
		tmp = (y0 * y3) * ((j * y5) - (z * c))
	elif k <= 2.8e-294:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif k <= 6e-155:
		tmp = t_2
	elif k <= 4.5e-151:
		tmp = (b * k) * t_1
	elif k <= 2e-53:
		tmp = x * (y2 * ((c * y0) - (a * y1)))
	elif k <= 4.5e+19:
		tmp = t_2
	elif k <= 1.6e+172:
		tmp = y2 * (y0 * ((x * c) - (k * y5)))
	else:
		tmp = b * (k * 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 * y0) - Float64(y * y4))
	t_2 = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))))
	tmp = 0.0
	if (k <= -25000000.0)
		tmp = Float64(y4 * Float64(k * Float64(Float64(y1 * y2) - Float64(y * b))));
	elseif (k <= -4.8e-95)
		tmp = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))));
	elseif (k <= -3.2e-242)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (k <= 3.9e-305)
		tmp = Float64(Float64(y0 * y3) * Float64(Float64(j * y5) - Float64(z * c)));
	elseif (k <= 2.8e-294)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (k <= 6e-155)
		tmp = t_2;
	elseif (k <= 4.5e-151)
		tmp = Float64(Float64(b * k) * t_1);
	elseif (k <= 2e-53)
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (k <= 4.5e+19)
		tmp = t_2;
	elseif (k <= 1.6e+172)
		tmp = Float64(y2 * Float64(y0 * Float64(Float64(x * c) - Float64(k * y5))));
	else
		tmp = Float64(b * Float64(k * 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 * y0) - (y * y4);
	t_2 = a * (y1 * ((z * y3) - (x * y2)));
	tmp = 0.0;
	if (k <= -25000000.0)
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	elseif (k <= -4.8e-95)
		tmp = i * (y5 * ((y * k) - (t * j)));
	elseif (k <= -3.2e-242)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	elseif (k <= 3.9e-305)
		tmp = (y0 * y3) * ((j * y5) - (z * c));
	elseif (k <= 2.8e-294)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (k <= 6e-155)
		tmp = t_2;
	elseif (k <= 4.5e-151)
		tmp = (b * k) * t_1;
	elseif (k <= 2e-53)
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	elseif (k <= 4.5e+19)
		tmp = t_2;
	elseif (k <= 1.6e+172)
		tmp = y2 * (y0 * ((x * c) - (k * y5)));
	else
		tmp = b * (k * 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 * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -25000000.0], N[(y4 * N[(k * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -4.8e-95], N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -3.2e-242], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 3.9e-305], N[(N[(y0 * y3), $MachinePrecision] * N[(N[(j * y5), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.8e-294], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 6e-155], t$95$2, If[LessEqual[k, 4.5e-151], N[(N[(b * k), $MachinePrecision] * t$95$1), $MachinePrecision], If[LessEqual[k, 2e-53], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 4.5e+19], t$95$2, If[LessEqual[k, 1.6e+172], N[(y2 * N[(y0 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(k * t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if k < -2.5e7

   1. Initial program 24.5%

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

   3. Taylor expanded in y4 around inf 46.4%

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

   4. Taylor expanded in k around inf 50.8%

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

      1. +-commutative 50.8%

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

      2. mul-1-neg 50.8%

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

      3. unsub-neg 50.8%

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

      4. *-commutative 50.8%

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

   6. Simplified 50.8%

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

   if -2.5e7 < k < -4.8e-95

   1. Initial program 47.5%

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

   3. Simplified 47.5%

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

   5. Taylor expanded in i around -inf 57.7%

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

   6. Taylor expanded in y5 around inf 43.6%

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

   if -4.8e-95 < k < -3.19999999999999999e-242

   1. Initial program 47.5%

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

   3. Simplified 47.5%

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

   5. Taylor expanded in a around inf 50.7%

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

   6. Taylor expanded in y5 around inf 39.1%

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

   if -3.19999999999999999e-242 < k < 3.90000000000000025e-305

   1. Initial program 29.7%

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

   3. Taylor expanded in y3 around -inf 51.4%

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

   4. Taylor expanded in y0 around inf 51.1%

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

      1. associate-*r* 57.9%

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

      2. +-commutative 57.9%

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

      3. mul-1-neg 57.9%

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

      4. unsub-neg 57.9%

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

      5. *-commutative 57.9%

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

      6. *-commutative 57.9%

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

   6. Simplified 57.9%

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

   if 3.90000000000000025e-305 < k < 2.79999999999999991e-294

   1. Initial program 50.0%

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

   3. Simplified 50.0%

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

   5. Taylor expanded in a around inf 76.3%

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

   6. Taylor expanded in y around inf 76.3%

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

   if 2.79999999999999991e-294 < k < 5.99999999999999967e-155 or 2.00000000000000006e-53 < k < 4.5e19

   1. Initial program 27.4%

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

   3. Simplified 27.4%

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

   5. Taylor expanded in a around inf 55.4%

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

   6. Taylor expanded in y1 around inf 58.1%

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

      1. mul-1-neg 58.1%

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

   8. Simplified 58.1%

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

   if 5.99999999999999967e-155 < k < 4.5000000000000002e-151

   1. Initial program 50.0%

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

   3. Simplified 50.0%

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

   5. Taylor expanded in b around inf 100.0%

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

   6. Taylor expanded in k around -inf 100.0%

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

      1. associate-*r* 100.0%

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

      2. neg-mul-1 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in b around 0 100.0%

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

       1. mul-1-neg 100.0%

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

       2. associate-*r* 100.0%

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

       3. *-commutative 100.0%

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

   11. Simplified 100.0%

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

   if 4.5000000000000002e-151 < k < 2.00000000000000006e-53

   1. Initial program 28.1%

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

   3. Taylor expanded in y2 around inf 58.1%

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

   4. Taylor expanded in x around inf 51.4%

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

   if 4.5e19 < k < 1.59999999999999993e172

   1. Initial program 34.4%

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

   3. Taylor expanded in y2 around inf 48.6%

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

   4. Taylor expanded in y0 around inf 66.2%

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

   if 1.59999999999999993e172 < k

   1. Initial program 14.8%

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

   3. Simplified 14.8%

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

   5. Taylor expanded in b around inf 44.6%

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

   6. Taylor expanded in k around -inf 71.0%

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

      1. associate-*r* 71.0%

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

      2. neg-mul-1 71.0%

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

   8. Simplified 71.0%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -25000000:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;k \leq -4.8 \cdot 10^{-95}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;k \leq -3.2 \cdot 10^{-242}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq 3.9 \cdot 10^{-305}:\\ \;\;\;\;\left(y0 \cdot y3\right) \cdot \left(j \cdot y5 - z \cdot c\right)\\ \mathbf{elif}\;k \leq 2.8 \cdot 10^{-294}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 6 \cdot 10^{-155}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 4.5 \cdot 10^{-151}:\\ \;\;\;\;\left(b \cdot k\right) \cdot \left(z \cdot y0 - y \cdot y4\right)\\ \mathbf{elif}\;k \leq 2 \cdot 10^{-53}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;k \leq 4.5 \cdot 10^{+19}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 1.6 \cdot 10^{+172}:\\ \;\;\;\;y2 \cdot \left(y0 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 29.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(x \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ t_2 := \left(b \cdot k\right) \cdot \left(z \cdot y0 - y \cdot y4\right)\\ \mathbf{if}\;i \leq -3.6 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -1.6 \cdot 10^{-142}:\\ \;\;\;\;\left(y3 \cdot y4\right) \cdot \left(y \cdot c - j \cdot y1\right)\\ \mathbf{elif}\;i \leq -3.65 \cdot 10^{-205}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq -3.8 \cdot 10^{-247}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -1.05 \cdot 10^{-290}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;i \leq 3.2 \cdot 10^{-296}:\\ \;\;\;\;y2 \cdot \left(a \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;i \leq 1.35 \cdot 10^{-255}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;i \leq 4.4 \cdot 10^{-124}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq 3.6 \cdot 10^{-22}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{+200}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* x (- (* j y1) (* y c)))))
        (t_2 (* (* b k) (- (* z y0) (* y y4)))))
   (if (<= i -3.6e+40)
     t_1
     (if (<= i -1.6e-142)
       (* (* y3 y4) (- (* y c) (* j y1)))
       (if (<= i -3.65e-205)
         (* b (* x (- (* y a) (* j y0))))
         (if (<= i -3.8e-247)
           t_2
           (if (<= i -1.05e-290)
             (* a (* y (- (* x b) (* y3 y5))))
             (if (<= i 3.2e-296)
               (* y2 (* a (- (* t y5) (* x y1))))
               (if (<= i 1.35e-255)
                 (* a (* y3 (- (* z y1) (* y y5))))
                 (if (<= i 4.4e-124)
                   (* c (* y2 (- (* x y0) (* t y4))))
                   (if (<= i 3.6e-22)
                     (* k (* y2 (- (* y1 y4) (* y0 y5))))
                     (if (<= i 4.8e+200) 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 = i * (x * ((j * y1) - (y * c)));
	double t_2 = (b * k) * ((z * y0) - (y * y4));
	double tmp;
	if (i <= -3.6e+40) {
		tmp = t_1;
	} else if (i <= -1.6e-142) {
		tmp = (y3 * y4) * ((y * c) - (j * y1));
	} else if (i <= -3.65e-205) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (i <= -3.8e-247) {
		tmp = t_2;
	} else if (i <= -1.05e-290) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (i <= 3.2e-296) {
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	} else if (i <= 1.35e-255) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (i <= 4.4e-124) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (i <= 3.6e-22) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (i <= 4.8e+200) {
		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 = i * (x * ((j * y1) - (y * c)))
    t_2 = (b * k) * ((z * y0) - (y * y4))
    if (i <= (-3.6d+40)) then
        tmp = t_1
    else if (i <= (-1.6d-142)) then
        tmp = (y3 * y4) * ((y * c) - (j * y1))
    else if (i <= (-3.65d-205)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (i <= (-3.8d-247)) then
        tmp = t_2
    else if (i <= (-1.05d-290)) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (i <= 3.2d-296) then
        tmp = y2 * (a * ((t * y5) - (x * y1)))
    else if (i <= 1.35d-255) then
        tmp = a * (y3 * ((z * y1) - (y * y5)))
    else if (i <= 4.4d-124) then
        tmp = c * (y2 * ((x * y0) - (t * y4)))
    else if (i <= 3.6d-22) then
        tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
    else if (i <= 4.8d+200) 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 = i * (x * ((j * y1) - (y * c)));
	double t_2 = (b * k) * ((z * y0) - (y * y4));
	double tmp;
	if (i <= -3.6e+40) {
		tmp = t_1;
	} else if (i <= -1.6e-142) {
		tmp = (y3 * y4) * ((y * c) - (j * y1));
	} else if (i <= -3.65e-205) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (i <= -3.8e-247) {
		tmp = t_2;
	} else if (i <= -1.05e-290) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (i <= 3.2e-296) {
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	} else if (i <= 1.35e-255) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (i <= 4.4e-124) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (i <= 3.6e-22) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (i <= 4.8e+200) {
		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 = i * (x * ((j * y1) - (y * c)))
	t_2 = (b * k) * ((z * y0) - (y * y4))
	tmp = 0
	if i <= -3.6e+40:
		tmp = t_1
	elif i <= -1.6e-142:
		tmp = (y3 * y4) * ((y * c) - (j * y1))
	elif i <= -3.65e-205:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif i <= -3.8e-247:
		tmp = t_2
	elif i <= -1.05e-290:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif i <= 3.2e-296:
		tmp = y2 * (a * ((t * y5) - (x * y1)))
	elif i <= 1.35e-255:
		tmp = a * (y3 * ((z * y1) - (y * y5)))
	elif i <= 4.4e-124:
		tmp = c * (y2 * ((x * y0) - (t * y4)))
	elif i <= 3.6e-22:
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
	elif i <= 4.8e+200:
		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(i * Float64(x * Float64(Float64(j * y1) - Float64(y * c))))
	t_2 = Float64(Float64(b * k) * Float64(Float64(z * y0) - Float64(y * y4)))
	tmp = 0.0
	if (i <= -3.6e+40)
		tmp = t_1;
	elseif (i <= -1.6e-142)
		tmp = Float64(Float64(y3 * y4) * Float64(Float64(y * c) - Float64(j * y1)));
	elseif (i <= -3.65e-205)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (i <= -3.8e-247)
		tmp = t_2;
	elseif (i <= -1.05e-290)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (i <= 3.2e-296)
		tmp = Float64(y2 * Float64(a * Float64(Float64(t * y5) - Float64(x * y1))));
	elseif (i <= 1.35e-255)
		tmp = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))));
	elseif (i <= 4.4e-124)
		tmp = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))));
	elseif (i <= 3.6e-22)
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	elseif (i <= 4.8e+200)
		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 = i * (x * ((j * y1) - (y * c)));
	t_2 = (b * k) * ((z * y0) - (y * y4));
	tmp = 0.0;
	if (i <= -3.6e+40)
		tmp = t_1;
	elseif (i <= -1.6e-142)
		tmp = (y3 * y4) * ((y * c) - (j * y1));
	elseif (i <= -3.65e-205)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (i <= -3.8e-247)
		tmp = t_2;
	elseif (i <= -1.05e-290)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (i <= 3.2e-296)
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	elseif (i <= 1.35e-255)
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	elseif (i <= 4.4e-124)
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	elseif (i <= 3.6e-22)
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	elseif (i <= 4.8e+200)
		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[(i * N[(x * N[(N[(j * y1), $MachinePrecision] - N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * k), $MachinePrecision] * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -3.6e+40], t$95$1, If[LessEqual[i, -1.6e-142], N[(N[(y3 * y4), $MachinePrecision] * N[(N[(y * c), $MachinePrecision] - N[(j * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -3.65e-205], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -3.8e-247], t$95$2, If[LessEqual[i, -1.05e-290], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.2e-296], N[(y2 * N[(a * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.35e-255], N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.4e-124], N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.6e-22], N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.8e+200], t$95$2, t$95$1]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if i < -3.59999999999999996e40 or 4.8000000000000001e200 < i

   1. Initial program 27.3%

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

   3. Simplified 28.7%

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

   5. Taylor expanded in i around -inf 69.9%

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

   6. Taylor expanded in x around inf 55.2%

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

   if -3.59999999999999996e40 < i < -1.5999999999999999e-142

   1. Initial program 33.6%

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

   3. Taylor expanded in y4 around inf 34.1%

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

   4. Taylor expanded in y3 around inf 34.7%

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

      1. associate-*r* 37.3%

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

      2. neg-mul-1 37.3%

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

      3. associate-*r* 37.3%

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

      4. neg-mul-1 37.3%

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

      5. cancel-sign-sub 37.3%

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

      6. +-commutative 37.3%

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

      7. fma-undefine 37.3%

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

      8. fma-neg 37.3%

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

      9. *-commutative 37.3%

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

   6. Simplified 37.3%

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

   if -1.5999999999999999e-142 < i < -3.64999999999999996e-205

   1. Initial program 11.8%

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

   3. Simplified 11.8%

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

   5. Taylor expanded in b around inf 17.8%

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

   6. Taylor expanded in x around inf 59.5%

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

   if -3.64999999999999996e-205 < i < -3.79999999999999988e-247 or 3.5999999999999998e-22 < i < 4.8000000000000001e200

   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%

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

   5. Taylor expanded in b around inf 52.6%

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

   6. Taylor expanded in k around -inf 49.4%

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

      1. associate-*r* 49.4%

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

      2. neg-mul-1 49.4%

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

   8. Simplified 49.4%

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

   9. Taylor expanded in b around 0 49.4%

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

       1. mul-1-neg 49.4%

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

       2. associate-*r* 49.4%

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

       3. *-commutative 49.4%

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

   11. Simplified 49.4%

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

   if -3.79999999999999988e-247 < i < -1.0500000000000001e-290

   1. Initial program 87.3%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in a around inf 51.9%

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

   6. Taylor expanded in y around inf 39.8%

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

   if -1.0500000000000001e-290 < i < 3.20000000000000013e-296

   1. Initial program 13.7%

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

   3. Taylor expanded in y2 around inf 38.4%

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

   4. Taylor expanded in a around -inf 63.1%

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

      1. mul-1-neg 63.1%

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

   6. Simplified 63.1%

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

   if 3.20000000000000013e-296 < i < 1.35000000000000008e-255

   1. Initial program 58.3%

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

   3. Simplified 58.3%

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

   5. Taylor expanded in a around inf 50.6%

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

   6. Taylor expanded in y3 around inf 75.1%

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

   if 1.35000000000000008e-255 < i < 4.3999999999999998e-124

   1. Initial program 30.9%

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

   3. Taylor expanded in y2 around inf 42.0%

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

   4. Taylor expanded in c around inf 56.1%

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

   if 4.3999999999999998e-124 < i < 3.5999999999999998e-22

   1. Initial program 27.3%

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

   3. Taylor expanded in y2 around inf 41.2%

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

   4. Taylor expanded in k around inf 50.5%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.6 \cdot 10^{+40}:\\ \;\;\;\;i \cdot \left(x \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;i \leq -1.6 \cdot 10^{-142}:\\ \;\;\;\;\left(y3 \cdot y4\right) \cdot \left(y \cdot c - j \cdot y1\right)\\ \mathbf{elif}\;i \leq -3.65 \cdot 10^{-205}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq -3.8 \cdot 10^{-247}:\\ \;\;\;\;\left(b \cdot k\right) \cdot \left(z \cdot y0 - y \cdot y4\right)\\ \mathbf{elif}\;i \leq -1.05 \cdot 10^{-290}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;i \leq 3.2 \cdot 10^{-296}:\\ \;\;\;\;y2 \cdot \left(a \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;i \leq 1.35 \cdot 10^{-255}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;i \leq 4.4 \cdot 10^{-124}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq 3.6 \cdot 10^{-22}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{+200}:\\ \;\;\;\;\left(b \cdot k\right) \cdot \left(z \cdot y0 - y \cdot y4\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(x \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 30.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ t_2 := b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ t_3 := a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{if}\;y0 \leq -9.8 \cdot 10^{+63}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y0 \leq -8.8 \cdot 10^{-69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y0 \leq -2.4 \cdot 10^{-141}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y0 \leq 4.5 \cdot 10^{-266}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y0 \leq 1.15 \cdot 10^{-212}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 1.5 \cdot 10^{-137}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y0 \leq 2.4 \cdot 10^{-42}:\\ \;\;\;\;i \cdot \left(y \cdot \left(c \cdot \left(-x\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 2.3 \cdot 10^{-15}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y0 \leq 1.8 \cdot 10^{+72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y0 \leq 3.7 \cdot 10^{+196}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* y4 (- (* t j) (* y k)))))
        (t_2 (* b (* y0 (- (* z k) (* x j)))))
        (t_3 (* a (* y3 (- (* z y1) (* y y5))))))
   (if (<= y0 -9.8e+63)
     t_2
     (if (<= y0 -8.8e-69)
       t_1
       (if (<= y0 -2.4e-141)
         t_3
         (if (<= y0 4.5e-266)
           t_1
           (if (<= y0 1.15e-212)
             (* k (* y2 (* y1 y4)))
             (if (<= y0 1.5e-137)
               (* i (* j (* x y1)))
               (if (<= y0 2.4e-42)
                 (* i (* y (* c (- x))))
                 (if (<= y0 2.3e-15)
                   t_3
                   (if (<= y0 1.8e+72)
                     t_1
                     (if (<= y0 3.7e+196)
                       (* a (* y5 (- (* t y2) (* y y3))))
                       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 = b * (y4 * ((t * j) - (y * k)));
	double t_2 = b * (y0 * ((z * k) - (x * j)));
	double t_3 = a * (y3 * ((z * y1) - (y * y5)));
	double tmp;
	if (y0 <= -9.8e+63) {
		tmp = t_2;
	} else if (y0 <= -8.8e-69) {
		tmp = t_1;
	} else if (y0 <= -2.4e-141) {
		tmp = t_3;
	} else if (y0 <= 4.5e-266) {
		tmp = t_1;
	} else if (y0 <= 1.15e-212) {
		tmp = k * (y2 * (y1 * y4));
	} else if (y0 <= 1.5e-137) {
		tmp = i * (j * (x * y1));
	} else if (y0 <= 2.4e-42) {
		tmp = i * (y * (c * -x));
	} else if (y0 <= 2.3e-15) {
		tmp = t_3;
	} else if (y0 <= 1.8e+72) {
		tmp = t_1;
	} else if (y0 <= 3.7e+196) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} 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 = b * (y4 * ((t * j) - (y * k)))
    t_2 = b * (y0 * ((z * k) - (x * j)))
    t_3 = a * (y3 * ((z * y1) - (y * y5)))
    if (y0 <= (-9.8d+63)) then
        tmp = t_2
    else if (y0 <= (-8.8d-69)) then
        tmp = t_1
    else if (y0 <= (-2.4d-141)) then
        tmp = t_3
    else if (y0 <= 4.5d-266) then
        tmp = t_1
    else if (y0 <= 1.15d-212) then
        tmp = k * (y2 * (y1 * y4))
    else if (y0 <= 1.5d-137) then
        tmp = i * (j * (x * y1))
    else if (y0 <= 2.4d-42) then
        tmp = i * (y * (c * -x))
    else if (y0 <= 2.3d-15) then
        tmp = t_3
    else if (y0 <= 1.8d+72) then
        tmp = t_1
    else if (y0 <= 3.7d+196) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    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 = b * (y4 * ((t * j) - (y * k)));
	double t_2 = b * (y0 * ((z * k) - (x * j)));
	double t_3 = a * (y3 * ((z * y1) - (y * y5)));
	double tmp;
	if (y0 <= -9.8e+63) {
		tmp = t_2;
	} else if (y0 <= -8.8e-69) {
		tmp = t_1;
	} else if (y0 <= -2.4e-141) {
		tmp = t_3;
	} else if (y0 <= 4.5e-266) {
		tmp = t_1;
	} else if (y0 <= 1.15e-212) {
		tmp = k * (y2 * (y1 * y4));
	} else if (y0 <= 1.5e-137) {
		tmp = i * (j * (x * y1));
	} else if (y0 <= 2.4e-42) {
		tmp = i * (y * (c * -x));
	} else if (y0 <= 2.3e-15) {
		tmp = t_3;
	} else if (y0 <= 1.8e+72) {
		tmp = t_1;
	} else if (y0 <= 3.7e+196) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} 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 = b * (y4 * ((t * j) - (y * k)))
	t_2 = b * (y0 * ((z * k) - (x * j)))
	t_3 = a * (y3 * ((z * y1) - (y * y5)))
	tmp = 0
	if y0 <= -9.8e+63:
		tmp = t_2
	elif y0 <= -8.8e-69:
		tmp = t_1
	elif y0 <= -2.4e-141:
		tmp = t_3
	elif y0 <= 4.5e-266:
		tmp = t_1
	elif y0 <= 1.15e-212:
		tmp = k * (y2 * (y1 * y4))
	elif y0 <= 1.5e-137:
		tmp = i * (j * (x * y1))
	elif y0 <= 2.4e-42:
		tmp = i * (y * (c * -x))
	elif y0 <= 2.3e-15:
		tmp = t_3
	elif y0 <= 1.8e+72:
		tmp = t_1
	elif y0 <= 3.7e+196:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	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(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))))
	t_2 = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))))
	t_3 = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))))
	tmp = 0.0
	if (y0 <= -9.8e+63)
		tmp = t_2;
	elseif (y0 <= -8.8e-69)
		tmp = t_1;
	elseif (y0 <= -2.4e-141)
		tmp = t_3;
	elseif (y0 <= 4.5e-266)
		tmp = t_1;
	elseif (y0 <= 1.15e-212)
		tmp = Float64(k * Float64(y2 * Float64(y1 * y4)));
	elseif (y0 <= 1.5e-137)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (y0 <= 2.4e-42)
		tmp = Float64(i * Float64(y * Float64(c * Float64(-x))));
	elseif (y0 <= 2.3e-15)
		tmp = t_3;
	elseif (y0 <= 1.8e+72)
		tmp = t_1;
	elseif (y0 <= 3.7e+196)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	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 = b * (y4 * ((t * j) - (y * k)));
	t_2 = b * (y0 * ((z * k) - (x * j)));
	t_3 = a * (y3 * ((z * y1) - (y * y5)));
	tmp = 0.0;
	if (y0 <= -9.8e+63)
		tmp = t_2;
	elseif (y0 <= -8.8e-69)
		tmp = t_1;
	elseif (y0 <= -2.4e-141)
		tmp = t_3;
	elseif (y0 <= 4.5e-266)
		tmp = t_1;
	elseif (y0 <= 1.15e-212)
		tmp = k * (y2 * (y1 * y4));
	elseif (y0 <= 1.5e-137)
		tmp = i * (j * (x * y1));
	elseif (y0 <= 2.4e-42)
		tmp = i * (y * (c * -x));
	elseif (y0 <= 2.3e-15)
		tmp = t_3;
	elseif (y0 <= 1.8e+72)
		tmp = t_1;
	elseif (y0 <= 3.7e+196)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	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[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -9.8e+63], t$95$2, If[LessEqual[y0, -8.8e-69], t$95$1, If[LessEqual[y0, -2.4e-141], t$95$3, If[LessEqual[y0, 4.5e-266], t$95$1, If[LessEqual[y0, 1.15e-212], N[(k * N[(y2 * N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.5e-137], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 2.4e-42], N[(i * N[(y * N[(c * (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 2.3e-15], t$95$3, If[LessEqual[y0, 1.8e+72], t$95$1, If[LessEqual[y0, 3.7e+196], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y0 < -9.7999999999999994e63 or 3.6999999999999999e196 < y0

   1. Initial program 27.5%

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

   3. Simplified 28.8%

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

   5. Taylor expanded in b around inf 36.9%

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

   6. Taylor expanded in y0 around inf 48.7%

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

   if -9.7999999999999994e63 < y0 < -8.8000000000000001e-69 or -2.4000000000000001e-141 < y0 < 4.5000000000000003e-266 or 2.2999999999999999e-15 < y0 < 1.80000000000000017e72

   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 38.7%

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

   5. Taylor expanded in b around inf 37.9%

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

   6. Taylor expanded in y4 around inf 42.4%

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

   if -8.8000000000000001e-69 < y0 < -2.4000000000000001e-141 or 2.40000000000000003e-42 < y0 < 2.2999999999999999e-15

   1. Initial program 28.6%

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

   3. Simplified 28.6%

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

   5. Taylor expanded in a around inf 61.0%

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

   6. Taylor expanded in y3 around inf 79.2%

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

   if 4.5000000000000003e-266 < y0 < 1.15e-212

   1. Initial program 45.5%

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

   3. Taylor expanded in y2 around inf 67.1%

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

   4. Taylor expanded in k around inf 45.0%

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

   5. Taylor expanded in y1 around inf 56.3%

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

      1. *-commutative 56.3%

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

   7. Simplified 56.3%

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

   if 1.15e-212 < y0 < 1.4999999999999999e-137

   1. Initial program 23.0%

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

   3. Simplified 23.0%

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

   5. Taylor expanded in i around -inf 31.2%

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

   6. Taylor expanded in x around inf 47.3%

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

   7. Taylor expanded in c around 0 47.3%

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

      1. mul-1-neg 47.3%

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

      2. *-commutative 47.3%

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

      3. distribute-rgt-neg-in 47.3%

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

      4. *-commutative 47.3%

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

   9. Simplified 47.3%

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

   if 1.4999999999999999e-137 < y0 < 2.40000000000000003e-42

   1. Initial program 33.3%

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

   3. Simplified 33.3%

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

   5. Taylor expanded in i around -inf 56.2%

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

   6. Taylor expanded in x around inf 39.8%

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

   7. Taylor expanded in c around inf 45.3%

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

      1. associate-*r* 45.3%

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

   9. Simplified 45.3%

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

   if 1.80000000000000017e72 < y0 < 3.6999999999999999e196

   1. Initial program 21.3%

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

   3. Simplified 21.3%

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

   5. Taylor expanded in a around inf 48.8%

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

   6. Taylor expanded in y5 around inf 49.4%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 50.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -9.8 \cdot 10^{+63}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -8.8 \cdot 10^{-69}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y0 \leq -2.4 \cdot 10^{-141}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 4.5 \cdot 10^{-266}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y0 \leq 1.15 \cdot 10^{-212}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 1.5 \cdot 10^{-137}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y0 \leq 2.4 \cdot 10^{-42}:\\ \;\;\;\;i \cdot \left(y \cdot \left(c \cdot \left(-x\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 2.3 \cdot 10^{-15}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 1.8 \cdot 10^{+72}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y0 \leq 3.7 \cdot 10^{+196}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 34.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{if}\;k \leq -1.32 \cdot 10^{+26}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;k \leq -1.45 \cdot 10^{-52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq -8 \cdot 10^{-185}:\\ \;\;\;\;z \cdot \left(c \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq -2.1 \cdot 10^{-238}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 7 \cdot 10^{-276}:\\ \;\;\;\;\left(y3 \cdot y5\right) \cdot \left(j \cdot y0 - y \cdot a\right)\\ \mathbf{elif}\;k \leq 5.6 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq 2.1 \cdot 10^{+168}:\\ \;\;\;\;y2 \cdot \left(y0 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0 - k \cdot \frac{y \cdot y4}{z}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          y2
          (+
           (+ (* k (- (* y1 y4) (* y0 y5))) (* x (- (* c y0) (* a y1))))
           (* t (- (* a y5) (* c y4)))))))
   (if (<= k -1.32e+26)
     (* y4 (* k (- (* y1 y2) (* y b))))
     (if (<= k -1.45e-52)
       t_1
       (if (<= k -8e-185)
         (* z (* c (- (* t i) (* y0 y3))))
         (if (<= k -2.1e-238)
           (*
            y4
            (+
             (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
             (* c (- (* y y3) (* t y2)))))
           (if (<= k 7e-276)
             (* (* y3 y5) (- (* j y0) (* y a)))
             (if (<= k 5.6e-15)
               t_1
               (if (<= k 2.1e+168)
                 (* y2 (* y0 (- (* x c) (* k y5))))
                 (* b (* z (- (* k y0) (* k (/ (* y y4) z))))))))))))))

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 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	double tmp;
	if (k <= -1.32e+26) {
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	} else if (k <= -1.45e-52) {
		tmp = t_1;
	} else if (k <= -8e-185) {
		tmp = z * (c * ((t * i) - (y0 * y3)));
	} else if (k <= -2.1e-238) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (k <= 7e-276) {
		tmp = (y3 * y5) * ((j * y0) - (y * a));
	} else if (k <= 5.6e-15) {
		tmp = t_1;
	} else if (k <= 2.1e+168) {
		tmp = y2 * (y0 * ((x * c) - (k * y5)));
	} else {
		tmp = b * (z * ((k * y0) - (k * ((y * y4) / z))));
	}
	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 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
    if (k <= (-1.32d+26)) then
        tmp = y4 * (k * ((y1 * y2) - (y * b)))
    else if (k <= (-1.45d-52)) then
        tmp = t_1
    else if (k <= (-8d-185)) then
        tmp = z * (c * ((t * i) - (y0 * y3)))
    else if (k <= (-2.1d-238)) then
        tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    else if (k <= 7d-276) then
        tmp = (y3 * y5) * ((j * y0) - (y * a))
    else if (k <= 5.6d-15) then
        tmp = t_1
    else if (k <= 2.1d+168) then
        tmp = y2 * (y0 * ((x * c) - (k * y5)))
    else
        tmp = b * (z * ((k * y0) - (k * ((y * y4) / z))))
    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 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	double tmp;
	if (k <= -1.32e+26) {
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	} else if (k <= -1.45e-52) {
		tmp = t_1;
	} else if (k <= -8e-185) {
		tmp = z * (c * ((t * i) - (y0 * y3)));
	} else if (k <= -2.1e-238) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (k <= 7e-276) {
		tmp = (y3 * y5) * ((j * y0) - (y * a));
	} else if (k <= 5.6e-15) {
		tmp = t_1;
	} else if (k <= 2.1e+168) {
		tmp = y2 * (y0 * ((x * c) - (k * y5)));
	} else {
		tmp = b * (z * ((k * y0) - (k * ((y * y4) / z))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
	tmp = 0
	if k <= -1.32e+26:
		tmp = y4 * (k * ((y1 * y2) - (y * b)))
	elif k <= -1.45e-52:
		tmp = t_1
	elif k <= -8e-185:
		tmp = z * (c * ((t * i) - (y0 * y3)))
	elif k <= -2.1e-238:
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	elif k <= 7e-276:
		tmp = (y3 * y5) * ((j * y0) - (y * a))
	elif k <= 5.6e-15:
		tmp = t_1
	elif k <= 2.1e+168:
		tmp = y2 * (y0 * ((x * c) - (k * y5)))
	else:
		tmp = b * (z * ((k * y0) - (k * ((y * y4) / z))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y2 * Float64(Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))))
	tmp = 0.0
	if (k <= -1.32e+26)
		tmp = Float64(y4 * Float64(k * Float64(Float64(y1 * y2) - Float64(y * b))));
	elseif (k <= -1.45e-52)
		tmp = t_1;
	elseif (k <= -8e-185)
		tmp = Float64(z * Float64(c * Float64(Float64(t * i) - Float64(y0 * y3))));
	elseif (k <= -2.1e-238)
		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 (k <= 7e-276)
		tmp = Float64(Float64(y3 * y5) * Float64(Float64(j * y0) - Float64(y * a)));
	elseif (k <= 5.6e-15)
		tmp = t_1;
	elseif (k <= 2.1e+168)
		tmp = Float64(y2 * Float64(y0 * Float64(Float64(x * c) - Float64(k * y5))));
	else
		tmp = Float64(b * Float64(z * Float64(Float64(k * y0) - Float64(k * Float64(Float64(y * y4) / z)))));
	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 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	tmp = 0.0;
	if (k <= -1.32e+26)
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	elseif (k <= -1.45e-52)
		tmp = t_1;
	elseif (k <= -8e-185)
		tmp = z * (c * ((t * i) - (y0 * y3)));
	elseif (k <= -2.1e-238)
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	elseif (k <= 7e-276)
		tmp = (y3 * y5) * ((j * y0) - (y * a));
	elseif (k <= 5.6e-15)
		tmp = t_1;
	elseif (k <= 2.1e+168)
		tmp = y2 * (y0 * ((x * c) - (k * y5)));
	else
		tmp = b * (z * ((k * y0) - (k * ((y * y4) / z))));
	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[(y2 * N[(N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -1.32e+26], N[(y4 * N[(k * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -1.45e-52], t$95$1, If[LessEqual[k, -8e-185], N[(z * N[(c * N[(N[(t * i), $MachinePrecision] - N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -2.1e-238], 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[k, 7e-276], N[(N[(y3 * y5), $MachinePrecision] * N[(N[(j * y0), $MachinePrecision] - N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 5.6e-15], t$95$1, If[LessEqual[k, 2.1e+168], N[(y2 * N[(y0 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(z * N[(N[(k * y0), $MachinePrecision] - N[(k * N[(N[(y * y4), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if k < -1.32e26

   1. Initial program 24.8%

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

   3. Taylor expanded in y4 around inf 45.4%

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

   4. Taylor expanded in k around inf 51.5%

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

      1. +-commutative 51.5%

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

      2. mul-1-neg 51.5%

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

      3. unsub-neg 51.5%

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

      4. *-commutative 51.5%

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

   6. Simplified 51.5%

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

   if -1.32e26 < k < -1.4500000000000001e-52 or 6.99999999999999986e-276 < k < 5.60000000000000028e-15

   1. Initial program 28.7%

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

   3. Taylor expanded in y2 around inf 52.0%

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

   if -1.4500000000000001e-52 < k < -7.9999999999999999e-185

   1. Initial program 60.7%

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

   3. Simplified 60.7%

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

   5. Taylor expanded in z around -inf 61.4%

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

   6. Taylor expanded in c around inf 54.1%

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

   if -7.9999999999999999e-185 < k < -2.1000000000000001e-238

   1. Initial program 34.6%

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

   3. Taylor expanded in y4 around inf 59.2%

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

   if -2.1000000000000001e-238 < k < 6.99999999999999986e-276

   1. Initial program 32.6%

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

   3. Taylor expanded in y3 around -inf 48.9%

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

   4. Taylor expanded in y5 around inf 49.1%

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

      1. associate-*r* 49.2%

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

      2. distribute-lft-out-- 49.2%

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

      3. *-commutative 49.2%

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

   6. Simplified 49.2%

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

   if 5.60000000000000028e-15 < k < 2.10000000000000003e168

   1. Initial program 34.5%

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

   3. Taylor expanded in y2 around inf 44.1%

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

   4. Taylor expanded in y0 around inf 60.1%

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

   if 2.10000000000000003e168 < k

   1. Initial program 14.8%

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

   3. Simplified 14.8%

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

   5. Taylor expanded in b around inf 44.6%

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

   6. Taylor expanded in k around -inf 71.0%

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

      1. associate-*r* 71.0%

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

      2. neg-mul-1 71.0%

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

   8. Simplified 71.0%

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

   9. Taylor expanded in z around inf 66.8%

      \[\leadsto b \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \frac{k \cdot \left(y \cdot y4\right)}{z} + k \cdot y0\right)\right)} \]
   10. Step-by-step derivation

       1. +-commutative 66.8%

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

       2. mul-1-neg 66.8%

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

       3. unsub-neg 66.8%

          \[\leadsto b \cdot \left(z \cdot \color{blue}{\left(k \cdot y0 - \frac{k \cdot \left(y \cdot y4\right)}{z}\right)}\right) \]

       4. *-commutative 66.8%

          \[\leadsto b \cdot \left(z \cdot \left(\color{blue}{y0 \cdot k} - \frac{k \cdot \left(y \cdot y4\right)}{z}\right)\right) \]

       5. associate-/l* 74.6%

          \[\leadsto b \cdot \left(z \cdot \left(y0 \cdot k - \color{blue}{k \cdot \frac{y \cdot y4}{z}}\right)\right) \]

   11. Simplified 74.6%

       \[\leadsto b \cdot \color{blue}{\left(z \cdot \left(y0 \cdot k - k \cdot \frac{y \cdot y4}{z}\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.32 \cdot 10^{+26}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;k \leq -1.45 \cdot 10^{-52}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq -8 \cdot 10^{-185}:\\ \;\;\;\;z \cdot \left(c \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq -2.1 \cdot 10^{-238}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 7 \cdot 10^{-276}:\\ \;\;\;\;\left(y3 \cdot y5\right) \cdot \left(j \cdot y0 - y \cdot a\right)\\ \mathbf{elif}\;k \leq 5.6 \cdot 10^{-15}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 2.1 \cdot 10^{+168}:\\ \;\;\;\;y2 \cdot \left(y0 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0 - k \cdot \frac{y \cdot y4}{z}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 33.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{if}\;k \leq -5.6 \cdot 10^{+26}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;k \leq -7.5 \cdot 10^{-53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq -3.6 \cdot 10^{-186}:\\ \;\;\;\;z \cdot \left(c \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq -3.5 \cdot 10^{-237}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;k \leq 7 \cdot 10^{-276}:\\ \;\;\;\;\left(y3 \cdot y5\right) \cdot \left(j \cdot y0 - y \cdot a\right)\\ \mathbf{elif}\;k \leq 5.6 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq 1.7 \cdot 10^{+168}:\\ \;\;\;\;y2 \cdot \left(y0 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0 - k \cdot \frac{y \cdot y4}{z}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          y2
          (+
           (+ (* k (- (* y1 y4) (* y0 y5))) (* x (- (* c y0) (* a y1))))
           (* t (- (* a y5) (* c y4)))))))
   (if (<= k -5.6e+26)
     (* y4 (* k (- (* y1 y2) (* y b))))
     (if (<= k -7.5e-53)
       t_1
       (if (<= k -3.6e-186)
         (* z (* c (- (* t i) (* y0 y3))))
         (if (<= k -3.5e-237)
           (* b (* y4 (- (* t j) (* y k))))
           (if (<= k 7e-276)
             (* (* y3 y5) (- (* j y0) (* y a)))
             (if (<= k 5.6e-15)
               t_1
               (if (<= k 1.7e+168)
                 (* y2 (* y0 (- (* x c) (* k y5))))
                 (* b (* z (- (* k y0) (* k (/ (* y y4) z))))))))))))))

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 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	double tmp;
	if (k <= -5.6e+26) {
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	} else if (k <= -7.5e-53) {
		tmp = t_1;
	} else if (k <= -3.6e-186) {
		tmp = z * (c * ((t * i) - (y0 * y3)));
	} else if (k <= -3.5e-237) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (k <= 7e-276) {
		tmp = (y3 * y5) * ((j * y0) - (y * a));
	} else if (k <= 5.6e-15) {
		tmp = t_1;
	} else if (k <= 1.7e+168) {
		tmp = y2 * (y0 * ((x * c) - (k * y5)));
	} else {
		tmp = b * (z * ((k * y0) - (k * ((y * y4) / z))));
	}
	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 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
    if (k <= (-5.6d+26)) then
        tmp = y4 * (k * ((y1 * y2) - (y * b)))
    else if (k <= (-7.5d-53)) then
        tmp = t_1
    else if (k <= (-3.6d-186)) then
        tmp = z * (c * ((t * i) - (y0 * y3)))
    else if (k <= (-3.5d-237)) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (k <= 7d-276) then
        tmp = (y3 * y5) * ((j * y0) - (y * a))
    else if (k <= 5.6d-15) then
        tmp = t_1
    else if (k <= 1.7d+168) then
        tmp = y2 * (y0 * ((x * c) - (k * y5)))
    else
        tmp = b * (z * ((k * y0) - (k * ((y * y4) / z))))
    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 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	double tmp;
	if (k <= -5.6e+26) {
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	} else if (k <= -7.5e-53) {
		tmp = t_1;
	} else if (k <= -3.6e-186) {
		tmp = z * (c * ((t * i) - (y0 * y3)));
	} else if (k <= -3.5e-237) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (k <= 7e-276) {
		tmp = (y3 * y5) * ((j * y0) - (y * a));
	} else if (k <= 5.6e-15) {
		tmp = t_1;
	} else if (k <= 1.7e+168) {
		tmp = y2 * (y0 * ((x * c) - (k * y5)));
	} else {
		tmp = b * (z * ((k * y0) - (k * ((y * y4) / z))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
	tmp = 0
	if k <= -5.6e+26:
		tmp = y4 * (k * ((y1 * y2) - (y * b)))
	elif k <= -7.5e-53:
		tmp = t_1
	elif k <= -3.6e-186:
		tmp = z * (c * ((t * i) - (y0 * y3)))
	elif k <= -3.5e-237:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif k <= 7e-276:
		tmp = (y3 * y5) * ((j * y0) - (y * a))
	elif k <= 5.6e-15:
		tmp = t_1
	elif k <= 1.7e+168:
		tmp = y2 * (y0 * ((x * c) - (k * y5)))
	else:
		tmp = b * (z * ((k * y0) - (k * ((y * y4) / z))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y2 * Float64(Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))))
	tmp = 0.0
	if (k <= -5.6e+26)
		tmp = Float64(y4 * Float64(k * Float64(Float64(y1 * y2) - Float64(y * b))));
	elseif (k <= -7.5e-53)
		tmp = t_1;
	elseif (k <= -3.6e-186)
		tmp = Float64(z * Float64(c * Float64(Float64(t * i) - Float64(y0 * y3))));
	elseif (k <= -3.5e-237)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (k <= 7e-276)
		tmp = Float64(Float64(y3 * y5) * Float64(Float64(j * y0) - Float64(y * a)));
	elseif (k <= 5.6e-15)
		tmp = t_1;
	elseif (k <= 1.7e+168)
		tmp = Float64(y2 * Float64(y0 * Float64(Float64(x * c) - Float64(k * y5))));
	else
		tmp = Float64(b * Float64(z * Float64(Float64(k * y0) - Float64(k * Float64(Float64(y * y4) / z)))));
	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 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	tmp = 0.0;
	if (k <= -5.6e+26)
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	elseif (k <= -7.5e-53)
		tmp = t_1;
	elseif (k <= -3.6e-186)
		tmp = z * (c * ((t * i) - (y0 * y3)));
	elseif (k <= -3.5e-237)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (k <= 7e-276)
		tmp = (y3 * y5) * ((j * y0) - (y * a));
	elseif (k <= 5.6e-15)
		tmp = t_1;
	elseif (k <= 1.7e+168)
		tmp = y2 * (y0 * ((x * c) - (k * y5)));
	else
		tmp = b * (z * ((k * y0) - (k * ((y * y4) / z))));
	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[(y2 * N[(N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -5.6e+26], N[(y4 * N[(k * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -7.5e-53], t$95$1, If[LessEqual[k, -3.6e-186], N[(z * N[(c * N[(N[(t * i), $MachinePrecision] - N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -3.5e-237], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 7e-276], N[(N[(y3 * y5), $MachinePrecision] * N[(N[(j * y0), $MachinePrecision] - N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 5.6e-15], t$95$1, If[LessEqual[k, 1.7e+168], N[(y2 * N[(y0 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(z * N[(N[(k * y0), $MachinePrecision] - N[(k * N[(N[(y * y4), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if k < -5.59999999999999999e26

   1. Initial program 24.8%

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

   3. Taylor expanded in y4 around inf 45.4%

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

   4. Taylor expanded in k around inf 51.5%

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

      1. +-commutative 51.5%

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

      2. mul-1-neg 51.5%

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

      3. unsub-neg 51.5%

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

      4. *-commutative 51.5%

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

   6. Simplified 51.5%

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

   if -5.59999999999999999e26 < k < -7.5000000000000001e-53 or 6.99999999999999986e-276 < k < 5.60000000000000028e-15

   1. Initial program 28.7%

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

   3. Taylor expanded in y2 around inf 52.0%

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

   if -7.5000000000000001e-53 < k < -3.5999999999999998e-186

   1. Initial program 60.7%

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

   3. Simplified 60.7%

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

   5. Taylor expanded in z around -inf 61.4%

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

   6. Taylor expanded in c around inf 54.1%

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

   if -3.5999999999999998e-186 < k < -3.49999999999999983e-237

   1. Initial program 34.6%

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

   3. Simplified 34.6%

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

   5. Taylor expanded in b around inf 50.3%

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

   6. Taylor expanded in y4 around inf 50.7%

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

   if -3.49999999999999983e-237 < k < 6.99999999999999986e-276

   1. Initial program 32.6%

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

   3. Taylor expanded in y3 around -inf 48.9%

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

   4. Taylor expanded in y5 around inf 49.1%

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

      1. associate-*r* 49.2%

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

      2. distribute-lft-out-- 49.2%

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

      3. *-commutative 49.2%

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

   6. Simplified 49.2%

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

   if 5.60000000000000028e-15 < k < 1.70000000000000001e168

   1. Initial program 34.5%

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

   3. Taylor expanded in y2 around inf 44.1%

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

   4. Taylor expanded in y0 around inf 60.1%

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

   if 1.70000000000000001e168 < k

   1. Initial program 14.8%

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

   3. Simplified 14.8%

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

   5. Taylor expanded in b around inf 44.6%

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

   6. Taylor expanded in k around -inf 71.0%

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

      1. associate-*r* 71.0%

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

      2. neg-mul-1 71.0%

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

   8. Simplified 71.0%

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

   9. Taylor expanded in z around inf 66.8%

      \[\leadsto b \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \frac{k \cdot \left(y \cdot y4\right)}{z} + k \cdot y0\right)\right)} \]
   10. Step-by-step derivation

       1. +-commutative 66.8%

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

       2. mul-1-neg 66.8%

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

       3. unsub-neg 66.8%

          \[\leadsto b \cdot \left(z \cdot \color{blue}{\left(k \cdot y0 - \frac{k \cdot \left(y \cdot y4\right)}{z}\right)}\right) \]

       4. *-commutative 66.8%

          \[\leadsto b \cdot \left(z \cdot \left(\color{blue}{y0 \cdot k} - \frac{k \cdot \left(y \cdot y4\right)}{z}\right)\right) \]

       5. associate-/l* 74.6%

          \[\leadsto b \cdot \left(z \cdot \left(y0 \cdot k - \color{blue}{k \cdot \frac{y \cdot y4}{z}}\right)\right) \]

   11. Simplified 74.6%

       \[\leadsto b \cdot \color{blue}{\left(z \cdot \left(y0 \cdot k - k \cdot \frac{y \cdot y4}{z}\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -5.6 \cdot 10^{+26}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;k \leq -7.5 \cdot 10^{-53}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq -3.6 \cdot 10^{-186}:\\ \;\;\;\;z \cdot \left(c \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq -3.5 \cdot 10^{-237}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;k \leq 7 \cdot 10^{-276}:\\ \;\;\;\;\left(y3 \cdot y5\right) \cdot \left(j \cdot y0 - y \cdot a\right)\\ \mathbf{elif}\;k \leq 5.6 \cdot 10^{-15}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 1.7 \cdot 10^{+168}:\\ \;\;\;\;y2 \cdot \left(y0 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0 - k \cdot \frac{y \cdot y4}{z}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 32.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{if}\;k \leq -9 \cdot 10^{-16}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;k \leq -1.6 \cdot 10^{-186}:\\ \;\;\;\;z \cdot \left(c \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq -3.8 \cdot 10^{-237}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;k \leq 2 \cdot 10^{-305}:\\ \;\;\;\;\left(y3 \cdot y5\right) \cdot \left(j \cdot y0 - y \cdot a\right)\\ \mathbf{elif}\;k \leq 4.6 \cdot 10^{-294}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq 7 \cdot 10^{-276}:\\ \;\;\;\;i \cdot \left(t \cdot \left(z \cdot c - j \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 1.85 \cdot 10^{-227}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq 1.75 \cdot 10^{+20}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 4.5 \cdot 10^{+165}:\\ \;\;\;\;y2 \cdot \left(y0 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0 - k \cdot \frac{y \cdot y4}{z}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* a (- (* x y) (* z t))))))
   (if (<= k -9e-16)
     (* y4 (* k (- (* y1 y2) (* y b))))
     (if (<= k -1.6e-186)
       (* z (* c (- (* t i) (* y0 y3))))
       (if (<= k -3.8e-237)
         (* b (* y4 (- (* t j) (* y k))))
         (if (<= k 2e-305)
           (* (* y3 y5) (- (* j y0) (* y a)))
           (if (<= k 4.6e-294)
             t_1
             (if (<= k 7e-276)
               (* i (* t (- (* z c) (* j y5))))
               (if (<= k 1.85e-227)
                 t_1
                 (if (<= k 1.75e+20)
                   (* a (* y1 (- (* z y3) (* x y2))))
                   (if (<= k 4.5e+165)
                     (* y2 (* y0 (- (* x c) (* k y5))))
                     (* b (* z (- (* k y0) (* k (/ (* y y4) z))))))))))))))))

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 * (a * ((x * y) - (z * t)));
	double tmp;
	if (k <= -9e-16) {
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	} else if (k <= -1.6e-186) {
		tmp = z * (c * ((t * i) - (y0 * y3)));
	} else if (k <= -3.8e-237) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (k <= 2e-305) {
		tmp = (y3 * y5) * ((j * y0) - (y * a));
	} else if (k <= 4.6e-294) {
		tmp = t_1;
	} else if (k <= 7e-276) {
		tmp = i * (t * ((z * c) - (j * y5)));
	} else if (k <= 1.85e-227) {
		tmp = t_1;
	} else if (k <= 1.75e+20) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (k <= 4.5e+165) {
		tmp = y2 * (y0 * ((x * c) - (k * y5)));
	} else {
		tmp = b * (z * ((k * y0) - (k * ((y * y4) / z))));
	}
	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 = b * (a * ((x * y) - (z * t)))
    if (k <= (-9d-16)) then
        tmp = y4 * (k * ((y1 * y2) - (y * b)))
    else if (k <= (-1.6d-186)) then
        tmp = z * (c * ((t * i) - (y0 * y3)))
    else if (k <= (-3.8d-237)) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (k <= 2d-305) then
        tmp = (y3 * y5) * ((j * y0) - (y * a))
    else if (k <= 4.6d-294) then
        tmp = t_1
    else if (k <= 7d-276) then
        tmp = i * (t * ((z * c) - (j * y5)))
    else if (k <= 1.85d-227) then
        tmp = t_1
    else if (k <= 1.75d+20) then
        tmp = a * (y1 * ((z * y3) - (x * y2)))
    else if (k <= 4.5d+165) then
        tmp = y2 * (y0 * ((x * c) - (k * y5)))
    else
        tmp = b * (z * ((k * y0) - (k * ((y * y4) / z))))
    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 * (a * ((x * y) - (z * t)));
	double tmp;
	if (k <= -9e-16) {
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	} else if (k <= -1.6e-186) {
		tmp = z * (c * ((t * i) - (y0 * y3)));
	} else if (k <= -3.8e-237) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (k <= 2e-305) {
		tmp = (y3 * y5) * ((j * y0) - (y * a));
	} else if (k <= 4.6e-294) {
		tmp = t_1;
	} else if (k <= 7e-276) {
		tmp = i * (t * ((z * c) - (j * y5)));
	} else if (k <= 1.85e-227) {
		tmp = t_1;
	} else if (k <= 1.75e+20) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (k <= 4.5e+165) {
		tmp = y2 * (y0 * ((x * c) - (k * y5)));
	} else {
		tmp = b * (z * ((k * y0) - (k * ((y * y4) / z))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (a * ((x * y) - (z * t)))
	tmp = 0
	if k <= -9e-16:
		tmp = y4 * (k * ((y1 * y2) - (y * b)))
	elif k <= -1.6e-186:
		tmp = z * (c * ((t * i) - (y0 * y3)))
	elif k <= -3.8e-237:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif k <= 2e-305:
		tmp = (y3 * y5) * ((j * y0) - (y * a))
	elif k <= 4.6e-294:
		tmp = t_1
	elif k <= 7e-276:
		tmp = i * (t * ((z * c) - (j * y5)))
	elif k <= 1.85e-227:
		tmp = t_1
	elif k <= 1.75e+20:
		tmp = a * (y1 * ((z * y3) - (x * y2)))
	elif k <= 4.5e+165:
		tmp = y2 * (y0 * ((x * c) - (k * y5)))
	else:
		tmp = b * (z * ((k * y0) - (k * ((y * y4) / z))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))))
	tmp = 0.0
	if (k <= -9e-16)
		tmp = Float64(y4 * Float64(k * Float64(Float64(y1 * y2) - Float64(y * b))));
	elseif (k <= -1.6e-186)
		tmp = Float64(z * Float64(c * Float64(Float64(t * i) - Float64(y0 * y3))));
	elseif (k <= -3.8e-237)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (k <= 2e-305)
		tmp = Float64(Float64(y3 * y5) * Float64(Float64(j * y0) - Float64(y * a)));
	elseif (k <= 4.6e-294)
		tmp = t_1;
	elseif (k <= 7e-276)
		tmp = Float64(i * Float64(t * Float64(Float64(z * c) - Float64(j * y5))));
	elseif (k <= 1.85e-227)
		tmp = t_1;
	elseif (k <= 1.75e+20)
		tmp = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))));
	elseif (k <= 4.5e+165)
		tmp = Float64(y2 * Float64(y0 * Float64(Float64(x * c) - Float64(k * y5))));
	else
		tmp = Float64(b * Float64(z * Float64(Float64(k * y0) - Float64(k * Float64(Float64(y * y4) / z)))));
	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 * (a * ((x * y) - (z * t)));
	tmp = 0.0;
	if (k <= -9e-16)
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	elseif (k <= -1.6e-186)
		tmp = z * (c * ((t * i) - (y0 * y3)));
	elseif (k <= -3.8e-237)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (k <= 2e-305)
		tmp = (y3 * y5) * ((j * y0) - (y * a));
	elseif (k <= 4.6e-294)
		tmp = t_1;
	elseif (k <= 7e-276)
		tmp = i * (t * ((z * c) - (j * y5)));
	elseif (k <= 1.85e-227)
		tmp = t_1;
	elseif (k <= 1.75e+20)
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	elseif (k <= 4.5e+165)
		tmp = y2 * (y0 * ((x * c) - (k * y5)));
	else
		tmp = b * (z * ((k * y0) - (k * ((y * y4) / z))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -9e-16], N[(y4 * N[(k * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -1.6e-186], N[(z * N[(c * N[(N[(t * i), $MachinePrecision] - N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -3.8e-237], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2e-305], N[(N[(y3 * y5), $MachinePrecision] * N[(N[(j * y0), $MachinePrecision] - N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 4.6e-294], t$95$1, If[LessEqual[k, 7e-276], N[(i * N[(t * N[(N[(z * c), $MachinePrecision] - N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.85e-227], t$95$1, If[LessEqual[k, 1.75e+20], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 4.5e+165], N[(y2 * N[(y0 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(z * N[(N[(k * y0), $MachinePrecision] - N[(k * N[(N[(y * y4), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if k < -9.0000000000000003e-16

   1. Initial program 24.5%

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

   3. Taylor expanded in y4 around inf 45.3%

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

   4. Taylor expanded in k around inf 49.4%

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

      1. +-commutative 49.4%

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

      2. mul-1-neg 49.4%

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

      3. unsub-neg 49.4%

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

      4. *-commutative 49.4%

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

   6. Simplified 49.4%

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

   if -9.0000000000000003e-16 < k < -1.6e-186

   1. Initial program 55.5%

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

   3. Simplified 55.5%

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

   5. Taylor expanded in z around -inf 56.3%

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

   6. Taylor expanded in c around inf 45.2%

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

   if -1.6e-186 < k < -3.80000000000000024e-237

   1. Initial program 34.6%

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

   3. Simplified 34.6%

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

   5. Taylor expanded in b around inf 50.3%

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

   6. Taylor expanded in y4 around inf 50.7%

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

   if -3.80000000000000024e-237 < k < 1.99999999999999999e-305

   1. Initial program 30.4%

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

   3. Taylor expanded in y3 around -inf 59.9%

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

   4. Taylor expanded in y5 around inf 48.2%

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

      1. associate-*r* 48.2%

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

      2. distribute-lft-out-- 48.2%

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

      3. *-commutative 48.2%

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

   6. Simplified 48.2%

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

   if 1.99999999999999999e-305 < k < 4.60000000000000032e-294 or 6.99999999999999986e-276 < k < 1.84999999999999989e-227

   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%

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

   5. Taylor expanded in b around inf 59.1%

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

   6. Taylor expanded in a around inf 59.8%

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

   if 4.60000000000000032e-294 < k < 6.99999999999999986e-276

   1. Initial program 33.3%

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

   3. Simplified 33.3%

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

   5. Taylor expanded in i around -inf 66.7%

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

   6. Taylor expanded in t around inf 100.0%

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

   if 1.84999999999999989e-227 < k < 1.75e20

   1. Initial program 26.4%

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

   3. Simplified 26.4%

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

   5. Taylor expanded in a around inf 43.6%

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

   6. Taylor expanded in y1 around inf 53.0%

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

      1. mul-1-neg 53.0%

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

   8. Simplified 53.0%

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

   if 1.75e20 < k < 4.4999999999999996e165

   1. Initial program 34.4%

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

   3. Taylor expanded in y2 around inf 48.6%

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

   4. Taylor expanded in y0 around inf 66.2%

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

   if 4.4999999999999996e165 < k

   1. Initial program 14.8%

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

   3. Simplified 14.8%

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

   5. Taylor expanded in b around inf 44.6%

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

   6. Taylor expanded in k around -inf 71.0%

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

      1. associate-*r* 71.0%

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

      2. neg-mul-1 71.0%

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

   8. Simplified 71.0%

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

   9. Taylor expanded in z around inf 66.8%

      \[\leadsto b \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \frac{k \cdot \left(y \cdot y4\right)}{z} + k \cdot y0\right)\right)} \]
   10. Step-by-step derivation

       1. +-commutative 66.8%

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

       2. mul-1-neg 66.8%

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

       3. unsub-neg 66.8%

          \[\leadsto b \cdot \left(z \cdot \color{blue}{\left(k \cdot y0 - \frac{k \cdot \left(y \cdot y4\right)}{z}\right)}\right) \]

       4. *-commutative 66.8%

          \[\leadsto b \cdot \left(z \cdot \left(\color{blue}{y0 \cdot k} - \frac{k \cdot \left(y \cdot y4\right)}{z}\right)\right) \]

       5. associate-/l* 74.6%

          \[\leadsto b \cdot \left(z \cdot \left(y0 \cdot k - \color{blue}{k \cdot \frac{y \cdot y4}{z}}\right)\right) \]

   11. Simplified 74.6%

       \[\leadsto b \cdot \color{blue}{\left(z \cdot \left(y0 \cdot k - k \cdot \frac{y \cdot y4}{z}\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -9 \cdot 10^{-16}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;k \leq -1.6 \cdot 10^{-186}:\\ \;\;\;\;z \cdot \left(c \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq -3.8 \cdot 10^{-237}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;k \leq 2 \cdot 10^{-305}:\\ \;\;\;\;\left(y3 \cdot y5\right) \cdot \left(j \cdot y0 - y \cdot a\right)\\ \mathbf{elif}\;k \leq 4.6 \cdot 10^{-294}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;k \leq 7 \cdot 10^{-276}:\\ \;\;\;\;i \cdot \left(t \cdot \left(z \cdot c - j \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 1.85 \cdot 10^{-227}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;k \leq 1.75 \cdot 10^{+20}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 4.5 \cdot 10^{+165}:\\ \;\;\;\;y2 \cdot \left(y0 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0 - k \cdot \frac{y \cdot y4}{z}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 32.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{if}\;k \leq -9 \cdot 10^{-16}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;k \leq -2.1 \cdot 10^{-186}:\\ \;\;\;\;z \cdot \left(c \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq -3.5 \cdot 10^{-237}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;k \leq 3.9 \cdot 10^{-305}:\\ \;\;\;\;\left(y3 \cdot y5\right) \cdot \left(j \cdot y0 - y \cdot a\right)\\ \mathbf{elif}\;k \leq 2.7 \cdot 10^{-292}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq 7.5 \cdot 10^{-276}:\\ \;\;\;\;i \cdot \left(t \cdot \left(z \cdot c - j \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 4.8 \cdot 10^{-229}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq 1.8 \cdot 10^{+20}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 1.25 \cdot 10^{+166}:\\ \;\;\;\;y2 \cdot \left(y0 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* a (- (* x y) (* z t))))))
   (if (<= k -9e-16)
     (* y4 (* k (- (* y1 y2) (* y b))))
     (if (<= k -2.1e-186)
       (* z (* c (- (* t i) (* y0 y3))))
       (if (<= k -3.5e-237)
         (* b (* y4 (- (* t j) (* y k))))
         (if (<= k 3.9e-305)
           (* (* y3 y5) (- (* j y0) (* y a)))
           (if (<= k 2.7e-292)
             t_1
             (if (<= k 7.5e-276)
               (* i (* t (- (* z c) (* j y5))))
               (if (<= k 4.8e-229)
                 t_1
                 (if (<= k 1.8e+20)
                   (* a (* y1 (- (* z y3) (* x y2))))
                   (if (<= k 1.25e+166)
                     (* y2 (* y0 (- (* x c) (* k y5))))
                     (* b (* k (- (* z y0) (* y y4)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (a * ((x * y) - (z * t)));
	double tmp;
	if (k <= -9e-16) {
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	} else if (k <= -2.1e-186) {
		tmp = z * (c * ((t * i) - (y0 * y3)));
	} else if (k <= -3.5e-237) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (k <= 3.9e-305) {
		tmp = (y3 * y5) * ((j * y0) - (y * a));
	} else if (k <= 2.7e-292) {
		tmp = t_1;
	} else if (k <= 7.5e-276) {
		tmp = i * (t * ((z * c) - (j * y5)));
	} else if (k <= 4.8e-229) {
		tmp = t_1;
	} else if (k <= 1.8e+20) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (k <= 1.25e+166) {
		tmp = y2 * (y0 * ((x * c) - (k * y5)));
	} else {
		tmp = b * (k * ((z * y0) - (y * y4)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a * ((x * y) - (z * t)))
    if (k <= (-9d-16)) then
        tmp = y4 * (k * ((y1 * y2) - (y * b)))
    else if (k <= (-2.1d-186)) then
        tmp = z * (c * ((t * i) - (y0 * y3)))
    else if (k <= (-3.5d-237)) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (k <= 3.9d-305) then
        tmp = (y3 * y5) * ((j * y0) - (y * a))
    else if (k <= 2.7d-292) then
        tmp = t_1
    else if (k <= 7.5d-276) then
        tmp = i * (t * ((z * c) - (j * y5)))
    else if (k <= 4.8d-229) then
        tmp = t_1
    else if (k <= 1.8d+20) then
        tmp = a * (y1 * ((z * y3) - (x * y2)))
    else if (k <= 1.25d+166) then
        tmp = y2 * (y0 * ((x * c) - (k * y5)))
    else
        tmp = b * (k * ((z * y0) - (y * y4)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (a * ((x * y) - (z * t)));
	double tmp;
	if (k <= -9e-16) {
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	} else if (k <= -2.1e-186) {
		tmp = z * (c * ((t * i) - (y0 * y3)));
	} else if (k <= -3.5e-237) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (k <= 3.9e-305) {
		tmp = (y3 * y5) * ((j * y0) - (y * a));
	} else if (k <= 2.7e-292) {
		tmp = t_1;
	} else if (k <= 7.5e-276) {
		tmp = i * (t * ((z * c) - (j * y5)));
	} else if (k <= 4.8e-229) {
		tmp = t_1;
	} else if (k <= 1.8e+20) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (k <= 1.25e+166) {
		tmp = y2 * (y0 * ((x * c) - (k * y5)));
	} else {
		tmp = b * (k * ((z * y0) - (y * y4)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (a * ((x * y) - (z * t)))
	tmp = 0
	if k <= -9e-16:
		tmp = y4 * (k * ((y1 * y2) - (y * b)))
	elif k <= -2.1e-186:
		tmp = z * (c * ((t * i) - (y0 * y3)))
	elif k <= -3.5e-237:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif k <= 3.9e-305:
		tmp = (y3 * y5) * ((j * y0) - (y * a))
	elif k <= 2.7e-292:
		tmp = t_1
	elif k <= 7.5e-276:
		tmp = i * (t * ((z * c) - (j * y5)))
	elif k <= 4.8e-229:
		tmp = t_1
	elif k <= 1.8e+20:
		tmp = a * (y1 * ((z * y3) - (x * y2)))
	elif k <= 1.25e+166:
		tmp = y2 * (y0 * ((x * c) - (k * y5)))
	else:
		tmp = b * (k * ((z * y0) - (y * y4)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))))
	tmp = 0.0
	if (k <= -9e-16)
		tmp = Float64(y4 * Float64(k * Float64(Float64(y1 * y2) - Float64(y * b))));
	elseif (k <= -2.1e-186)
		tmp = Float64(z * Float64(c * Float64(Float64(t * i) - Float64(y0 * y3))));
	elseif (k <= -3.5e-237)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (k <= 3.9e-305)
		tmp = Float64(Float64(y3 * y5) * Float64(Float64(j * y0) - Float64(y * a)));
	elseif (k <= 2.7e-292)
		tmp = t_1;
	elseif (k <= 7.5e-276)
		tmp = Float64(i * Float64(t * Float64(Float64(z * c) - Float64(j * y5))));
	elseif (k <= 4.8e-229)
		tmp = t_1;
	elseif (k <= 1.8e+20)
		tmp = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))));
	elseif (k <= 1.25e+166)
		tmp = Float64(y2 * Float64(y0 * Float64(Float64(x * c) - Float64(k * y5))));
	else
		tmp = Float64(b * Float64(k * Float64(Float64(z * y0) - Float64(y * y4))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (a * ((x * y) - (z * t)));
	tmp = 0.0;
	if (k <= -9e-16)
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	elseif (k <= -2.1e-186)
		tmp = z * (c * ((t * i) - (y0 * y3)));
	elseif (k <= -3.5e-237)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (k <= 3.9e-305)
		tmp = (y3 * y5) * ((j * y0) - (y * a));
	elseif (k <= 2.7e-292)
		tmp = t_1;
	elseif (k <= 7.5e-276)
		tmp = i * (t * ((z * c) - (j * y5)));
	elseif (k <= 4.8e-229)
		tmp = t_1;
	elseif (k <= 1.8e+20)
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	elseif (k <= 1.25e+166)
		tmp = y2 * (y0 * ((x * c) - (k * y5)));
	else
		tmp = b * (k * ((z * y0) - (y * y4)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -9e-16], N[(y4 * N[(k * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -2.1e-186], N[(z * N[(c * N[(N[(t * i), $MachinePrecision] - N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -3.5e-237], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 3.9e-305], N[(N[(y3 * y5), $MachinePrecision] * N[(N[(j * y0), $MachinePrecision] - N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.7e-292], t$95$1, If[LessEqual[k, 7.5e-276], N[(i * N[(t * N[(N[(z * c), $MachinePrecision] - N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 4.8e-229], t$95$1, If[LessEqual[k, 1.8e+20], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.25e+166], N[(y2 * N[(y0 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if k < -9.0000000000000003e-16

   1. Initial program 24.5%

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

   3. Taylor expanded in y4 around inf 45.3%

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

   4. Taylor expanded in k around inf 49.4%

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

      1. +-commutative 49.4%

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

      2. mul-1-neg 49.4%

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

      3. unsub-neg 49.4%

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

      4. *-commutative 49.4%

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

   6. Simplified 49.4%

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

   if -9.0000000000000003e-16 < k < -2.1000000000000002e-186

   1. Initial program 55.5%

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

   3. Simplified 55.5%

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

   5. Taylor expanded in z around -inf 56.3%

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

   6. Taylor expanded in c around inf 45.2%

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

   if -2.1000000000000002e-186 < k < -3.49999999999999983e-237

   1. Initial program 34.6%

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

   3. Simplified 34.6%

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

   5. Taylor expanded in b around inf 50.3%

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

   6. Taylor expanded in y4 around inf 50.7%

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

   if -3.49999999999999983e-237 < k < 3.90000000000000025e-305

   1. Initial program 30.4%

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

   3. Taylor expanded in y3 around -inf 59.9%

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

   4. Taylor expanded in y5 around inf 48.2%

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

      1. associate-*r* 48.2%

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

      2. distribute-lft-out-- 48.2%

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

      3. *-commutative 48.2%

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

   6. Simplified 48.2%

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

   if 3.90000000000000025e-305 < k < 2.6999999999999999e-292 or 7.500000000000001e-276 < k < 4.8e-229

   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%

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

   5. Taylor expanded in b around inf 59.1%

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

   6. Taylor expanded in a around inf 59.8%

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

   if 2.6999999999999999e-292 < k < 7.500000000000001e-276

   1. Initial program 33.3%

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

   3. Simplified 33.3%

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

   5. Taylor expanded in i around -inf 66.7%

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

   6. Taylor expanded in t around inf 100.0%

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

   if 4.8e-229 < k < 1.8e20

   1. Initial program 26.4%

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

   3. Simplified 26.4%

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

   5. Taylor expanded in a around inf 43.6%

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

   6. Taylor expanded in y1 around inf 53.0%

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

      1. mul-1-neg 53.0%

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

   8. Simplified 53.0%

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

   if 1.8e20 < k < 1.25e166

   1. Initial program 34.4%

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

   3. Taylor expanded in y2 around inf 48.6%

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

   4. Taylor expanded in y0 around inf 66.2%

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

   if 1.25e166 < k

   1. Initial program 14.8%

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

   3. Simplified 14.8%

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

   5. Taylor expanded in b around inf 44.6%

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

   6. Taylor expanded in k around -inf 71.0%

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

      1. associate-*r* 71.0%

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

      2. neg-mul-1 71.0%

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

   8. Simplified 71.0%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -9 \cdot 10^{-16}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;k \leq -2.1 \cdot 10^{-186}:\\ \;\;\;\;z \cdot \left(c \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq -3.5 \cdot 10^{-237}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;k \leq 3.9 \cdot 10^{-305}:\\ \;\;\;\;\left(y3 \cdot y5\right) \cdot \left(j \cdot y0 - y \cdot a\right)\\ \mathbf{elif}\;k \leq 2.7 \cdot 10^{-292}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;k \leq 7.5 \cdot 10^{-276}:\\ \;\;\;\;i \cdot \left(t \cdot \left(z \cdot c - j \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 4.8 \cdot 10^{-229}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;k \leq 1.8 \cdot 10^{+20}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 1.25 \cdot 10^{+166}:\\ \;\;\;\;y2 \cdot \left(y0 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 31.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{if}\;k \leq -61000000:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;k \leq -3 \cdot 10^{-94}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;k \leq -1.9 \cdot 10^{-273}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 6 \cdot 10^{-142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq 1.35 \cdot 10^{-88}:\\ \;\;\;\;i \cdot \left(x \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;k \leq 1.45 \cdot 10^{-53}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;k \leq 2 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq 3.6 \cdot 10^{+122}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 3.5 \cdot 10^{+165}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y1 (- (* z y3) (* x y2))))))
   (if (<= k -61000000.0)
     (* y4 (* k (- (* y1 y2) (* y b))))
     (if (<= k -3e-94)
       (* i (* y5 (- (* y k) (* t j))))
       (if (<= k -1.9e-273)
         (* a (* y3 (- (* z y1) (* y y5))))
         (if (<= k 6e-142)
           t_1
           (if (<= k 1.35e-88)
             (* i (* x (- (* j y1) (* y c))))
             (if (<= k 1.45e-53)
               (* y2 (* x (- (* c y0) (* a y1))))
               (if (<= k 2e+20)
                 t_1
                 (if (<= k 3.6e+122)
                   (* k (* y2 (- (* y1 y4) (* y0 y5))))
                   (if (<= k 3.5e+165)
                     (* a (* y (- (* x b) (* y3 y5))))
                     (* b (* k (- (* z y0) (* y y4)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y1 * ((z * y3) - (x * y2)));
	double tmp;
	if (k <= -61000000.0) {
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	} else if (k <= -3e-94) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (k <= -1.9e-273) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (k <= 6e-142) {
		tmp = t_1;
	} else if (k <= 1.35e-88) {
		tmp = i * (x * ((j * y1) - (y * c)));
	} else if (k <= 1.45e-53) {
		tmp = y2 * (x * ((c * y0) - (a * y1)));
	} else if (k <= 2e+20) {
		tmp = t_1;
	} else if (k <= 3.6e+122) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (k <= 3.5e+165) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else {
		tmp = b * (k * ((z * y0) - (y * y4)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (y1 * ((z * y3) - (x * y2)))
    if (k <= (-61000000.0d0)) then
        tmp = y4 * (k * ((y1 * y2) - (y * b)))
    else if (k <= (-3d-94)) then
        tmp = i * (y5 * ((y * k) - (t * j)))
    else if (k <= (-1.9d-273)) then
        tmp = a * (y3 * ((z * y1) - (y * y5)))
    else if (k <= 6d-142) then
        tmp = t_1
    else if (k <= 1.35d-88) then
        tmp = i * (x * ((j * y1) - (y * c)))
    else if (k <= 1.45d-53) then
        tmp = y2 * (x * ((c * y0) - (a * y1)))
    else if (k <= 2d+20) then
        tmp = t_1
    else if (k <= 3.6d+122) then
        tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
    else if (k <= 3.5d+165) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else
        tmp = b * (k * ((z * y0) - (y * y4)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y1 * ((z * y3) - (x * y2)));
	double tmp;
	if (k <= -61000000.0) {
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	} else if (k <= -3e-94) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (k <= -1.9e-273) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (k <= 6e-142) {
		tmp = t_1;
	} else if (k <= 1.35e-88) {
		tmp = i * (x * ((j * y1) - (y * c)));
	} else if (k <= 1.45e-53) {
		tmp = y2 * (x * ((c * y0) - (a * y1)));
	} else if (k <= 2e+20) {
		tmp = t_1;
	} else if (k <= 3.6e+122) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (k <= 3.5e+165) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else {
		tmp = b * (k * ((z * y0) - (y * y4)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y1 * ((z * y3) - (x * y2)))
	tmp = 0
	if k <= -61000000.0:
		tmp = y4 * (k * ((y1 * y2) - (y * b)))
	elif k <= -3e-94:
		tmp = i * (y5 * ((y * k) - (t * j)))
	elif k <= -1.9e-273:
		tmp = a * (y3 * ((z * y1) - (y * y5)))
	elif k <= 6e-142:
		tmp = t_1
	elif k <= 1.35e-88:
		tmp = i * (x * ((j * y1) - (y * c)))
	elif k <= 1.45e-53:
		tmp = y2 * (x * ((c * y0) - (a * y1)))
	elif k <= 2e+20:
		tmp = t_1
	elif k <= 3.6e+122:
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
	elif k <= 3.5e+165:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	else:
		tmp = b * (k * ((z * y0) - (y * y4)))
	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(y1 * Float64(Float64(z * y3) - Float64(x * y2))))
	tmp = 0.0
	if (k <= -61000000.0)
		tmp = Float64(y4 * Float64(k * Float64(Float64(y1 * y2) - Float64(y * b))));
	elseif (k <= -3e-94)
		tmp = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))));
	elseif (k <= -1.9e-273)
		tmp = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))));
	elseif (k <= 6e-142)
		tmp = t_1;
	elseif (k <= 1.35e-88)
		tmp = Float64(i * Float64(x * Float64(Float64(j * y1) - Float64(y * c))));
	elseif (k <= 1.45e-53)
		tmp = Float64(y2 * Float64(x * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (k <= 2e+20)
		tmp = t_1;
	elseif (k <= 3.6e+122)
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	elseif (k <= 3.5e+165)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	else
		tmp = Float64(b * Float64(k * Float64(Float64(z * y0) - Float64(y * y4))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y1 * ((z * y3) - (x * y2)));
	tmp = 0.0;
	if (k <= -61000000.0)
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	elseif (k <= -3e-94)
		tmp = i * (y5 * ((y * k) - (t * j)));
	elseif (k <= -1.9e-273)
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	elseif (k <= 6e-142)
		tmp = t_1;
	elseif (k <= 1.35e-88)
		tmp = i * (x * ((j * y1) - (y * c)));
	elseif (k <= 1.45e-53)
		tmp = y2 * (x * ((c * y0) - (a * y1)));
	elseif (k <= 2e+20)
		tmp = t_1;
	elseif (k <= 3.6e+122)
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	elseif (k <= 3.5e+165)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	else
		tmp = b * (k * ((z * y0) - (y * y4)));
	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[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -61000000.0], N[(y4 * N[(k * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -3e-94], N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -1.9e-273], N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 6e-142], t$95$1, If[LessEqual[k, 1.35e-88], N[(i * N[(x * N[(N[(j * y1), $MachinePrecision] - N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.45e-53], N[(y2 * N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2e+20], t$95$1, If[LessEqual[k, 3.6e+122], N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 3.5e+165], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if k < -6.1e7

   1. Initial program 24.5%

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

   3. Taylor expanded in y4 around inf 46.4%

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

   4. Taylor expanded in k around inf 50.8%

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

      1. +-commutative 50.8%

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

      2. mul-1-neg 50.8%

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

      3. unsub-neg 50.8%

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

      4. *-commutative 50.8%

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

   6. Simplified 50.8%

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

   if -6.1e7 < k < -3.0000000000000001e-94

   1. Initial program 47.5%

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

   3. Simplified 47.5%

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

   5. Taylor expanded in i around -inf 57.7%

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

   6. Taylor expanded in y5 around inf 43.6%

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

   if -3.0000000000000001e-94 < k < -1.9000000000000002e-273

   1. Initial program 42.8%

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

   3. Simplified 45.0%

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

   5. Taylor expanded in a around inf 38.5%

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

   6. Taylor expanded in y3 around inf 36.8%

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

   if -1.9000000000000002e-273 < k < 6.0000000000000002e-142 or 1.4499999999999999e-53 < k < 2e20

   1. Initial program 32.1%

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

   3. Simplified 32.1%

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

   5. Taylor expanded in a around inf 53.1%

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

   6. Taylor expanded in y1 around inf 50.7%

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

      1. mul-1-neg 50.7%

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

   8. Simplified 50.7%

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

   if 6.0000000000000002e-142 < k < 1.34999999999999997e-88

   1. Initial program 12.5%

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

   3. Simplified 12.5%

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

   5. Taylor expanded in i around -inf 50.4%

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

   6. Taylor expanded in x around inf 51.3%

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

   if 1.34999999999999997e-88 < k < 1.4499999999999999e-53

   1. Initial program 38.2%

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

   3. Taylor expanded in y2 around inf 54.7%

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

   4. Taylor expanded in x around inf 63.6%

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

   if 2e20 < k < 3.6000000000000003e122

   1. Initial program 44.4%

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

   3. Taylor expanded in y2 around inf 61.3%

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

   4. Taylor expanded in k around inf 62.4%

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

   if 3.6000000000000003e122 < k < 3.49999999999999996e165

   1. Initial program 18.0%

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

   3. Simplified 18.0%

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

   5. Taylor expanded in a around inf 63.7%

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

   6. Taylor expanded in y around inf 64.2%

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

   if 3.49999999999999996e165 < k

   1. Initial program 14.8%

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

   3. Simplified 14.8%

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

   5. Taylor expanded in b around inf 44.6%

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

   6. Taylor expanded in k around -inf 71.0%

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

      1. associate-*r* 71.0%

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

      2. neg-mul-1 71.0%

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

   8. Simplified 71.0%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -61000000:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;k \leq -3 \cdot 10^{-94}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;k \leq -1.9 \cdot 10^{-273}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 6 \cdot 10^{-142}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 1.35 \cdot 10^{-88}:\\ \;\;\;\;i \cdot \left(x \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;k \leq 1.45 \cdot 10^{-53}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;k \leq 2 \cdot 10^{+20}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 3.6 \cdot 10^{+122}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 3.5 \cdot 10^{+165}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 29.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ t_2 := b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{if}\;a \leq -1.35 \cdot 10^{+119}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-160}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-224}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-296}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 10^{+32}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+100}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+149}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+266}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (* y2 (- (* y1 y4) (* y0 y5)))))
        (t_2 (* b (* y4 (- (* t j) (* y k))))))
   (if (<= a -1.35e+119)
     (* t (* y2 (- (* a y5) (* c y4))))
     (if (<= a -3.2e-91)
       t_1
       (if (<= a -5e-160)
         t_2
         (if (<= a -4.5e-224)
           (* b (* y0 (- (* z k) (* x j))))
           (if (<= a 1.9e-296)
             t_1
             (if (<= a 1e+32)
               (* b (* k (- (* z y0) (* y y4))))
               (if (<= a 1.2e+100)
                 (* y4 (* j (- (* t b) (* y1 y3))))
                 (if (<= a 1.6e+149)
                   (* a (* y1 (- (* z y3) (* x y2))))
                   (if (<= a 5.2e+266)
                     t_2
                     (* b (* x (- (* y a) (* j y0)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (y2 * ((y1 * y4) - (y0 * y5)));
	double t_2 = b * (y4 * ((t * j) - (y * k)));
	double tmp;
	if (a <= -1.35e+119) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (a <= -3.2e-91) {
		tmp = t_1;
	} else if (a <= -5e-160) {
		tmp = t_2;
	} else if (a <= -4.5e-224) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (a <= 1.9e-296) {
		tmp = t_1;
	} else if (a <= 1e+32) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (a <= 1.2e+100) {
		tmp = y4 * (j * ((t * b) - (y1 * y3)));
	} else if (a <= 1.6e+149) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (a <= 5.2e+266) {
		tmp = t_2;
	} else {
		tmp = b * (x * ((y * a) - (j * y0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = k * (y2 * ((y1 * y4) - (y0 * y5)))
    t_2 = b * (y4 * ((t * j) - (y * k)))
    if (a <= (-1.35d+119)) then
        tmp = t * (y2 * ((a * y5) - (c * y4)))
    else if (a <= (-3.2d-91)) then
        tmp = t_1
    else if (a <= (-5d-160)) then
        tmp = t_2
    else if (a <= (-4.5d-224)) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (a <= 1.9d-296) then
        tmp = t_1
    else if (a <= 1d+32) then
        tmp = b * (k * ((z * y0) - (y * y4)))
    else if (a <= 1.2d+100) then
        tmp = y4 * (j * ((t * b) - (y1 * y3)))
    else if (a <= 1.6d+149) then
        tmp = a * (y1 * ((z * y3) - (x * y2)))
    else if (a <= 5.2d+266) then
        tmp = t_2
    else
        tmp = b * (x * ((y * a) - (j * y0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (y2 * ((y1 * y4) - (y0 * y5)));
	double t_2 = b * (y4 * ((t * j) - (y * k)));
	double tmp;
	if (a <= -1.35e+119) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (a <= -3.2e-91) {
		tmp = t_1;
	} else if (a <= -5e-160) {
		tmp = t_2;
	} else if (a <= -4.5e-224) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (a <= 1.9e-296) {
		tmp = t_1;
	} else if (a <= 1e+32) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (a <= 1.2e+100) {
		tmp = y4 * (j * ((t * b) - (y1 * y3)));
	} else if (a <= 1.6e+149) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (a <= 5.2e+266) {
		tmp = t_2;
	} else {
		tmp = b * (x * ((y * a) - (j * y0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = k * (y2 * ((y1 * y4) - (y0 * y5)))
	t_2 = b * (y4 * ((t * j) - (y * k)))
	tmp = 0
	if a <= -1.35e+119:
		tmp = t * (y2 * ((a * y5) - (c * y4)))
	elif a <= -3.2e-91:
		tmp = t_1
	elif a <= -5e-160:
		tmp = t_2
	elif a <= -4.5e-224:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif a <= 1.9e-296:
		tmp = t_1
	elif a <= 1e+32:
		tmp = b * (k * ((z * y0) - (y * y4)))
	elif a <= 1.2e+100:
		tmp = y4 * (j * ((t * b) - (y1 * y3)))
	elif a <= 1.6e+149:
		tmp = a * (y1 * ((z * y3) - (x * y2)))
	elif a <= 5.2e+266:
		tmp = t_2
	else:
		tmp = b * (x * ((y * a) - (j * y0)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))))
	t_2 = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))))
	tmp = 0.0
	if (a <= -1.35e+119)
		tmp = Float64(t * Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))));
	elseif (a <= -3.2e-91)
		tmp = t_1;
	elseif (a <= -5e-160)
		tmp = t_2;
	elseif (a <= -4.5e-224)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (a <= 1.9e-296)
		tmp = t_1;
	elseif (a <= 1e+32)
		tmp = Float64(b * Float64(k * Float64(Float64(z * y0) - Float64(y * y4))));
	elseif (a <= 1.2e+100)
		tmp = Float64(y4 * Float64(j * Float64(Float64(t * b) - Float64(y1 * y3))));
	elseif (a <= 1.6e+149)
		tmp = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))));
	elseif (a <= 5.2e+266)
		tmp = t_2;
	else
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = k * (y2 * ((y1 * y4) - (y0 * y5)));
	t_2 = b * (y4 * ((t * j) - (y * k)));
	tmp = 0.0;
	if (a <= -1.35e+119)
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	elseif (a <= -3.2e-91)
		tmp = t_1;
	elseif (a <= -5e-160)
		tmp = t_2;
	elseif (a <= -4.5e-224)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (a <= 1.9e-296)
		tmp = t_1;
	elseif (a <= 1e+32)
		tmp = b * (k * ((z * y0) - (y * y4)));
	elseif (a <= 1.2e+100)
		tmp = y4 * (j * ((t * b) - (y1 * y3)));
	elseif (a <= 1.6e+149)
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	elseif (a <= 5.2e+266)
		tmp = t_2;
	else
		tmp = b * (x * ((y * a) - (j * y0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.35e+119], N[(t * N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.2e-91], t$95$1, If[LessEqual[a, -5e-160], t$95$2, If[LessEqual[a, -4.5e-224], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.9e-296], t$95$1, If[LessEqual[a, 1e+32], N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.2e+100], N[(y4 * N[(j * N[(N[(t * b), $MachinePrecision] - N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.6e+149], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.2e+266], t$95$2, N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if a < -1.3499999999999999e119

   1. Initial program 31.7%

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

   3. Taylor expanded in y2 around inf 41.8%

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

   4. Taylor expanded in t around inf 51.8%

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

   if -1.3499999999999999e119 < a < -3.19999999999999996e-91 or -4.5000000000000004e-224 < a < 1.9000000000000001e-296

   1. Initial program 37.5%

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

   3. Taylor expanded in y2 around inf 40.0%

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

   4. Taylor expanded in k around inf 42.1%

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

   if -3.19999999999999996e-91 < a < -4.99999999999999994e-160 or 1.6000000000000001e149 < a < 5.20000000000000027e266

   1. Initial program 26.9%

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

   3. Simplified 26.9%

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

   5. Taylor expanded in b around inf 41.9%

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

   6. Taylor expanded in y4 around inf 54.0%

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

   if -4.99999999999999994e-160 < a < -4.5000000000000004e-224

   1. Initial program 42.9%

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

   3. Simplified 42.9%

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

   5. Taylor expanded in b around inf 43.2%

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

   6. Taylor expanded in y0 around inf 50.5%

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

   if 1.9000000000000001e-296 < a < 1.00000000000000005e32

   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 28.2%

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

   5. Taylor expanded in b around inf 39.6%

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

   6. Taylor expanded in k around -inf 44.0%

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

      1. associate-*r* 44.0%

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

      2. neg-mul-1 44.0%

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

   8. Simplified 44.0%

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

   if 1.00000000000000005e32 < a < 1.20000000000000006e100

   1. Initial program 27.8%

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

   3. Taylor expanded in y4 around inf 55.9%

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

   4. Taylor expanded in j around inf 61.9%

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

      1. +-commutative 61.9%

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

      2. mul-1-neg 61.9%

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

      3. unsub-neg 61.9%

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

      4. *-commutative 61.9%

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

   6. Simplified 61.9%

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

   if 1.20000000000000006e100 < a < 1.6000000000000001e149

   1. Initial program 27.3%

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

   3. Simplified 27.3%

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

   5. Taylor expanded in a around inf 55.4%

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

   6. Taylor expanded in y1 around inf 83.0%

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

      1. mul-1-neg 83.0%

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

   8. Simplified 83.0%

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

   if 5.20000000000000027e266 < a

   1. Initial program 22.2%

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

   3. Simplified 22.2%

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

   5. Taylor expanded in b around inf 55.6%

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

   6. Taylor expanded in x around inf 67.0%

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

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{+119}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-91}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-160}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-224}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-296}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 10^{+32}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+100}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+149}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+266}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 28.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ t_2 := b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{if}\;a \leq -6 \cdot 10^{+118}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-157}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-225}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;a \leq 10^{-296}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 8.4 \cdot 10^{+30}:\\ \;\;\;\;\left(b \cdot k\right) \cdot \left(z \cdot y0 - y \cdot y4\right)\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+94}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+151}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+268}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (* y2 (- (* y1 y4) (* y0 y5)))))
        (t_2 (* b (* y4 (- (* t j) (* y k))))))
   (if (<= a -6e+118)
     (* t (* y2 (- (* a y5) (* c y4))))
     (if (<= a -2.6e-95)
       t_1
       (if (<= a -1.15e-157)
         t_2
         (if (<= a -1.3e-225)
           (* b (* y0 (- (* z k) (* x j))))
           (if (<= a 1e-296)
             t_1
             (if (<= a 8.4e+30)
               (* (* b k) (- (* z y0) (* y y4)))
               (if (<= a 2.7e+94)
                 (* y4 (* j (- (* t b) (* y1 y3))))
                 (if (<= a 4.8e+151)
                   (* a (* y1 (- (* z y3) (* x y2))))
                   (if (<= a 1.4e+268)
                     t_2
                     (* b (* x (- (* y a) (* j y0)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (y2 * ((y1 * y4) - (y0 * y5)));
	double t_2 = b * (y4 * ((t * j) - (y * k)));
	double tmp;
	if (a <= -6e+118) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (a <= -2.6e-95) {
		tmp = t_1;
	} else if (a <= -1.15e-157) {
		tmp = t_2;
	} else if (a <= -1.3e-225) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (a <= 1e-296) {
		tmp = t_1;
	} else if (a <= 8.4e+30) {
		tmp = (b * k) * ((z * y0) - (y * y4));
	} else if (a <= 2.7e+94) {
		tmp = y4 * (j * ((t * b) - (y1 * y3)));
	} else if (a <= 4.8e+151) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (a <= 1.4e+268) {
		tmp = t_2;
	} else {
		tmp = b * (x * ((y * a) - (j * y0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = k * (y2 * ((y1 * y4) - (y0 * y5)))
    t_2 = b * (y4 * ((t * j) - (y * k)))
    if (a <= (-6d+118)) then
        tmp = t * (y2 * ((a * y5) - (c * y4)))
    else if (a <= (-2.6d-95)) then
        tmp = t_1
    else if (a <= (-1.15d-157)) then
        tmp = t_2
    else if (a <= (-1.3d-225)) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (a <= 1d-296) then
        tmp = t_1
    else if (a <= 8.4d+30) then
        tmp = (b * k) * ((z * y0) - (y * y4))
    else if (a <= 2.7d+94) then
        tmp = y4 * (j * ((t * b) - (y1 * y3)))
    else if (a <= 4.8d+151) then
        tmp = a * (y1 * ((z * y3) - (x * y2)))
    else if (a <= 1.4d+268) then
        tmp = t_2
    else
        tmp = b * (x * ((y * a) - (j * y0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (y2 * ((y1 * y4) - (y0 * y5)));
	double t_2 = b * (y4 * ((t * j) - (y * k)));
	double tmp;
	if (a <= -6e+118) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (a <= -2.6e-95) {
		tmp = t_1;
	} else if (a <= -1.15e-157) {
		tmp = t_2;
	} else if (a <= -1.3e-225) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (a <= 1e-296) {
		tmp = t_1;
	} else if (a <= 8.4e+30) {
		tmp = (b * k) * ((z * y0) - (y * y4));
	} else if (a <= 2.7e+94) {
		tmp = y4 * (j * ((t * b) - (y1 * y3)));
	} else if (a <= 4.8e+151) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (a <= 1.4e+268) {
		tmp = t_2;
	} else {
		tmp = b * (x * ((y * a) - (j * y0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = k * (y2 * ((y1 * y4) - (y0 * y5)))
	t_2 = b * (y4 * ((t * j) - (y * k)))
	tmp = 0
	if a <= -6e+118:
		tmp = t * (y2 * ((a * y5) - (c * y4)))
	elif a <= -2.6e-95:
		tmp = t_1
	elif a <= -1.15e-157:
		tmp = t_2
	elif a <= -1.3e-225:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif a <= 1e-296:
		tmp = t_1
	elif a <= 8.4e+30:
		tmp = (b * k) * ((z * y0) - (y * y4))
	elif a <= 2.7e+94:
		tmp = y4 * (j * ((t * b) - (y1 * y3)))
	elif a <= 4.8e+151:
		tmp = a * (y1 * ((z * y3) - (x * y2)))
	elif a <= 1.4e+268:
		tmp = t_2
	else:
		tmp = b * (x * ((y * a) - (j * y0)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))))
	t_2 = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))))
	tmp = 0.0
	if (a <= -6e+118)
		tmp = Float64(t * Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))));
	elseif (a <= -2.6e-95)
		tmp = t_1;
	elseif (a <= -1.15e-157)
		tmp = t_2;
	elseif (a <= -1.3e-225)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (a <= 1e-296)
		tmp = t_1;
	elseif (a <= 8.4e+30)
		tmp = Float64(Float64(b * k) * Float64(Float64(z * y0) - Float64(y * y4)));
	elseif (a <= 2.7e+94)
		tmp = Float64(y4 * Float64(j * Float64(Float64(t * b) - Float64(y1 * y3))));
	elseif (a <= 4.8e+151)
		tmp = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))));
	elseif (a <= 1.4e+268)
		tmp = t_2;
	else
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = k * (y2 * ((y1 * y4) - (y0 * y5)));
	t_2 = b * (y4 * ((t * j) - (y * k)));
	tmp = 0.0;
	if (a <= -6e+118)
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	elseif (a <= -2.6e-95)
		tmp = t_1;
	elseif (a <= -1.15e-157)
		tmp = t_2;
	elseif (a <= -1.3e-225)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (a <= 1e-296)
		tmp = t_1;
	elseif (a <= 8.4e+30)
		tmp = (b * k) * ((z * y0) - (y * y4));
	elseif (a <= 2.7e+94)
		tmp = y4 * (j * ((t * b) - (y1 * y3)));
	elseif (a <= 4.8e+151)
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	elseif (a <= 1.4e+268)
		tmp = t_2;
	else
		tmp = b * (x * ((y * a) - (j * y0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6e+118], N[(t * N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.6e-95], t$95$1, If[LessEqual[a, -1.15e-157], t$95$2, If[LessEqual[a, -1.3e-225], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1e-296], t$95$1, If[LessEqual[a, 8.4e+30], N[(N[(b * k), $MachinePrecision] * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.7e+94], N[(y4 * N[(j * N[(N[(t * b), $MachinePrecision] - N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.8e+151], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.4e+268], t$95$2, N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if a < -6e118

   1. Initial program 31.7%

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

   3. Taylor expanded in y2 around inf 41.8%

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

   4. Taylor expanded in t around inf 51.8%

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

   if -6e118 < a < -2.60000000000000001e-95 or -1.30000000000000007e-225 < a < 1e-296

   1. Initial program 37.5%

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

   3. Taylor expanded in y2 around inf 40.0%

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

   4. Taylor expanded in k around inf 42.1%

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

   if -2.60000000000000001e-95 < a < -1.14999999999999994e-157 or 4.8000000000000002e151 < a < 1.4e268

   1. Initial program 26.9%

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

   3. Simplified 26.9%

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

   5. Taylor expanded in b around inf 41.9%

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

   6. Taylor expanded in y4 around inf 54.0%

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

   if -1.14999999999999994e-157 < a < -1.30000000000000007e-225

   1. Initial program 42.9%

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

   3. Simplified 42.9%

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

   5. Taylor expanded in b around inf 43.2%

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

   6. Taylor expanded in y0 around inf 50.5%

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

   if 1e-296 < a < 8.4000000000000001e30

   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 28.2%

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

   5. Taylor expanded in b around inf 39.6%

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

   6. Taylor expanded in k around -inf 44.0%

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

      1. associate-*r* 44.0%

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

      2. neg-mul-1 44.0%

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

   8. Simplified 44.0%

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

   9. Taylor expanded in b around 0 44.0%

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

       1. mul-1-neg 44.0%

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

       2. associate-*r* 42.4%

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

       3. *-commutative 42.4%

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

   11. Simplified 42.4%

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

   if 8.4000000000000001e30 < a < 2.7000000000000001e94

   1. Initial program 27.8%

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

   3. Taylor expanded in y4 around inf 55.9%

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

   4. Taylor expanded in j around inf 61.9%

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

      1. +-commutative 61.9%

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

      2. mul-1-neg 61.9%

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

      3. unsub-neg 61.9%

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

      4. *-commutative 61.9%

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

   6. Simplified 61.9%

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

   if 2.7000000000000001e94 < a < 4.8000000000000002e151

   1. Initial program 27.3%

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

   3. Simplified 27.3%

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

   5. Taylor expanded in a around inf 55.4%

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

   6. Taylor expanded in y1 around inf 83.0%

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

      1. mul-1-neg 83.0%

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

   8. Simplified 83.0%

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

   if 1.4e268 < a

   1. Initial program 22.2%

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

   3. Simplified 22.2%

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

   5. Taylor expanded in b around inf 55.6%

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

   6. Taylor expanded in x around inf 67.0%

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

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+118}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-95}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-157}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-225}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;a \leq 10^{-296}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 8.4 \cdot 10^{+30}:\\ \;\;\;\;\left(b \cdot k\right) \cdot \left(z \cdot y0 - y \cdot y4\right)\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+94}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+151}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+268}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 31.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ t_2 := y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right)\right)\\ t_3 := a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{if}\;y0 \leq -1.05 \cdot 10^{+73}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y0 \leq -3.8 \cdot 10^{-53}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;y0 \leq -2 \cdot 10^{-140}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y0 \leq 7.5 \cdot 10^{-282}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y0 \leq 1.68 \cdot 10^{-136}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;y0 \leq 1.9 \cdot 10^{-42}:\\ \;\;\;\;i \cdot \left(y \cdot \left(c \cdot \left(-x\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 2.1 \cdot 10^{-15}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y0 \leq 1.7 \cdot 10^{+93}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y0 \leq 5.5 \cdot 10^{+196}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* y0 (- (* z k) (* x j)))))
        (t_2 (* y4 (* b (- (* t j) (* y k)))))
        (t_3 (* a (* y3 (- (* z y1) (* y y5))))))
   (if (<= y0 -1.05e+73)
     t_1
     (if (<= y0 -3.8e-53)
       (* y4 (* k (- (* y1 y2) (* y b))))
       (if (<= y0 -2e-140)
         t_3
         (if (<= y0 7.5e-282)
           t_2
           (if (<= y0 1.68e-136)
             (* y2 (* y4 (- (* k y1) (* t c))))
             (if (<= y0 1.9e-42)
               (* i (* y (* c (- x))))
               (if (<= y0 2.1e-15)
                 t_3
                 (if (<= y0 1.7e+93)
                   t_2
                   (if (<= y0 5.5e+196)
                     (* a (* y5 (- (* t y2) (* y 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 = b * (y0 * ((z * k) - (x * j)));
	double t_2 = y4 * (b * ((t * j) - (y * k)));
	double t_3 = a * (y3 * ((z * y1) - (y * y5)));
	double tmp;
	if (y0 <= -1.05e+73) {
		tmp = t_1;
	} else if (y0 <= -3.8e-53) {
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	} else if (y0 <= -2e-140) {
		tmp = t_3;
	} else if (y0 <= 7.5e-282) {
		tmp = t_2;
	} else if (y0 <= 1.68e-136) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (y0 <= 1.9e-42) {
		tmp = i * (y * (c * -x));
	} else if (y0 <= 2.1e-15) {
		tmp = t_3;
	} else if (y0 <= 1.7e+93) {
		tmp = t_2;
	} else if (y0 <= 5.5e+196) {
		tmp = a * (y5 * ((t * y2) - (y * 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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * (y0 * ((z * k) - (x * j)))
    t_2 = y4 * (b * ((t * j) - (y * k)))
    t_3 = a * (y3 * ((z * y1) - (y * y5)))
    if (y0 <= (-1.05d+73)) then
        tmp = t_1
    else if (y0 <= (-3.8d-53)) then
        tmp = y4 * (k * ((y1 * y2) - (y * b)))
    else if (y0 <= (-2d-140)) then
        tmp = t_3
    else if (y0 <= 7.5d-282) then
        tmp = t_2
    else if (y0 <= 1.68d-136) then
        tmp = y2 * (y4 * ((k * y1) - (t * c)))
    else if (y0 <= 1.9d-42) then
        tmp = i * (y * (c * -x))
    else if (y0 <= 2.1d-15) then
        tmp = t_3
    else if (y0 <= 1.7d+93) then
        tmp = t_2
    else if (y0 <= 5.5d+196) then
        tmp = a * (y5 * ((t * y2) - (y * 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 = b * (y0 * ((z * k) - (x * j)));
	double t_2 = y4 * (b * ((t * j) - (y * k)));
	double t_3 = a * (y3 * ((z * y1) - (y * y5)));
	double tmp;
	if (y0 <= -1.05e+73) {
		tmp = t_1;
	} else if (y0 <= -3.8e-53) {
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	} else if (y0 <= -2e-140) {
		tmp = t_3;
	} else if (y0 <= 7.5e-282) {
		tmp = t_2;
	} else if (y0 <= 1.68e-136) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (y0 <= 1.9e-42) {
		tmp = i * (y * (c * -x));
	} else if (y0 <= 2.1e-15) {
		tmp = t_3;
	} else if (y0 <= 1.7e+93) {
		tmp = t_2;
	} else if (y0 <= 5.5e+196) {
		tmp = a * (y5 * ((t * y2) - (y * 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 = b * (y0 * ((z * k) - (x * j)))
	t_2 = y4 * (b * ((t * j) - (y * k)))
	t_3 = a * (y3 * ((z * y1) - (y * y5)))
	tmp = 0
	if y0 <= -1.05e+73:
		tmp = t_1
	elif y0 <= -3.8e-53:
		tmp = y4 * (k * ((y1 * y2) - (y * b)))
	elif y0 <= -2e-140:
		tmp = t_3
	elif y0 <= 7.5e-282:
		tmp = t_2
	elif y0 <= 1.68e-136:
		tmp = y2 * (y4 * ((k * y1) - (t * c)))
	elif y0 <= 1.9e-42:
		tmp = i * (y * (c * -x))
	elif y0 <= 2.1e-15:
		tmp = t_3
	elif y0 <= 1.7e+93:
		tmp = t_2
	elif y0 <= 5.5e+196:
		tmp = a * (y5 * ((t * y2) - (y * 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(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))))
	t_2 = Float64(y4 * Float64(b * Float64(Float64(t * j) - Float64(y * k))))
	t_3 = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))))
	tmp = 0.0
	if (y0 <= -1.05e+73)
		tmp = t_1;
	elseif (y0 <= -3.8e-53)
		tmp = Float64(y4 * Float64(k * Float64(Float64(y1 * y2) - Float64(y * b))));
	elseif (y0 <= -2e-140)
		tmp = t_3;
	elseif (y0 <= 7.5e-282)
		tmp = t_2;
	elseif (y0 <= 1.68e-136)
		tmp = Float64(y2 * Float64(y4 * Float64(Float64(k * y1) - Float64(t * c))));
	elseif (y0 <= 1.9e-42)
		tmp = Float64(i * Float64(y * Float64(c * Float64(-x))));
	elseif (y0 <= 2.1e-15)
		tmp = t_3;
	elseif (y0 <= 1.7e+93)
		tmp = t_2;
	elseif (y0 <= 5.5e+196)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * 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 = b * (y0 * ((z * k) - (x * j)));
	t_2 = y4 * (b * ((t * j) - (y * k)));
	t_3 = a * (y3 * ((z * y1) - (y * y5)));
	tmp = 0.0;
	if (y0 <= -1.05e+73)
		tmp = t_1;
	elseif (y0 <= -3.8e-53)
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	elseif (y0 <= -2e-140)
		tmp = t_3;
	elseif (y0 <= 7.5e-282)
		tmp = t_2;
	elseif (y0 <= 1.68e-136)
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	elseif (y0 <= 1.9e-42)
		tmp = i * (y * (c * -x));
	elseif (y0 <= 2.1e-15)
		tmp = t_3;
	elseif (y0 <= 1.7e+93)
		tmp = t_2;
	elseif (y0 <= 5.5e+196)
		tmp = a * (y5 * ((t * y2) - (y * 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[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y4 * N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -1.05e+73], t$95$1, If[LessEqual[y0, -3.8e-53], N[(y4 * N[(k * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -2e-140], t$95$3, If[LessEqual[y0, 7.5e-282], t$95$2, If[LessEqual[y0, 1.68e-136], N[(y2 * N[(y4 * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.9e-42], N[(i * N[(y * N[(c * (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 2.1e-15], t$95$3, If[LessEqual[y0, 1.7e+93], t$95$2, If[LessEqual[y0, 5.5e+196], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y0 < -1.0500000000000001e73 or 5.49999999999999973e196 < y0

   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 29.6%

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

   5. Taylor expanded in b around inf 36.5%

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

   6. Taylor expanded in y0 around inf 48.6%

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

   if -1.0500000000000001e73 < y0 < -3.7999999999999998e-53

   1. Initial program 33.3%

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

   3. Taylor expanded in y4 around inf 57.2%

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

   4. Taylor expanded in k around inf 58.3%

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

      1. +-commutative 58.3%

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

      2. mul-1-neg 58.3%

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

      3. unsub-neg 58.3%

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

      4. *-commutative 58.3%

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

   6. Simplified 58.3%

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

   if -3.7999999999999998e-53 < y0 < -2e-140 or 1.90000000000000009e-42 < y0 < 2.09999999999999981e-15

   1. Initial program 28.1%

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

   3. Simplified 28.1%

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

   5. Taylor expanded in a around inf 59.6%

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

   6. Taylor expanded in y3 around inf 72.7%

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

   if -2e-140 < y0 < 7.49999999999999937e-282 or 2.09999999999999981e-15 < y0 < 1.7e93

   1. Initial program 38.2%

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

   3. Taylor expanded in y4 around inf 44.2%

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

   4. Taylor expanded in b around inf 42.6%

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

   if 7.49999999999999937e-282 < y0 < 1.67999999999999993e-136

   1. Initial program 35.2%

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

   3. Taylor expanded in y2 around inf 43.9%

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

   4. Taylor expanded in y4 around inf 44.6%

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

   if 1.67999999999999993e-136 < y0 < 1.90000000000000009e-42

   1. Initial program 29.4%

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

   3. Simplified 29.4%

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

   5. Taylor expanded in i around -inf 53.7%

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

   6. Taylor expanded in x around inf 42.1%

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

   7. Taylor expanded in c around inf 47.9%

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

      1. associate-*r* 47.9%

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

   9. Simplified 47.9%

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

   if 1.7e93 < y0 < 5.49999999999999973e196

   1. Initial program 22.2%

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

   3. Simplified 22.2%

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

   5. Taylor expanded in a around inf 52.2%

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

   6. Taylor expanded in y5 around inf 52.9%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -1.05 \cdot 10^{+73}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -3.8 \cdot 10^{-53}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;y0 \leq -2 \cdot 10^{-140}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 7.5 \cdot 10^{-282}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y0 \leq 1.68 \cdot 10^{-136}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;y0 \leq 1.9 \cdot 10^{-42}:\\ \;\;\;\;i \cdot \left(y \cdot \left(c \cdot \left(-x\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 2.1 \cdot 10^{-15}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 1.7 \cdot 10^{+93}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y0 \leq 5.5 \cdot 10^{+196}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 39.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ t_2 := y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;y4 \leq -1.52 \cdot 10^{+209}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;y4 \leq -7 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq -7.5 \cdot 10^{-92}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y4 \leq -1.2 \cdot 10^{-144}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq 5.8 \cdot 10^{-6}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          y3
          (+
           (* y (- (* c y4) (* a y5)))
           (+ (* j (- (* y0 y5) (* y1 y4))) (* z (- (* a y1) (* c y0)))))))
        (t_2
         (*
          y4
          (+
           (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
           (* c (- (* y y3) (* t y2)))))))
   (if (<= y4 -1.52e+209)
     (* j (* y4 (- (* t b) (* y1 y3))))
     (if (<= y4 -7e+39)
       t_1
       (if (<= y4 -7.5e-92)
         t_2
         (if (<= y4 -1.2e-144)
           t_1
           (if (<= y4 5.8e-6)
             (*
              y5
              (+
               (* a (- (* t y2) (* y y3)))
               (+ (* i (- (* y k) (* t j))) (* y0 (- (* j y3) (* k y2))))))
             t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	double t_2 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double tmp;
	if (y4 <= -1.52e+209) {
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	} else if (y4 <= -7e+39) {
		tmp = t_1;
	} else if (y4 <= -7.5e-92) {
		tmp = t_2;
	} else if (y4 <= -1.2e-144) {
		tmp = t_1;
	} else if (y4 <= 5.8e-6) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))))
    t_2 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    if (y4 <= (-1.52d+209)) then
        tmp = j * (y4 * ((t * b) - (y1 * y3)))
    else if (y4 <= (-7d+39)) then
        tmp = t_1
    else if (y4 <= (-7.5d-92)) then
        tmp = t_2
    else if (y4 <= (-1.2d-144)) then
        tmp = t_1
    else if (y4 <= 5.8d-6) then
        tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	double t_2 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double tmp;
	if (y4 <= -1.52e+209) {
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	} else if (y4 <= -7e+39) {
		tmp = t_1;
	} else if (y4 <= -7.5e-92) {
		tmp = t_2;
	} else if (y4 <= -1.2e-144) {
		tmp = t_1;
	} else if (y4 <= 5.8e-6) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))))
	t_2 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	tmp = 0
	if y4 <= -1.52e+209:
		tmp = j * (y4 * ((t * b) - (y1 * y3)))
	elif y4 <= -7e+39:
		tmp = t_1
	elif y4 <= -7.5e-92:
		tmp = t_2
	elif y4 <= -1.2e-144:
		tmp = t_1
	elif y4 <= 5.8e-6:
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(z * Float64(Float64(a * y1) - Float64(c * y0))))))
	t_2 = 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 (y4 <= -1.52e+209)
		tmp = Float64(j * Float64(y4 * Float64(Float64(t * b) - Float64(y1 * y3))));
	elseif (y4 <= -7e+39)
		tmp = t_1;
	elseif (y4 <= -7.5e-92)
		tmp = t_2;
	elseif (y4 <= -1.2e-144)
		tmp = t_1;
	elseif (y4 <= 5.8e-6)
		tmp = Float64(y5 * Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(Float64(i * Float64(Float64(y * k) - Float64(t * j))) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	t_2 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	tmp = 0.0;
	if (y4 <= -1.52e+209)
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	elseif (y4 <= -7e+39)
		tmp = t_1;
	elseif (y4 <= -7.5e-92)
		tmp = t_2;
	elseif (y4 <= -1.2e-144)
		tmp = t_1;
	elseif (y4 <= 5.8e-6)
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(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 * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = 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[y4, -1.52e+209], N[(j * N[(y4 * N[(N[(t * b), $MachinePrecision] - N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -7e+39], t$95$1, If[LessEqual[y4, -7.5e-92], t$95$2, If[LessEqual[y4, -1.2e-144], t$95$1, If[LessEqual[y4, 5.8e-6], N[(y5 * N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y4 < -1.5200000000000001e209

   1. Initial program 21.4%

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

   3. Taylor expanded in y4 around inf 64.7%

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

   4. Taylor expanded in j around -inf 78.6%

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

      1. mul-1-neg 78.6%

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

      2. *-commutative 78.6%

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

      3. distribute-rgt-neg-in 78.6%

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

      4. +-commutative 78.6%

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

      5. mul-1-neg 78.6%

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

      6. unsub-neg 78.6%

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

      7. *-commutative 78.6%

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

   6. Simplified 78.6%

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

   if -1.5200000000000001e209 < y4 < -7.0000000000000003e39 or -7.5000000000000005e-92 < y4 < -1.19999999999999997e-144

   1. Initial program 23.4%

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

   3. Taylor expanded in y3 around -inf 57.5%

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

   if -7.0000000000000003e39 < y4 < -7.5000000000000005e-92 or 5.8000000000000004e-6 < y4

   1. Initial program 28.9%

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

   3. Taylor expanded in y4 around inf 55.9%

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

   if -1.19999999999999997e-144 < y4 < 5.8000000000000004e-6

   1. Initial program 39.1%

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

   3. Taylor expanded in y5 around -inf 54.3%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -1.52 \cdot 10^{+209}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;y4 \leq -7 \cdot 10^{+39}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;y4 \leq -7.5 \cdot 10^{-92}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq -1.2 \cdot 10^{-144}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 5.8 \cdot 10^{-6}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 39.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y4 \leq -3.7 \cdot 10^{+206}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;y4 \leq -1.38 \cdot 10^{+41} \lor \neg \left(y4 \leq -4.6 \cdot 10^{-94}\right) \land y4 \leq 0.125:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y4 -3.7e+206)
   (* j (* y4 (- (* t b) (* y1 y3))))
   (if (or (<= y4 -1.38e+41) (and (not (<= y4 -4.6e-94)) (<= y4 0.125)))
     (*
      y3
      (+
       (* y (- (* c y4) (* a y5)))
       (+ (* j (- (* y0 y5) (* y1 y4))) (* z (- (* a y1) (* c y0))))))
     (*
      y4
      (+
       (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
       (* c (- (* y y3) (* t y2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -3.7e+206) {
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	} else if ((y4 <= -1.38e+41) || (!(y4 <= -4.6e-94) && (y4 <= 0.125))) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	} else {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y4 <= (-3.7d+206)) then
        tmp = j * (y4 * ((t * b) - (y1 * y3)))
    else if ((y4 <= (-1.38d+41)) .or. (.not. (y4 <= (-4.6d-94))) .and. (y4 <= 0.125d0)) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))))
    else
        tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -3.7e+206) {
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	} else if ((y4 <= -1.38e+41) || (!(y4 <= -4.6e-94) && (y4 <= 0.125))) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	} else {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y4 <= -3.7e+206:
		tmp = j * (y4 * ((t * b) - (y1 * y3)))
	elif (y4 <= -1.38e+41) or (not (y4 <= -4.6e-94) and (y4 <= 0.125)):
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))))
	else:
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y4 <= -3.7e+206)
		tmp = Float64(j * Float64(y4 * Float64(Float64(t * b) - Float64(y1 * y3))));
	elseif ((y4 <= -1.38e+41) || (!(y4 <= -4.6e-94) && (y4 <= 0.125)))
		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 * Float64(Float64(a * y1) - Float64(c * y0))))));
	else
		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)))));
	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 (y4 <= -3.7e+206)
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	elseif ((y4 <= -1.38e+41) || (~((y4 <= -4.6e-94)) && (y4 <= 0.125)))
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	else
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y4, -3.7e+206], N[(j * N[(y4 * N[(N[(t * b), $MachinePrecision] - N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y4, -1.38e+41], And[N[Not[LessEqual[y4, -4.6e-94]], $MachinePrecision], LessEqual[y4, 0.125]]], 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 * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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]]]

Derivation

1. Split input into 3 regimes

2. if y4 < -3.6999999999999997e206

   1. Initial program 21.4%

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

   3. Taylor expanded in y4 around inf 64.7%

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

   4. Taylor expanded in j around -inf 78.6%

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

      1. mul-1-neg 78.6%

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

      2. *-commutative 78.6%

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

      3. distribute-rgt-neg-in 78.6%

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

      4. +-commutative 78.6%

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

      5. mul-1-neg 78.6%

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

      6. unsub-neg 78.6%

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

      7. *-commutative 78.6%

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

   6. Simplified 78.6%

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

   if -3.6999999999999997e206 < y4 < -1.3800000000000001e41 or -4.5999999999999999e-94 < y4 < 0.125

   1. Initial program 33.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y3 around -inf 44.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   if -1.3800000000000001e41 < y4 < -4.5999999999999999e-94 or 0.125 < y4

   1. Initial program 29.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf 56.0%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -3.7 \cdot 10^{+206}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;y4 \leq -1.38 \cdot 10^{+41} \lor \neg \left(y4 \leq -4.6 \cdot 10^{-94}\right) \land y4 \leq 0.125:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 30.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ t_2 := t \cdot b - y1 \cdot y3\\ \mathbf{if}\;a \leq -5.6 \cdot 10^{+119}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-161}:\\ \;\;\;\;j \cdot \left(y4 \cdot t\_2\right)\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-224}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-298}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6.3 \cdot 10^{+31}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+110}:\\ \;\;\;\;y4 \cdot \left(j \cdot t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(a \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (* y2 (- (* y1 y4) (* y0 y5))))) (t_2 (- (* t b) (* y1 y3))))
   (if (<= a -5.6e+119)
     (* t (* y2 (- (* a y5) (* c y4))))
     (if (<= a -3.5e-100)
       t_1
       (if (<= a -1.2e-161)
         (* j (* y4 t_2))
         (if (<= a -2.5e-224)
           (* b (* y0 (- (* z k) (* x j))))
           (if (<= a 9.5e-298)
             t_1
             (if (<= a 6.3e+31)
               (* b (* k (- (* z y0) (* y y4))))
               (if (<= a 1.85e+110)
                 (* y4 (* j t_2))
                 (* y2 (* a (- (* t y5) (* x y1)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (y2 * ((y1 * y4) - (y0 * y5)));
	double t_2 = (t * b) - (y1 * y3);
	double tmp;
	if (a <= -5.6e+119) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (a <= -3.5e-100) {
		tmp = t_1;
	} else if (a <= -1.2e-161) {
		tmp = j * (y4 * t_2);
	} else if (a <= -2.5e-224) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (a <= 9.5e-298) {
		tmp = t_1;
	} else if (a <= 6.3e+31) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (a <= 1.85e+110) {
		tmp = y4 * (j * t_2);
	} else {
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = k * (y2 * ((y1 * y4) - (y0 * y5)))
    t_2 = (t * b) - (y1 * y3)
    if (a <= (-5.6d+119)) then
        tmp = t * (y2 * ((a * y5) - (c * y4)))
    else if (a <= (-3.5d-100)) then
        tmp = t_1
    else if (a <= (-1.2d-161)) then
        tmp = j * (y4 * t_2)
    else if (a <= (-2.5d-224)) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (a <= 9.5d-298) then
        tmp = t_1
    else if (a <= 6.3d+31) then
        tmp = b * (k * ((z * y0) - (y * y4)))
    else if (a <= 1.85d+110) then
        tmp = y4 * (j * t_2)
    else
        tmp = y2 * (a * ((t * y5) - (x * y1)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (y2 * ((y1 * y4) - (y0 * y5)));
	double t_2 = (t * b) - (y1 * y3);
	double tmp;
	if (a <= -5.6e+119) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (a <= -3.5e-100) {
		tmp = t_1;
	} else if (a <= -1.2e-161) {
		tmp = j * (y4 * t_2);
	} else if (a <= -2.5e-224) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (a <= 9.5e-298) {
		tmp = t_1;
	} else if (a <= 6.3e+31) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (a <= 1.85e+110) {
		tmp = y4 * (j * t_2);
	} else {
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = k * (y2 * ((y1 * y4) - (y0 * y5)))
	t_2 = (t * b) - (y1 * y3)
	tmp = 0
	if a <= -5.6e+119:
		tmp = t * (y2 * ((a * y5) - (c * y4)))
	elif a <= -3.5e-100:
		tmp = t_1
	elif a <= -1.2e-161:
		tmp = j * (y4 * t_2)
	elif a <= -2.5e-224:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif a <= 9.5e-298:
		tmp = t_1
	elif a <= 6.3e+31:
		tmp = b * (k * ((z * y0) - (y * y4)))
	elif a <= 1.85e+110:
		tmp = y4 * (j * t_2)
	else:
		tmp = y2 * (a * ((t * y5) - (x * y1)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))))
	t_2 = Float64(Float64(t * b) - Float64(y1 * y3))
	tmp = 0.0
	if (a <= -5.6e+119)
		tmp = Float64(t * Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))));
	elseif (a <= -3.5e-100)
		tmp = t_1;
	elseif (a <= -1.2e-161)
		tmp = Float64(j * Float64(y4 * t_2));
	elseif (a <= -2.5e-224)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (a <= 9.5e-298)
		tmp = t_1;
	elseif (a <= 6.3e+31)
		tmp = Float64(b * Float64(k * Float64(Float64(z * y0) - Float64(y * y4))));
	elseif (a <= 1.85e+110)
		tmp = Float64(y4 * Float64(j * t_2));
	else
		tmp = Float64(y2 * Float64(a * Float64(Float64(t * y5) - Float64(x * y1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = k * (y2 * ((y1 * y4) - (y0 * y5)));
	t_2 = (t * b) - (y1 * y3);
	tmp = 0.0;
	if (a <= -5.6e+119)
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	elseif (a <= -3.5e-100)
		tmp = t_1;
	elseif (a <= -1.2e-161)
		tmp = j * (y4 * t_2);
	elseif (a <= -2.5e-224)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (a <= 9.5e-298)
		tmp = t_1;
	elseif (a <= 6.3e+31)
		tmp = b * (k * ((z * y0) - (y * y4)));
	elseif (a <= 1.85e+110)
		tmp = y4 * (j * t_2);
	else
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * b), $MachinePrecision] - N[(y1 * y3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.6e+119], N[(t * N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.5e-100], t$95$1, If[LessEqual[a, -1.2e-161], N[(j * N[(y4 * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.5e-224], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e-298], t$95$1, If[LessEqual[a, 6.3e+31], N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.85e+110], N[(y4 * N[(j * t$95$2), $MachinePrecision]), $MachinePrecision], N[(y2 * N[(a * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if a < -5.60000000000000026e119

   1. Initial program 31.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 41.8%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 51.8%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   if -5.60000000000000026e119 < a < -3.5000000000000001e-100 or -2.4999999999999999e-224 < a < 9.50000000000000012e-298

   1. Initial program 37.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 40.0%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in k around inf 42.1%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   if -3.5000000000000001e-100 < a < -1.19999999999999999e-161

   1. Initial program 41.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf 41.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in j around -inf 61.9%

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(y4 \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 61.9%

         \[\leadsto \color{blue}{-j \cdot \left(y4 \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right)} \]

      2. *-commutative 61.9%

         \[\leadsto -\color{blue}{\left(y4 \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right) \cdot j} \]

      3. distribute-rgt-neg-in 61.9%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right) \cdot \left(-j\right)} \]

      4. +-commutative 61.9%

         \[\leadsto \left(y4 \cdot \color{blue}{\left(y1 \cdot y3 + -1 \cdot \left(b \cdot t\right)\right)}\right) \cdot \left(-j\right) \]

      5. mul-1-neg 61.9%

         \[\leadsto \left(y4 \cdot \left(y1 \cdot y3 + \color{blue}{\left(-b \cdot t\right)}\right)\right) \cdot \left(-j\right) \]

      6. unsub-neg 61.9%

         \[\leadsto \left(y4 \cdot \color{blue}{\left(y1 \cdot y3 - b \cdot t\right)}\right) \cdot \left(-j\right) \]

      7. *-commutative 61.9%

         \[\leadsto \left(y4 \cdot \left(y1 \cdot y3 - \color{blue}{t \cdot b}\right)\right) \cdot \left(-j\right) \]

   6. Simplified 61.9%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(y1 \cdot y3 - t \cdot b\right)\right) \cdot \left(-j\right)} \]

   if -1.19999999999999999e-161 < a < -2.4999999999999999e-224

   1. Initial program 42.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 42.9%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 43.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y0 around inf 50.5%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   if 9.50000000000000012e-298 < a < 6.2999999999999998e31

   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 28.2%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 39.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in k around -inf 44.0%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 44.0%

         \[\leadsto b \cdot \color{blue}{\left(\left(-1 \cdot k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

      2. neg-mul-1 44.0%

         \[\leadsto b \cdot \left(\color{blue}{\left(-k\right)} \cdot \left(y \cdot y4 - y0 \cdot z\right)\right) \]

   8. Simplified 44.0%

      \[\leadsto b \cdot \color{blue}{\left(\left(-k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

   if 6.2999999999999998e31 < a < 1.85000000000000006e110

   1. Initial program 28.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf 52.7%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in j around inf 62.6%

      \[\leadsto y4 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 62.6%

         \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      2. mul-1-neg 62.6%

         \[\leadsto y4 \cdot \left(j \cdot \left(b \cdot t + \color{blue}{\left(-y1 \cdot y3\right)}\right)\right) \]

      3. unsub-neg 62.6%

         \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t - y1 \cdot y3\right)}\right) \]

      4. *-commutative 62.6%

         \[\leadsto y4 \cdot \left(j \cdot \left(\color{blue}{t \cdot b} - y1 \cdot y3\right)\right) \]

   6. Simplified 62.6%

      \[\leadsto y4 \cdot \color{blue}{\left(j \cdot \left(t \cdot b - y1 \cdot y3\right)\right)} \]

   if 1.85000000000000006e110 < a

   1. Initial program 19.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 28.3%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in a around -inf 53.5%

      \[\leadsto y2 \cdot \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y1 - t \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 53.5%

         \[\leadsto y2 \cdot \color{blue}{\left(-a \cdot \left(x \cdot y1 - t \cdot y5\right)\right)} \]

   6. Simplified 53.5%

      \[\leadsto y2 \cdot \color{blue}{\left(-a \cdot \left(x \cdot y1 - t \cdot y5\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{+119}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-100}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-161}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-224}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-298}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 6.3 \cdot 10^{+31}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+110}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(a \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 30.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{if}\;a \leq -5.1 \cdot 10^{+119}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{-166}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-225}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-296}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+31}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{+115}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(a \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (* y2 (- (* y1 y4) (* y0 y5))))))
   (if (<= a -5.1e+119)
     (* t (* y2 (- (* a y5) (* c y4))))
     (if (<= a -1.7e-96)
       t_1
       (if (<= a -6.6e-166)
         (* b (* y4 (- (* t j) (* y k))))
         (if (<= a -1.45e-225)
           (* b (* y0 (- (* z k) (* x j))))
           (if (<= a 4.6e-296)
             t_1
             (if (<= a 2.2e+31)
               (* b (* k (- (* z y0) (* y y4))))
               (if (<= a 1.95e+115)
                 (* y4 (* j (- (* t b) (* y1 y3))))
                 (* y2 (* a (- (* t y5) (* x y1)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (y2 * ((y1 * y4) - (y0 * y5)));
	double tmp;
	if (a <= -5.1e+119) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (a <= -1.7e-96) {
		tmp = t_1;
	} else if (a <= -6.6e-166) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (a <= -1.45e-225) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (a <= 4.6e-296) {
		tmp = t_1;
	} else if (a <= 2.2e+31) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (a <= 1.95e+115) {
		tmp = y4 * (j * ((t * b) - (y1 * y3)));
	} else {
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = k * (y2 * ((y1 * y4) - (y0 * y5)))
    if (a <= (-5.1d+119)) then
        tmp = t * (y2 * ((a * y5) - (c * y4)))
    else if (a <= (-1.7d-96)) then
        tmp = t_1
    else if (a <= (-6.6d-166)) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (a <= (-1.45d-225)) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (a <= 4.6d-296) then
        tmp = t_1
    else if (a <= 2.2d+31) then
        tmp = b * (k * ((z * y0) - (y * y4)))
    else if (a <= 1.95d+115) then
        tmp = y4 * (j * ((t * b) - (y1 * y3)))
    else
        tmp = y2 * (a * ((t * y5) - (x * y1)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (y2 * ((y1 * y4) - (y0 * y5)));
	double tmp;
	if (a <= -5.1e+119) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (a <= -1.7e-96) {
		tmp = t_1;
	} else if (a <= -6.6e-166) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (a <= -1.45e-225) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (a <= 4.6e-296) {
		tmp = t_1;
	} else if (a <= 2.2e+31) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (a <= 1.95e+115) {
		tmp = y4 * (j * ((t * b) - (y1 * y3)));
	} else {
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = k * (y2 * ((y1 * y4) - (y0 * y5)))
	tmp = 0
	if a <= -5.1e+119:
		tmp = t * (y2 * ((a * y5) - (c * y4)))
	elif a <= -1.7e-96:
		tmp = t_1
	elif a <= -6.6e-166:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif a <= -1.45e-225:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif a <= 4.6e-296:
		tmp = t_1
	elif a <= 2.2e+31:
		tmp = b * (k * ((z * y0) - (y * y4)))
	elif a <= 1.95e+115:
		tmp = y4 * (j * ((t * b) - (y1 * y3)))
	else:
		tmp = y2 * (a * ((t * y5) - (x * y1)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))))
	tmp = 0.0
	if (a <= -5.1e+119)
		tmp = Float64(t * Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))));
	elseif (a <= -1.7e-96)
		tmp = t_1;
	elseif (a <= -6.6e-166)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (a <= -1.45e-225)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (a <= 4.6e-296)
		tmp = t_1;
	elseif (a <= 2.2e+31)
		tmp = Float64(b * Float64(k * Float64(Float64(z * y0) - Float64(y * y4))));
	elseif (a <= 1.95e+115)
		tmp = Float64(y4 * Float64(j * Float64(Float64(t * b) - Float64(y1 * y3))));
	else
		tmp = Float64(y2 * Float64(a * Float64(Float64(t * y5) - Float64(x * y1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = k * (y2 * ((y1 * y4) - (y0 * y5)));
	tmp = 0.0;
	if (a <= -5.1e+119)
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	elseif (a <= -1.7e-96)
		tmp = t_1;
	elseif (a <= -6.6e-166)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (a <= -1.45e-225)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (a <= 4.6e-296)
		tmp = t_1;
	elseif (a <= 2.2e+31)
		tmp = b * (k * ((z * y0) - (y * y4)));
	elseif (a <= 1.95e+115)
		tmp = y4 * (j * ((t * b) - (y1 * y3)));
	else
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.1e+119], N[(t * N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.7e-96], t$95$1, If[LessEqual[a, -6.6e-166], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.45e-225], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.6e-296], t$95$1, If[LessEqual[a, 2.2e+31], N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.95e+115], N[(y4 * N[(j * N[(N[(t * b), $MachinePrecision] - N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y2 * N[(a * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if a < -5.09999999999999984e119

   1. Initial program 31.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 41.8%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 51.8%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   if -5.09999999999999984e119 < a < -1.7e-96 or -1.4499999999999999e-225 < a < 4.60000000000000008e-296

   1. Initial program 37.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 40.0%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in k around inf 42.1%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   if -1.7e-96 < a < -6.60000000000000036e-166

   1. Initial program 41.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 41.0%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 60.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y4 around inf 54.9%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   if -6.60000000000000036e-166 < a < -1.4499999999999999e-225

   1. Initial program 42.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 42.9%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 43.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y0 around inf 50.5%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   if 4.60000000000000008e-296 < a < 2.2000000000000001e31

   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 28.2%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 39.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in k around -inf 44.0%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 44.0%

         \[\leadsto b \cdot \color{blue}{\left(\left(-1 \cdot k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

      2. neg-mul-1 44.0%

         \[\leadsto b \cdot \left(\color{blue}{\left(-k\right)} \cdot \left(y \cdot y4 - y0 \cdot z\right)\right) \]

   8. Simplified 44.0%

      \[\leadsto b \cdot \color{blue}{\left(\left(-k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

   if 2.2000000000000001e31 < a < 1.95000000000000003e115

   1. Initial program 28.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf 52.7%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in j around inf 62.6%

      \[\leadsto y4 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 62.6%

         \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      2. mul-1-neg 62.6%

         \[\leadsto y4 \cdot \left(j \cdot \left(b \cdot t + \color{blue}{\left(-y1 \cdot y3\right)}\right)\right) \]

      3. unsub-neg 62.6%

         \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t - y1 \cdot y3\right)}\right) \]

      4. *-commutative 62.6%

         \[\leadsto y4 \cdot \left(j \cdot \left(\color{blue}{t \cdot b} - y1 \cdot y3\right)\right) \]

   6. Simplified 62.6%

      \[\leadsto y4 \cdot \color{blue}{\left(j \cdot \left(t \cdot b - y1 \cdot y3\right)\right)} \]

   if 1.95000000000000003e115 < a

   1. Initial program 19.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 28.3%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in a around -inf 53.5%

      \[\leadsto y2 \cdot \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y1 - t \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 53.5%

         \[\leadsto y2 \cdot \color{blue}{\left(-a \cdot \left(x \cdot y1 - t \cdot y5\right)\right)} \]

   6. Simplified 53.5%

      \[\leadsto y2 \cdot \color{blue}{\left(-a \cdot \left(x \cdot y1 - t \cdot y5\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 48.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.1 \cdot 10^{+119}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-96}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{-166}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-225}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-296}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+31}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{+115}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(a \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 26.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.3 \cdot 10^{+50}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;i \leq -4.5 \cdot 10^{-147}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;i \leq -1.42 \cdot 10^{-207}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq -2.6 \cdot 10^{-297}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;i \leq 7.5 \cdot 10^{-127}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq 1.02 \cdot 10^{-23}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{+205}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(c \cdot \left(-x\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= i -1.3e+50)
   (* i (* j (* x y1)))
   (if (<= i -4.5e-147)
     (* a (* y3 (- (* z y1) (* y y5))))
     (if (<= i -1.42e-207)
       (* b (* x (- (* y a) (* j y0))))
       (if (<= i -2.6e-297)
         (* b (* y0 (- (* z k) (* x j))))
         (if (<= i 7.5e-127)
           (* c (* y2 (- (* x y0) (* t y4))))
           (if (<= i 1.02e-23)
             (* k (* y2 (- (* y1 y4) (* y0 y5))))
             (if (<= i 1.3e+205)
               (* b (* y4 (- (* t j) (* y k))))
               (* i (* y (* c (- x))))))))))))

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 (i <= -1.3e+50) {
		tmp = i * (j * (x * y1));
	} else if (i <= -4.5e-147) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (i <= -1.42e-207) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (i <= -2.6e-297) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (i <= 7.5e-127) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (i <= 1.02e-23) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (i <= 1.3e+205) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else {
		tmp = i * (y * (c * -x));
	}
	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 (i <= (-1.3d+50)) then
        tmp = i * (j * (x * y1))
    else if (i <= (-4.5d-147)) then
        tmp = a * (y3 * ((z * y1) - (y * y5)))
    else if (i <= (-1.42d-207)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (i <= (-2.6d-297)) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (i <= 7.5d-127) then
        tmp = c * (y2 * ((x * y0) - (t * y4)))
    else if (i <= 1.02d-23) then
        tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
    else if (i <= 1.3d+205) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else
        tmp = i * (y * (c * -x))
    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 (i <= -1.3e+50) {
		tmp = i * (j * (x * y1));
	} else if (i <= -4.5e-147) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (i <= -1.42e-207) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (i <= -2.6e-297) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (i <= 7.5e-127) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (i <= 1.02e-23) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (i <= 1.3e+205) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else {
		tmp = i * (y * (c * -x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if i <= -1.3e+50:
		tmp = i * (j * (x * y1))
	elif i <= -4.5e-147:
		tmp = a * (y3 * ((z * y1) - (y * y5)))
	elif i <= -1.42e-207:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif i <= -2.6e-297:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif i <= 7.5e-127:
		tmp = c * (y2 * ((x * y0) - (t * y4)))
	elif i <= 1.02e-23:
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
	elif i <= 1.3e+205:
		tmp = b * (y4 * ((t * j) - (y * k)))
	else:
		tmp = i * (y * (c * -x))
	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 (i <= -1.3e+50)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (i <= -4.5e-147)
		tmp = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))));
	elseif (i <= -1.42e-207)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (i <= -2.6e-297)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (i <= 7.5e-127)
		tmp = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))));
	elseif (i <= 1.02e-23)
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	elseif (i <= 1.3e+205)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	else
		tmp = Float64(i * Float64(y * Float64(c * Float64(-x))));
	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 (i <= -1.3e+50)
		tmp = i * (j * (x * y1));
	elseif (i <= -4.5e-147)
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	elseif (i <= -1.42e-207)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (i <= -2.6e-297)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (i <= 7.5e-127)
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	elseif (i <= 1.02e-23)
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	elseif (i <= 1.3e+205)
		tmp = b * (y4 * ((t * j) - (y * k)));
	else
		tmp = i * (y * (c * -x));
	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[i, -1.3e+50], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -4.5e-147], N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.42e-207], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -2.6e-297], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 7.5e-127], N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.02e-23], N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.3e+205], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(y * N[(c * (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if i < -1.3000000000000001e50

   1. Initial program 23.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.6%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 64.6%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   6. Taylor expanded in x around inf 51.9%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right)\right)\right)} \]

   7. Taylor expanded in c around 0 46.7%

      \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 46.7%

         \[\leadsto -1 \cdot \color{blue}{\left(-i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\right)} \]

      2. *-commutative 46.7%

         \[\leadsto -1 \cdot \left(-\color{blue}{\left(j \cdot \left(x \cdot y1\right)\right) \cdot i}\right) \]

      3. distribute-rgt-neg-in 46.7%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(j \cdot \left(x \cdot y1\right)\right) \cdot \left(-i\right)\right)} \]

      4. *-commutative 46.7%

         \[\leadsto -1 \cdot \left(\left(j \cdot \color{blue}{\left(y1 \cdot x\right)}\right) \cdot \left(-i\right)\right) \]

   9. Simplified 46.7%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(j \cdot \left(y1 \cdot x\right)\right) \cdot \left(-i\right)\right)} \]

   if -1.3000000000000001e50 < i < -4.49999999999999973e-147

   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%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 40.6%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in y3 around inf 32.8%

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]

   if -4.49999999999999973e-147 < i < -1.42e-207

   1. Initial program 13.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 13.3%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 20.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 66.9%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   if -1.42e-207 < i < -2.6000000000000001e-297

   1. Initial program 50.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 50.6%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 40.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y0 around inf 36.5%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   if -2.6000000000000001e-297 < i < 7.5000000000000004e-127

   1. Initial program 35.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 42.5%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 46.9%

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)} \]

   if 7.5000000000000004e-127 < i < 1.02000000000000005e-23

   1. Initial program 27.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 41.2%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in k around inf 50.5%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   if 1.02000000000000005e-23 < i < 1.2999999999999999e205

   1. Initial program 30.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.4%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 58.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y4 around inf 39.1%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   if 1.2999999999999999e205 < i

   1. Initial program 37.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 37.2%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 84.0%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   6. Taylor expanded in x around inf 64.2%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right)\right)\right)} \]

   7. Taylor expanded in c around inf 56.2%

      \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(c \cdot \left(x \cdot y\right)\right)}\right) \]
   8. Step-by-step derivation

      1. associate-*r* 56.5%

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(c \cdot x\right) \cdot y\right)}\right) \]

   9. Simplified 56.5%

      \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(c \cdot x\right) \cdot y\right)}\right) \]
3. Recombined 8 regimes into one program.

4. Final simplification 44.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.3 \cdot 10^{+50}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;i \leq -4.5 \cdot 10^{-147}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;i \leq -1.42 \cdot 10^{-207}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq -2.6 \cdot 10^{-297}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;i \leq 7.5 \cdot 10^{-127}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq 1.02 \cdot 10^{-23}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{+205}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(c \cdot \left(-x\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 21.0% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{if}\;y0 \leq -2.35 \cdot 10^{-67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y0 \leq -1.05 \cdot 10^{-121}:\\ \;\;\;\;a \cdot \left(y \cdot \left(y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 2.15 \cdot 10^{-151}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 1.1 \cdot 10^{-101}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \mathbf{elif}\;y0 \leq 2.35 \cdot 10^{+20}:\\ \;\;\;\;b \cdot \left(k \cdot \left(y \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 6.8 \cdot 10^{+71}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y0 \leq 3.7 \cdot 10^{+196}:\\ \;\;\;\;a \cdot \left(\left(y \cdot y3\right) \cdot \left(-y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* k (* z y0)))))
   (if (<= y0 -2.35e-67)
     t_1
     (if (<= y0 -1.05e-121)
       (* a (* y (* y3 (- y5))))
       (if (<= y0 2.15e-151)
         (* k (* y2 (* y1 y4)))
         (if (<= y0 1.1e-101)
           (* b (* (* x y) a))
           (if (<= y0 2.35e+20)
             (* b (* k (* y (- y4))))
             (if (<= y0 6.8e+71)
               (* a (* (* x y) b))
               (if (<= y0 3.7e+196) (* a (* (* y y3) (- y5))) t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (k * (z * y0));
	double tmp;
	if (y0 <= -2.35e-67) {
		tmp = t_1;
	} else if (y0 <= -1.05e-121) {
		tmp = a * (y * (y3 * -y5));
	} else if (y0 <= 2.15e-151) {
		tmp = k * (y2 * (y1 * y4));
	} else if (y0 <= 1.1e-101) {
		tmp = b * ((x * y) * a);
	} else if (y0 <= 2.35e+20) {
		tmp = b * (k * (y * -y4));
	} else if (y0 <= 6.8e+71) {
		tmp = a * ((x * y) * b);
	} else if (y0 <= 3.7e+196) {
		tmp = a * ((y * y3) * -y5);
	} 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 = b * (k * (z * y0))
    if (y0 <= (-2.35d-67)) then
        tmp = t_1
    else if (y0 <= (-1.05d-121)) then
        tmp = a * (y * (y3 * -y5))
    else if (y0 <= 2.15d-151) then
        tmp = k * (y2 * (y1 * y4))
    else if (y0 <= 1.1d-101) then
        tmp = b * ((x * y) * a)
    else if (y0 <= 2.35d+20) then
        tmp = b * (k * (y * -y4))
    else if (y0 <= 6.8d+71) then
        tmp = a * ((x * y) * b)
    else if (y0 <= 3.7d+196) then
        tmp = a * ((y * y3) * -y5)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (k * (z * y0));
	double tmp;
	if (y0 <= -2.35e-67) {
		tmp = t_1;
	} else if (y0 <= -1.05e-121) {
		tmp = a * (y * (y3 * -y5));
	} else if (y0 <= 2.15e-151) {
		tmp = k * (y2 * (y1 * y4));
	} else if (y0 <= 1.1e-101) {
		tmp = b * ((x * y) * a);
	} else if (y0 <= 2.35e+20) {
		tmp = b * (k * (y * -y4));
	} else if (y0 <= 6.8e+71) {
		tmp = a * ((x * y) * b);
	} else if (y0 <= 3.7e+196) {
		tmp = a * ((y * y3) * -y5);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (k * (z * y0))
	tmp = 0
	if y0 <= -2.35e-67:
		tmp = t_1
	elif y0 <= -1.05e-121:
		tmp = a * (y * (y3 * -y5))
	elif y0 <= 2.15e-151:
		tmp = k * (y2 * (y1 * y4))
	elif y0 <= 1.1e-101:
		tmp = b * ((x * y) * a)
	elif y0 <= 2.35e+20:
		tmp = b * (k * (y * -y4))
	elif y0 <= 6.8e+71:
		tmp = a * ((x * y) * b)
	elif y0 <= 3.7e+196:
		tmp = a * ((y * y3) * -y5)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(k * Float64(z * y0)))
	tmp = 0.0
	if (y0 <= -2.35e-67)
		tmp = t_1;
	elseif (y0 <= -1.05e-121)
		tmp = Float64(a * Float64(y * Float64(y3 * Float64(-y5))));
	elseif (y0 <= 2.15e-151)
		tmp = Float64(k * Float64(y2 * Float64(y1 * y4)));
	elseif (y0 <= 1.1e-101)
		tmp = Float64(b * Float64(Float64(x * y) * a));
	elseif (y0 <= 2.35e+20)
		tmp = Float64(b * Float64(k * Float64(y * Float64(-y4))));
	elseif (y0 <= 6.8e+71)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	elseif (y0 <= 3.7e+196)
		tmp = Float64(a * Float64(Float64(y * y3) * Float64(-y5)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (k * (z * y0));
	tmp = 0.0;
	if (y0 <= -2.35e-67)
		tmp = t_1;
	elseif (y0 <= -1.05e-121)
		tmp = a * (y * (y3 * -y5));
	elseif (y0 <= 2.15e-151)
		tmp = k * (y2 * (y1 * y4));
	elseif (y0 <= 1.1e-101)
		tmp = b * ((x * y) * a);
	elseif (y0 <= 2.35e+20)
		tmp = b * (k * (y * -y4));
	elseif (y0 <= 6.8e+71)
		tmp = a * ((x * y) * b);
	elseif (y0 <= 3.7e+196)
		tmp = a * ((y * y3) * -y5);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(k * N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -2.35e-67], t$95$1, If[LessEqual[y0, -1.05e-121], N[(a * N[(y * N[(y3 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 2.15e-151], N[(k * N[(y2 * N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.1e-101], N[(b * N[(N[(x * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 2.35e+20], N[(b * N[(k * N[(y * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 6.8e+71], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 3.7e+196], N[(a * N[(N[(y * y3), $MachinePrecision] * (-y5)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y0 < -2.35000000000000002e-67 or 3.6999999999999999e196 < y0

   1. Initial program 29.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.2%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 39.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in k around -inf 43.6%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 43.6%

         \[\leadsto b \cdot \color{blue}{\left(\left(-1 \cdot k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

      2. neg-mul-1 43.6%

         \[\leadsto b \cdot \left(\color{blue}{\left(-k\right)} \cdot \left(y \cdot y4 - y0 \cdot z\right)\right) \]

   8. Simplified 43.6%

      \[\leadsto b \cdot \color{blue}{\left(\left(-k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

   9. Taylor expanded in y around 0 35.9%

      \[\leadsto b \cdot \color{blue}{\left(k \cdot \left(y0 \cdot z\right)\right)} \]

   if -2.35000000000000002e-67 < y0 < -1.0499999999999999e-121

   1. Initial program 20.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 20.0%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 60.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in y around inf 67.3%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]

   7. Taylor expanded in b around 0 60.8%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 60.8%

         \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot y\right) \cdot \left(y3 \cdot y5\right)\right)} \]

      2. neg-mul-1 60.8%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y\right)} \cdot \left(y3 \cdot y5\right)\right) \]

   9. Simplified 60.8%

      \[\leadsto a \cdot \color{blue}{\left(\left(-y\right) \cdot \left(y3 \cdot y5\right)\right)} \]

   if -1.0499999999999999e-121 < y0 < 2.15000000000000009e-151

   1. Initial program 42.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 41.6%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in k around inf 25.8%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   5. Taylor expanded in y1 around inf 27.6%

      \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y1 \cdot y4\right)}\right) \]
   6. Step-by-step derivation

      1. *-commutative 27.6%

         \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y4 \cdot y1\right)}\right) \]

   7. Simplified 27.6%

      \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y4 \cdot y1\right)}\right) \]

   if 2.15000000000000009e-151 < y0 < 1.0999999999999999e-101

   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%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 40.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 40.9%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right)} \]

   7. Taylor expanded in t around 0 51.0%

      \[\leadsto b \cdot \left(a \cdot \color{blue}{\left(x \cdot y\right)}\right) \]
   8. Step-by-step derivation

      1. *-commutative 51.0%

         \[\leadsto b \cdot \left(a \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

   9. Simplified 51.0%

      \[\leadsto b \cdot \left(a \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

   if 1.0999999999999999e-101 < y0 < 2.35e20

   1. Initial program 30.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.9%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 27.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in k around -inf 28.0%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 28.0%

         \[\leadsto b \cdot \color{blue}{\left(\left(-1 \cdot k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

      2. neg-mul-1 28.0%

         \[\leadsto b \cdot \left(\color{blue}{\left(-k\right)} \cdot \left(y \cdot y4 - y0 \cdot z\right)\right) \]

   8. Simplified 28.0%

      \[\leadsto b \cdot \color{blue}{\left(\left(-k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

   9. Taylor expanded in y around inf 24.5%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 24.5%

          \[\leadsto b \cdot \color{blue}{\left(-k \cdot \left(y \cdot y4\right)\right)} \]

       2. *-commutative 24.5%

          \[\leadsto b \cdot \left(-\color{blue}{\left(y \cdot y4\right) \cdot k}\right) \]

       3. distribute-rgt-neg-in 24.5%

          \[\leadsto b \cdot \color{blue}{\left(\left(y \cdot y4\right) \cdot \left(-k\right)\right)} \]

   11. Simplified 24.5%

       \[\leadsto b \cdot \color{blue}{\left(\left(y \cdot y4\right) \cdot \left(-k\right)\right)} \]

   if 2.35e20 < y0 < 6.7999999999999997e71

   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%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 40.1%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in y around inf 41.4%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]

   7. Taylor expanded in b around inf 50.4%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 50.4%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

   9. Simplified 50.4%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(y \cdot x\right)\right)} \]

   if 6.7999999999999997e71 < y0 < 3.6999999999999999e196

   1. Initial program 21.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 21.3%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 48.8%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in y around inf 34.9%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]

   7. Taylor expanded in b around 0 35.0%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 35.0%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)} \]

      2. mul-1-neg 35.0%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(y \cdot \left(y3 \cdot y5\right)\right) \]

      3. associate-*r* 37.8%

         \[\leadsto \left(-a\right) \cdot \color{blue}{\left(\left(y \cdot y3\right) \cdot y5\right)} \]

      4. *-commutative 37.8%

         \[\leadsto \left(-a\right) \cdot \left(\color{blue}{\left(y3 \cdot y\right)} \cdot y5\right) \]

   9. Simplified 37.8%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(\left(y3 \cdot y\right) \cdot y5\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 35.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -2.35 \cdot 10^{-67}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -1.05 \cdot 10^{-121}:\\ \;\;\;\;a \cdot \left(y \cdot \left(y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 2.15 \cdot 10^{-151}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 1.1 \cdot 10^{-101}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \mathbf{elif}\;y0 \leq 2.35 \cdot 10^{+20}:\\ \;\;\;\;b \cdot \left(k \cdot \left(y \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 6.8 \cdot 10^{+71}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y0 \leq 3.7 \cdot 10^{+196}:\\ \;\;\;\;a \cdot \left(\left(y \cdot y3\right) \cdot \left(-y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 24.4% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \mathbf{if}\;y1 \leq -2.5 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq -1.45 \cdot 10^{-222}:\\ \;\;\;\;c \cdot \left(i \cdot \left(y \cdot \left(-x\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 1.45 \cdot 10^{-243}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 1.5 \cdot 10^{-123}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq 1.7 \cdot 10^{-67}:\\ \;\;\;\;i \cdot \left(y \cdot \left(c \cdot \left(-x\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 1.16 \cdot 10^{+75}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq 1.06 \cdot 10^{+243}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (* y2 (* y1 y4)))))
   (if (<= y1 -2.5e+15)
     t_1
     (if (<= y1 -1.45e-222)
       (* c (* i (* y (- x))))
       (if (<= y1 1.45e-243)
         (* b (* k (* z y0)))
         (if (<= y1 1.5e-123)
           (* a (* y5 (- (* t y2) (* y y3))))
           (if (<= y1 1.7e-67)
             (* i (* y (* c (- x))))
             (if (<= y1 1.16e+75)
               (* a (* y3 (- (* z y1) (* y y5))))
               (if (<= y1 1.06e+243) t_1 (* i (* j (* x y1))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (y2 * (y1 * y4));
	double tmp;
	if (y1 <= -2.5e+15) {
		tmp = t_1;
	} else if (y1 <= -1.45e-222) {
		tmp = c * (i * (y * -x));
	} else if (y1 <= 1.45e-243) {
		tmp = b * (k * (z * y0));
	} else if (y1 <= 1.5e-123) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (y1 <= 1.7e-67) {
		tmp = i * (y * (c * -x));
	} else if (y1 <= 1.16e+75) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (y1 <= 1.06e+243) {
		tmp = t_1;
	} else {
		tmp = i * (j * (x * y1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = k * (y2 * (y1 * y4))
    if (y1 <= (-2.5d+15)) then
        tmp = t_1
    else if (y1 <= (-1.45d-222)) then
        tmp = c * (i * (y * -x))
    else if (y1 <= 1.45d-243) then
        tmp = b * (k * (z * y0))
    else if (y1 <= 1.5d-123) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else if (y1 <= 1.7d-67) then
        tmp = i * (y * (c * -x))
    else if (y1 <= 1.16d+75) then
        tmp = a * (y3 * ((z * y1) - (y * y5)))
    else if (y1 <= 1.06d+243) then
        tmp = t_1
    else
        tmp = i * (j * (x * y1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (y2 * (y1 * y4));
	double tmp;
	if (y1 <= -2.5e+15) {
		tmp = t_1;
	} else if (y1 <= -1.45e-222) {
		tmp = c * (i * (y * -x));
	} else if (y1 <= 1.45e-243) {
		tmp = b * (k * (z * y0));
	} else if (y1 <= 1.5e-123) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (y1 <= 1.7e-67) {
		tmp = i * (y * (c * -x));
	} else if (y1 <= 1.16e+75) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (y1 <= 1.06e+243) {
		tmp = t_1;
	} else {
		tmp = i * (j * (x * y1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = k * (y2 * (y1 * y4))
	tmp = 0
	if y1 <= -2.5e+15:
		tmp = t_1
	elif y1 <= -1.45e-222:
		tmp = c * (i * (y * -x))
	elif y1 <= 1.45e-243:
		tmp = b * (k * (z * y0))
	elif y1 <= 1.5e-123:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	elif y1 <= 1.7e-67:
		tmp = i * (y * (c * -x))
	elif y1 <= 1.16e+75:
		tmp = a * (y3 * ((z * y1) - (y * y5)))
	elif y1 <= 1.06e+243:
		tmp = t_1
	else:
		tmp = i * (j * (x * y1))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(k * Float64(y2 * Float64(y1 * y4)))
	tmp = 0.0
	if (y1 <= -2.5e+15)
		tmp = t_1;
	elseif (y1 <= -1.45e-222)
		tmp = Float64(c * Float64(i * Float64(y * Float64(-x))));
	elseif (y1 <= 1.45e-243)
		tmp = Float64(b * Float64(k * Float64(z * y0)));
	elseif (y1 <= 1.5e-123)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (y1 <= 1.7e-67)
		tmp = Float64(i * Float64(y * Float64(c * Float64(-x))));
	elseif (y1 <= 1.16e+75)
		tmp = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))));
	elseif (y1 <= 1.06e+243)
		tmp = t_1;
	else
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = k * (y2 * (y1 * y4));
	tmp = 0.0;
	if (y1 <= -2.5e+15)
		tmp = t_1;
	elseif (y1 <= -1.45e-222)
		tmp = c * (i * (y * -x));
	elseif (y1 <= 1.45e-243)
		tmp = b * (k * (z * y0));
	elseif (y1 <= 1.5e-123)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	elseif (y1 <= 1.7e-67)
		tmp = i * (y * (c * -x));
	elseif (y1 <= 1.16e+75)
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	elseif (y1 <= 1.06e+243)
		tmp = t_1;
	else
		tmp = i * (j * (x * y1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(k * N[(y2 * N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -2.5e+15], t$95$1, If[LessEqual[y1, -1.45e-222], N[(c * N[(i * N[(y * (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.45e-243], N[(b * N[(k * N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.5e-123], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.7e-67], N[(i * N[(y * N[(c * (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.16e+75], N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.06e+243], t$95$1, N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y1 < -2.5e15 or 1.1600000000000001e75 < y1 < 1.06e243

   1. Initial program 27.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 45.8%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in k around inf 43.0%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   5. Taylor expanded in y1 around inf 38.6%

      \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y1 \cdot y4\right)}\right) \]
   6. Step-by-step derivation

      1. *-commutative 38.6%

         \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y4 \cdot y1\right)}\right) \]

   7. Simplified 38.6%

      \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y4 \cdot y1\right)}\right) \]

   if -2.5e15 < y1 < -1.4500000000000001e-222

   1. Initial program 18.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 18.7%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 53.2%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   6. Taylor expanded in x around inf 35.9%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right)\right)\right)} \]

   7. Taylor expanded in c around inf 38.3%

      \[\leadsto -1 \cdot \color{blue}{\left(c \cdot \left(i \cdot \left(x \cdot y\right)\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 38.3%

         \[\leadsto -1 \cdot \left(c \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot i\right)}\right) \]

      2. *-commutative 38.3%

         \[\leadsto -1 \cdot \left(c \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot i\right)\right) \]

   9. Simplified 38.3%

      \[\leadsto -1 \cdot \color{blue}{\left(c \cdot \left(\left(y \cdot x\right) \cdot i\right)\right)} \]

   if -1.4500000000000001e-222 < y1 < 1.44999999999999988e-243

   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 42.5%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 39.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in k around -inf 43.5%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 43.5%

         \[\leadsto b \cdot \color{blue}{\left(\left(-1 \cdot k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

      2. neg-mul-1 43.5%

         \[\leadsto b \cdot \left(\color{blue}{\left(-k\right)} \cdot \left(y \cdot y4 - y0 \cdot z\right)\right) \]

   8. Simplified 43.5%

      \[\leadsto b \cdot \color{blue}{\left(\left(-k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

   9. Taylor expanded in y around 0 40.1%

      \[\leadsto b \cdot \color{blue}{\left(k \cdot \left(y0 \cdot z\right)\right)} \]

   if 1.44999999999999988e-243 < y1 < 1.49999999999999992e-123

   1. Initial program 37.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 37.6%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 32.6%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in y5 around inf 35.8%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   if 1.49999999999999992e-123 < y1 < 1.70000000000000005e-67

   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 43.3%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 58.3%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   6. Taylor expanded in x around inf 37.4%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right)\right)\right)} \]

   7. Taylor expanded in c around inf 37.2%

      \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(c \cdot \left(x \cdot y\right)\right)}\right) \]
   8. Step-by-step derivation

      1. associate-*r* 44.3%

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(c \cdot x\right) \cdot y\right)}\right) \]

   9. Simplified 44.3%

      \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(c \cdot x\right) \cdot y\right)}\right) \]

   if 1.70000000000000005e-67 < y1 < 1.1600000000000001e75

   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 37.5%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 44.0%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in y3 around inf 38.7%

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]

   if 1.06e243 < y1

   1. Initial program 31.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.3%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 44.0%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   6. Taylor expanded in x around inf 50.5%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right)\right)\right)} \]

   7. Taylor expanded in c around 0 63.0%

      \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 63.0%

         \[\leadsto -1 \cdot \color{blue}{\left(-i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\right)} \]

      2. *-commutative 63.0%

         \[\leadsto -1 \cdot \left(-\color{blue}{\left(j \cdot \left(x \cdot y1\right)\right) \cdot i}\right) \]

      3. distribute-rgt-neg-in 63.0%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(j \cdot \left(x \cdot y1\right)\right) \cdot \left(-i\right)\right)} \]

      4. *-commutative 63.0%

         \[\leadsto -1 \cdot \left(\left(j \cdot \color{blue}{\left(y1 \cdot x\right)}\right) \cdot \left(-i\right)\right) \]

   9. Simplified 63.0%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(j \cdot \left(y1 \cdot x\right)\right) \cdot \left(-i\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 40.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -2.5 \cdot 10^{+15}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq -1.45 \cdot 10^{-222}:\\ \;\;\;\;c \cdot \left(i \cdot \left(y \cdot \left(-x\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 1.45 \cdot 10^{-243}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 1.5 \cdot 10^{-123}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq 1.7 \cdot 10^{-67}:\\ \;\;\;\;i \cdot \left(y \cdot \left(c \cdot \left(-x\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 1.16 \cdot 10^{+75}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq 1.06 \cdot 10^{+243}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 22.9% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \mathbf{if}\;y1 \leq -4 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq -1.65 \cdot 10^{-223}:\\ \;\;\;\;c \cdot \left(i \cdot \left(y \cdot \left(-x\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 3.1 \cdot 10^{-174}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 9.5 \cdot 10^{-137}:\\ \;\;\;\;c \cdot \left(t \cdot \left(y2 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 2 \cdot 10^{-46}:\\ \;\;\;\;b \cdot \left(k \cdot \left(y \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 225:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq 1.46 \cdot 10^{+243}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (* y2 (* y1 y4)))))
   (if (<= y1 -4e+19)
     t_1
     (if (<= y1 -1.65e-223)
       (* c (* i (* y (- x))))
       (if (<= y1 3.1e-174)
         (* b (* k (* z y0)))
         (if (<= y1 9.5e-137)
           (* c (* t (* y2 (- y4))))
           (if (<= y1 2e-46)
             (* b (* k (* y (- y4))))
             (if (<= y1 225.0)
               (* a (* y (- (* x b) (* y3 y5))))
               (if (<= y1 1.46e+243) t_1 (* i (* j (* x y1))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (y2 * (y1 * y4));
	double tmp;
	if (y1 <= -4e+19) {
		tmp = t_1;
	} else if (y1 <= -1.65e-223) {
		tmp = c * (i * (y * -x));
	} else if (y1 <= 3.1e-174) {
		tmp = b * (k * (z * y0));
	} else if (y1 <= 9.5e-137) {
		tmp = c * (t * (y2 * -y4));
	} else if (y1 <= 2e-46) {
		tmp = b * (k * (y * -y4));
	} else if (y1 <= 225.0) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (y1 <= 1.46e+243) {
		tmp = t_1;
	} else {
		tmp = i * (j * (x * y1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = k * (y2 * (y1 * y4))
    if (y1 <= (-4d+19)) then
        tmp = t_1
    else if (y1 <= (-1.65d-223)) then
        tmp = c * (i * (y * -x))
    else if (y1 <= 3.1d-174) then
        tmp = b * (k * (z * y0))
    else if (y1 <= 9.5d-137) then
        tmp = c * (t * (y2 * -y4))
    else if (y1 <= 2d-46) then
        tmp = b * (k * (y * -y4))
    else if (y1 <= 225.0d0) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (y1 <= 1.46d+243) then
        tmp = t_1
    else
        tmp = i * (j * (x * y1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (y2 * (y1 * y4));
	double tmp;
	if (y1 <= -4e+19) {
		tmp = t_1;
	} else if (y1 <= -1.65e-223) {
		tmp = c * (i * (y * -x));
	} else if (y1 <= 3.1e-174) {
		tmp = b * (k * (z * y0));
	} else if (y1 <= 9.5e-137) {
		tmp = c * (t * (y2 * -y4));
	} else if (y1 <= 2e-46) {
		tmp = b * (k * (y * -y4));
	} else if (y1 <= 225.0) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (y1 <= 1.46e+243) {
		tmp = t_1;
	} else {
		tmp = i * (j * (x * y1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = k * (y2 * (y1 * y4))
	tmp = 0
	if y1 <= -4e+19:
		tmp = t_1
	elif y1 <= -1.65e-223:
		tmp = c * (i * (y * -x))
	elif y1 <= 3.1e-174:
		tmp = b * (k * (z * y0))
	elif y1 <= 9.5e-137:
		tmp = c * (t * (y2 * -y4))
	elif y1 <= 2e-46:
		tmp = b * (k * (y * -y4))
	elif y1 <= 225.0:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif y1 <= 1.46e+243:
		tmp = t_1
	else:
		tmp = i * (j * (x * y1))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(k * Float64(y2 * Float64(y1 * y4)))
	tmp = 0.0
	if (y1 <= -4e+19)
		tmp = t_1;
	elseif (y1 <= -1.65e-223)
		tmp = Float64(c * Float64(i * Float64(y * Float64(-x))));
	elseif (y1 <= 3.1e-174)
		tmp = Float64(b * Float64(k * Float64(z * y0)));
	elseif (y1 <= 9.5e-137)
		tmp = Float64(c * Float64(t * Float64(y2 * Float64(-y4))));
	elseif (y1 <= 2e-46)
		tmp = Float64(b * Float64(k * Float64(y * Float64(-y4))));
	elseif (y1 <= 225.0)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (y1 <= 1.46e+243)
		tmp = t_1;
	else
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = k * (y2 * (y1 * y4));
	tmp = 0.0;
	if (y1 <= -4e+19)
		tmp = t_1;
	elseif (y1 <= -1.65e-223)
		tmp = c * (i * (y * -x));
	elseif (y1 <= 3.1e-174)
		tmp = b * (k * (z * y0));
	elseif (y1 <= 9.5e-137)
		tmp = c * (t * (y2 * -y4));
	elseif (y1 <= 2e-46)
		tmp = b * (k * (y * -y4));
	elseif (y1 <= 225.0)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (y1 <= 1.46e+243)
		tmp = t_1;
	else
		tmp = i * (j * (x * y1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(k * N[(y2 * N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -4e+19], t$95$1, If[LessEqual[y1, -1.65e-223], N[(c * N[(i * N[(y * (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 3.1e-174], N[(b * N[(k * N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 9.5e-137], N[(c * N[(t * N[(y2 * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 2e-46], N[(b * N[(k * N[(y * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 225.0], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.46e+243], t$95$1, N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y1 < -4e19 or 225 < y1 < 1.46000000000000009e243

   1. Initial program 28.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 44.4%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in k around inf 42.0%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   5. Taylor expanded in y1 around inf 37.2%

      \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y1 \cdot y4\right)}\right) \]
   6. Step-by-step derivation

      1. *-commutative 37.2%

         \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y4 \cdot y1\right)}\right) \]

   7. Simplified 37.2%

      \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y4 \cdot y1\right)}\right) \]

   if -4e19 < y1 < -1.64999999999999997e-223

   1. Initial program 18.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 18.7%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 53.2%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   6. Taylor expanded in x around inf 35.9%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right)\right)\right)} \]

   7. Taylor expanded in c around inf 38.3%

      \[\leadsto -1 \cdot \color{blue}{\left(c \cdot \left(i \cdot \left(x \cdot y\right)\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 38.3%

         \[\leadsto -1 \cdot \left(c \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot i\right)}\right) \]

      2. *-commutative 38.3%

         \[\leadsto -1 \cdot \left(c \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot i\right)\right) \]

   9. Simplified 38.3%

      \[\leadsto -1 \cdot \color{blue}{\left(c \cdot \left(\left(y \cdot x\right) \cdot i\right)\right)} \]

   if -1.64999999999999997e-223 < y1 < 3.0999999999999999e-174

   1. Initial program 39.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 41.2%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 35.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in k around -inf 35.5%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 35.5%

         \[\leadsto b \cdot \color{blue}{\left(\left(-1 \cdot k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

      2. neg-mul-1 35.5%

         \[\leadsto b \cdot \left(\color{blue}{\left(-k\right)} \cdot \left(y \cdot y4 - y0 \cdot z\right)\right) \]

   8. Simplified 35.5%

      \[\leadsto b \cdot \color{blue}{\left(\left(-k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

   9. Taylor expanded in y around 0 35.4%

      \[\leadsto b \cdot \color{blue}{\left(k \cdot \left(y0 \cdot z\right)\right)} \]

   if 3.0999999999999999e-174 < y1 < 9.5000000000000007e-137

   1. Initial program 36.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 29.3%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 44.8%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   5. Taylor expanded in a around 0 37.1%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 37.1%

         \[\leadsto \color{blue}{-c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)} \]

      2. *-commutative 37.1%

         \[\leadsto -\color{blue}{\left(t \cdot \left(y2 \cdot y4\right)\right) \cdot c} \]

      3. distribute-rgt-neg-in 37.1%

         \[\leadsto \color{blue}{\left(t \cdot \left(y2 \cdot y4\right)\right) \cdot \left(-c\right)} \]

      4. *-commutative 37.1%

         \[\leadsto \left(t \cdot \color{blue}{\left(y4 \cdot y2\right)}\right) \cdot \left(-c\right) \]

   7. Simplified 37.1%

      \[\leadsto \color{blue}{\left(t \cdot \left(y4 \cdot y2\right)\right) \cdot \left(-c\right)} \]

   if 9.5000000000000007e-137 < y1 < 2.00000000000000005e-46

   1. Initial program 41.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 41.8%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 42.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in k around -inf 47.1%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 47.1%

         \[\leadsto b \cdot \color{blue}{\left(\left(-1 \cdot k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

      2. neg-mul-1 47.1%

         \[\leadsto b \cdot \left(\color{blue}{\left(-k\right)} \cdot \left(y \cdot y4 - y0 \cdot z\right)\right) \]

   8. Simplified 47.1%

      \[\leadsto b \cdot \color{blue}{\left(\left(-k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

   9. Taylor expanded in y around inf 34.8%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 34.8%

          \[\leadsto b \cdot \color{blue}{\left(-k \cdot \left(y \cdot y4\right)\right)} \]

       2. *-commutative 34.8%

          \[\leadsto b \cdot \left(-\color{blue}{\left(y \cdot y4\right) \cdot k}\right) \]

       3. distribute-rgt-neg-in 34.8%

          \[\leadsto b \cdot \color{blue}{\left(\left(y \cdot y4\right) \cdot \left(-k\right)\right)} \]

   11. Simplified 34.8%

       \[\leadsto b \cdot \color{blue}{\left(\left(y \cdot y4\right) \cdot \left(-k\right)\right)} \]

   if 2.00000000000000005e-46 < y1 < 225

   1. Initial program 40.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 40.0%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 27.0%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in y around inf 53.8%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]

   if 1.46000000000000009e243 < y1

   1. Initial program 31.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.3%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 44.0%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   6. Taylor expanded in x around inf 50.5%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right)\right)\right)} \]

   7. Taylor expanded in c around 0 63.0%

      \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 63.0%

         \[\leadsto -1 \cdot \color{blue}{\left(-i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\right)} \]

      2. *-commutative 63.0%

         \[\leadsto -1 \cdot \left(-\color{blue}{\left(j \cdot \left(x \cdot y1\right)\right) \cdot i}\right) \]

      3. distribute-rgt-neg-in 63.0%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(j \cdot \left(x \cdot y1\right)\right) \cdot \left(-i\right)\right)} \]

      4. *-commutative 63.0%

         \[\leadsto -1 \cdot \left(\left(j \cdot \color{blue}{\left(y1 \cdot x\right)}\right) \cdot \left(-i\right)\right) \]

   9. Simplified 63.0%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(j \cdot \left(y1 \cdot x\right)\right) \cdot \left(-i\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -4 \cdot 10^{+19}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq -1.65 \cdot 10^{-223}:\\ \;\;\;\;c \cdot \left(i \cdot \left(y \cdot \left(-x\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 3.1 \cdot 10^{-174}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 9.5 \cdot 10^{-137}:\\ \;\;\;\;c \cdot \left(t \cdot \left(y2 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 2 \cdot 10^{-46}:\\ \;\;\;\;b \cdot \left(k \cdot \left(y \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 225:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq 1.46 \cdot 10^{+243}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 31: 22.5% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot \left(y2 \cdot \left(-y4\right)\right)\right)\\ t_2 := k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \mathbf{if}\;y1 \leq -4 \cdot 10^{+17}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y1 \leq -9.5 \cdot 10^{-216}:\\ \;\;\;\;c \cdot \left(i \cdot \left(y \cdot \left(-x\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 3.1 \cdot 10^{-174}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 7.6 \cdot 10^{-137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq 3.8 \cdot 10^{-44}:\\ \;\;\;\;b \cdot \left(k \cdot \left(y \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 6 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq 7.6 \cdot 10^{+242}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* t (* y2 (- y4))))) (t_2 (* k (* y2 (* y1 y4)))))
   (if (<= y1 -4e+17)
     t_2
     (if (<= y1 -9.5e-216)
       (* c (* i (* y (- x))))
       (if (<= y1 3.1e-174)
         (* b (* k (* z y0)))
         (if (<= y1 7.6e-137)
           t_1
           (if (<= y1 3.8e-44)
             (* b (* k (* y (- y4))))
             (if (<= y1 6e-14)
               t_1
               (if (<= y1 7.6e+242) t_2 (* i (* j (* x y1))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (t * (y2 * -y4));
	double t_2 = k * (y2 * (y1 * y4));
	double tmp;
	if (y1 <= -4e+17) {
		tmp = t_2;
	} else if (y1 <= -9.5e-216) {
		tmp = c * (i * (y * -x));
	} else if (y1 <= 3.1e-174) {
		tmp = b * (k * (z * y0));
	} else if (y1 <= 7.6e-137) {
		tmp = t_1;
	} else if (y1 <= 3.8e-44) {
		tmp = b * (k * (y * -y4));
	} else if (y1 <= 6e-14) {
		tmp = t_1;
	} else if (y1 <= 7.6e+242) {
		tmp = t_2;
	} else {
		tmp = i * (j * (x * y1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * (t * (y2 * -y4))
    t_2 = k * (y2 * (y1 * y4))
    if (y1 <= (-4d+17)) then
        tmp = t_2
    else if (y1 <= (-9.5d-216)) then
        tmp = c * (i * (y * -x))
    else if (y1 <= 3.1d-174) then
        tmp = b * (k * (z * y0))
    else if (y1 <= 7.6d-137) then
        tmp = t_1
    else if (y1 <= 3.8d-44) then
        tmp = b * (k * (y * -y4))
    else if (y1 <= 6d-14) then
        tmp = t_1
    else if (y1 <= 7.6d+242) then
        tmp = t_2
    else
        tmp = i * (j * (x * y1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (t * (y2 * -y4));
	double t_2 = k * (y2 * (y1 * y4));
	double tmp;
	if (y1 <= -4e+17) {
		tmp = t_2;
	} else if (y1 <= -9.5e-216) {
		tmp = c * (i * (y * -x));
	} else if (y1 <= 3.1e-174) {
		tmp = b * (k * (z * y0));
	} else if (y1 <= 7.6e-137) {
		tmp = t_1;
	} else if (y1 <= 3.8e-44) {
		tmp = b * (k * (y * -y4));
	} else if (y1 <= 6e-14) {
		tmp = t_1;
	} else if (y1 <= 7.6e+242) {
		tmp = t_2;
	} else {
		tmp = i * (j * (x * y1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (t * (y2 * -y4))
	t_2 = k * (y2 * (y1 * y4))
	tmp = 0
	if y1 <= -4e+17:
		tmp = t_2
	elif y1 <= -9.5e-216:
		tmp = c * (i * (y * -x))
	elif y1 <= 3.1e-174:
		tmp = b * (k * (z * y0))
	elif y1 <= 7.6e-137:
		tmp = t_1
	elif y1 <= 3.8e-44:
		tmp = b * (k * (y * -y4))
	elif y1 <= 6e-14:
		tmp = t_1
	elif y1 <= 7.6e+242:
		tmp = t_2
	else:
		tmp = i * (j * (x * y1))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(t * Float64(y2 * Float64(-y4))))
	t_2 = Float64(k * Float64(y2 * Float64(y1 * y4)))
	tmp = 0.0
	if (y1 <= -4e+17)
		tmp = t_2;
	elseif (y1 <= -9.5e-216)
		tmp = Float64(c * Float64(i * Float64(y * Float64(-x))));
	elseif (y1 <= 3.1e-174)
		tmp = Float64(b * Float64(k * Float64(z * y0)));
	elseif (y1 <= 7.6e-137)
		tmp = t_1;
	elseif (y1 <= 3.8e-44)
		tmp = Float64(b * Float64(k * Float64(y * Float64(-y4))));
	elseif (y1 <= 6e-14)
		tmp = t_1;
	elseif (y1 <= 7.6e+242)
		tmp = t_2;
	else
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (t * (y2 * -y4));
	t_2 = k * (y2 * (y1 * y4));
	tmp = 0.0;
	if (y1 <= -4e+17)
		tmp = t_2;
	elseif (y1 <= -9.5e-216)
		tmp = c * (i * (y * -x));
	elseif (y1 <= 3.1e-174)
		tmp = b * (k * (z * y0));
	elseif (y1 <= 7.6e-137)
		tmp = t_1;
	elseif (y1 <= 3.8e-44)
		tmp = b * (k * (y * -y4));
	elseif (y1 <= 6e-14)
		tmp = t_1;
	elseif (y1 <= 7.6e+242)
		tmp = t_2;
	else
		tmp = i * (j * (x * y1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(t * N[(y2 * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(y2 * N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -4e+17], t$95$2, If[LessEqual[y1, -9.5e-216], N[(c * N[(i * N[(y * (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 3.1e-174], N[(b * N[(k * N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 7.6e-137], t$95$1, If[LessEqual[y1, 3.8e-44], N[(b * N[(k * N[(y * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 6e-14], t$95$1, If[LessEqual[y1, 7.6e+242], t$95$2, N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y1 < -4e17 or 5.9999999999999997e-14 < y1 < 7.60000000000000015e242

   1. Initial program 28.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 47.0%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in k around inf 41.9%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   5. Taylor expanded in y1 around inf 37.4%

      \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y1 \cdot y4\right)}\right) \]
   6. Step-by-step derivation

      1. *-commutative 37.4%

         \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y4 \cdot y1\right)}\right) \]

   7. Simplified 37.4%

      \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y4 \cdot y1\right)}\right) \]

   if -4e17 < y1 < -9.49999999999999943e-216

   1. Initial program 18.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 18.7%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 53.2%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   6. Taylor expanded in x around inf 35.9%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right)\right)\right)} \]

   7. Taylor expanded in c around inf 38.3%

      \[\leadsto -1 \cdot \color{blue}{\left(c \cdot \left(i \cdot \left(x \cdot y\right)\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 38.3%

         \[\leadsto -1 \cdot \left(c \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot i\right)}\right) \]

      2. *-commutative 38.3%

         \[\leadsto -1 \cdot \left(c \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot i\right)\right) \]

   9. Simplified 38.3%

      \[\leadsto -1 \cdot \color{blue}{\left(c \cdot \left(\left(y \cdot x\right) \cdot i\right)\right)} \]

   if -9.49999999999999943e-216 < y1 < 3.0999999999999999e-174

   1. Initial program 39.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 41.2%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 35.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in k around -inf 35.5%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 35.5%

         \[\leadsto b \cdot \color{blue}{\left(\left(-1 \cdot k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

      2. neg-mul-1 35.5%

         \[\leadsto b \cdot \left(\color{blue}{\left(-k\right)} \cdot \left(y \cdot y4 - y0 \cdot z\right)\right) \]

   8. Simplified 35.5%

      \[\leadsto b \cdot \color{blue}{\left(\left(-k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

   9. Taylor expanded in y around 0 35.4%

      \[\leadsto b \cdot \color{blue}{\left(k \cdot \left(y0 \cdot z\right)\right)} \]

   if 3.0999999999999999e-174 < y1 < 7.59999999999999997e-137 or 3.8000000000000001e-44 < y1 < 5.9999999999999997e-14

   1. Initial program 32.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 24.0%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 38.4%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   5. Taylor expanded in a around 0 42.1%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 42.1%

         \[\leadsto \color{blue}{-c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)} \]

      2. *-commutative 42.1%

         \[\leadsto -\color{blue}{\left(t \cdot \left(y2 \cdot y4\right)\right) \cdot c} \]

      3. distribute-rgt-neg-in 42.1%

         \[\leadsto \color{blue}{\left(t \cdot \left(y2 \cdot y4\right)\right) \cdot \left(-c\right)} \]

      4. *-commutative 42.1%

         \[\leadsto \left(t \cdot \color{blue}{\left(y4 \cdot y2\right)}\right) \cdot \left(-c\right) \]

   7. Simplified 42.1%

      \[\leadsto \color{blue}{\left(t \cdot \left(y4 \cdot y2\right)\right) \cdot \left(-c\right)} \]

   if 7.59999999999999997e-137 < y1 < 3.8000000000000001e-44

   1. Initial program 46.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 46.3%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 39.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in k around -inf 43.6%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 43.6%

         \[\leadsto b \cdot \color{blue}{\left(\left(-1 \cdot k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

      2. neg-mul-1 43.6%

         \[\leadsto b \cdot \left(\color{blue}{\left(-k\right)} \cdot \left(y \cdot y4 - y0 \cdot z\right)\right) \]

   8. Simplified 43.6%

      \[\leadsto b \cdot \color{blue}{\left(\left(-k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

   9. Taylor expanded in y around inf 32.3%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 32.3%

          \[\leadsto b \cdot \color{blue}{\left(-k \cdot \left(y \cdot y4\right)\right)} \]

       2. *-commutative 32.3%

          \[\leadsto b \cdot \left(-\color{blue}{\left(y \cdot y4\right) \cdot k}\right) \]

       3. distribute-rgt-neg-in 32.3%

          \[\leadsto b \cdot \color{blue}{\left(\left(y \cdot y4\right) \cdot \left(-k\right)\right)} \]

   11. Simplified 32.3%

       \[\leadsto b \cdot \color{blue}{\left(\left(y \cdot y4\right) \cdot \left(-k\right)\right)} \]

   if 7.60000000000000015e242 < y1

   1. Initial program 31.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.3%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 44.0%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   6. Taylor expanded in x around inf 50.5%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right)\right)\right)} \]

   7. Taylor expanded in c around 0 63.0%

      \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 63.0%

         \[\leadsto -1 \cdot \color{blue}{\left(-i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\right)} \]

      2. *-commutative 63.0%

         \[\leadsto -1 \cdot \left(-\color{blue}{\left(j \cdot \left(x \cdot y1\right)\right) \cdot i}\right) \]

      3. distribute-rgt-neg-in 63.0%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(j \cdot \left(x \cdot y1\right)\right) \cdot \left(-i\right)\right)} \]

      4. *-commutative 63.0%

         \[\leadsto -1 \cdot \left(\left(j \cdot \color{blue}{\left(y1 \cdot x\right)}\right) \cdot \left(-i\right)\right) \]

   9. Simplified 63.0%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(j \cdot \left(y1 \cdot x\right)\right) \cdot \left(-i\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 38.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -4 \cdot 10^{+17}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq -9.5 \cdot 10^{-216}:\\ \;\;\;\;c \cdot \left(i \cdot \left(y \cdot \left(-x\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 3.1 \cdot 10^{-174}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 7.6 \cdot 10^{-137}:\\ \;\;\;\;c \cdot \left(t \cdot \left(y2 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 3.8 \cdot 10^{-44}:\\ \;\;\;\;b \cdot \left(k \cdot \left(y \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 6 \cdot 10^{-14}:\\ \;\;\;\;c \cdot \left(t \cdot \left(y2 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 7.6 \cdot 10^{+242}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 32: 31.8% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq -8.8 \cdot 10^{-16}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;k \leq -1.6 \cdot 10^{-186}:\\ \;\;\;\;z \cdot \left(c \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq -1.45 \cdot 10^{-241}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;k \leq 4.2 \cdot 10^{-227}:\\ \;\;\;\;\left(y0 \cdot y3\right) \cdot \left(j \cdot y5 - z \cdot c\right)\\ \mathbf{elif}\;k \leq 8.8 \cdot 10^{+20}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 9.2 \cdot 10^{+166}:\\ \;\;\;\;y2 \cdot \left(y0 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= k -8.8e-16)
   (* y4 (* k (- (* y1 y2) (* y b))))
   (if (<= k -1.6e-186)
     (* z (* c (- (* t i) (* y0 y3))))
     (if (<= k -1.45e-241)
       (* b (* y4 (- (* t j) (* y k))))
       (if (<= k 4.2e-227)
         (* (* y0 y3) (- (* j y5) (* z c)))
         (if (<= k 8.8e+20)
           (* a (* y1 (- (* z y3) (* x y2))))
           (if (<= k 9.2e+166)
             (* y2 (* y0 (- (* x c) (* k y5))))
             (* b (* k (- (* z y0) (* y y4)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (k <= -8.8e-16) {
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	} else if (k <= -1.6e-186) {
		tmp = z * (c * ((t * i) - (y0 * y3)));
	} else if (k <= -1.45e-241) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (k <= 4.2e-227) {
		tmp = (y0 * y3) * ((j * y5) - (z * c));
	} else if (k <= 8.8e+20) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (k <= 9.2e+166) {
		tmp = y2 * (y0 * ((x * c) - (k * y5)));
	} else {
		tmp = b * (k * ((z * y0) - (y * y4)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (k <= (-8.8d-16)) then
        tmp = y4 * (k * ((y1 * y2) - (y * b)))
    else if (k <= (-1.6d-186)) then
        tmp = z * (c * ((t * i) - (y0 * y3)))
    else if (k <= (-1.45d-241)) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (k <= 4.2d-227) then
        tmp = (y0 * y3) * ((j * y5) - (z * c))
    else if (k <= 8.8d+20) then
        tmp = a * (y1 * ((z * y3) - (x * y2)))
    else if (k <= 9.2d+166) then
        tmp = y2 * (y0 * ((x * c) - (k * y5)))
    else
        tmp = b * (k * ((z * y0) - (y * y4)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (k <= -8.8e-16) {
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	} else if (k <= -1.6e-186) {
		tmp = z * (c * ((t * i) - (y0 * y3)));
	} else if (k <= -1.45e-241) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (k <= 4.2e-227) {
		tmp = (y0 * y3) * ((j * y5) - (z * c));
	} else if (k <= 8.8e+20) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (k <= 9.2e+166) {
		tmp = y2 * (y0 * ((x * c) - (k * y5)));
	} else {
		tmp = b * (k * ((z * y0) - (y * y4)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if k <= -8.8e-16:
		tmp = y4 * (k * ((y1 * y2) - (y * b)))
	elif k <= -1.6e-186:
		tmp = z * (c * ((t * i) - (y0 * y3)))
	elif k <= -1.45e-241:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif k <= 4.2e-227:
		tmp = (y0 * y3) * ((j * y5) - (z * c))
	elif k <= 8.8e+20:
		tmp = a * (y1 * ((z * y3) - (x * y2)))
	elif k <= 9.2e+166:
		tmp = y2 * (y0 * ((x * c) - (k * y5)))
	else:
		tmp = b * (k * ((z * y0) - (y * y4)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (k <= -8.8e-16)
		tmp = Float64(y4 * Float64(k * Float64(Float64(y1 * y2) - Float64(y * b))));
	elseif (k <= -1.6e-186)
		tmp = Float64(z * Float64(c * Float64(Float64(t * i) - Float64(y0 * y3))));
	elseif (k <= -1.45e-241)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (k <= 4.2e-227)
		tmp = Float64(Float64(y0 * y3) * Float64(Float64(j * y5) - Float64(z * c)));
	elseif (k <= 8.8e+20)
		tmp = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))));
	elseif (k <= 9.2e+166)
		tmp = Float64(y2 * Float64(y0 * Float64(Float64(x * c) - Float64(k * y5))));
	else
		tmp = Float64(b * Float64(k * Float64(Float64(z * y0) - Float64(y * y4))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (k <= -8.8e-16)
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	elseif (k <= -1.6e-186)
		tmp = z * (c * ((t * i) - (y0 * y3)));
	elseif (k <= -1.45e-241)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (k <= 4.2e-227)
		tmp = (y0 * y3) * ((j * y5) - (z * c));
	elseif (k <= 8.8e+20)
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	elseif (k <= 9.2e+166)
		tmp = y2 * (y0 * ((x * c) - (k * y5)));
	else
		tmp = b * (k * ((z * y0) - (y * y4)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[k, -8.8e-16], N[(y4 * N[(k * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -1.6e-186], N[(z * N[(c * N[(N[(t * i), $MachinePrecision] - N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -1.45e-241], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 4.2e-227], N[(N[(y0 * y3), $MachinePrecision] * N[(N[(j * y5), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 8.8e+20], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 9.2e+166], N[(y2 * N[(y0 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if k < -8.80000000000000001e-16

   1. Initial program 24.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf 45.3%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in k around inf 49.4%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(b \cdot y\right) + y1 \cdot y2\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 49.4%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(b \cdot y\right)\right)}\right) \]

      2. mul-1-neg 49.4%

         \[\leadsto y4 \cdot \left(k \cdot \left(y1 \cdot y2 + \color{blue}{\left(-b \cdot y\right)}\right)\right) \]

      3. unsub-neg 49.4%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 - b \cdot y\right)}\right) \]

      4. *-commutative 49.4%

         \[\leadsto y4 \cdot \left(k \cdot \left(y1 \cdot y2 - \color{blue}{y \cdot b}\right)\right) \]

   6. Simplified 49.4%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)} \]

   if -8.80000000000000001e-16 < k < -1.6e-186

   1. Initial program 55.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 55.5%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around -inf 56.3%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   6. Taylor expanded in c around inf 45.2%

      \[\leadsto -1 \cdot \left(z \cdot \color{blue}{\left(c \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)}\right) \]

   if -1.6e-186 < k < -1.45e-241

   1. Initial program 34.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 34.3%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 40.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y4 around inf 41.0%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   if -1.45e-241 < k < 4.1999999999999999e-227

   1. Initial program 35.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y3 around -inf 45.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 46.0%

      \[\leadsto -1 \cdot \color{blue}{\left(y0 \cdot \left(y3 \cdot \left(-1 \cdot \left(j \cdot y5\right) + c \cdot z\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 49.2%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(y0 \cdot y3\right) \cdot \left(-1 \cdot \left(j \cdot y5\right) + c \cdot z\right)\right)} \]

      2. +-commutative 49.2%

         \[\leadsto -1 \cdot \left(\left(y0 \cdot y3\right) \cdot \color{blue}{\left(c \cdot z + -1 \cdot \left(j \cdot y5\right)\right)}\right) \]

      3. mul-1-neg 49.2%

         \[\leadsto -1 \cdot \left(\left(y0 \cdot y3\right) \cdot \left(c \cdot z + \color{blue}{\left(-j \cdot y5\right)}\right)\right) \]

      4. unsub-neg 49.2%

         \[\leadsto -1 \cdot \left(\left(y0 \cdot y3\right) \cdot \color{blue}{\left(c \cdot z - j \cdot y5\right)}\right) \]

      5. *-commutative 49.2%

         \[\leadsto -1 \cdot \left(\left(y0 \cdot y3\right) \cdot \left(\color{blue}{z \cdot c} - j \cdot y5\right)\right) \]

      6. *-commutative 49.2%

         \[\leadsto -1 \cdot \left(\left(y0 \cdot y3\right) \cdot \left(z \cdot c - \color{blue}{y5 \cdot j}\right)\right) \]

   6. Simplified 49.2%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(y0 \cdot y3\right) \cdot \left(z \cdot c - y5 \cdot j\right)\right)} \]

   if 4.1999999999999999e-227 < k < 8.8e20

   1. Initial program 26.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 26.4%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 43.6%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in y1 around inf 53.0%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 53.0%

         \[\leadsto \color{blue}{-a \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   8. Simplified 53.0%

      \[\leadsto \color{blue}{-a \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   if 8.8e20 < k < 9.2000000000000003e166

   1. Initial program 34.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 48.6%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in y0 around inf 66.2%

      \[\leadsto y2 \cdot \color{blue}{\left(y0 \cdot \left(-1 \cdot \left(k \cdot y5\right) + c \cdot x\right)\right)} \]

   if 9.2000000000000003e166 < k

   1. Initial program 14.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 14.8%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 44.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in k around -inf 71.0%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 71.0%

         \[\leadsto b \cdot \color{blue}{\left(\left(-1 \cdot k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

      2. neg-mul-1 71.0%

         \[\leadsto b \cdot \left(\color{blue}{\left(-k\right)} \cdot \left(y \cdot y4 - y0 \cdot z\right)\right) \]

   8. Simplified 71.0%

      \[\leadsto b \cdot \color{blue}{\left(\left(-k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -8.8 \cdot 10^{-16}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;k \leq -1.6 \cdot 10^{-186}:\\ \;\;\;\;z \cdot \left(c \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq -1.45 \cdot 10^{-241}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;k \leq 4.2 \cdot 10^{-227}:\\ \;\;\;\;\left(y0 \cdot y3\right) \cdot \left(j \cdot y5 - z \cdot c\right)\\ \mathbf{elif}\;k \leq 8.8 \cdot 10^{+20}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 9.2 \cdot 10^{+166}:\\ \;\;\;\;y2 \cdot \left(y0 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 33: 26.9% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -3.8 \cdot 10^{+51}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;i \leq -5.5 \cdot 10^{-147}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;i \leq -4.4 \cdot 10^{-205}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq -5.2 \cdot 10^{-300}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;i \leq 8.6 \cdot 10^{-128}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq 3.2 \cdot 10^{+205}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(c \cdot \left(-x\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= i -3.8e+51)
   (* i (* j (* x y1)))
   (if (<= i -5.5e-147)
     (* a (* y3 (- (* z y1) (* y y5))))
     (if (<= i -4.4e-205)
       (* b (* x (- (* y a) (* j y0))))
       (if (<= i -5.2e-300)
         (* b (* y0 (- (* z k) (* x j))))
         (if (<= i 8.6e-128)
           (* c (* y2 (- (* x y0) (* t y4))))
           (if (<= i 3.2e+205)
             (* y4 (* b (- (* t j) (* y k))))
             (* i (* y (* c (- x)))))))))))

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 (i <= -3.8e+51) {
		tmp = i * (j * (x * y1));
	} else if (i <= -5.5e-147) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (i <= -4.4e-205) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (i <= -5.2e-300) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (i <= 8.6e-128) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (i <= 3.2e+205) {
		tmp = y4 * (b * ((t * j) - (y * k)));
	} else {
		tmp = i * (y * (c * -x));
	}
	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 (i <= (-3.8d+51)) then
        tmp = i * (j * (x * y1))
    else if (i <= (-5.5d-147)) then
        tmp = a * (y3 * ((z * y1) - (y * y5)))
    else if (i <= (-4.4d-205)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (i <= (-5.2d-300)) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (i <= 8.6d-128) then
        tmp = c * (y2 * ((x * y0) - (t * y4)))
    else if (i <= 3.2d+205) then
        tmp = y4 * (b * ((t * j) - (y * k)))
    else
        tmp = i * (y * (c * -x))
    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 (i <= -3.8e+51) {
		tmp = i * (j * (x * y1));
	} else if (i <= -5.5e-147) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (i <= -4.4e-205) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (i <= -5.2e-300) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (i <= 8.6e-128) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (i <= 3.2e+205) {
		tmp = y4 * (b * ((t * j) - (y * k)));
	} else {
		tmp = i * (y * (c * -x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if i <= -3.8e+51:
		tmp = i * (j * (x * y1))
	elif i <= -5.5e-147:
		tmp = a * (y3 * ((z * y1) - (y * y5)))
	elif i <= -4.4e-205:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif i <= -5.2e-300:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif i <= 8.6e-128:
		tmp = c * (y2 * ((x * y0) - (t * y4)))
	elif i <= 3.2e+205:
		tmp = y4 * (b * ((t * j) - (y * k)))
	else:
		tmp = i * (y * (c * -x))
	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 (i <= -3.8e+51)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (i <= -5.5e-147)
		tmp = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))));
	elseif (i <= -4.4e-205)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (i <= -5.2e-300)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (i <= 8.6e-128)
		tmp = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))));
	elseif (i <= 3.2e+205)
		tmp = Float64(y4 * Float64(b * Float64(Float64(t * j) - Float64(y * k))));
	else
		tmp = Float64(i * Float64(y * Float64(c * Float64(-x))));
	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 (i <= -3.8e+51)
		tmp = i * (j * (x * y1));
	elseif (i <= -5.5e-147)
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	elseif (i <= -4.4e-205)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (i <= -5.2e-300)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (i <= 8.6e-128)
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	elseif (i <= 3.2e+205)
		tmp = y4 * (b * ((t * j) - (y * k)));
	else
		tmp = i * (y * (c * -x));
	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[i, -3.8e+51], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -5.5e-147], N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -4.4e-205], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -5.2e-300], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 8.6e-128], N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.2e+205], N[(y4 * N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(y * N[(c * (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if i < -3.7999999999999997e51

   1. Initial program 23.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.6%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 64.6%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   6. Taylor expanded in x around inf 51.9%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right)\right)\right)} \]

   7. Taylor expanded in c around 0 46.7%

      \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 46.7%

         \[\leadsto -1 \cdot \color{blue}{\left(-i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\right)} \]

      2. *-commutative 46.7%

         \[\leadsto -1 \cdot \left(-\color{blue}{\left(j \cdot \left(x \cdot y1\right)\right) \cdot i}\right) \]

      3. distribute-rgt-neg-in 46.7%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(j \cdot \left(x \cdot y1\right)\right) \cdot \left(-i\right)\right)} \]

      4. *-commutative 46.7%

         \[\leadsto -1 \cdot \left(\left(j \cdot \color{blue}{\left(y1 \cdot x\right)}\right) \cdot \left(-i\right)\right) \]

   9. Simplified 46.7%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(j \cdot \left(y1 \cdot x\right)\right) \cdot \left(-i\right)\right)} \]

   if -3.7999999999999997e51 < i < -5.5e-147

   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%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 40.6%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in y3 around inf 32.8%

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]

   if -5.5e-147 < i < -4.40000000000000018e-205

   1. Initial program 13.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 13.3%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 20.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 66.9%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   if -4.40000000000000018e-205 < i < -5.19999999999999993e-300

   1. Initial program 50.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 50.6%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 40.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y0 around inf 36.5%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   if -5.19999999999999993e-300 < i < 8.59999999999999988e-128

   1. Initial program 36.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 43.4%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 45.7%

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)} \]

   if 8.59999999999999988e-128 < i < 3.19999999999999996e205

   1. Initial program 28.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf 44.4%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in b around inf 42.2%

      \[\leadsto y4 \cdot \color{blue}{\left(b \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   if 3.19999999999999996e205 < i

   1. Initial program 37.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 37.2%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 84.0%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   6. Taylor expanded in x around inf 64.2%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right)\right)\right)} \]

   7. Taylor expanded in c around inf 56.2%

      \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(c \cdot \left(x \cdot y\right)\right)}\right) \]
   8. Step-by-step derivation

      1. associate-*r* 56.5%

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(c \cdot x\right) \cdot y\right)}\right) \]

   9. Simplified 56.5%

      \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(c \cdot x\right) \cdot y\right)}\right) \]
3. Recombined 7 regimes into one program.

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.8 \cdot 10^{+51}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;i \leq -5.5 \cdot 10^{-147}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;i \leq -4.4 \cdot 10^{-205}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq -5.2 \cdot 10^{-300}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;i \leq 8.6 \cdot 10^{-128}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq 3.2 \cdot 10^{+205}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(c \cdot \left(-x\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 34: 29.7% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{if}\;y0 \leq -3.8 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y0 \leq -1.35 \cdot 10^{-26}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq -1.02 \cdot 10^{-50}:\\ \;\;\;\;b \cdot \left(k \cdot \left(y \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 4.4 \cdot 10^{-219}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 5 \cdot 10^{-43}:\\ \;\;\;\;i \cdot \left(y \cdot \left(c \cdot \left(-x\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 4.1 \cdot 10^{+196}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* y0 (- (* z k) (* x j))))))
   (if (<= y0 -3.8e+58)
     t_1
     (if (<= y0 -1.35e-26)
       (* k (* y2 (* y1 y4)))
       (if (<= y0 -1.02e-50)
         (* b (* k (* y (- y4))))
         (if (<= y0 4.4e-219)
           (* a (* y3 (- (* z y1) (* y y5))))
           (if (<= y0 5e-43)
             (* i (* y (* c (- x))))
             (if (<= y0 4.1e+196)
               (* a (* y5 (- (* t y2) (* y 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 = b * (y0 * ((z * k) - (x * j)));
	double tmp;
	if (y0 <= -3.8e+58) {
		tmp = t_1;
	} else if (y0 <= -1.35e-26) {
		tmp = k * (y2 * (y1 * y4));
	} else if (y0 <= -1.02e-50) {
		tmp = b * (k * (y * -y4));
	} else if (y0 <= 4.4e-219) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (y0 <= 5e-43) {
		tmp = i * (y * (c * -x));
	} else if (y0 <= 4.1e+196) {
		tmp = a * (y5 * ((t * y2) - (y * 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 = b * (y0 * ((z * k) - (x * j)))
    if (y0 <= (-3.8d+58)) then
        tmp = t_1
    else if (y0 <= (-1.35d-26)) then
        tmp = k * (y2 * (y1 * y4))
    else if (y0 <= (-1.02d-50)) then
        tmp = b * (k * (y * -y4))
    else if (y0 <= 4.4d-219) then
        tmp = a * (y3 * ((z * y1) - (y * y5)))
    else if (y0 <= 5d-43) then
        tmp = i * (y * (c * -x))
    else if (y0 <= 4.1d+196) then
        tmp = a * (y5 * ((t * y2) - (y * 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 = b * (y0 * ((z * k) - (x * j)));
	double tmp;
	if (y0 <= -3.8e+58) {
		tmp = t_1;
	} else if (y0 <= -1.35e-26) {
		tmp = k * (y2 * (y1 * y4));
	} else if (y0 <= -1.02e-50) {
		tmp = b * (k * (y * -y4));
	} else if (y0 <= 4.4e-219) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (y0 <= 5e-43) {
		tmp = i * (y * (c * -x));
	} else if (y0 <= 4.1e+196) {
		tmp = a * (y5 * ((t * y2) - (y * 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 = b * (y0 * ((z * k) - (x * j)))
	tmp = 0
	if y0 <= -3.8e+58:
		tmp = t_1
	elif y0 <= -1.35e-26:
		tmp = k * (y2 * (y1 * y4))
	elif y0 <= -1.02e-50:
		tmp = b * (k * (y * -y4))
	elif y0 <= 4.4e-219:
		tmp = a * (y3 * ((z * y1) - (y * y5)))
	elif y0 <= 5e-43:
		tmp = i * (y * (c * -x))
	elif y0 <= 4.1e+196:
		tmp = a * (y5 * ((t * y2) - (y * 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(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))))
	tmp = 0.0
	if (y0 <= -3.8e+58)
		tmp = t_1;
	elseif (y0 <= -1.35e-26)
		tmp = Float64(k * Float64(y2 * Float64(y1 * y4)));
	elseif (y0 <= -1.02e-50)
		tmp = Float64(b * Float64(k * Float64(y * Float64(-y4))));
	elseif (y0 <= 4.4e-219)
		tmp = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))));
	elseif (y0 <= 5e-43)
		tmp = Float64(i * Float64(y * Float64(c * Float64(-x))));
	elseif (y0 <= 4.1e+196)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * 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 = b * (y0 * ((z * k) - (x * j)));
	tmp = 0.0;
	if (y0 <= -3.8e+58)
		tmp = t_1;
	elseif (y0 <= -1.35e-26)
		tmp = k * (y2 * (y1 * y4));
	elseif (y0 <= -1.02e-50)
		tmp = b * (k * (y * -y4));
	elseif (y0 <= 4.4e-219)
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	elseif (y0 <= 5e-43)
		tmp = i * (y * (c * -x));
	elseif (y0 <= 4.1e+196)
		tmp = a * (y5 * ((t * y2) - (y * 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[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -3.8e+58], t$95$1, If[LessEqual[y0, -1.35e-26], N[(k * N[(y2 * N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1.02e-50], N[(b * N[(k * N[(y * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 4.4e-219], N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 5e-43], N[(i * N[(y * N[(c * (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 4.1e+196], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y0 < -3.7999999999999999e58 or 4.0999999999999996e196 < y0

   1. Initial program 27.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.8%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 36.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y0 around inf 48.7%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   if -3.7999999999999999e58 < y0 < -1.34999999999999991e-26

   1. Initial program 40.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 40.9%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in k around inf 41.2%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   5. Taylor expanded in y1 around inf 41.1%

      \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y1 \cdot y4\right)}\right) \]
   6. Step-by-step derivation

      1. *-commutative 41.1%

         \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y4 \cdot y1\right)}\right) \]

   7. Simplified 41.1%

      \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y4 \cdot y1\right)}\right) \]

   if -1.34999999999999991e-26 < y0 < -1.0199999999999999e-50

   1. Initial program 24.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 24.6%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 74.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in k around -inf 99.6%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 99.6%

         \[\leadsto b \cdot \color{blue}{\left(\left(-1 \cdot k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

      2. neg-mul-1 99.6%

         \[\leadsto b \cdot \left(\color{blue}{\left(-k\right)} \cdot \left(y \cdot y4 - y0 \cdot z\right)\right) \]

   8. Simplified 99.6%

      \[\leadsto b \cdot \color{blue}{\left(\left(-k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

   9. Taylor expanded in y around inf 76.0%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 76.0%

          \[\leadsto b \cdot \color{blue}{\left(-k \cdot \left(y \cdot y4\right)\right)} \]

       2. *-commutative 76.0%

          \[\leadsto b \cdot \left(-\color{blue}{\left(y \cdot y4\right) \cdot k}\right) \]

       3. distribute-rgt-neg-in 76.0%

          \[\leadsto b \cdot \color{blue}{\left(\left(y \cdot y4\right) \cdot \left(-k\right)\right)} \]

   11. Simplified 76.0%

       \[\leadsto b \cdot \color{blue}{\left(\left(y \cdot y4\right) \cdot \left(-k\right)\right)} \]

   if -1.0199999999999999e-50 < y0 < 4.3999999999999999e-219

   1. Initial program 38.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 38.6%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 36.4%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in y3 around inf 38.0%

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]

   if 4.3999999999999999e-219 < y0 < 5.00000000000000019e-43

   1. Initial program 30.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.3%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 46.0%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   6. Taylor expanded in x around inf 46.3%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right)\right)\right)} \]

   7. Taylor expanded in c around inf 39.3%

      \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(c \cdot \left(x \cdot y\right)\right)}\right) \]
   8. Step-by-step derivation

      1. associate-*r* 42.0%

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(c \cdot x\right) \cdot y\right)}\right) \]

   9. Simplified 42.0%

      \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(c \cdot x\right) \cdot y\right)}\right) \]

   if 5.00000000000000019e-43 < y0 < 4.0999999999999996e196

   1. Initial program 25.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.5%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 44.5%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in y5 around inf 38.4%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -3.8 \cdot 10^{+58}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -1.35 \cdot 10^{-26}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq -1.02 \cdot 10^{-50}:\\ \;\;\;\;b \cdot \left(k \cdot \left(y \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 4.4 \cdot 10^{-219}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 5 \cdot 10^{-43}:\\ \;\;\;\;i \cdot \left(y \cdot \left(c \cdot \left(-x\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 4.1 \cdot 10^{+196}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 35: 22.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot \left(y2 \cdot \left(-y4\right)\right)\right)\\ t_2 := k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \mathbf{if}\;y1 \leq -4 \cdot 10^{+19}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y1 \leq -1.2 \cdot 10^{-215}:\\ \;\;\;\;c \cdot \left(i \cdot \left(y \cdot \left(-x\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 3.2 \cdot 10^{-174}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 1.65 \cdot 10^{-136}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq 3.8 \cdot 10^{-44}:\\ \;\;\;\;b \cdot \left(k \cdot \left(y \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 9.6 \cdot 10^{-13}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* t (* y2 (- y4))))) (t_2 (* k (* y2 (* y1 y4)))))
   (if (<= y1 -4e+19)
     t_2
     (if (<= y1 -1.2e-215)
       (* c (* i (* y (- x))))
       (if (<= y1 3.2e-174)
         (* b (* k (* z y0)))
         (if (<= y1 1.65e-136)
           t_1
           (if (<= y1 3.8e-44)
             (* b (* k (* y (- y4))))
             (if (<= y1 9.6e-13) 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 = c * (t * (y2 * -y4));
	double t_2 = k * (y2 * (y1 * y4));
	double tmp;
	if (y1 <= -4e+19) {
		tmp = t_2;
	} else if (y1 <= -1.2e-215) {
		tmp = c * (i * (y * -x));
	} else if (y1 <= 3.2e-174) {
		tmp = b * (k * (z * y0));
	} else if (y1 <= 1.65e-136) {
		tmp = t_1;
	} else if (y1 <= 3.8e-44) {
		tmp = b * (k * (y * -y4));
	} else if (y1 <= 9.6e-13) {
		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) :: tmp
    t_1 = c * (t * (y2 * -y4))
    t_2 = k * (y2 * (y1 * y4))
    if (y1 <= (-4d+19)) then
        tmp = t_2
    else if (y1 <= (-1.2d-215)) then
        tmp = c * (i * (y * -x))
    else if (y1 <= 3.2d-174) then
        tmp = b * (k * (z * y0))
    else if (y1 <= 1.65d-136) then
        tmp = t_1
    else if (y1 <= 3.8d-44) then
        tmp = b * (k * (y * -y4))
    else if (y1 <= 9.6d-13) 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 = c * (t * (y2 * -y4));
	double t_2 = k * (y2 * (y1 * y4));
	double tmp;
	if (y1 <= -4e+19) {
		tmp = t_2;
	} else if (y1 <= -1.2e-215) {
		tmp = c * (i * (y * -x));
	} else if (y1 <= 3.2e-174) {
		tmp = b * (k * (z * y0));
	} else if (y1 <= 1.65e-136) {
		tmp = t_1;
	} else if (y1 <= 3.8e-44) {
		tmp = b * (k * (y * -y4));
	} else if (y1 <= 9.6e-13) {
		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 = c * (t * (y2 * -y4))
	t_2 = k * (y2 * (y1 * y4))
	tmp = 0
	if y1 <= -4e+19:
		tmp = t_2
	elif y1 <= -1.2e-215:
		tmp = c * (i * (y * -x))
	elif y1 <= 3.2e-174:
		tmp = b * (k * (z * y0))
	elif y1 <= 1.65e-136:
		tmp = t_1
	elif y1 <= 3.8e-44:
		tmp = b * (k * (y * -y4))
	elif y1 <= 9.6e-13:
		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(c * Float64(t * Float64(y2 * Float64(-y4))))
	t_2 = Float64(k * Float64(y2 * Float64(y1 * y4)))
	tmp = 0.0
	if (y1 <= -4e+19)
		tmp = t_2;
	elseif (y1 <= -1.2e-215)
		tmp = Float64(c * Float64(i * Float64(y * Float64(-x))));
	elseif (y1 <= 3.2e-174)
		tmp = Float64(b * Float64(k * Float64(z * y0)));
	elseif (y1 <= 1.65e-136)
		tmp = t_1;
	elseif (y1 <= 3.8e-44)
		tmp = Float64(b * Float64(k * Float64(y * Float64(-y4))));
	elseif (y1 <= 9.6e-13)
		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 = c * (t * (y2 * -y4));
	t_2 = k * (y2 * (y1 * y4));
	tmp = 0.0;
	if (y1 <= -4e+19)
		tmp = t_2;
	elseif (y1 <= -1.2e-215)
		tmp = c * (i * (y * -x));
	elseif (y1 <= 3.2e-174)
		tmp = b * (k * (z * y0));
	elseif (y1 <= 1.65e-136)
		tmp = t_1;
	elseif (y1 <= 3.8e-44)
		tmp = b * (k * (y * -y4));
	elseif (y1 <= 9.6e-13)
		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[(c * N[(t * N[(y2 * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(y2 * N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -4e+19], t$95$2, If[LessEqual[y1, -1.2e-215], N[(c * N[(i * N[(y * (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 3.2e-174], N[(b * N[(k * N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.65e-136], t$95$1, If[LessEqual[y1, 3.8e-44], N[(b * N[(k * N[(y * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 9.6e-13], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y1 < -4e19 or 9.5999999999999995e-13 < y1

   1. Initial program 29.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 45.8%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in k around inf 39.8%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   5. Taylor expanded in y1 around inf 35.1%

      \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y1 \cdot y4\right)}\right) \]
   6. Step-by-step derivation

      1. *-commutative 35.1%

         \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y4 \cdot y1\right)}\right) \]

   7. Simplified 35.1%

      \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y4 \cdot y1\right)}\right) \]

   if -4e19 < y1 < -1.20000000000000005e-215

   1. Initial program 18.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 18.7%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 53.2%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   6. Taylor expanded in x around inf 35.9%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right)\right)\right)} \]

   7. Taylor expanded in c around inf 38.3%

      \[\leadsto -1 \cdot \color{blue}{\left(c \cdot \left(i \cdot \left(x \cdot y\right)\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 38.3%

         \[\leadsto -1 \cdot \left(c \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot i\right)}\right) \]

      2. *-commutative 38.3%

         \[\leadsto -1 \cdot \left(c \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot i\right)\right) \]

   9. Simplified 38.3%

      \[\leadsto -1 \cdot \color{blue}{\left(c \cdot \left(\left(y \cdot x\right) \cdot i\right)\right)} \]

   if -1.20000000000000005e-215 < y1 < 3.2e-174

   1. Initial program 39.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 41.2%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 35.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in k around -inf 35.5%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 35.5%

         \[\leadsto b \cdot \color{blue}{\left(\left(-1 \cdot k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

      2. neg-mul-1 35.5%

         \[\leadsto b \cdot \left(\color{blue}{\left(-k\right)} \cdot \left(y \cdot y4 - y0 \cdot z\right)\right) \]

   8. Simplified 35.5%

      \[\leadsto b \cdot \color{blue}{\left(\left(-k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

   9. Taylor expanded in y around 0 35.4%

      \[\leadsto b \cdot \color{blue}{\left(k \cdot \left(y0 \cdot z\right)\right)} \]

   if 3.2e-174 < y1 < 1.65000000000000009e-136 or 3.8000000000000001e-44 < y1 < 9.5999999999999995e-13

   1. Initial program 32.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 24.0%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 38.4%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   5. Taylor expanded in a around 0 42.1%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 42.1%

         \[\leadsto \color{blue}{-c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)} \]

      2. *-commutative 42.1%

         \[\leadsto -\color{blue}{\left(t \cdot \left(y2 \cdot y4\right)\right) \cdot c} \]

      3. distribute-rgt-neg-in 42.1%

         \[\leadsto \color{blue}{\left(t \cdot \left(y2 \cdot y4\right)\right) \cdot \left(-c\right)} \]

      4. *-commutative 42.1%

         \[\leadsto \left(t \cdot \color{blue}{\left(y4 \cdot y2\right)}\right) \cdot \left(-c\right) \]

   7. Simplified 42.1%

      \[\leadsto \color{blue}{\left(t \cdot \left(y4 \cdot y2\right)\right) \cdot \left(-c\right)} \]

   if 1.65000000000000009e-136 < y1 < 3.8000000000000001e-44

   1. Initial program 46.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 46.3%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 39.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in k around -inf 43.6%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 43.6%

         \[\leadsto b \cdot \color{blue}{\left(\left(-1 \cdot k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

      2. neg-mul-1 43.6%

         \[\leadsto b \cdot \left(\color{blue}{\left(-k\right)} \cdot \left(y \cdot y4 - y0 \cdot z\right)\right) \]

   8. Simplified 43.6%

      \[\leadsto b \cdot \color{blue}{\left(\left(-k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

   9. Taylor expanded in y around inf 32.3%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 32.3%

          \[\leadsto b \cdot \color{blue}{\left(-k \cdot \left(y \cdot y4\right)\right)} \]

       2. *-commutative 32.3%

          \[\leadsto b \cdot \left(-\color{blue}{\left(y \cdot y4\right) \cdot k}\right) \]

       3. distribute-rgt-neg-in 32.3%

          \[\leadsto b \cdot \color{blue}{\left(\left(y \cdot y4\right) \cdot \left(-k\right)\right)} \]

   11. Simplified 32.3%

       \[\leadsto b \cdot \color{blue}{\left(\left(y \cdot y4\right) \cdot \left(-k\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 36.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -4 \cdot 10^{+19}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq -1.2 \cdot 10^{-215}:\\ \;\;\;\;c \cdot \left(i \cdot \left(y \cdot \left(-x\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 3.2 \cdot 10^{-174}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 1.65 \cdot 10^{-136}:\\ \;\;\;\;c \cdot \left(t \cdot \left(y2 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 3.8 \cdot 10^{-44}:\\ \;\;\;\;b \cdot \left(k \cdot \left(y \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 9.6 \cdot 10^{-13}:\\ \;\;\;\;c \cdot \left(t \cdot \left(y2 \cdot \left(-y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 36: 22.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ t_2 := c \cdot \left(t \cdot \left(y2 \cdot \left(-y4\right)\right)\right)\\ \mathbf{if}\;y1 \leq -6800:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq -7.4 \cdot 10^{-149}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \mathbf{elif}\;y1 \leq 3.1 \cdot 10^{-174}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 5.8 \cdot 10^{-137}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y1 \leq 1.95 \cdot 10^{-43}:\\ \;\;\;\;b \cdot \left(k \cdot \left(y \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 4 \cdot 10^{-13}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (* y2 (* y1 y4)))) (t_2 (* c (* t (* y2 (- y4))))))
   (if (<= y1 -6800.0)
     t_1
     (if (<= y1 -7.4e-149)
       (* b (* (* x y) a))
       (if (<= y1 3.1e-174)
         (* b (* k (* z y0)))
         (if (<= y1 5.8e-137)
           t_2
           (if (<= y1 1.95e-43)
             (* b (* k (* y (- y4))))
             (if (<= y1 4e-13) 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 = k * (y2 * (y1 * y4));
	double t_2 = c * (t * (y2 * -y4));
	double tmp;
	if (y1 <= -6800.0) {
		tmp = t_1;
	} else if (y1 <= -7.4e-149) {
		tmp = b * ((x * y) * a);
	} else if (y1 <= 3.1e-174) {
		tmp = b * (k * (z * y0));
	} else if (y1 <= 5.8e-137) {
		tmp = t_2;
	} else if (y1 <= 1.95e-43) {
		tmp = b * (k * (y * -y4));
	} else if (y1 <= 4e-13) {
		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 = k * (y2 * (y1 * y4))
    t_2 = c * (t * (y2 * -y4))
    if (y1 <= (-6800.0d0)) then
        tmp = t_1
    else if (y1 <= (-7.4d-149)) then
        tmp = b * ((x * y) * a)
    else if (y1 <= 3.1d-174) then
        tmp = b * (k * (z * y0))
    else if (y1 <= 5.8d-137) then
        tmp = t_2
    else if (y1 <= 1.95d-43) then
        tmp = b * (k * (y * -y4))
    else if (y1 <= 4d-13) 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 = k * (y2 * (y1 * y4));
	double t_2 = c * (t * (y2 * -y4));
	double tmp;
	if (y1 <= -6800.0) {
		tmp = t_1;
	} else if (y1 <= -7.4e-149) {
		tmp = b * ((x * y) * a);
	} else if (y1 <= 3.1e-174) {
		tmp = b * (k * (z * y0));
	} else if (y1 <= 5.8e-137) {
		tmp = t_2;
	} else if (y1 <= 1.95e-43) {
		tmp = b * (k * (y * -y4));
	} else if (y1 <= 4e-13) {
		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 = k * (y2 * (y1 * y4))
	t_2 = c * (t * (y2 * -y4))
	tmp = 0
	if y1 <= -6800.0:
		tmp = t_1
	elif y1 <= -7.4e-149:
		tmp = b * ((x * y) * a)
	elif y1 <= 3.1e-174:
		tmp = b * (k * (z * y0))
	elif y1 <= 5.8e-137:
		tmp = t_2
	elif y1 <= 1.95e-43:
		tmp = b * (k * (y * -y4))
	elif y1 <= 4e-13:
		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(k * Float64(y2 * Float64(y1 * y4)))
	t_2 = Float64(c * Float64(t * Float64(y2 * Float64(-y4))))
	tmp = 0.0
	if (y1 <= -6800.0)
		tmp = t_1;
	elseif (y1 <= -7.4e-149)
		tmp = Float64(b * Float64(Float64(x * y) * a));
	elseif (y1 <= 3.1e-174)
		tmp = Float64(b * Float64(k * Float64(z * y0)));
	elseif (y1 <= 5.8e-137)
		tmp = t_2;
	elseif (y1 <= 1.95e-43)
		tmp = Float64(b * Float64(k * Float64(y * Float64(-y4))));
	elseif (y1 <= 4e-13)
		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 = k * (y2 * (y1 * y4));
	t_2 = c * (t * (y2 * -y4));
	tmp = 0.0;
	if (y1 <= -6800.0)
		tmp = t_1;
	elseif (y1 <= -7.4e-149)
		tmp = b * ((x * y) * a);
	elseif (y1 <= 3.1e-174)
		tmp = b * (k * (z * y0));
	elseif (y1 <= 5.8e-137)
		tmp = t_2;
	elseif (y1 <= 1.95e-43)
		tmp = b * (k * (y * -y4));
	elseif (y1 <= 4e-13)
		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[(k * N[(y2 * N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(t * N[(y2 * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -6800.0], t$95$1, If[LessEqual[y1, -7.4e-149], N[(b * N[(N[(x * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 3.1e-174], N[(b * N[(k * N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 5.8e-137], t$95$2, If[LessEqual[y1, 1.95e-43], N[(b * N[(k * N[(y * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 4e-13], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y1 < -6800 or 4.0000000000000001e-13 < y1

   1. Initial program 28.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 46.7%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in k around inf 39.2%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   5. Taylor expanded in y1 around inf 34.5%

      \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y1 \cdot y4\right)}\right) \]
   6. Step-by-step derivation

      1. *-commutative 34.5%

         \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y4 \cdot y1\right)}\right) \]

   7. Simplified 34.5%

      \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y4 \cdot y1\right)}\right) \]

   if -6800 < y1 < -7.3999999999999998e-149

   1. Initial program 12.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 12.7%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 38.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 47.0%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right)} \]

   7. Taylor expanded in t around 0 42.5%

      \[\leadsto b \cdot \left(a \cdot \color{blue}{\left(x \cdot y\right)}\right) \]
   8. Step-by-step derivation

      1. *-commutative 42.5%

         \[\leadsto b \cdot \left(a \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

   9. Simplified 42.5%

      \[\leadsto b \cdot \left(a \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

   if -7.3999999999999998e-149 < y1 < 3.0999999999999999e-174

   1. Initial program 36.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 37.9%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 33.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in k around -inf 35.7%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 35.7%

         \[\leadsto b \cdot \color{blue}{\left(\left(-1 \cdot k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

      2. neg-mul-1 35.7%

         \[\leadsto b \cdot \left(\color{blue}{\left(-k\right)} \cdot \left(y \cdot y4 - y0 \cdot z\right)\right) \]

   8. Simplified 35.7%

      \[\leadsto b \cdot \color{blue}{\left(\left(-k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

   9. Taylor expanded in y around 0 30.8%

      \[\leadsto b \cdot \color{blue}{\left(k \cdot \left(y0 \cdot z\right)\right)} \]

   if 3.0999999999999999e-174 < y1 < 5.7999999999999997e-137 or 1.95e-43 < y1 < 4.0000000000000001e-13

   1. Initial program 32.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 24.0%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 38.4%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   5. Taylor expanded in a around 0 42.1%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 42.1%

         \[\leadsto \color{blue}{-c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)} \]

      2. *-commutative 42.1%

         \[\leadsto -\color{blue}{\left(t \cdot \left(y2 \cdot y4\right)\right) \cdot c} \]

      3. distribute-rgt-neg-in 42.1%

         \[\leadsto \color{blue}{\left(t \cdot \left(y2 \cdot y4\right)\right) \cdot \left(-c\right)} \]

      4. *-commutative 42.1%

         \[\leadsto \left(t \cdot \color{blue}{\left(y4 \cdot y2\right)}\right) \cdot \left(-c\right) \]

   7. Simplified 42.1%

      \[\leadsto \color{blue}{\left(t \cdot \left(y4 \cdot y2\right)\right) \cdot \left(-c\right)} \]

   if 5.7999999999999997e-137 < y1 < 1.95e-43

   1. Initial program 46.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 46.3%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 39.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in k around -inf 43.6%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 43.6%

         \[\leadsto b \cdot \color{blue}{\left(\left(-1 \cdot k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

      2. neg-mul-1 43.6%

         \[\leadsto b \cdot \left(\color{blue}{\left(-k\right)} \cdot \left(y \cdot y4 - y0 \cdot z\right)\right) \]

   8. Simplified 43.6%

      \[\leadsto b \cdot \color{blue}{\left(\left(-k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

   9. Taylor expanded in y around inf 32.3%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 32.3%

          \[\leadsto b \cdot \color{blue}{\left(-k \cdot \left(y \cdot y4\right)\right)} \]

       2. *-commutative 32.3%

          \[\leadsto b \cdot \left(-\color{blue}{\left(y \cdot y4\right) \cdot k}\right) \]

       3. distribute-rgt-neg-in 32.3%

          \[\leadsto b \cdot \color{blue}{\left(\left(y \cdot y4\right) \cdot \left(-k\right)\right)} \]

   11. Simplified 32.3%

       \[\leadsto b \cdot \color{blue}{\left(\left(y \cdot y4\right) \cdot \left(-k\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 34.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -6800:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq -7.4 \cdot 10^{-149}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \mathbf{elif}\;y1 \leq 3.1 \cdot 10^{-174}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 5.8 \cdot 10^{-137}:\\ \;\;\;\;c \cdot \left(t \cdot \left(y2 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 1.95 \cdot 10^{-43}:\\ \;\;\;\;b \cdot \left(k \cdot \left(y \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 4 \cdot 10^{-13}:\\ \;\;\;\;c \cdot \left(t \cdot \left(y2 \cdot \left(-y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 37: 20.6% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ t_2 := a \cdot \left(y \cdot \left(y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{if}\;y0 \leq -2.1 \cdot 10^{-67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y0 \leq -7.5 \cdot 10^{-121}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y0 \leq 1.16 \cdot 10^{-155}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 4.1 \cdot 10^{-80}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \mathbf{elif}\;y0 \leq 2.35 \cdot 10^{+94}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(y2 \cdot y5\right)\\ \mathbf{elif}\;y0 \leq 3.9 \cdot 10^{+196}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* k (* z y0)))) (t_2 (* a (* y (* y3 (- y5))))))
   (if (<= y0 -2.1e-67)
     t_1
     (if (<= y0 -7.5e-121)
       t_2
       (if (<= y0 1.16e-155)
         (* k (* y2 (* y1 y4)))
         (if (<= y0 4.1e-80)
           (* b (* (* x y) a))
           (if (<= y0 2.35e+94)
             (* (* t a) (* y2 y5))
             (if (<= y0 3.9e+196) t_2 t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (k * (z * y0));
	double t_2 = a * (y * (y3 * -y5));
	double tmp;
	if (y0 <= -2.1e-67) {
		tmp = t_1;
	} else if (y0 <= -7.5e-121) {
		tmp = t_2;
	} else if (y0 <= 1.16e-155) {
		tmp = k * (y2 * (y1 * y4));
	} else if (y0 <= 4.1e-80) {
		tmp = b * ((x * y) * a);
	} else if (y0 <= 2.35e+94) {
		tmp = (t * a) * (y2 * y5);
	} else if (y0 <= 3.9e+196) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (k * (z * y0))
    t_2 = a * (y * (y3 * -y5))
    if (y0 <= (-2.1d-67)) then
        tmp = t_1
    else if (y0 <= (-7.5d-121)) then
        tmp = t_2
    else if (y0 <= 1.16d-155) then
        tmp = k * (y2 * (y1 * y4))
    else if (y0 <= 4.1d-80) then
        tmp = b * ((x * y) * a)
    else if (y0 <= 2.35d+94) then
        tmp = (t * a) * (y2 * y5)
    else if (y0 <= 3.9d+196) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (k * (z * y0));
	double t_2 = a * (y * (y3 * -y5));
	double tmp;
	if (y0 <= -2.1e-67) {
		tmp = t_1;
	} else if (y0 <= -7.5e-121) {
		tmp = t_2;
	} else if (y0 <= 1.16e-155) {
		tmp = k * (y2 * (y1 * y4));
	} else if (y0 <= 4.1e-80) {
		tmp = b * ((x * y) * a);
	} else if (y0 <= 2.35e+94) {
		tmp = (t * a) * (y2 * y5);
	} else if (y0 <= 3.9e+196) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (k * (z * y0))
	t_2 = a * (y * (y3 * -y5))
	tmp = 0
	if y0 <= -2.1e-67:
		tmp = t_1
	elif y0 <= -7.5e-121:
		tmp = t_2
	elif y0 <= 1.16e-155:
		tmp = k * (y2 * (y1 * y4))
	elif y0 <= 4.1e-80:
		tmp = b * ((x * y) * a)
	elif y0 <= 2.35e+94:
		tmp = (t * a) * (y2 * y5)
	elif y0 <= 3.9e+196:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(k * Float64(z * y0)))
	t_2 = Float64(a * Float64(y * Float64(y3 * Float64(-y5))))
	tmp = 0.0
	if (y0 <= -2.1e-67)
		tmp = t_1;
	elseif (y0 <= -7.5e-121)
		tmp = t_2;
	elseif (y0 <= 1.16e-155)
		tmp = Float64(k * Float64(y2 * Float64(y1 * y4)));
	elseif (y0 <= 4.1e-80)
		tmp = Float64(b * Float64(Float64(x * y) * a));
	elseif (y0 <= 2.35e+94)
		tmp = Float64(Float64(t * a) * Float64(y2 * y5));
	elseif (y0 <= 3.9e+196)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (k * (z * y0));
	t_2 = a * (y * (y3 * -y5));
	tmp = 0.0;
	if (y0 <= -2.1e-67)
		tmp = t_1;
	elseif (y0 <= -7.5e-121)
		tmp = t_2;
	elseif (y0 <= 1.16e-155)
		tmp = k * (y2 * (y1 * y4));
	elseif (y0 <= 4.1e-80)
		tmp = b * ((x * y) * a);
	elseif (y0 <= 2.35e+94)
		tmp = (t * a) * (y2 * y5);
	elseif (y0 <= 3.9e+196)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(k * N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(y * N[(y3 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -2.1e-67], t$95$1, If[LessEqual[y0, -7.5e-121], t$95$2, If[LessEqual[y0, 1.16e-155], N[(k * N[(y2 * N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 4.1e-80], N[(b * N[(N[(x * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 2.35e+94], N[(N[(t * a), $MachinePrecision] * N[(y2 * y5), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 3.9e+196], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y0 < -2.1000000000000002e-67 or 3.9e196 < y0

   1. Initial program 29.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.2%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 39.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in k around -inf 43.6%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 43.6%

         \[\leadsto b \cdot \color{blue}{\left(\left(-1 \cdot k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

      2. neg-mul-1 43.6%

         \[\leadsto b \cdot \left(\color{blue}{\left(-k\right)} \cdot \left(y \cdot y4 - y0 \cdot z\right)\right) \]

   8. Simplified 43.6%

      \[\leadsto b \cdot \color{blue}{\left(\left(-k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

   9. Taylor expanded in y around 0 35.9%

      \[\leadsto b \cdot \color{blue}{\left(k \cdot \left(y0 \cdot z\right)\right)} \]

   if -2.1000000000000002e-67 < y0 < -7.50000000000000027e-121 or 2.35000000000000008e94 < y0 < 3.9e196

   1. Initial program 22.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 22.0%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 56.4%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in y around inf 50.1%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]

   7. Taylor expanded in b around 0 47.8%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 47.8%

         \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot y\right) \cdot \left(y3 \cdot y5\right)\right)} \]

      2. neg-mul-1 47.8%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y\right)} \cdot \left(y3 \cdot y5\right)\right) \]

   9. Simplified 47.8%

      \[\leadsto a \cdot \color{blue}{\left(\left(-y\right) \cdot \left(y3 \cdot y5\right)\right)} \]

   if -7.50000000000000027e-121 < y0 < 1.16000000000000008e-155

   1. Initial program 42.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 41.6%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in k around inf 25.8%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   5. Taylor expanded in y1 around inf 27.6%

      \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y1 \cdot y4\right)}\right) \]
   6. Step-by-step derivation

      1. *-commutative 27.6%

         \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y4 \cdot y1\right)}\right) \]

   7. Simplified 27.6%

      \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y4 \cdot y1\right)}\right) \]

   if 1.16000000000000008e-155 < y0 < 4.0999999999999999e-80

   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%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 43.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 36.6%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right)} \]

   7. Taylor expanded in t around 0 43.8%

      \[\leadsto b \cdot \left(a \cdot \color{blue}{\left(x \cdot y\right)}\right) \]
   8. Step-by-step derivation

      1. *-commutative 43.8%

         \[\leadsto b \cdot \left(a \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

   9. Simplified 43.8%

      \[\leadsto b \cdot \left(a \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

   if 4.0999999999999999e-80 < y0 < 2.35000000000000008e94

   1. Initial program 25.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 29.1%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 22.6%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   5. Taylor expanded in a around inf 17.2%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 21.9%

         \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot \left(y2 \cdot y5\right)} \]

      2. *-commutative 21.9%

         \[\leadsto \left(a \cdot t\right) \cdot \color{blue}{\left(y5 \cdot y2\right)} \]

   7. Simplified 21.9%

      \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot \left(y5 \cdot y2\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 34.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -2.1 \cdot 10^{-67}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -7.5 \cdot 10^{-121}:\\ \;\;\;\;a \cdot \left(y \cdot \left(y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 1.16 \cdot 10^{-155}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 4.1 \cdot 10^{-80}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \mathbf{elif}\;y0 \leq 2.35 \cdot 10^{+94}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(y2 \cdot y5\right)\\ \mathbf{elif}\;y0 \leq 3.9 \cdot 10^{+196}:\\ \;\;\;\;a \cdot \left(y \cdot \left(y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 38: 21.1% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ t_2 := b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{if}\;y0 \leq -3 \cdot 10^{-70}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y0 \leq -1.4 \cdot 10^{-118}:\\ \;\;\;\;a \cdot \left(y \cdot \left(y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 2.1 \cdot 10^{-151}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 10^{-101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y0 \leq 1.4 \cdot 10^{+21}:\\ \;\;\;\;b \cdot \left(k \cdot \left(y \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 3 \cdot 10^{+211}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* (* x y) a))) (t_2 (* b (* k (* z y0)))))
   (if (<= y0 -3e-70)
     t_2
     (if (<= y0 -1.4e-118)
       (* a (* y (* y3 (- y5))))
       (if (<= y0 2.1e-151)
         (* k (* y2 (* y1 y4)))
         (if (<= y0 1e-101)
           t_1
           (if (<= y0 1.4e+21)
             (* b (* k (* y (- y4))))
             (if (<= y0 3e+211) 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 = b * ((x * y) * a);
	double t_2 = b * (k * (z * y0));
	double tmp;
	if (y0 <= -3e-70) {
		tmp = t_2;
	} else if (y0 <= -1.4e-118) {
		tmp = a * (y * (y3 * -y5));
	} else if (y0 <= 2.1e-151) {
		tmp = k * (y2 * (y1 * y4));
	} else if (y0 <= 1e-101) {
		tmp = t_1;
	} else if (y0 <= 1.4e+21) {
		tmp = b * (k * (y * -y4));
	} else if (y0 <= 3e+211) {
		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) :: tmp
    t_1 = b * ((x * y) * a)
    t_2 = b * (k * (z * y0))
    if (y0 <= (-3d-70)) then
        tmp = t_2
    else if (y0 <= (-1.4d-118)) then
        tmp = a * (y * (y3 * -y5))
    else if (y0 <= 2.1d-151) then
        tmp = k * (y2 * (y1 * y4))
    else if (y0 <= 1d-101) then
        tmp = t_1
    else if (y0 <= 1.4d+21) then
        tmp = b * (k * (y * -y4))
    else if (y0 <= 3d+211) 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 = b * ((x * y) * a);
	double t_2 = b * (k * (z * y0));
	double tmp;
	if (y0 <= -3e-70) {
		tmp = t_2;
	} else if (y0 <= -1.4e-118) {
		tmp = a * (y * (y3 * -y5));
	} else if (y0 <= 2.1e-151) {
		tmp = k * (y2 * (y1 * y4));
	} else if (y0 <= 1e-101) {
		tmp = t_1;
	} else if (y0 <= 1.4e+21) {
		tmp = b * (k * (y * -y4));
	} else if (y0 <= 3e+211) {
		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 = b * ((x * y) * a)
	t_2 = b * (k * (z * y0))
	tmp = 0
	if y0 <= -3e-70:
		tmp = t_2
	elif y0 <= -1.4e-118:
		tmp = a * (y * (y3 * -y5))
	elif y0 <= 2.1e-151:
		tmp = k * (y2 * (y1 * y4))
	elif y0 <= 1e-101:
		tmp = t_1
	elif y0 <= 1.4e+21:
		tmp = b * (k * (y * -y4))
	elif y0 <= 3e+211:
		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(b * Float64(Float64(x * y) * a))
	t_2 = Float64(b * Float64(k * Float64(z * y0)))
	tmp = 0.0
	if (y0 <= -3e-70)
		tmp = t_2;
	elseif (y0 <= -1.4e-118)
		tmp = Float64(a * Float64(y * Float64(y3 * Float64(-y5))));
	elseif (y0 <= 2.1e-151)
		tmp = Float64(k * Float64(y2 * Float64(y1 * y4)));
	elseif (y0 <= 1e-101)
		tmp = t_1;
	elseif (y0 <= 1.4e+21)
		tmp = Float64(b * Float64(k * Float64(y * Float64(-y4))));
	elseif (y0 <= 3e+211)
		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 = b * ((x * y) * a);
	t_2 = b * (k * (z * y0));
	tmp = 0.0;
	if (y0 <= -3e-70)
		tmp = t_2;
	elseif (y0 <= -1.4e-118)
		tmp = a * (y * (y3 * -y5));
	elseif (y0 <= 2.1e-151)
		tmp = k * (y2 * (y1 * y4));
	elseif (y0 <= 1e-101)
		tmp = t_1;
	elseif (y0 <= 1.4e+21)
		tmp = b * (k * (y * -y4));
	elseif (y0 <= 3e+211)
		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[(b * N[(N[(x * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(k * N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -3e-70], t$95$2, If[LessEqual[y0, -1.4e-118], N[(a * N[(y * N[(y3 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 2.1e-151], N[(k * N[(y2 * N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1e-101], t$95$1, If[LessEqual[y0, 1.4e+21], N[(b * N[(k * N[(y * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 3e+211], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y0 < -3.0000000000000001e-70 or 3e211 < y0

   1. Initial program 29.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.4%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 37.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in k around -inf 44.4%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 44.4%

         \[\leadsto b \cdot \color{blue}{\left(\left(-1 \cdot k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

      2. neg-mul-1 44.4%

         \[\leadsto b \cdot \left(\color{blue}{\left(-k\right)} \cdot \left(y \cdot y4 - y0 \cdot z\right)\right) \]

   8. Simplified 44.4%

      \[\leadsto b \cdot \color{blue}{\left(\left(-k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

   9. Taylor expanded in y around 0 36.3%

      \[\leadsto b \cdot \color{blue}{\left(k \cdot \left(y0 \cdot z\right)\right)} \]

   if -3.0000000000000001e-70 < y0 < -1.4e-118

   1. Initial program 20.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 20.0%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 60.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in y around inf 67.3%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]

   7. Taylor expanded in b around 0 60.8%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 60.8%

         \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot y\right) \cdot \left(y3 \cdot y5\right)\right)} \]

      2. neg-mul-1 60.8%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y\right)} \cdot \left(y3 \cdot y5\right)\right) \]

   9. Simplified 60.8%

      \[\leadsto a \cdot \color{blue}{\left(\left(-y\right) \cdot \left(y3 \cdot y5\right)\right)} \]

   if -1.4e-118 < y0 < 2.0999999999999999e-151

   1. Initial program 42.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 41.6%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in k around inf 25.8%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   5. Taylor expanded in y1 around inf 27.6%

      \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y1 \cdot y4\right)}\right) \]
   6. Step-by-step derivation

      1. *-commutative 27.6%

         \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y4 \cdot y1\right)}\right) \]

   7. Simplified 27.6%

      \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y4 \cdot y1\right)}\right) \]

   if 2.0999999999999999e-151 < y0 < 1.00000000000000005e-101 or 1.4e21 < y0 < 3e211

   1. Initial program 24.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 24.6%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 42.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 37.6%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right)} \]

   7. Taylor expanded in t around 0 34.5%

      \[\leadsto b \cdot \left(a \cdot \color{blue}{\left(x \cdot y\right)}\right) \]
   8. Step-by-step derivation

      1. *-commutative 34.5%

         \[\leadsto b \cdot \left(a \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

   9. Simplified 34.5%

      \[\leadsto b \cdot \left(a \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

   if 1.00000000000000005e-101 < y0 < 1.4e21

   1. Initial program 30.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.9%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 27.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in k around -inf 28.0%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 28.0%

         \[\leadsto b \cdot \color{blue}{\left(\left(-1 \cdot k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

      2. neg-mul-1 28.0%

         \[\leadsto b \cdot \left(\color{blue}{\left(-k\right)} \cdot \left(y \cdot y4 - y0 \cdot z\right)\right) \]

   8. Simplified 28.0%

      \[\leadsto b \cdot \color{blue}{\left(\left(-k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

   9. Taylor expanded in y around inf 24.5%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 24.5%

          \[\leadsto b \cdot \color{blue}{\left(-k \cdot \left(y \cdot y4\right)\right)} \]

       2. *-commutative 24.5%

          \[\leadsto b \cdot \left(-\color{blue}{\left(y \cdot y4\right) \cdot k}\right) \]

       3. distribute-rgt-neg-in 24.5%

          \[\leadsto b \cdot \color{blue}{\left(\left(y \cdot y4\right) \cdot \left(-k\right)\right)} \]

   11. Simplified 24.5%

       \[\leadsto b \cdot \color{blue}{\left(\left(y \cdot y4\right) \cdot \left(-k\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 34.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -3 \cdot 10^{-70}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -1.4 \cdot 10^{-118}:\\ \;\;\;\;a \cdot \left(y \cdot \left(y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 2.1 \cdot 10^{-151}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 10^{-101}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \mathbf{elif}\;y0 \leq 1.4 \cdot 10^{+21}:\\ \;\;\;\;b \cdot \left(k \cdot \left(y \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 3 \cdot 10^{+211}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 39: 32.0% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq -8.8 \cdot 10^{-16}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;k \leq -3.8 \cdot 10^{-120}:\\ \;\;\;\;i \cdot \left(t \cdot \left(z \cdot c - j \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 1.8 \cdot 10^{-228}:\\ \;\;\;\;\left(y0 \cdot y3\right) \cdot \left(j \cdot y5 - z \cdot c\right)\\ \mathbf{elif}\;k \leq 2.8 \cdot 10^{+20}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 1.6 \cdot 10^{+172}:\\ \;\;\;\;y2 \cdot \left(y0 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= k -8.8e-16)
   (* y4 (* k (- (* y1 y2) (* y b))))
   (if (<= k -3.8e-120)
     (* i (* t (- (* z c) (* j y5))))
     (if (<= k 1.8e-228)
       (* (* y0 y3) (- (* j y5) (* z c)))
       (if (<= k 2.8e+20)
         (* a (* y1 (- (* z y3) (* x y2))))
         (if (<= k 1.6e+172)
           (* y2 (* y0 (- (* x c) (* k y5))))
           (* b (* k (- (* z y0) (* y y4))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (k <= -8.8e-16) {
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	} else if (k <= -3.8e-120) {
		tmp = i * (t * ((z * c) - (j * y5)));
	} else if (k <= 1.8e-228) {
		tmp = (y0 * y3) * ((j * y5) - (z * c));
	} else if (k <= 2.8e+20) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (k <= 1.6e+172) {
		tmp = y2 * (y0 * ((x * c) - (k * y5)));
	} else {
		tmp = b * (k * ((z * y0) - (y * y4)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (k <= (-8.8d-16)) then
        tmp = y4 * (k * ((y1 * y2) - (y * b)))
    else if (k <= (-3.8d-120)) then
        tmp = i * (t * ((z * c) - (j * y5)))
    else if (k <= 1.8d-228) then
        tmp = (y0 * y3) * ((j * y5) - (z * c))
    else if (k <= 2.8d+20) then
        tmp = a * (y1 * ((z * y3) - (x * y2)))
    else if (k <= 1.6d+172) then
        tmp = y2 * (y0 * ((x * c) - (k * y5)))
    else
        tmp = b * (k * ((z * y0) - (y * y4)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (k <= -8.8e-16) {
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	} else if (k <= -3.8e-120) {
		tmp = i * (t * ((z * c) - (j * y5)));
	} else if (k <= 1.8e-228) {
		tmp = (y0 * y3) * ((j * y5) - (z * c));
	} else if (k <= 2.8e+20) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (k <= 1.6e+172) {
		tmp = y2 * (y0 * ((x * c) - (k * y5)));
	} else {
		tmp = b * (k * ((z * y0) - (y * y4)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if k <= -8.8e-16:
		tmp = y4 * (k * ((y1 * y2) - (y * b)))
	elif k <= -3.8e-120:
		tmp = i * (t * ((z * c) - (j * y5)))
	elif k <= 1.8e-228:
		tmp = (y0 * y3) * ((j * y5) - (z * c))
	elif k <= 2.8e+20:
		tmp = a * (y1 * ((z * y3) - (x * y2)))
	elif k <= 1.6e+172:
		tmp = y2 * (y0 * ((x * c) - (k * y5)))
	else:
		tmp = b * (k * ((z * y0) - (y * y4)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (k <= -8.8e-16)
		tmp = Float64(y4 * Float64(k * Float64(Float64(y1 * y2) - Float64(y * b))));
	elseif (k <= -3.8e-120)
		tmp = Float64(i * Float64(t * Float64(Float64(z * c) - Float64(j * y5))));
	elseif (k <= 1.8e-228)
		tmp = Float64(Float64(y0 * y3) * Float64(Float64(j * y5) - Float64(z * c)));
	elseif (k <= 2.8e+20)
		tmp = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))));
	elseif (k <= 1.6e+172)
		tmp = Float64(y2 * Float64(y0 * Float64(Float64(x * c) - Float64(k * y5))));
	else
		tmp = Float64(b * Float64(k * Float64(Float64(z * y0) - Float64(y * y4))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (k <= -8.8e-16)
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	elseif (k <= -3.8e-120)
		tmp = i * (t * ((z * c) - (j * y5)));
	elseif (k <= 1.8e-228)
		tmp = (y0 * y3) * ((j * y5) - (z * c));
	elseif (k <= 2.8e+20)
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	elseif (k <= 1.6e+172)
		tmp = y2 * (y0 * ((x * c) - (k * y5)));
	else
		tmp = b * (k * ((z * y0) - (y * y4)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[k, -8.8e-16], N[(y4 * N[(k * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -3.8e-120], N[(i * N[(t * N[(N[(z * c), $MachinePrecision] - N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.8e-228], N[(N[(y0 * y3), $MachinePrecision] * N[(N[(j * y5), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.8e+20], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.6e+172], N[(y2 * N[(y0 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if k < -8.80000000000000001e-16

   1. Initial program 24.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf 45.3%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in k around inf 49.4%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(b \cdot y\right) + y1 \cdot y2\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 49.4%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(b \cdot y\right)\right)}\right) \]

      2. mul-1-neg 49.4%

         \[\leadsto y4 \cdot \left(k \cdot \left(y1 \cdot y2 + \color{blue}{\left(-b \cdot y\right)}\right)\right) \]

      3. unsub-neg 49.4%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 - b \cdot y\right)}\right) \]

      4. *-commutative 49.4%

         \[\leadsto y4 \cdot \left(k \cdot \left(y1 \cdot y2 - \color{blue}{y \cdot b}\right)\right) \]

   6. Simplified 49.4%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)} \]

   if -8.80000000000000001e-16 < k < -3.7999999999999997e-120

   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%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 55.4%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   6. Taylor expanded in t around inf 46.1%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(t \cdot \left(-1 \cdot \left(c \cdot z\right) + j \cdot y5\right)\right)\right)} \]

   if -3.7999999999999997e-120 < k < 1.8000000000000001e-228

   1. Initial program 40.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y3 around -inf 54.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 35.8%

      \[\leadsto -1 \cdot \color{blue}{\left(y0 \cdot \left(y3 \cdot \left(-1 \cdot \left(j \cdot y5\right) + c \cdot z\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 37.2%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(y0 \cdot y3\right) \cdot \left(-1 \cdot \left(j \cdot y5\right) + c \cdot z\right)\right)} \]

      2. +-commutative 37.2%

         \[\leadsto -1 \cdot \left(\left(y0 \cdot y3\right) \cdot \color{blue}{\left(c \cdot z + -1 \cdot \left(j \cdot y5\right)\right)}\right) \]

      3. mul-1-neg 37.2%

         \[\leadsto -1 \cdot \left(\left(y0 \cdot y3\right) \cdot \left(c \cdot z + \color{blue}{\left(-j \cdot y5\right)}\right)\right) \]

      4. unsub-neg 37.2%

         \[\leadsto -1 \cdot \left(\left(y0 \cdot y3\right) \cdot \color{blue}{\left(c \cdot z - j \cdot y5\right)}\right) \]

      5. *-commutative 37.2%

         \[\leadsto -1 \cdot \left(\left(y0 \cdot y3\right) \cdot \left(\color{blue}{z \cdot c} - j \cdot y5\right)\right) \]

      6. *-commutative 37.2%

         \[\leadsto -1 \cdot \left(\left(y0 \cdot y3\right) \cdot \left(z \cdot c - \color{blue}{y5 \cdot j}\right)\right) \]

   6. Simplified 37.2%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(y0 \cdot y3\right) \cdot \left(z \cdot c - y5 \cdot j\right)\right)} \]

   if 1.8000000000000001e-228 < k < 2.8e20

   1. Initial program 26.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 26.4%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 43.6%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in y1 around inf 53.0%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 53.0%

         \[\leadsto \color{blue}{-a \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   8. Simplified 53.0%

      \[\leadsto \color{blue}{-a \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   if 2.8e20 < k < 1.59999999999999993e172

   1. Initial program 34.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 48.6%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in y0 around inf 66.2%

      \[\leadsto y2 \cdot \color{blue}{\left(y0 \cdot \left(-1 \cdot \left(k \cdot y5\right) + c \cdot x\right)\right)} \]

   if 1.59999999999999993e172 < k

   1. Initial program 14.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 14.8%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 44.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in k around -inf 71.0%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 71.0%

         \[\leadsto b \cdot \color{blue}{\left(\left(-1 \cdot k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

      2. neg-mul-1 71.0%

         \[\leadsto b \cdot \left(\color{blue}{\left(-k\right)} \cdot \left(y \cdot y4 - y0 \cdot z\right)\right) \]

   8. Simplified 71.0%

      \[\leadsto b \cdot \color{blue}{\left(\left(-k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -8.8 \cdot 10^{-16}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;k \leq -3.8 \cdot 10^{-120}:\\ \;\;\;\;i \cdot \left(t \cdot \left(z \cdot c - j \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 1.8 \cdot 10^{-228}:\\ \;\;\;\;\left(y0 \cdot y3\right) \cdot \left(j \cdot y5 - z \cdot c\right)\\ \mathbf{elif}\;k \leq 2.8 \cdot 10^{+20}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 1.6 \cdot 10^{+172}:\\ \;\;\;\;y2 \cdot \left(y0 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 40: 29.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y5 \leq -0.000125:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq -2.1 \cdot 10^{-82}:\\ \;\;\;\;c \cdot \left(i \cdot \left(y \cdot \left(-x\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 3.7 \cdot 10^{-193}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 3.5 \cdot 10^{-154}:\\ \;\;\;\;b \cdot \left(k \cdot \left(y \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 3 \cdot 10^{+61}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y5 -0.000125)
   (* a (* y5 (- (* t y2) (* y y3))))
   (if (<= y5 -2.1e-82)
     (* c (* i (* y (- x))))
     (if (<= y5 3.7e-193)
       (* b (* j (- (* t y4) (* x y0))))
       (if (<= y5 3.5e-154)
         (* b (* k (* y (- y4))))
         (if (<= y5 3e+61)
           (* b (* x (- (* y a) (* j y0))))
           (* a (* y3 (- (* z y1) (* y y5))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -0.000125) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (y5 <= -2.1e-82) {
		tmp = c * (i * (y * -x));
	} else if (y5 <= 3.7e-193) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y5 <= 3.5e-154) {
		tmp = b * (k * (y * -y4));
	} else if (y5 <= 3e+61) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y5 <= (-0.000125d0)) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else if (y5 <= (-2.1d-82)) then
        tmp = c * (i * (y * -x))
    else if (y5 <= 3.7d-193) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (y5 <= 3.5d-154) then
        tmp = b * (k * (y * -y4))
    else if (y5 <= 3d+61) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else
        tmp = a * (y3 * ((z * y1) - (y * y5)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -0.000125) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (y5 <= -2.1e-82) {
		tmp = c * (i * (y * -x));
	} else if (y5 <= 3.7e-193) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y5 <= 3.5e-154) {
		tmp = b * (k * (y * -y4));
	} else if (y5 <= 3e+61) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y5 <= -0.000125:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	elif y5 <= -2.1e-82:
		tmp = c * (i * (y * -x))
	elif y5 <= 3.7e-193:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif y5 <= 3.5e-154:
		tmp = b * (k * (y * -y4))
	elif y5 <= 3e+61:
		tmp = b * (x * ((y * a) - (j * y0)))
	else:
		tmp = a * (y3 * ((z * y1) - (y * y5)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y5 <= -0.000125)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (y5 <= -2.1e-82)
		tmp = Float64(c * Float64(i * Float64(y * Float64(-x))));
	elseif (y5 <= 3.7e-193)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (y5 <= 3.5e-154)
		tmp = Float64(b * Float64(k * Float64(y * Float64(-y4))));
	elseif (y5 <= 3e+61)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	else
		tmp = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y5 <= -0.000125)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	elseif (y5 <= -2.1e-82)
		tmp = c * (i * (y * -x));
	elseif (y5 <= 3.7e-193)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (y5 <= 3.5e-154)
		tmp = b * (k * (y * -y4));
	elseif (y5 <= 3e+61)
		tmp = b * (x * ((y * a) - (j * y0)));
	else
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y5, -0.000125], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -2.1e-82], N[(c * N[(i * N[(y * (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 3.7e-193], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 3.5e-154], N[(b * N[(k * N[(y * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 3e+61], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y5 < -1.25e-4

   1. Initial program 17.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 18.7%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 36.1%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in y5 around inf 39.8%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   if -1.25e-4 < y5 < -2.1e-82

   1. Initial program 16.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 16.4%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 62.2%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   6. Taylor expanded in x around inf 54.6%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right)\right)\right)} \]

   7. Taylor expanded in c around inf 61.8%

      \[\leadsto -1 \cdot \color{blue}{\left(c \cdot \left(i \cdot \left(x \cdot y\right)\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 61.8%

         \[\leadsto -1 \cdot \left(c \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot i\right)}\right) \]

      2. *-commutative 61.8%

         \[\leadsto -1 \cdot \left(c \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot i\right)\right) \]

   9. Simplified 61.8%

      \[\leadsto -1 \cdot \color{blue}{\left(c \cdot \left(\left(y \cdot x\right) \cdot i\right)\right)} \]

   if -2.1e-82 < y5 < 3.7000000000000002e-193

   1. Initial program 37.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 37.3%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 37.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 32.6%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if 3.7000000000000002e-193 < y5 < 3.5000000000000001e-154

   1. Initial program 54.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 54.6%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 54.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in k around -inf 54.7%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 54.7%

         \[\leadsto b \cdot \color{blue}{\left(\left(-1 \cdot k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

      2. neg-mul-1 54.7%

         \[\leadsto b \cdot \left(\color{blue}{\left(-k\right)} \cdot \left(y \cdot y4 - y0 \cdot z\right)\right) \]

   8. Simplified 54.7%

      \[\leadsto b \cdot \color{blue}{\left(\left(-k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

   9. Taylor expanded in y around inf 46.4%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 46.4%

          \[\leadsto b \cdot \color{blue}{\left(-k \cdot \left(y \cdot y4\right)\right)} \]

       2. *-commutative 46.4%

          \[\leadsto b \cdot \left(-\color{blue}{\left(y \cdot y4\right) \cdot k}\right) \]

       3. distribute-rgt-neg-in 46.4%

          \[\leadsto b \cdot \color{blue}{\left(\left(y \cdot y4\right) \cdot \left(-k\right)\right)} \]

   11. Simplified 46.4%

       \[\leadsto b \cdot \color{blue}{\left(\left(y \cdot y4\right) \cdot \left(-k\right)\right)} \]

   if 3.5000000000000001e-154 < y5 < 3e61

   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%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 31.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 27.9%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   if 3e61 < y5

   1. Initial program 31.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.5%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 43.4%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in y3 around inf 47.4%

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 38.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -0.000125:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq -2.1 \cdot 10^{-82}:\\ \;\;\;\;c \cdot \left(i \cdot \left(y \cdot \left(-x\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 3.7 \cdot 10^{-193}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 3.5 \cdot 10^{-154}:\\ \;\;\;\;b \cdot \left(k \cdot \left(y \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 3 \cdot 10^{+61}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 41: 29.4% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y5 \leq -1.36 \cdot 10^{-5}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq -1.8 \cdot 10^{-82}:\\ \;\;\;\;c \cdot \left(i \cdot \left(y \cdot \left(-x\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 1.86 \cdot 10^{-193}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 1.9 \cdot 10^{-145}:\\ \;\;\;\;b \cdot \left(\left(y \cdot k\right) \cdot \left(-y4\right)\right)\\ \mathbf{elif}\;y5 \leq 1.8 \cdot 10^{-75}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y5 -1.36e-5)
   (* a (* y5 (- (* t y2) (* y y3))))
   (if (<= y5 -1.8e-82)
     (* c (* i (* y (- x))))
     (if (<= y5 1.86e-193)
       (* b (* j (- (* t y4) (* x y0))))
       (if (<= y5 1.9e-145)
         (* b (* (* y k) (- y4)))
         (if (<= y5 1.8e-75)
           (* k (* y2 (* y1 y4)))
           (* a (* y3 (- (* z y1) (* y y5))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -1.36e-5) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (y5 <= -1.8e-82) {
		tmp = c * (i * (y * -x));
	} else if (y5 <= 1.86e-193) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y5 <= 1.9e-145) {
		tmp = b * ((y * k) * -y4);
	} else if (y5 <= 1.8e-75) {
		tmp = k * (y2 * (y1 * y4));
	} else {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y5 <= (-1.36d-5)) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else if (y5 <= (-1.8d-82)) then
        tmp = c * (i * (y * -x))
    else if (y5 <= 1.86d-193) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (y5 <= 1.9d-145) then
        tmp = b * ((y * k) * -y4)
    else if (y5 <= 1.8d-75) then
        tmp = k * (y2 * (y1 * y4))
    else
        tmp = a * (y3 * ((z * y1) - (y * y5)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -1.36e-5) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (y5 <= -1.8e-82) {
		tmp = c * (i * (y * -x));
	} else if (y5 <= 1.86e-193) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y5 <= 1.9e-145) {
		tmp = b * ((y * k) * -y4);
	} else if (y5 <= 1.8e-75) {
		tmp = k * (y2 * (y1 * y4));
	} else {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y5 <= -1.36e-5:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	elif y5 <= -1.8e-82:
		tmp = c * (i * (y * -x))
	elif y5 <= 1.86e-193:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif y5 <= 1.9e-145:
		tmp = b * ((y * k) * -y4)
	elif y5 <= 1.8e-75:
		tmp = k * (y2 * (y1 * y4))
	else:
		tmp = a * (y3 * ((z * y1) - (y * y5)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y5 <= -1.36e-5)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (y5 <= -1.8e-82)
		tmp = Float64(c * Float64(i * Float64(y * Float64(-x))));
	elseif (y5 <= 1.86e-193)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (y5 <= 1.9e-145)
		tmp = Float64(b * Float64(Float64(y * k) * Float64(-y4)));
	elseif (y5 <= 1.8e-75)
		tmp = Float64(k * Float64(y2 * Float64(y1 * y4)));
	else
		tmp = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y5 <= -1.36e-5)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	elseif (y5 <= -1.8e-82)
		tmp = c * (i * (y * -x));
	elseif (y5 <= 1.86e-193)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (y5 <= 1.9e-145)
		tmp = b * ((y * k) * -y4);
	elseif (y5 <= 1.8e-75)
		tmp = k * (y2 * (y1 * y4));
	else
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y5, -1.36e-5], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.8e-82], N[(c * N[(i * N[(y * (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.86e-193], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.9e-145], N[(b * N[(N[(y * k), $MachinePrecision] * (-y4)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.8e-75], N[(k * N[(y2 * N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y5 < -1.36000000000000002e-5

   1. Initial program 17.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 18.7%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 36.1%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in y5 around inf 39.8%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   if -1.36000000000000002e-5 < y5 < -1.79999999999999999e-82

   1. Initial program 16.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 16.4%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 62.2%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   6. Taylor expanded in x around inf 54.6%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right)\right)\right)} \]

   7. Taylor expanded in c around inf 61.8%

      \[\leadsto -1 \cdot \color{blue}{\left(c \cdot \left(i \cdot \left(x \cdot y\right)\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 61.8%

         \[\leadsto -1 \cdot \left(c \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot i\right)}\right) \]

      2. *-commutative 61.8%

         \[\leadsto -1 \cdot \left(c \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot i\right)\right) \]

   9. Simplified 61.8%

      \[\leadsto -1 \cdot \color{blue}{\left(c \cdot \left(\left(y \cdot x\right) \cdot i\right)\right)} \]

   if -1.79999999999999999e-82 < y5 < 1.8599999999999999e-193

   1. Initial program 37.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 37.3%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 37.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 32.6%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if 1.8599999999999999e-193 < y5 < 1.9000000000000001e-145

   1. Initial program 53.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 53.9%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 54.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in k around -inf 46.3%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 46.3%

         \[\leadsto b \cdot \color{blue}{\left(\left(-1 \cdot k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

      2. neg-mul-1 46.3%

         \[\leadsto b \cdot \left(\color{blue}{\left(-k\right)} \cdot \left(y \cdot y4 - y0 \cdot z\right)\right) \]

   8. Simplified 46.3%

      \[\leadsto b \cdot \color{blue}{\left(\left(-k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

   9. Taylor expanded in y around inf 39.4%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(k \cdot \left(y \cdot y4\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 39.4%

          \[\leadsto \color{blue}{-b \cdot \left(k \cdot \left(y \cdot y4\right)\right)} \]

       2. *-commutative 39.4%

          \[\leadsto -\color{blue}{\left(k \cdot \left(y \cdot y4\right)\right) \cdot b} \]

       3. distribute-rgt-neg-in 39.4%

          \[\leadsto \color{blue}{\left(k \cdot \left(y \cdot y4\right)\right) \cdot \left(-b\right)} \]

       4. associate-*r* 39.4%

          \[\leadsto \color{blue}{\left(\left(k \cdot y\right) \cdot y4\right)} \cdot \left(-b\right) \]

       5. *-commutative 39.4%

          \[\leadsto \left(\color{blue}{\left(y \cdot k\right)} \cdot y4\right) \cdot \left(-b\right) \]

   11. Simplified 39.4%

       \[\leadsto \color{blue}{\left(\left(y \cdot k\right) \cdot y4\right) \cdot \left(-b\right)} \]

   if 1.9000000000000001e-145 < y5 < 1.8e-75

   1. Initial program 42.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 37.9%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in k around inf 33.3%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   5. Taylor expanded in y1 around inf 27.7%

      \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y1 \cdot y4\right)}\right) \]
   6. Step-by-step derivation

      1. *-commutative 27.7%

         \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y4 \cdot y1\right)}\right) \]

   7. Simplified 27.7%

      \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y4 \cdot y1\right)}\right) \]

   if 1.8e-75 < y5

   1. Initial program 31.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.8%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 35.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in y3 around inf 39.1%

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 37.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -1.36 \cdot 10^{-5}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq -1.8 \cdot 10^{-82}:\\ \;\;\;\;c \cdot \left(i \cdot \left(y \cdot \left(-x\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 1.86 \cdot 10^{-193}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 1.9 \cdot 10^{-145}:\\ \;\;\;\;b \cdot \left(\left(y \cdot k\right) \cdot \left(-y4\right)\right)\\ \mathbf{elif}\;y5 \leq 1.8 \cdot 10^{-75}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 42: 21.7% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ t_2 := k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \mathbf{if}\;a \leq -9.8 \cdot 10^{+154}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-39}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-235}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-292}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 6.1 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* k (* z y0)))) (t_2 (* k (* y2 (* y1 y4)))))
   (if (<= a -9.8e+154)
     (* t (* y2 (* a y5)))
     (if (<= a -2.3e-39)
       t_2
       (if (<= a -1.65e-235)
         t_1
         (if (<= a 3.2e-292)
           t_2
           (if (<= a 6.1e+50) t_1 (* b (* (* x y) a)))))))))

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 * (k * (z * y0));
	double t_2 = k * (y2 * (y1 * y4));
	double tmp;
	if (a <= -9.8e+154) {
		tmp = t * (y2 * (a * y5));
	} else if (a <= -2.3e-39) {
		tmp = t_2;
	} else if (a <= -1.65e-235) {
		tmp = t_1;
	} else if (a <= 3.2e-292) {
		tmp = t_2;
	} else if (a <= 6.1e+50) {
		tmp = t_1;
	} else {
		tmp = b * ((x * y) * a);
	}
	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 * (k * (z * y0))
    t_2 = k * (y2 * (y1 * y4))
    if (a <= (-9.8d+154)) then
        tmp = t * (y2 * (a * y5))
    else if (a <= (-2.3d-39)) then
        tmp = t_2
    else if (a <= (-1.65d-235)) then
        tmp = t_1
    else if (a <= 3.2d-292) then
        tmp = t_2
    else if (a <= 6.1d+50) then
        tmp = t_1
    else
        tmp = b * ((x * y) * a)
    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 * (k * (z * y0));
	double t_2 = k * (y2 * (y1 * y4));
	double tmp;
	if (a <= -9.8e+154) {
		tmp = t * (y2 * (a * y5));
	} else if (a <= -2.3e-39) {
		tmp = t_2;
	} else if (a <= -1.65e-235) {
		tmp = t_1;
	} else if (a <= 3.2e-292) {
		tmp = t_2;
	} else if (a <= 6.1e+50) {
		tmp = t_1;
	} else {
		tmp = b * ((x * y) * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (k * (z * y0))
	t_2 = k * (y2 * (y1 * y4))
	tmp = 0
	if a <= -9.8e+154:
		tmp = t * (y2 * (a * y5))
	elif a <= -2.3e-39:
		tmp = t_2
	elif a <= -1.65e-235:
		tmp = t_1
	elif a <= 3.2e-292:
		tmp = t_2
	elif a <= 6.1e+50:
		tmp = t_1
	else:
		tmp = b * ((x * y) * a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(k * Float64(z * y0)))
	t_2 = Float64(k * Float64(y2 * Float64(y1 * y4)))
	tmp = 0.0
	if (a <= -9.8e+154)
		tmp = Float64(t * Float64(y2 * Float64(a * y5)));
	elseif (a <= -2.3e-39)
		tmp = t_2;
	elseif (a <= -1.65e-235)
		tmp = t_1;
	elseif (a <= 3.2e-292)
		tmp = t_2;
	elseif (a <= 6.1e+50)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(Float64(x * y) * a));
	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 * (k * (z * y0));
	t_2 = k * (y2 * (y1 * y4));
	tmp = 0.0;
	if (a <= -9.8e+154)
		tmp = t * (y2 * (a * y5));
	elseif (a <= -2.3e-39)
		tmp = t_2;
	elseif (a <= -1.65e-235)
		tmp = t_1;
	elseif (a <= 3.2e-292)
		tmp = t_2;
	elseif (a <= 6.1e+50)
		tmp = t_1;
	else
		tmp = b * ((x * y) * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(k * N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(y2 * N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9.8e+154], N[(t * N[(y2 * N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.3e-39], t$95$2, If[LessEqual[a, -1.65e-235], t$95$1, If[LessEqual[a, 3.2e-292], t$95$2, If[LessEqual[a, 6.1e+50], t$95$1, N[(b * N[(N[(x * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -9.8000000000000003e154

   1. Initial program 28.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 40.8%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 56.5%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   5. Taylor expanded in a around inf 47.4%

      \[\leadsto t \cdot \left(y2 \cdot \color{blue}{\left(a \cdot y5\right)}\right) \]

   if -9.8000000000000003e154 < a < -2.30000000000000008e-39 or -1.65000000000000014e-235 < a < 3.2000000000000002e-292

   1. Initial program 35.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 39.2%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in k around inf 44.7%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   5. Taylor expanded in y1 around inf 40.0%

      \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y1 \cdot y4\right)}\right) \]
   6. Step-by-step derivation

      1. *-commutative 40.0%

         \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y4 \cdot y1\right)}\right) \]

   7. Simplified 40.0%

      \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y4 \cdot y1\right)}\right) \]

   if -2.30000000000000008e-39 < a < -1.65000000000000014e-235 or 3.2000000000000002e-292 < a < 6.10000000000000026e50

   1. Initial program 34.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 34.9%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 39.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in k around -inf 38.3%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 38.3%

         \[\leadsto b \cdot \color{blue}{\left(\left(-1 \cdot k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

      2. neg-mul-1 38.3%

         \[\leadsto b \cdot \left(\color{blue}{\left(-k\right)} \cdot \left(y \cdot y4 - y0 \cdot z\right)\right) \]

   8. Simplified 38.3%

      \[\leadsto b \cdot \color{blue}{\left(\left(-k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

   9. Taylor expanded in y around 0 26.2%

      \[\leadsto b \cdot \color{blue}{\left(k \cdot \left(y0 \cdot z\right)\right)} \]

   if 6.10000000000000026e50 < a

   1. Initial program 21.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 21.6%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 31.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 45.9%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right)} \]

   7. Taylor expanded in t around 0 30.5%

      \[\leadsto b \cdot \left(a \cdot \color{blue}{\left(x \cdot y\right)}\right) \]
   8. Step-by-step derivation

      1. *-commutative 30.5%

         \[\leadsto b \cdot \left(a \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

   9. Simplified 30.5%

      \[\leadsto b \cdot \left(a \cdot \color{blue}{\left(y \cdot x\right)}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 33.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.8 \cdot 10^{+154}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-39}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-235}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-292}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 6.1 \cdot 10^{+50}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 43: 21.3% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ t_2 := k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \mathbf{if}\;a \leq -3 \cdot 10^{+155}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-39}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-236}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-292}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* k (* z y0)))) (t_2 (* k (* y2 (* y1 y4)))))
   (if (<= a -3e+155)
     (* t (* a (* y2 y5)))
     (if (<= a -1.2e-39)
       t_2
       (if (<= a -1.6e-236)
         t_1
         (if (<= a 2.8e-292)
           t_2
           (if (<= a 1.75e+46) t_1 (* b (* (* x y) a)))))))))

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 * (k * (z * y0));
	double t_2 = k * (y2 * (y1 * y4));
	double tmp;
	if (a <= -3e+155) {
		tmp = t * (a * (y2 * y5));
	} else if (a <= -1.2e-39) {
		tmp = t_2;
	} else if (a <= -1.6e-236) {
		tmp = t_1;
	} else if (a <= 2.8e-292) {
		tmp = t_2;
	} else if (a <= 1.75e+46) {
		tmp = t_1;
	} else {
		tmp = b * ((x * y) * a);
	}
	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 * (k * (z * y0))
    t_2 = k * (y2 * (y1 * y4))
    if (a <= (-3d+155)) then
        tmp = t * (a * (y2 * y5))
    else if (a <= (-1.2d-39)) then
        tmp = t_2
    else if (a <= (-1.6d-236)) then
        tmp = t_1
    else if (a <= 2.8d-292) then
        tmp = t_2
    else if (a <= 1.75d+46) then
        tmp = t_1
    else
        tmp = b * ((x * y) * a)
    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 * (k * (z * y0));
	double t_2 = k * (y2 * (y1 * y4));
	double tmp;
	if (a <= -3e+155) {
		tmp = t * (a * (y2 * y5));
	} else if (a <= -1.2e-39) {
		tmp = t_2;
	} else if (a <= -1.6e-236) {
		tmp = t_1;
	} else if (a <= 2.8e-292) {
		tmp = t_2;
	} else if (a <= 1.75e+46) {
		tmp = t_1;
	} else {
		tmp = b * ((x * y) * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (k * (z * y0))
	t_2 = k * (y2 * (y1 * y4))
	tmp = 0
	if a <= -3e+155:
		tmp = t * (a * (y2 * y5))
	elif a <= -1.2e-39:
		tmp = t_2
	elif a <= -1.6e-236:
		tmp = t_1
	elif a <= 2.8e-292:
		tmp = t_2
	elif a <= 1.75e+46:
		tmp = t_1
	else:
		tmp = b * ((x * y) * a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(k * Float64(z * y0)))
	t_2 = Float64(k * Float64(y2 * Float64(y1 * y4)))
	tmp = 0.0
	if (a <= -3e+155)
		tmp = Float64(t * Float64(a * Float64(y2 * y5)));
	elseif (a <= -1.2e-39)
		tmp = t_2;
	elseif (a <= -1.6e-236)
		tmp = t_1;
	elseif (a <= 2.8e-292)
		tmp = t_2;
	elseif (a <= 1.75e+46)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(Float64(x * y) * a));
	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 * (k * (z * y0));
	t_2 = k * (y2 * (y1 * y4));
	tmp = 0.0;
	if (a <= -3e+155)
		tmp = t * (a * (y2 * y5));
	elseif (a <= -1.2e-39)
		tmp = t_2;
	elseif (a <= -1.6e-236)
		tmp = t_1;
	elseif (a <= 2.8e-292)
		tmp = t_2;
	elseif (a <= 1.75e+46)
		tmp = t_1;
	else
		tmp = b * ((x * y) * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(k * N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(y2 * N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3e+155], N[(t * N[(a * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.2e-39], t$95$2, If[LessEqual[a, -1.6e-236], t$95$1, If[LessEqual[a, 2.8e-292], t$95$2, If[LessEqual[a, 1.75e+46], t$95$1, N[(b * N[(N[(x * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.0000000000000001e155

   1. Initial program 28.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 40.8%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 56.5%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   5. Taylor expanded in a around inf 44.4%

      \[\leadsto t \cdot \color{blue}{\left(a \cdot \left(y2 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 44.4%

         \[\leadsto t \cdot \left(a \cdot \color{blue}{\left(y5 \cdot y2\right)}\right) \]

   7. Simplified 44.4%

      \[\leadsto t \cdot \color{blue}{\left(a \cdot \left(y5 \cdot y2\right)\right)} \]

   if -3.0000000000000001e155 < a < -1.20000000000000008e-39 or -1.6e-236 < a < 2.8000000000000001e-292

   1. Initial program 35.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 39.2%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in k around inf 44.7%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   5. Taylor expanded in y1 around inf 40.0%

      \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y1 \cdot y4\right)}\right) \]
   6. Step-by-step derivation

      1. *-commutative 40.0%

         \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y4 \cdot y1\right)}\right) \]

   7. Simplified 40.0%

      \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y4 \cdot y1\right)}\right) \]

   if -1.20000000000000008e-39 < a < -1.6e-236 or 2.8000000000000001e-292 < a < 1.74999999999999992e46

   1. Initial program 34.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 34.9%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 39.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in k around -inf 38.3%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 38.3%

         \[\leadsto b \cdot \color{blue}{\left(\left(-1 \cdot k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

      2. neg-mul-1 38.3%

         \[\leadsto b \cdot \left(\color{blue}{\left(-k\right)} \cdot \left(y \cdot y4 - y0 \cdot z\right)\right) \]

   8. Simplified 38.3%

      \[\leadsto b \cdot \color{blue}{\left(\left(-k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

   9. Taylor expanded in y around 0 26.2%

      \[\leadsto b \cdot \color{blue}{\left(k \cdot \left(y0 \cdot z\right)\right)} \]

   if 1.74999999999999992e46 < a

   1. Initial program 21.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 21.6%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 31.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 45.9%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right)} \]

   7. Taylor expanded in t around 0 30.5%

      \[\leadsto b \cdot \left(a \cdot \color{blue}{\left(x \cdot y\right)}\right) \]
   8. Step-by-step derivation

      1. *-commutative 30.5%

         \[\leadsto b \cdot \left(a \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

   9. Simplified 30.5%

      \[\leadsto b \cdot \left(a \cdot \color{blue}{\left(y \cdot x\right)}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 32.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{+155}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-39}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-236}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-292}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{+46}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 44: 27.8% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{if}\;y3 \leq -2 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y3 \leq -2.75 \cdot 10^{-70}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y3 \leq -1 \cdot 10^{-71} \lor \neg \left(y3 \leq 7 \cdot 10^{-176}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y3 (- (* z y1) (* y y5))))))
   (if (<= y3 -2e+34)
     t_1
     (if (<= y3 -2.75e-70)
       (* i (* j (* x y1)))
       (if (or (<= y3 -1e-71) (not (<= y3 7e-176)))
         t_1
         (* k (* y2 (* y1 y4))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y3 * ((z * y1) - (y * y5)));
	double tmp;
	if (y3 <= -2e+34) {
		tmp = t_1;
	} else if (y3 <= -2.75e-70) {
		tmp = i * (j * (x * y1));
	} else if ((y3 <= -1e-71) || !(y3 <= 7e-176)) {
		tmp = t_1;
	} else {
		tmp = k * (y2 * (y1 * y4));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (y3 * ((z * y1) - (y * y5)))
    if (y3 <= (-2d+34)) then
        tmp = t_1
    else if (y3 <= (-2.75d-70)) then
        tmp = i * (j * (x * y1))
    else if ((y3 <= (-1d-71)) .or. (.not. (y3 <= 7d-176))) then
        tmp = t_1
    else
        tmp = k * (y2 * (y1 * y4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y3 * ((z * y1) - (y * y5)));
	double tmp;
	if (y3 <= -2e+34) {
		tmp = t_1;
	} else if (y3 <= -2.75e-70) {
		tmp = i * (j * (x * y1));
	} else if ((y3 <= -1e-71) || !(y3 <= 7e-176)) {
		tmp = t_1;
	} else {
		tmp = k * (y2 * (y1 * y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y3 * ((z * y1) - (y * y5)))
	tmp = 0
	if y3 <= -2e+34:
		tmp = t_1
	elif y3 <= -2.75e-70:
		tmp = i * (j * (x * y1))
	elif (y3 <= -1e-71) or not (y3 <= 7e-176):
		tmp = t_1
	else:
		tmp = k * (y2 * (y1 * y4))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))))
	tmp = 0.0
	if (y3 <= -2e+34)
		tmp = t_1;
	elseif (y3 <= -2.75e-70)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif ((y3 <= -1e-71) || !(y3 <= 7e-176))
		tmp = t_1;
	else
		tmp = Float64(k * Float64(y2 * Float64(y1 * y4)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y3 * ((z * y1) - (y * y5)));
	tmp = 0.0;
	if (y3 <= -2e+34)
		tmp = t_1;
	elseif (y3 <= -2.75e-70)
		tmp = i * (j * (x * y1));
	elseif ((y3 <= -1e-71) || ~((y3 <= 7e-176)))
		tmp = t_1;
	else
		tmp = k * (y2 * (y1 * y4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -2e+34], t$95$1, If[LessEqual[y3, -2.75e-70], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y3, -1e-71], N[Not[LessEqual[y3, 7e-176]], $MachinePrecision]], t$95$1, N[(k * N[(y2 * N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y3 < -1.99999999999999989e34 or -2.75e-70 < y3 < -9.9999999999999992e-72 or 7e-176 < y3

   1. Initial program 22.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 23.2%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 38.0%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in y3 around inf 37.1%

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]

   if -1.99999999999999989e34 < y3 < -2.75e-70

   1. Initial program 48.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 48.1%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 40.4%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   6. Taylor expanded in x around inf 34.2%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right)\right)\right)} \]

   7. Taylor expanded in c around 0 38.2%

      \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 38.2%

         \[\leadsto -1 \cdot \color{blue}{\left(-i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\right)} \]

      2. *-commutative 38.2%

         \[\leadsto -1 \cdot \left(-\color{blue}{\left(j \cdot \left(x \cdot y1\right)\right) \cdot i}\right) \]

      3. distribute-rgt-neg-in 38.2%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(j \cdot \left(x \cdot y1\right)\right) \cdot \left(-i\right)\right)} \]

      4. *-commutative 38.2%

         \[\leadsto -1 \cdot \left(\left(j \cdot \color{blue}{\left(y1 \cdot x\right)}\right) \cdot \left(-i\right)\right) \]

   9. Simplified 38.2%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(j \cdot \left(y1 \cdot x\right)\right) \cdot \left(-i\right)\right)} \]

   if -9.9999999999999992e-72 < y3 < 7e-176

   1. Initial program 41.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 45.2%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in k around inf 43.0%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   5. Taylor expanded in y1 around inf 32.8%

      \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y1 \cdot y4\right)}\right) \]
   6. Step-by-step derivation

      1. *-commutative 32.8%

         \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y4 \cdot y1\right)}\right) \]

   7. Simplified 32.8%

      \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y4 \cdot y1\right)}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 35.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -2 \cdot 10^{+34}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y3 \leq -2.75 \cdot 10^{-70}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y3 \leq -1 \cdot 10^{-71} \lor \neg \left(y3 \leq 7 \cdot 10^{-176}\right):\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 45: 22.1% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \mathbf{if}\;y1 \leq -5000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq -3.5 \cdot 10^{-149}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \mathbf{elif}\;y1 \leq 1.2 \cdot 10^{-12}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (* y2 (* y1 y4)))))
   (if (<= y1 -5000.0)
     t_1
     (if (<= y1 -3.5e-149)
       (* b (* (* x y) a))
       (if (<= y1 1.2e-12) (* b (* k (* z y0))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (y2 * (y1 * y4));
	double tmp;
	if (y1 <= -5000.0) {
		tmp = t_1;
	} else if (y1 <= -3.5e-149) {
		tmp = b * ((x * y) * a);
	} else if (y1 <= 1.2e-12) {
		tmp = b * (k * (z * y0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = k * (y2 * (y1 * y4))
    if (y1 <= (-5000.0d0)) then
        tmp = t_1
    else if (y1 <= (-3.5d-149)) then
        tmp = b * ((x * y) * a)
    else if (y1 <= 1.2d-12) then
        tmp = b * (k * (z * y0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (y2 * (y1 * y4));
	double tmp;
	if (y1 <= -5000.0) {
		tmp = t_1;
	} else if (y1 <= -3.5e-149) {
		tmp = b * ((x * y) * a);
	} else if (y1 <= 1.2e-12) {
		tmp = b * (k * (z * y0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = k * (y2 * (y1 * y4))
	tmp = 0
	if y1 <= -5000.0:
		tmp = t_1
	elif y1 <= -3.5e-149:
		tmp = b * ((x * y) * a)
	elif y1 <= 1.2e-12:
		tmp = b * (k * (z * y0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(k * Float64(y2 * Float64(y1 * y4)))
	tmp = 0.0
	if (y1 <= -5000.0)
		tmp = t_1;
	elseif (y1 <= -3.5e-149)
		tmp = Float64(b * Float64(Float64(x * y) * a));
	elseif (y1 <= 1.2e-12)
		tmp = Float64(b * Float64(k * Float64(z * y0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = k * (y2 * (y1 * y4));
	tmp = 0.0;
	if (y1 <= -5000.0)
		tmp = t_1;
	elseif (y1 <= -3.5e-149)
		tmp = b * ((x * y) * a);
	elseif (y1 <= 1.2e-12)
		tmp = b * (k * (z * y0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(k * N[(y2 * N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -5000.0], t$95$1, If[LessEqual[y1, -3.5e-149], N[(b * N[(N[(x * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.2e-12], N[(b * N[(k * N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y1 < -5e3 or 1.19999999999999994e-12 < y1

   1. Initial program 28.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 46.7%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in k around inf 39.2%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   5. Taylor expanded in y1 around inf 34.5%

      \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y1 \cdot y4\right)}\right) \]
   6. Step-by-step derivation

      1. *-commutative 34.5%

         \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y4 \cdot y1\right)}\right) \]

   7. Simplified 34.5%

      \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y4 \cdot y1\right)}\right) \]

   if -5e3 < y1 < -3.5e-149

   1. Initial program 12.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 12.7%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 38.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 47.0%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right)} \]

   7. Taylor expanded in t around 0 42.5%

      \[\leadsto b \cdot \left(a \cdot \color{blue}{\left(x \cdot y\right)}\right) \]
   8. Step-by-step derivation

      1. *-commutative 42.5%

         \[\leadsto b \cdot \left(a \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

   9. Simplified 42.5%

      \[\leadsto b \cdot \left(a \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

   if -3.5e-149 < y1 < 1.19999999999999994e-12

   1. Initial program 37.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 38.7%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 32.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in k around -inf 32.5%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 32.5%

         \[\leadsto b \cdot \color{blue}{\left(\left(-1 \cdot k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

      2. neg-mul-1 32.5%

         \[\leadsto b \cdot \left(\color{blue}{\left(-k\right)} \cdot \left(y \cdot y4 - y0 \cdot z\right)\right) \]

   8. Simplified 32.5%

      \[\leadsto b \cdot \color{blue}{\left(\left(-k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

   9. Taylor expanded in y around 0 22.5%

      \[\leadsto b \cdot \color{blue}{\left(k \cdot \left(y0 \cdot z\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 30.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -5000:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq -3.5 \cdot 10^{-149}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \mathbf{elif}\;y1 \leq 1.2 \cdot 10^{-12}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 46: 21.0% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{if}\;y1 \leq -9000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq -2.55 \cdot 10^{-148}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \mathbf{elif}\;y1 \leq 9 \cdot 10^{-13}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (* y1 (* y2 y4)))))
   (if (<= y1 -9000.0)
     t_1
     (if (<= y1 -2.55e-148)
       (* b (* (* x y) a))
       (if (<= y1 9e-13) (* b (* k (* z y0))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (y1 * (y2 * y4));
	double tmp;
	if (y1 <= -9000.0) {
		tmp = t_1;
	} else if (y1 <= -2.55e-148) {
		tmp = b * ((x * y) * a);
	} else if (y1 <= 9e-13) {
		tmp = b * (k * (z * y0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = k * (y1 * (y2 * y4))
    if (y1 <= (-9000.0d0)) then
        tmp = t_1
    else if (y1 <= (-2.55d-148)) then
        tmp = b * ((x * y) * a)
    else if (y1 <= 9d-13) then
        tmp = b * (k * (z * y0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (y1 * (y2 * y4));
	double tmp;
	if (y1 <= -9000.0) {
		tmp = t_1;
	} else if (y1 <= -2.55e-148) {
		tmp = b * ((x * y) * a);
	} else if (y1 <= 9e-13) {
		tmp = b * (k * (z * y0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = k * (y1 * (y2 * y4))
	tmp = 0
	if y1 <= -9000.0:
		tmp = t_1
	elif y1 <= -2.55e-148:
		tmp = b * ((x * y) * a)
	elif y1 <= 9e-13:
		tmp = b * (k * (z * y0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(k * Float64(y1 * Float64(y2 * y4)))
	tmp = 0.0
	if (y1 <= -9000.0)
		tmp = t_1;
	elseif (y1 <= -2.55e-148)
		tmp = Float64(b * Float64(Float64(x * y) * a));
	elseif (y1 <= 9e-13)
		tmp = Float64(b * Float64(k * Float64(z * y0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = k * (y1 * (y2 * y4));
	tmp = 0.0;
	if (y1 <= -9000.0)
		tmp = t_1;
	elseif (y1 <= -2.55e-148)
		tmp = b * ((x * y) * a);
	elseif (y1 <= 9e-13)
		tmp = b * (k * (z * y0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -9000.0], t$95$1, If[LessEqual[y1, -2.55e-148], N[(b * N[(N[(x * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 9e-13], N[(b * N[(k * N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y1 < -9e3 or 9e-13 < y1

   1. Initial program 28.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 46.7%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in k around inf 39.2%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   5. Taylor expanded in y1 around inf 30.7%

      \[\leadsto k \cdot \color{blue}{\left(y1 \cdot \left(y2 \cdot y4\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 30.7%

         \[\leadsto k \cdot \left(y1 \cdot \color{blue}{\left(y4 \cdot y2\right)}\right) \]

   7. Simplified 30.7%

      \[\leadsto k \cdot \color{blue}{\left(y1 \cdot \left(y4 \cdot y2\right)\right)} \]

   if -9e3 < y1 < -2.55e-148

   1. Initial program 12.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 12.7%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 38.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 47.0%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right)} \]

   7. Taylor expanded in t around 0 42.5%

      \[\leadsto b \cdot \left(a \cdot \color{blue}{\left(x \cdot y\right)}\right) \]
   8. Step-by-step derivation

      1. *-commutative 42.5%

         \[\leadsto b \cdot \left(a \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

   9. Simplified 42.5%

      \[\leadsto b \cdot \left(a \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

   if -2.55e-148 < y1 < 9e-13

   1. Initial program 37.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 38.7%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 32.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in k around -inf 32.5%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 32.5%

         \[\leadsto b \cdot \color{blue}{\left(\left(-1 \cdot k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

      2. neg-mul-1 32.5%

         \[\leadsto b \cdot \left(\color{blue}{\left(-k\right)} \cdot \left(y \cdot y4 - y0 \cdot z\right)\right) \]

   8. Simplified 32.5%

      \[\leadsto b \cdot \color{blue}{\left(\left(-k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

   9. Taylor expanded in y around 0 22.5%

      \[\leadsto b \cdot \color{blue}{\left(k \cdot \left(y0 \cdot z\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 28.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -9000:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq -2.55 \cdot 10^{-148}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \mathbf{elif}\;y1 \leq 9 \cdot 10^{-13}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 47: 21.6% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y0 \leq -1.2 \cdot 10^{-83} \lor \neg \left(y0 \leq 6.5 \cdot 10^{+211}\right):\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= y0 -1.2e-83) (not (<= y0 6.5e+211)))
   (* b (* k (* z y0)))
   (* b (* (* x y) a))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y0 <= -1.2e-83) || !(y0 <= 6.5e+211)) {
		tmp = b * (k * (z * y0));
	} else {
		tmp = b * ((x * y) * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((y0 <= (-1.2d-83)) .or. (.not. (y0 <= 6.5d+211))) then
        tmp = b * (k * (z * y0))
    else
        tmp = b * ((x * y) * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y0 <= -1.2e-83) || !(y0 <= 6.5e+211)) {
		tmp = b * (k * (z * y0));
	} else {
		tmp = b * ((x * y) * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (y0 <= -1.2e-83) or not (y0 <= 6.5e+211):
		tmp = b * (k * (z * y0))
	else:
		tmp = b * ((x * y) * a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((y0 <= -1.2e-83) || !(y0 <= 6.5e+211))
		tmp = Float64(b * Float64(k * Float64(z * y0)));
	else
		tmp = Float64(b * Float64(Float64(x * y) * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((y0 <= -1.2e-83) || ~((y0 <= 6.5e+211)))
		tmp = b * (k * (z * y0));
	else
		tmp = b * ((x * y) * a);
	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[y0, -1.2e-83], N[Not[LessEqual[y0, 6.5e+211]], $MachinePrecision]], N[(b * N[(k * N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(x * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y0 < -1.2e-83 or 6.4999999999999996e211 < y0

   1. Initial program 29.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.2%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 37.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in k around -inf 43.7%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 43.7%

         \[\leadsto b \cdot \color{blue}{\left(\left(-1 \cdot k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

      2. neg-mul-1 43.7%

         \[\leadsto b \cdot \left(\color{blue}{\left(-k\right)} \cdot \left(y \cdot y4 - y0 \cdot z\right)\right) \]

   8. Simplified 43.7%

      \[\leadsto b \cdot \color{blue}{\left(\left(-k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

   9. Taylor expanded in y around 0 35.9%

      \[\leadsto b \cdot \color{blue}{\left(k \cdot \left(y0 \cdot z\right)\right)} \]

   if -1.2e-83 < y0 < 6.4999999999999996e211

   1. Initial program 32.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 32.3%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 33.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 23.6%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right)} \]

   7. Taylor expanded in t around 0 18.0%

      \[\leadsto b \cdot \left(a \cdot \color{blue}{\left(x \cdot y\right)}\right) \]
   8. Step-by-step derivation

      1. *-commutative 18.0%

         \[\leadsto b \cdot \left(a \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

   9. Simplified 18.0%

      \[\leadsto b \cdot \left(a \cdot \color{blue}{\left(y \cdot x\right)}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 25.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -1.2 \cdot 10^{-83} \lor \neg \left(y0 \leq 6.5 \cdot 10^{+211}\right):\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 48: 17.4% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ b \cdot \left(\left(x \cdot y\right) \cdot a\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* b (* (* x y) a)))

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 b * ((x * y) * a);
}

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 = b * ((x * y) * a)
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 b * ((x * y) * a);
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return b * ((x * y) * a)

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(b * Float64(Float64(x * y) * a))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = b * ((x * y) * a);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(b * N[(N[(x * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 31.0%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

3. Simplified 31.4%

   \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
4. Add Preprocessing

5. Taylor expanded in b around inf 35.0%

   \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

6. Taylor expanded in a around inf 20.7%

   \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right)} \]

7. Taylor expanded in t around 0 14.3%

   \[\leadsto b \cdot \left(a \cdot \color{blue}{\left(x \cdot y\right)}\right) \]
8. Step-by-step derivation

   1. *-commutative 14.3%

      \[\leadsto b \cdot \left(a \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

9. Simplified 14.3%

   \[\leadsto b \cdot \left(a \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

10. Final simplification 14.3%

    \[\leadsto b \cdot \left(\left(x \cdot y\right) \cdot a\right) \]
11. Add Preprocessing

Alternative 49: 17.0% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(\left(x \cdot y\right) \cdot b\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* (* x y) b)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * ((x * y) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = a * ((x * y) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * ((x * y) * b);
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * ((x * y) * b)

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(Float64(x * y) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * ((x * y) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 31.0%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

3. Simplified 31.4%

   \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
4. Add Preprocessing

5. Taylor expanded in a around inf 32.9%

   \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

6. Taylor expanded in y around inf 24.8%

   \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]

7. Taylor expanded in b around inf 13.2%

   \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
8. Step-by-step derivation

   1. *-commutative 13.2%

      \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

9. Simplified 13.2%

   \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(y \cdot x\right)\right)} \]

10. Final simplification 13.2%

    \[\leadsto a \cdot \left(\left(x \cdot y\right) \cdot b\right) \]
11. Add Preprocessing

Developer target: 27.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot c - y5 \cdot a\\ t_2 := x \cdot y2 - z \cdot y3\\ t_3 := y2 \cdot t - y3 \cdot y\\ t_4 := k \cdot y2 - j \cdot y3\\ t_5 := y4 \cdot b - y5 \cdot i\\ t_6 := \left(j \cdot t - k \cdot y\right) \cdot t\_5\\ t_7 := b \cdot a - i \cdot c\\ t_8 := t\_7 \cdot \left(y \cdot x - t \cdot z\right)\\ t_9 := j \cdot x - k \cdot z\\ t_10 := \left(b \cdot y0 - i \cdot y1\right) \cdot t\_9\\ t_11 := t\_9 \cdot \left(y0 \cdot b - i \cdot y1\right)\\ t_12 := y4 \cdot y1 - y5 \cdot y0\\ t_13 := t\_4 \cdot t\_12\\ t_14 := \left(y2 \cdot k - y3 \cdot j\right) \cdot t\_12\\ t_15 := \left(\left(\left(\left(k \cdot y\right) \cdot \left(y5 \cdot i\right) - \left(y \cdot b\right) \cdot \left(y4 \cdot k\right)\right) - \left(y5 \cdot t\right) \cdot \left(i \cdot j\right)\right) - \left(t\_3 \cdot t\_1 - t\_14\right)\right) + \left(t\_8 - \left(t\_11 - \left(y2 \cdot x - y3 \cdot z\right) \cdot \left(c \cdot y0 - y1 \cdot a\right)\right)\right)\\ t_16 := \left(\left(t\_6 - \left(y3 \cdot y\right) \cdot \left(y5 \cdot a - y4 \cdot c\right)\right) + \left(\left(y5 \cdot a\right) \cdot \left(t \cdot y2\right) + t\_13\right)\right) + \left(t\_2 \cdot \left(c \cdot y0 - a \cdot y1\right) - \left(t\_10 - \left(y \cdot x - z \cdot t\right) \cdot t\_7\right)\right)\\ t_17 := t \cdot y2 - y \cdot y3\\ \mathbf{if}\;y4 < -7.206256231996481 \cdot 10^{+60}:\\ \;\;\;\;\left(t\_8 - \left(t\_11 - t\_6\right)\right) - \left(\frac{t\_3}{\frac{1}{t\_1}} - t\_14\right)\\ \mathbf{elif}\;y4 < -3.364603505246317 \cdot 10^{-66}:\\ \;\;\;\;\left(\left(\left(\left(t \cdot c\right) \cdot \left(i \cdot z\right) - \left(a \cdot t\right) \cdot \left(b \cdot z\right)\right) - \left(y \cdot c\right) \cdot \left(i \cdot x\right)\right) - t\_10\right) + \left(\left(y0 \cdot c - a \cdot y1\right) \cdot t\_2 - \left(t\_17 \cdot \left(y4 \cdot c - a \cdot y5\right) - \left(y1 \cdot y4 - y5 \cdot y0\right) \cdot t\_4\right)\right)\\ \mathbf{elif}\;y4 < -1.2000065055686116 \cdot 10^{-105}:\\ \;\;\;\;t\_16\\ \mathbf{elif}\;y4 < 6.718963124057495 \cdot 10^{-279}:\\ \;\;\;\;t\_15\\ \mathbf{elif}\;y4 < 4.77962681403792 \cdot 10^{-222}:\\ \;\;\;\;t\_16\\ \mathbf{elif}\;y4 < 2.2852241541266835 \cdot 10^{-175}:\\ \;\;\;\;t\_15\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(k \cdot \left(i \cdot \left(z \cdot y1\right)\right) - \left(j \cdot \left(i \cdot \left(x \cdot y1\right)\right) + y0 \cdot \left(k \cdot \left(z \cdot b\right)\right)\right)\right)\right) + \left(z \cdot \left(y3 \cdot \left(a \cdot y1\right)\right) - \left(y2 \cdot \left(x \cdot \left(a \cdot y1\right)\right) + y0 \cdot \left(z \cdot \left(c \cdot y3\right)\right)\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot t\_5\right) - t\_17 \cdot t\_1\right) + t\_13\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y4 c) (* y5 a)))
        (t_2 (- (* x y2) (* z y3)))
        (t_3 (- (* y2 t) (* y3 y)))
        (t_4 (- (* k y2) (* j y3)))
        (t_5 (- (* y4 b) (* y5 i)))
        (t_6 (* (- (* j t) (* k y)) t_5))
        (t_7 (- (* b a) (* i c)))
        (t_8 (* t_7 (- (* y x) (* t z))))
        (t_9 (- (* j x) (* k z)))
        (t_10 (* (- (* b y0) (* i y1)) t_9))
        (t_11 (* t_9 (- (* y0 b) (* i y1))))
        (t_12 (- (* y4 y1) (* y5 y0)))
        (t_13 (* t_4 t_12))
        (t_14 (* (- (* y2 k) (* y3 j)) t_12))
        (t_15
         (+
          (-
           (-
            (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k)))
            (* (* y5 t) (* i j)))
           (- (* t_3 t_1) t_14))
          (- t_8 (- t_11 (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))))
        (t_16
         (+
          (+
           (- t_6 (* (* y3 y) (- (* y5 a) (* y4 c))))
           (+ (* (* y5 a) (* t y2)) t_13))
          (-
           (* t_2 (- (* c y0) (* a y1)))
           (- t_10 (* (- (* y x) (* z t)) t_7)))))
        (t_17 (- (* t y2) (* y y3))))
   (if (< y4 -7.206256231996481e+60)
     (- (- t_8 (- t_11 t_6)) (- (/ t_3 (/ 1.0 t_1)) t_14))
     (if (< y4 -3.364603505246317e-66)
       (+
        (-
         (- (- (* (* t c) (* i z)) (* (* a t) (* b z))) (* (* y c) (* i x)))
         t_10)
        (-
         (* (- (* y0 c) (* a y1)) t_2)
         (- (* t_17 (- (* y4 c) (* a y5))) (* (- (* y1 y4) (* y5 y0)) t_4))))
       (if (< y4 -1.2000065055686116e-105)
         t_16
         (if (< y4 6.718963124057495e-279)
           t_15
           (if (< y4 4.77962681403792e-222)
             t_16
             (if (< y4 2.2852241541266835e-175)
               t_15
               (+
                (-
                 (+
                  (+
                   (-
                    (* (- (* x y) (* z t)) (- (* a b) (* c i)))
                    (-
                     (* k (* i (* z y1)))
                     (+ (* j (* i (* x y1))) (* y0 (* k (* z b))))))
                   (-
                    (* z (* y3 (* a y1)))
                    (+ (* y2 (* x (* a y1))) (* y0 (* z (* c y3))))))
                  (* (- (* t j) (* y k)) t_5))
                 (* t_17 t_1))
                t_13)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y4 * c) - (y5 * a);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (y2 * t) - (y3 * y);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = (y4 * b) - (y5 * i);
	double t_6 = ((j * t) - (k * y)) * t_5;
	double t_7 = (b * a) - (i * c);
	double t_8 = t_7 * ((y * x) - (t * z));
	double t_9 = (j * x) - (k * z);
	double t_10 = ((b * y0) - (i * y1)) * t_9;
	double t_11 = t_9 * ((y0 * b) - (i * y1));
	double t_12 = (y4 * y1) - (y5 * y0);
	double t_13 = t_4 * t_12;
	double t_14 = ((y2 * k) - (y3 * j)) * t_12;
	double t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	double t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	double t_17 = (t * y2) - (y * y3);
	double tmp;
	if (y4 < -7.206256231996481e+60) {
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	} else if (y4 < -3.364603505246317e-66) {
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	} else if (y4 < -1.2000065055686116e-105) {
		tmp = t_16;
	} else if (y4 < 6.718963124057495e-279) {
		tmp = t_15;
	} else if (y4 < 4.77962681403792e-222) {
		tmp = t_16;
	} else if (y4 < 2.2852241541266835e-175) {
		tmp = t_15;
	} else {
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_10
    real(8) :: t_11
    real(8) :: t_12
    real(8) :: t_13
    real(8) :: t_14
    real(8) :: t_15
    real(8) :: t_16
    real(8) :: t_17
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = (y4 * c) - (y5 * a)
    t_2 = (x * y2) - (z * y3)
    t_3 = (y2 * t) - (y3 * y)
    t_4 = (k * y2) - (j * y3)
    t_5 = (y4 * b) - (y5 * i)
    t_6 = ((j * t) - (k * y)) * t_5
    t_7 = (b * a) - (i * c)
    t_8 = t_7 * ((y * x) - (t * z))
    t_9 = (j * x) - (k * z)
    t_10 = ((b * y0) - (i * y1)) * t_9
    t_11 = t_9 * ((y0 * b) - (i * y1))
    t_12 = (y4 * y1) - (y5 * y0)
    t_13 = t_4 * t_12
    t_14 = ((y2 * k) - (y3 * j)) * t_12
    t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))))
    t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)))
    t_17 = (t * y2) - (y * y3)
    if (y4 < (-7.206256231996481d+60)) then
        tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0d0 / t_1)) - t_14)
    else if (y4 < (-3.364603505246317d-66)) then
        tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)))
    else if (y4 < (-1.2000065055686116d-105)) then
        tmp = t_16
    else if (y4 < 6.718963124057495d-279) then
        tmp = t_15
    else if (y4 < 4.77962681403792d-222) then
        tmp = t_16
    else if (y4 < 2.2852241541266835d-175) then
        tmp = t_15
    else
        tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y4 * c) - (y5 * a);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (y2 * t) - (y3 * y);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = (y4 * b) - (y5 * i);
	double t_6 = ((j * t) - (k * y)) * t_5;
	double t_7 = (b * a) - (i * c);
	double t_8 = t_7 * ((y * x) - (t * z));
	double t_9 = (j * x) - (k * z);
	double t_10 = ((b * y0) - (i * y1)) * t_9;
	double t_11 = t_9 * ((y0 * b) - (i * y1));
	double t_12 = (y4 * y1) - (y5 * y0);
	double t_13 = t_4 * t_12;
	double t_14 = ((y2 * k) - (y3 * j)) * t_12;
	double t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	double t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	double t_17 = (t * y2) - (y * y3);
	double tmp;
	if (y4 < -7.206256231996481e+60) {
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	} else if (y4 < -3.364603505246317e-66) {
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	} else if (y4 < -1.2000065055686116e-105) {
		tmp = t_16;
	} else if (y4 < 6.718963124057495e-279) {
		tmp = t_15;
	} else if (y4 < 4.77962681403792e-222) {
		tmp = t_16;
	} else if (y4 < 2.2852241541266835e-175) {
		tmp = t_15;
	} else {
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y4 * c) - (y5 * a)
	t_2 = (x * y2) - (z * y3)
	t_3 = (y2 * t) - (y3 * y)
	t_4 = (k * y2) - (j * y3)
	t_5 = (y4 * b) - (y5 * i)
	t_6 = ((j * t) - (k * y)) * t_5
	t_7 = (b * a) - (i * c)
	t_8 = t_7 * ((y * x) - (t * z))
	t_9 = (j * x) - (k * z)
	t_10 = ((b * y0) - (i * y1)) * t_9
	t_11 = t_9 * ((y0 * b) - (i * y1))
	t_12 = (y4 * y1) - (y5 * y0)
	t_13 = t_4 * t_12
	t_14 = ((y2 * k) - (y3 * j)) * t_12
	t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))))
	t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)))
	t_17 = (t * y2) - (y * y3)
	tmp = 0
	if y4 < -7.206256231996481e+60:
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14)
	elif y4 < -3.364603505246317e-66:
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)))
	elif y4 < -1.2000065055686116e-105:
		tmp = t_16
	elif y4 < 6.718963124057495e-279:
		tmp = t_15
	elif y4 < 4.77962681403792e-222:
		tmp = t_16
	elif y4 < 2.2852241541266835e-175:
		tmp = t_15
	else:
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y4 * c) - Float64(y5 * a))
	t_2 = Float64(Float64(x * y2) - Float64(z * y3))
	t_3 = Float64(Float64(y2 * t) - Float64(y3 * y))
	t_4 = Float64(Float64(k * y2) - Float64(j * y3))
	t_5 = Float64(Float64(y4 * b) - Float64(y5 * i))
	t_6 = Float64(Float64(Float64(j * t) - Float64(k * y)) * t_5)
	t_7 = Float64(Float64(b * a) - Float64(i * c))
	t_8 = Float64(t_7 * Float64(Float64(y * x) - Float64(t * z)))
	t_9 = Float64(Float64(j * x) - Float64(k * z))
	t_10 = Float64(Float64(Float64(b * y0) - Float64(i * y1)) * t_9)
	t_11 = Float64(t_9 * Float64(Float64(y0 * b) - Float64(i * y1)))
	t_12 = Float64(Float64(y4 * y1) - Float64(y5 * y0))
	t_13 = Float64(t_4 * t_12)
	t_14 = Float64(Float64(Float64(y2 * k) - Float64(y3 * j)) * t_12)
	t_15 = Float64(Float64(Float64(Float64(Float64(Float64(k * y) * Float64(y5 * i)) - Float64(Float64(y * b) * Float64(y4 * k))) - Float64(Float64(y5 * t) * Float64(i * j))) - Float64(Float64(t_3 * t_1) - t_14)) + Float64(t_8 - Float64(t_11 - Float64(Float64(Float64(y2 * x) - Float64(y3 * z)) * Float64(Float64(c * y0) - Float64(y1 * a))))))
	t_16 = Float64(Float64(Float64(t_6 - Float64(Float64(y3 * y) * Float64(Float64(y5 * a) - Float64(y4 * c)))) + Float64(Float64(Float64(y5 * a) * Float64(t * y2)) + t_13)) + Float64(Float64(t_2 * Float64(Float64(c * y0) - Float64(a * y1))) - Float64(t_10 - Float64(Float64(Float64(y * x) - Float64(z * t)) * t_7))))
	t_17 = Float64(Float64(t * y2) - Float64(y * y3))
	tmp = 0.0
	if (y4 < -7.206256231996481e+60)
		tmp = Float64(Float64(t_8 - Float64(t_11 - t_6)) - Float64(Float64(t_3 / Float64(1.0 / t_1)) - t_14));
	elseif (y4 < -3.364603505246317e-66)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(t * c) * Float64(i * z)) - Float64(Float64(a * t) * Float64(b * z))) - Float64(Float64(y * c) * Float64(i * x))) - t_10) + Float64(Float64(Float64(Float64(y0 * c) - Float64(a * y1)) * t_2) - Float64(Float64(t_17 * Float64(Float64(y4 * c) - Float64(a * y5))) - Float64(Float64(Float64(y1 * y4) - Float64(y5 * y0)) * t_4))));
	elseif (y4 < -1.2000065055686116e-105)
		tmp = t_16;
	elseif (y4 < 6.718963124057495e-279)
		tmp = t_15;
	elseif (y4 < 4.77962681403792e-222)
		tmp = t_16;
	elseif (y4 < 2.2852241541266835e-175)
		tmp = t_15;
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) - Float64(z * t)) * Float64(Float64(a * b) - Float64(c * i))) - Float64(Float64(k * Float64(i * Float64(z * y1))) - Float64(Float64(j * Float64(i * Float64(x * y1))) + Float64(y0 * Float64(k * Float64(z * b)))))) + Float64(Float64(z * Float64(y3 * Float64(a * y1))) - Float64(Float64(y2 * Float64(x * Float64(a * y1))) + Float64(y0 * Float64(z * Float64(c * y3)))))) + Float64(Float64(Float64(t * j) - Float64(y * k)) * t_5)) - Float64(t_17 * t_1)) + t_13);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y4 * c) - (y5 * a);
	t_2 = (x * y2) - (z * y3);
	t_3 = (y2 * t) - (y3 * y);
	t_4 = (k * y2) - (j * y3);
	t_5 = (y4 * b) - (y5 * i);
	t_6 = ((j * t) - (k * y)) * t_5;
	t_7 = (b * a) - (i * c);
	t_8 = t_7 * ((y * x) - (t * z));
	t_9 = (j * x) - (k * z);
	t_10 = ((b * y0) - (i * y1)) * t_9;
	t_11 = t_9 * ((y0 * b) - (i * y1));
	t_12 = (y4 * y1) - (y5 * y0);
	t_13 = t_4 * t_12;
	t_14 = ((y2 * k) - (y3 * j)) * t_12;
	t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	t_17 = (t * y2) - (y * y3);
	tmp = 0.0;
	if (y4 < -7.206256231996481e+60)
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	elseif (y4 < -3.364603505246317e-66)
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	elseif (y4 < -1.2000065055686116e-105)
		tmp = t_16;
	elseif (y4 < 6.718963124057495e-279)
		tmp = t_15;
	elseif (y4 < 4.77962681403792e-222)
		tmp = t_16;
	elseif (y4 < 2.2852241541266835e-175)
		tmp = t_15;
	else
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y4 * c), $MachinePrecision] - N[(y5 * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y2 * t), $MachinePrecision] - N[(y3 * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(y4 * b), $MachinePrecision] - N[(y5 * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision] * t$95$5), $MachinePrecision]}, Block[{t$95$7 = N[(N[(b * a), $MachinePrecision] - N[(i * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(t$95$7 * N[(N[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$10 = N[(N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision] * t$95$9), $MachinePrecision]}, Block[{t$95$11 = N[(t$95$9 * N[(N[(y0 * b), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$12 = N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$13 = N[(t$95$4 * t$95$12), $MachinePrecision]}, Block[{t$95$14 = N[(N[(N[(y2 * k), $MachinePrecision] - N[(y3 * j), $MachinePrecision]), $MachinePrecision] * t$95$12), $MachinePrecision]}, Block[{t$95$15 = N[(N[(N[(N[(N[(N[(k * y), $MachinePrecision] * N[(y5 * i), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] * N[(y4 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y5 * t), $MachinePrecision] * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$3 * t$95$1), $MachinePrecision] - t$95$14), $MachinePrecision]), $MachinePrecision] + N[(t$95$8 - N[(t$95$11 - N[(N[(N[(y2 * x), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision] * N[(N[(c * y0), $MachinePrecision] - N[(y1 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$16 = N[(N[(N[(t$95$6 - N[(N[(y3 * y), $MachinePrecision] * N[(N[(y5 * a), $MachinePrecision] - N[(y4 * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y5 * a), $MachinePrecision] * N[(t * y2), $MachinePrecision]), $MachinePrecision] + t$95$13), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$10 - N[(N[(N[(y * x), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$17 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, If[Less[y4, -7.206256231996481e+60], N[(N[(t$95$8 - N[(t$95$11 - t$95$6), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$3 / N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision] - t$95$14), $MachinePrecision]), $MachinePrecision], If[Less[y4, -3.364603505246317e-66], N[(N[(N[(N[(N[(N[(t * c), $MachinePrecision] * N[(i * z), $MachinePrecision]), $MachinePrecision] - N[(N[(a * t), $MachinePrecision] * N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * c), $MachinePrecision] * N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$10), $MachinePrecision] + N[(N[(N[(N[(y0 * c), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision] - N[(N[(t$95$17 * N[(N[(y4 * c), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(y1 * y4), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision] * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[y4, -1.2000065055686116e-105], t$95$16, If[Less[y4, 6.718963124057495e-279], t$95$15, If[Less[y4, 4.77962681403792e-222], t$95$16, If[Less[y4, 2.2852241541266835e-175], t$95$15, N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(k * N[(i * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * N[(i * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(k * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(y3 * N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y2 * N[(x * N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(z * N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * t$95$5), $MachinePrecision]), $MachinePrecision] - N[(t$95$17 * t$95$1), $MachinePrecision]), $MachinePrecision] + t$95$13), $MachinePrecision]]]]]]]]]]]]]]]]]]]]]]]]

Reproduce

herbie shell --seed 2024086 
(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :name "Linear.Matrix:det44 from linear-1.19.1.3"
  :precision binary64

  :alt
  (if (< y4 -7.206256231996481e+60) (- (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))))) (- (/ (- (* y2 t) (* y3 y)) (/ 1.0 (- (* y4 c) (* y5 a)))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (if (< y4 -3.364603505246317e-66) (+ (- (- (- (* (* t c) (* i z)) (* (* a t) (* b z))) (* (* y c) (* i x))) (* (- (* b y0) (* i y1)) (- (* j x) (* k z)))) (- (* (- (* y0 c) (* a y1)) (- (* x y2) (* z y3))) (- (* (- (* t y2) (* y y3)) (- (* y4 c) (* a y5))) (* (- (* y1 y4) (* y5 y0)) (- (* k y2) (* j y3)))))) (if (< y4 -1.2000065055686116e-105) (+ (+ (- (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))) (* (* y3 y) (- (* y5 a) (* y4 c)))) (+ (* (* y5 a) (* t y2)) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* x y2) (* z y3)) (- (* c y0) (* a y1))) (- (* (- (* b y0) (* i y1)) (- (* j x) (* k z))) (* (- (* y x) (* z t)) (- (* b a) (* i c)))))) (if (< y4 6.718963124057495e-279) (+ (- (- (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k))) (* (* y5 t) (* i j))) (- (* (- (* y2 t) (* y3 y)) (- (* y4 c) (* y5 a))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))) (if (< y4 4.77962681403792e-222) (+ (+ (- (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))) (* (* y3 y) (- (* y5 a) (* y4 c)))) (+ (* (* y5 a) (* t y2)) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* x y2) (* z y3)) (- (* c y0) (* a y1))) (- (* (- (* b y0) (* i y1)) (- (* j x) (* k z))) (* (- (* y x) (* z t)) (- (* b a) (* i c)))))) (if (< y4 2.2852241541266835e-175) (+ (- (- (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k))) (* (* y5 t) (* i j))) (- (* (- (* y2 t) (* y3 y)) (- (* y4 c) (* y5 a))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))) (+ (- (+ (+ (- (* (- (* x y) (* z t)) (- (* a b) (* c i))) (- (* k (* i (* z y1))) (+ (* j (* i (* x y1))) (* y0 (* k (* z b)))))) (- (* z (* y3 (* a y1))) (+ (* y2 (* x (* a y1))) (* y0 (* z (* c y3)))))) (* (- (* t j) (* y k)) (- (* y4 b) (* y5 i)))) (* (- (* t y2) (* y y3)) (- (* y4 c) (* y5 a)))) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))))))))

  (+ (- (+ (+ (- (* (- (* x y) (* z t)) (- (* a b) (* c i))) (* (- (* x j) (* z k)) (- (* y0 b) (* y1 i)))) (* (- (* x y2) (* z y3)) (- (* y0 c) (* y1 a)))) (* (- (* t j) (* y k)) (- (* y4 b) (* y5 i)))) (* (- (* t y2) (* y y3)) (- (* y4 c) (* y5 a)))) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0)))))