Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 30.5% → 37.3%

Time: 1.7min

Alternatives: 33

Speedup: 1.4×

• 89.3% 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: 30.5% 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: 37.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ t_2 := k \cdot y2 - j \cdot y3\\ t_3 := y1 \cdot y4 - y0 \cdot y5\\ t_4 := t_2 \cdot t_3 + t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ t_5 := y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot t_2\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ t_6 := a \cdot \left(\left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right) + b \cdot \left(x \cdot y - z \cdot t\right)\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{if}\;i \leq -6.6 \cdot 10^{+210}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -1.1 \cdot 10^{+106}:\\ \;\;\;\;y5 \cdot \left(t \cdot \left(a \cdot y2 - i \cdot j\right)\right)\\ \mathbf{elif}\;i \leq -2.8 \cdot 10^{+18}:\\ \;\;\;\;k \cdot \left(\left(y \cdot \left(i \cdot y5 - b \cdot y4\right) + y2 \cdot t_3\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;i \leq -5 \cdot 10^{-15}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq -5.2 \cdot 10^{-63}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq -3.2 \cdot 10^{-127}:\\ \;\;\;\;\left(y1 \cdot y2\right) \cdot \left(k \cdot y4 - x \cdot a\right)\\ \mathbf{elif}\;i \leq -2.5 \cdot 10^{-229}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq 4 \cdot 10^{-284}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{-38}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq 8.5 \cdot 10^{+26}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;i \leq 6.5 \cdot 10^{+153}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{+197}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \mathbf{elif}\;i \leq 4.3 \cdot 10^{+260}:\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y1 (* i (- (* x j) (* z k)))))
        (t_2 (- (* k y2) (* j y3)))
        (t_3 (- (* y1 y4) (* y0 y5)))
        (t_4
         (+
          (* t_2 t_3)
          (*
           t
           (+
            (+ (* z (- (* c i) (* a b))) (* j (- (* b y4) (* i y5))))
            (* y2 (- (* a y5) (* c y4)))))))
        (t_5
         (*
          y4
          (+
           (+ (* b (- (* t j) (* y k))) (* y1 t_2))
           (* c (- (* y y3) (* t y2))))))
        (t_6
         (*
          a
          (+
           (+ (* y1 (- (* z y3) (* x y2))) (* b (- (* x y) (* z t))))
           (* y5 (- (* t y2) (* y y3)))))))
   (if (<= i -6.6e+210)
     t_1
     (if (<= i -1.1e+106)
       (* y5 (* t (- (* a y2) (* i j))))
       (if (<= i -2.8e+18)
         (*
          k
          (+
           (+ (* y (- (* i y5) (* b y4))) (* y2 t_3))
           (* z (- (* b y0) (* i y1)))))
         (if (<= i -5e-15)
           t_4
           (if (<= i -5.2e-63)
             t_5
             (if (<= i -3.2e-127)
               (* (* y1 y2) (- (* k y4) (* x a)))
               (if (<= i -2.5e-229)
                 t_4
                 (if (<= i 4e-284)
                   (* a (* y (- (* x b) (* y3 y5))))
                   (if (<= i 4.8e-38)
                     t_4
                     (if (<= i 8.5e+26)
                       t_6
                       (if (<= i 6.5e+153)
                         t_5
                         (if (<= i 2.2e+197)
                           (* y (* y5 (- (* i k) (* a y3))))
                           (if (<= i 4.3e+260) t_6 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 = y1 * (i * ((x * j) - (z * k)));
	double t_2 = (k * y2) - (j * y3);
	double t_3 = (y1 * y4) - (y0 * y5);
	double t_4 = (t_2 * t_3) + (t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * ((a * y5) - (c * y4)))));
	double t_5 = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_2)) + (c * ((y * y3) - (t * y2))));
	double t_6 = a * (((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t)))) + (y5 * ((t * y2) - (y * y3))));
	double tmp;
	if (i <= -6.6e+210) {
		tmp = t_1;
	} else if (i <= -1.1e+106) {
		tmp = y5 * (t * ((a * y2) - (i * j)));
	} else if (i <= -2.8e+18) {
		tmp = k * (((y * ((i * y5) - (b * y4))) + (y2 * t_3)) + (z * ((b * y0) - (i * y1))));
	} else if (i <= -5e-15) {
		tmp = t_4;
	} else if (i <= -5.2e-63) {
		tmp = t_5;
	} else if (i <= -3.2e-127) {
		tmp = (y1 * y2) * ((k * y4) - (x * a));
	} else if (i <= -2.5e-229) {
		tmp = t_4;
	} else if (i <= 4e-284) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (i <= 4.8e-38) {
		tmp = t_4;
	} else if (i <= 8.5e+26) {
		tmp = t_6;
	} else if (i <= 6.5e+153) {
		tmp = t_5;
	} else if (i <= 2.2e+197) {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	} else if (i <= 4.3e+260) {
		tmp = t_6;
	} 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) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = y1 * (i * ((x * j) - (z * k)))
    t_2 = (k * y2) - (j * y3)
    t_3 = (y1 * y4) - (y0 * y5)
    t_4 = (t_2 * t_3) + (t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * ((a * y5) - (c * y4)))))
    t_5 = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_2)) + (c * ((y * y3) - (t * y2))))
    t_6 = a * (((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t)))) + (y5 * ((t * y2) - (y * y3))))
    if (i <= (-6.6d+210)) then
        tmp = t_1
    else if (i <= (-1.1d+106)) then
        tmp = y5 * (t * ((a * y2) - (i * j)))
    else if (i <= (-2.8d+18)) then
        tmp = k * (((y * ((i * y5) - (b * y4))) + (y2 * t_3)) + (z * ((b * y0) - (i * y1))))
    else if (i <= (-5d-15)) then
        tmp = t_4
    else if (i <= (-5.2d-63)) then
        tmp = t_5
    else if (i <= (-3.2d-127)) then
        tmp = (y1 * y2) * ((k * y4) - (x * a))
    else if (i <= (-2.5d-229)) then
        tmp = t_4
    else if (i <= 4d-284) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (i <= 4.8d-38) then
        tmp = t_4
    else if (i <= 8.5d+26) then
        tmp = t_6
    else if (i <= 6.5d+153) then
        tmp = t_5
    else if (i <= 2.2d+197) then
        tmp = y * (y5 * ((i * k) - (a * y3)))
    else if (i <= 4.3d+260) then
        tmp = t_6
    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 = y1 * (i * ((x * j) - (z * k)));
	double t_2 = (k * y2) - (j * y3);
	double t_3 = (y1 * y4) - (y0 * y5);
	double t_4 = (t_2 * t_3) + (t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * ((a * y5) - (c * y4)))));
	double t_5 = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_2)) + (c * ((y * y3) - (t * y2))));
	double t_6 = a * (((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t)))) + (y5 * ((t * y2) - (y * y3))));
	double tmp;
	if (i <= -6.6e+210) {
		tmp = t_1;
	} else if (i <= -1.1e+106) {
		tmp = y5 * (t * ((a * y2) - (i * j)));
	} else if (i <= -2.8e+18) {
		tmp = k * (((y * ((i * y5) - (b * y4))) + (y2 * t_3)) + (z * ((b * y0) - (i * y1))));
	} else if (i <= -5e-15) {
		tmp = t_4;
	} else if (i <= -5.2e-63) {
		tmp = t_5;
	} else if (i <= -3.2e-127) {
		tmp = (y1 * y2) * ((k * y4) - (x * a));
	} else if (i <= -2.5e-229) {
		tmp = t_4;
	} else if (i <= 4e-284) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (i <= 4.8e-38) {
		tmp = t_4;
	} else if (i <= 8.5e+26) {
		tmp = t_6;
	} else if (i <= 6.5e+153) {
		tmp = t_5;
	} else if (i <= 2.2e+197) {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	} else if (i <= 4.3e+260) {
		tmp = t_6;
	} 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 = y1 * (i * ((x * j) - (z * k)))
	t_2 = (k * y2) - (j * y3)
	t_3 = (y1 * y4) - (y0 * y5)
	t_4 = (t_2 * t_3) + (t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * ((a * y5) - (c * y4)))))
	t_5 = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_2)) + (c * ((y * y3) - (t * y2))))
	t_6 = a * (((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t)))) + (y5 * ((t * y2) - (y * y3))))
	tmp = 0
	if i <= -6.6e+210:
		tmp = t_1
	elif i <= -1.1e+106:
		tmp = y5 * (t * ((a * y2) - (i * j)))
	elif i <= -2.8e+18:
		tmp = k * (((y * ((i * y5) - (b * y4))) + (y2 * t_3)) + (z * ((b * y0) - (i * y1))))
	elif i <= -5e-15:
		tmp = t_4
	elif i <= -5.2e-63:
		tmp = t_5
	elif i <= -3.2e-127:
		tmp = (y1 * y2) * ((k * y4) - (x * a))
	elif i <= -2.5e-229:
		tmp = t_4
	elif i <= 4e-284:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif i <= 4.8e-38:
		tmp = t_4
	elif i <= 8.5e+26:
		tmp = t_6
	elif i <= 6.5e+153:
		tmp = t_5
	elif i <= 2.2e+197:
		tmp = y * (y5 * ((i * k) - (a * y3)))
	elif i <= 4.3e+260:
		tmp = t_6
	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(y1 * Float64(i * Float64(Float64(x * j) - Float64(z * k))))
	t_2 = Float64(Float64(k * y2) - Float64(j * y3))
	t_3 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_4 = Float64(Float64(t_2 * t_3) + Float64(t * Float64(Float64(Float64(z * Float64(Float64(c * i) - Float64(a * b))) + Float64(j * Float64(Float64(b * y4) - Float64(i * y5)))) + Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))))))
	t_5 = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * t_2)) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))))
	t_6 = Float64(a * Float64(Float64(Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))) + Float64(b * Float64(Float64(x * y) - Float64(z * t)))) + Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3)))))
	tmp = 0.0
	if (i <= -6.6e+210)
		tmp = t_1;
	elseif (i <= -1.1e+106)
		tmp = Float64(y5 * Float64(t * Float64(Float64(a * y2) - Float64(i * j))));
	elseif (i <= -2.8e+18)
		tmp = Float64(k * Float64(Float64(Float64(y * Float64(Float64(i * y5) - Float64(b * y4))) + Float64(y2 * t_3)) + Float64(z * Float64(Float64(b * y0) - Float64(i * y1)))));
	elseif (i <= -5e-15)
		tmp = t_4;
	elseif (i <= -5.2e-63)
		tmp = t_5;
	elseif (i <= -3.2e-127)
		tmp = Float64(Float64(y1 * y2) * Float64(Float64(k * y4) - Float64(x * a)));
	elseif (i <= -2.5e-229)
		tmp = t_4;
	elseif (i <= 4e-284)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (i <= 4.8e-38)
		tmp = t_4;
	elseif (i <= 8.5e+26)
		tmp = t_6;
	elseif (i <= 6.5e+153)
		tmp = t_5;
	elseif (i <= 2.2e+197)
		tmp = Float64(y * Float64(y5 * Float64(Float64(i * k) - Float64(a * y3))));
	elseif (i <= 4.3e+260)
		tmp = t_6;
	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 = y1 * (i * ((x * j) - (z * k)));
	t_2 = (k * y2) - (j * y3);
	t_3 = (y1 * y4) - (y0 * y5);
	t_4 = (t_2 * t_3) + (t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * ((a * y5) - (c * y4)))));
	t_5 = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_2)) + (c * ((y * y3) - (t * y2))));
	t_6 = a * (((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t)))) + (y5 * ((t * y2) - (y * y3))));
	tmp = 0.0;
	if (i <= -6.6e+210)
		tmp = t_1;
	elseif (i <= -1.1e+106)
		tmp = y5 * (t * ((a * y2) - (i * j)));
	elseif (i <= -2.8e+18)
		tmp = k * (((y * ((i * y5) - (b * y4))) + (y2 * t_3)) + (z * ((b * y0) - (i * y1))));
	elseif (i <= -5e-15)
		tmp = t_4;
	elseif (i <= -5.2e-63)
		tmp = t_5;
	elseif (i <= -3.2e-127)
		tmp = (y1 * y2) * ((k * y4) - (x * a));
	elseif (i <= -2.5e-229)
		tmp = t_4;
	elseif (i <= 4e-284)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (i <= 4.8e-38)
		tmp = t_4;
	elseif (i <= 8.5e+26)
		tmp = t_6;
	elseif (i <= 6.5e+153)
		tmp = t_5;
	elseif (i <= 2.2e+197)
		tmp = y * (y5 * ((i * k) - (a * y3)));
	elseif (i <= 4.3e+260)
		tmp = t_6;
	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[(y1 * N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$2 * t$95$3), $MachinePrecision] + N[(t * N[(N[(N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(a * N[(N[(N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -6.6e+210], t$95$1, If[LessEqual[i, -1.1e+106], N[(y5 * N[(t * N[(N[(a * y2), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -2.8e+18], N[(k * N[(N[(N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -5e-15], t$95$4, If[LessEqual[i, -5.2e-63], t$95$5, If[LessEqual[i, -3.2e-127], N[(N[(y1 * y2), $MachinePrecision] * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -2.5e-229], t$95$4, If[LessEqual[i, 4e-284], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.8e-38], t$95$4, If[LessEqual[i, 8.5e+26], t$95$6, If[LessEqual[i, 6.5e+153], t$95$5, If[LessEqual[i, 2.2e+197], N[(y * N[(y5 * N[(N[(i * k), $MachinePrecision] - N[(a * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.3e+260], t$95$6, t$95$1]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if i < -6.5999999999999999e210 or 4.30000000000000024e260 < i

   1. Initial program 13.5%

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

   3. Taylor expanded in y1 around inf 52.2%

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

   4. Taylor expanded in i around inf 63.2%

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

   if -6.5999999999999999e210 < i < -1.09999999999999996e106

   1. Initial program 12.5%

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

   3. Taylor expanded in y5 around -inf 45.0%

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

      1. associate-*r* 45.0%

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

      2. neg-mul-1 45.0%

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

      3. fma-def 45.0%

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

      4. *-commutative 45.0%

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

      5. *-commutative 45.0%

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

      6. *-commutative 45.0%

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

   5. Simplified 45.0%

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

   6. Taylor expanded in t around inf 57.2%

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

      1. *-commutative 57.2%

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

   8. Simplified 57.2%

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

   if -1.09999999999999996e106 < i < -2.8e18

   1. Initial program 57.1%

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

   3. Taylor expanded in k around inf 71.6%

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

   if -2.8e18 < i < -4.99999999999999999e-15 or -3.20000000000000017e-127 < i < -2.50000000000000008e-229 or 4.00000000000000015e-284 < i < 4.80000000000000044e-38

   1. Initial program 37.6%

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

   3. Taylor expanded in t around inf 61.9%

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

   if -4.99999999999999999e-15 < i < -5.2000000000000003e-63 or 8.5e26 < i < 6.49999999999999972e153

   1. Initial program 43.9%

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

   3. Taylor expanded in y4 around inf 59.1%

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

   if -5.2000000000000003e-63 < i < -3.20000000000000017e-127

   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 33.3%

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

   4. Taylor expanded in y1 around inf 61.9%

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

      1. associate-*r* 67.8%

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

      2. *-commutative 67.8%

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

      3. +-commutative 67.8%

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

      4. mul-1-neg 67.8%

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

      5. unsub-neg 67.8%

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

   6. Simplified 67.8%

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

   if -2.50000000000000008e-229 < i < 4.00000000000000015e-284

   1. Initial program 27.8%

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

   3. Simplified 27.8%

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

   5. Taylor expanded in a around inf 35.2%

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

   6. Taylor expanded in y around inf 55.9%

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

      1. *-commutative 55.9%

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

      2. *-commutative 55.9%

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

   8. Simplified 55.9%

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

   if 4.80000000000000044e-38 < i < 8.5e26 or 2.19999999999999989e197 < i < 4.30000000000000024e260

   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 a around inf 74.1%

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

   if 6.49999999999999972e153 < i < 2.19999999999999989e197

   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 y5 around -inf 54.3%

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

      1. associate-*r* 54.3%

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

      2. neg-mul-1 54.3%

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

      3. fma-def 54.3%

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

      4. *-commutative 54.3%

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

      5. *-commutative 54.3%

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

      6. *-commutative 54.3%

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

   5. Simplified 54.3%

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

   6. Taylor expanded in y around -inf 73.7%

      \[\leadsto \color{blue}{y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 73.7%

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

   8. Simplified 73.7%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -6.6 \cdot 10^{+210}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;i \leq -1.1 \cdot 10^{+106}:\\ \;\;\;\;y5 \cdot \left(t \cdot \left(a \cdot y2 - i \cdot j\right)\right)\\ \mathbf{elif}\;i \leq -2.8 \cdot 10^{+18}:\\ \;\;\;\;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}\;i \leq -5 \cdot 10^{-15}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq -5.2 \cdot 10^{-63}:\\ \;\;\;\;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}\;i \leq -3.2 \cdot 10^{-127}:\\ \;\;\;\;\left(y1 \cdot y2\right) \cdot \left(k \cdot y4 - x \cdot a\right)\\ \mathbf{elif}\;i \leq -2.5 \cdot 10^{-229}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq 4 \cdot 10^{-284}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{-38}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq 8.5 \cdot 10^{+26}:\\ \;\;\;\;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}\;i \leq 6.5 \cdot 10^{+153}:\\ \;\;\;\;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}\;i \leq 2.2 \cdot 10^{+197}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \mathbf{elif}\;i \leq 4.3 \cdot 10^{+260}:\\ \;\;\;\;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{else}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 53.7% accurate, 0.5× speedup

Math

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

FPCore

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 96.4%

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

   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 36.3%

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

4. Final simplification 55.3%

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

Alternative 3: 39.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y2 - z \cdot y3\\ t_2 := j \cdot y3 - k \cdot y2\\ t_3 := y \cdot y3 - t \cdot y2\\ t_4 := y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot t_3\right)\\ t_5 := y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ t_6 := 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)\\ t_7 := y0 \cdot \left(\left(y5 \cdot t_2 + c \cdot t_1\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ t_8 := y1 \cdot y4 - y0 \cdot y5\\ \mathbf{if}\;y0 \leq -3.6 \cdot 10^{+221}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot t_1\right) + y4 \cdot t_3\right)\\ \mathbf{elif}\;y0 \leq -1.4 \cdot 10^{+104}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;y0 \leq -5.8 \cdot 10^{+54}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) - \left(a \cdot t_1 + y4 \cdot t_2\right)\right)\\ \mathbf{elif}\;y0 \leq -2.35 \cdot 10^{-90}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y0 \leq -2.05 \cdot 10^{-206}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y0 \leq -4.6 \cdot 10^{-254}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq -6.2 \cdot 10^{-294}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y0 \leq 1.55 \cdot 10^{-214}:\\ \;\;\;\;k \cdot \left(\left(y \cdot \left(i \cdot y5 - b \cdot y4\right) + y2 \cdot t_8\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y0 \leq 5.4 \cdot 10^{-144}:\\ \;\;\;\;y2 \cdot \left(k \cdot t_8 + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 5.4 \cdot 10^{-76}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y0 \leq 1.25 \cdot 10^{-59}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y0 \leq 1.45 \cdot 10^{+69}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y0 \leq 1.42 \cdot 10^{+105}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_7\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* x y2) (* z y3)))
        (t_2 (- (* j y3) (* k y2)))
        (t_3 (- (* y y3) (* t y2)))
        (t_4
         (*
          y4
          (+
           (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
           (* c t_3))))
        (t_5 (* y (* y5 (- (* i k) (* a y3)))))
        (t_6
         (*
          a
          (+
           (+ (* y1 (- (* z y3) (* x y2))) (* b (- (* x y) (* z t))))
           (* y5 (- (* t y2) (* y y3))))))
        (t_7 (* y0 (+ (+ (* y5 t_2) (* c t_1)) (* b (- (* z k) (* x j))))))
        (t_8 (- (* y1 y4) (* y0 y5))))
   (if (<= y0 -3.6e+221)
     (* c (+ (+ (* i (- (* z t) (* x y))) (* y0 t_1)) (* y4 t_3)))
     (if (<= y0 -1.4e+104)
       t_7
       (if (<= y0 -5.8e+54)
         (* y1 (- (* i (- (* x j) (* z k))) (+ (* a t_1) (* y4 t_2))))
         (if (<= y0 -2.35e-90)
           t_4
           (if (<= y0 -2.05e-206)
             t_5
             (if (<= y0 -4.6e-254)
               (* y1 (* y3 (- (* z a) (* j y4))))
               (if (<= y0 -6.2e-294)
                 t_6
                 (if (<= y0 1.55e-214)
                   (*
                    k
                    (+
                     (+ (* y (- (* i y5) (* b y4))) (* y2 t_8))
                     (* z (- (* b y0) (* i y1)))))
                   (if (<= y0 5.4e-144)
                     (* y2 (+ (* k t_8) (* t (- (* a y5) (* c y4)))))
                     (if (<= y0 5.4e-76)
                       t_6
                       (if (<= y0 1.25e-59)
                         t_5
                         (if (<= y0 1.45e+69)
                           t_4
                           (if (<= y0 1.42e+105)
                             (* y1 (* y2 (- (* k y4) (* x a))))
                             t_7)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (x * y2) - (z * y3);
	double t_2 = (j * y3) - (k * y2);
	double t_3 = (y * y3) - (t * y2);
	double t_4 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_3));
	double t_5 = y * (y5 * ((i * k) - (a * y3)));
	double t_6 = a * (((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t)))) + (y5 * ((t * y2) - (y * y3))));
	double t_7 = y0 * (((y5 * t_2) + (c * t_1)) + (b * ((z * k) - (x * j))));
	double t_8 = (y1 * y4) - (y0 * y5);
	double tmp;
	if (y0 <= -3.6e+221) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_1)) + (y4 * t_3));
	} else if (y0 <= -1.4e+104) {
		tmp = t_7;
	} else if (y0 <= -5.8e+54) {
		tmp = y1 * ((i * ((x * j) - (z * k))) - ((a * t_1) + (y4 * t_2)));
	} else if (y0 <= -2.35e-90) {
		tmp = t_4;
	} else if (y0 <= -2.05e-206) {
		tmp = t_5;
	} else if (y0 <= -4.6e-254) {
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	} else if (y0 <= -6.2e-294) {
		tmp = t_6;
	} else if (y0 <= 1.55e-214) {
		tmp = k * (((y * ((i * y5) - (b * y4))) + (y2 * t_8)) + (z * ((b * y0) - (i * y1))));
	} else if (y0 <= 5.4e-144) {
		tmp = y2 * ((k * t_8) + (t * ((a * y5) - (c * y4))));
	} else if (y0 <= 5.4e-76) {
		tmp = t_6;
	} else if (y0 <= 1.25e-59) {
		tmp = t_5;
	} else if (y0 <= 1.45e+69) {
		tmp = t_4;
	} else if (y0 <= 1.42e+105) {
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	} else {
		tmp = t_7;
	}
	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) :: t_8
    real(8) :: tmp
    t_1 = (x * y2) - (z * y3)
    t_2 = (j * y3) - (k * y2)
    t_3 = (y * y3) - (t * y2)
    t_4 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_3))
    t_5 = y * (y5 * ((i * k) - (a * y3)))
    t_6 = a * (((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t)))) + (y5 * ((t * y2) - (y * y3))))
    t_7 = y0 * (((y5 * t_2) + (c * t_1)) + (b * ((z * k) - (x * j))))
    t_8 = (y1 * y4) - (y0 * y5)
    if (y0 <= (-3.6d+221)) then
        tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_1)) + (y4 * t_3))
    else if (y0 <= (-1.4d+104)) then
        tmp = t_7
    else if (y0 <= (-5.8d+54)) then
        tmp = y1 * ((i * ((x * j) - (z * k))) - ((a * t_1) + (y4 * t_2)))
    else if (y0 <= (-2.35d-90)) then
        tmp = t_4
    else if (y0 <= (-2.05d-206)) then
        tmp = t_5
    else if (y0 <= (-4.6d-254)) then
        tmp = y1 * (y3 * ((z * a) - (j * y4)))
    else if (y0 <= (-6.2d-294)) then
        tmp = t_6
    else if (y0 <= 1.55d-214) then
        tmp = k * (((y * ((i * y5) - (b * y4))) + (y2 * t_8)) + (z * ((b * y0) - (i * y1))))
    else if (y0 <= 5.4d-144) then
        tmp = y2 * ((k * t_8) + (t * ((a * y5) - (c * y4))))
    else if (y0 <= 5.4d-76) then
        tmp = t_6
    else if (y0 <= 1.25d-59) then
        tmp = t_5
    else if (y0 <= 1.45d+69) then
        tmp = t_4
    else if (y0 <= 1.42d+105) then
        tmp = y1 * (y2 * ((k * y4) - (x * a)))
    else
        tmp = t_7
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (x * y2) - (z * y3);
	double t_2 = (j * y3) - (k * y2);
	double t_3 = (y * y3) - (t * y2);
	double t_4 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_3));
	double t_5 = y * (y5 * ((i * k) - (a * y3)));
	double t_6 = a * (((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t)))) + (y5 * ((t * y2) - (y * y3))));
	double t_7 = y0 * (((y5 * t_2) + (c * t_1)) + (b * ((z * k) - (x * j))));
	double t_8 = (y1 * y4) - (y0 * y5);
	double tmp;
	if (y0 <= -3.6e+221) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_1)) + (y4 * t_3));
	} else if (y0 <= -1.4e+104) {
		tmp = t_7;
	} else if (y0 <= -5.8e+54) {
		tmp = y1 * ((i * ((x * j) - (z * k))) - ((a * t_1) + (y4 * t_2)));
	} else if (y0 <= -2.35e-90) {
		tmp = t_4;
	} else if (y0 <= -2.05e-206) {
		tmp = t_5;
	} else if (y0 <= -4.6e-254) {
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	} else if (y0 <= -6.2e-294) {
		tmp = t_6;
	} else if (y0 <= 1.55e-214) {
		tmp = k * (((y * ((i * y5) - (b * y4))) + (y2 * t_8)) + (z * ((b * y0) - (i * y1))));
	} else if (y0 <= 5.4e-144) {
		tmp = y2 * ((k * t_8) + (t * ((a * y5) - (c * y4))));
	} else if (y0 <= 5.4e-76) {
		tmp = t_6;
	} else if (y0 <= 1.25e-59) {
		tmp = t_5;
	} else if (y0 <= 1.45e+69) {
		tmp = t_4;
	} else if (y0 <= 1.42e+105) {
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	} else {
		tmp = t_7;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (x * y2) - (z * y3)
	t_2 = (j * y3) - (k * y2)
	t_3 = (y * y3) - (t * y2)
	t_4 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_3))
	t_5 = y * (y5 * ((i * k) - (a * y3)))
	t_6 = a * (((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t)))) + (y5 * ((t * y2) - (y * y3))))
	t_7 = y0 * (((y5 * t_2) + (c * t_1)) + (b * ((z * k) - (x * j))))
	t_8 = (y1 * y4) - (y0 * y5)
	tmp = 0
	if y0 <= -3.6e+221:
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_1)) + (y4 * t_3))
	elif y0 <= -1.4e+104:
		tmp = t_7
	elif y0 <= -5.8e+54:
		tmp = y1 * ((i * ((x * j) - (z * k))) - ((a * t_1) + (y4 * t_2)))
	elif y0 <= -2.35e-90:
		tmp = t_4
	elif y0 <= -2.05e-206:
		tmp = t_5
	elif y0 <= -4.6e-254:
		tmp = y1 * (y3 * ((z * a) - (j * y4)))
	elif y0 <= -6.2e-294:
		tmp = t_6
	elif y0 <= 1.55e-214:
		tmp = k * (((y * ((i * y5) - (b * y4))) + (y2 * t_8)) + (z * ((b * y0) - (i * y1))))
	elif y0 <= 5.4e-144:
		tmp = y2 * ((k * t_8) + (t * ((a * y5) - (c * y4))))
	elif y0 <= 5.4e-76:
		tmp = t_6
	elif y0 <= 1.25e-59:
		tmp = t_5
	elif y0 <= 1.45e+69:
		tmp = t_4
	elif y0 <= 1.42e+105:
		tmp = y1 * (y2 * ((k * y4) - (x * a)))
	else:
		tmp = t_7
	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(x * y2) - Float64(z * y3))
	t_2 = Float64(Float64(j * y3) - Float64(k * y2))
	t_3 = Float64(Float64(y * y3) - Float64(t * y2))
	t_4 = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * t_3)))
	t_5 = Float64(y * Float64(y5 * Float64(Float64(i * k) - Float64(a * y3))))
	t_6 = Float64(a * Float64(Float64(Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))) + Float64(b * Float64(Float64(x * y) - Float64(z * t)))) + Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3)))))
	t_7 = Float64(y0 * Float64(Float64(Float64(y5 * t_2) + Float64(c * t_1)) + Float64(b * Float64(Float64(z * k) - Float64(x * j)))))
	t_8 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	tmp = 0.0
	if (y0 <= -3.6e+221)
		tmp = Float64(c * Float64(Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(y0 * t_1)) + Float64(y4 * t_3)));
	elseif (y0 <= -1.4e+104)
		tmp = t_7;
	elseif (y0 <= -5.8e+54)
		tmp = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) - Float64(Float64(a * t_1) + Float64(y4 * t_2))));
	elseif (y0 <= -2.35e-90)
		tmp = t_4;
	elseif (y0 <= -2.05e-206)
		tmp = t_5;
	elseif (y0 <= -4.6e-254)
		tmp = Float64(y1 * Float64(y3 * Float64(Float64(z * a) - Float64(j * y4))));
	elseif (y0 <= -6.2e-294)
		tmp = t_6;
	elseif (y0 <= 1.55e-214)
		tmp = Float64(k * Float64(Float64(Float64(y * Float64(Float64(i * y5) - Float64(b * y4))) + Float64(y2 * t_8)) + Float64(z * Float64(Float64(b * y0) - Float64(i * y1)))));
	elseif (y0 <= 5.4e-144)
		tmp = Float64(y2 * Float64(Float64(k * t_8) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y0 <= 5.4e-76)
		tmp = t_6;
	elseif (y0 <= 1.25e-59)
		tmp = t_5;
	elseif (y0 <= 1.45e+69)
		tmp = t_4;
	elseif (y0 <= 1.42e+105)
		tmp = Float64(y1 * Float64(y2 * Float64(Float64(k * y4) - Float64(x * a))));
	else
		tmp = t_7;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (x * y2) - (z * y3);
	t_2 = (j * y3) - (k * y2);
	t_3 = (y * y3) - (t * y2);
	t_4 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_3));
	t_5 = y * (y5 * ((i * k) - (a * y3)));
	t_6 = a * (((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t)))) + (y5 * ((t * y2) - (y * y3))));
	t_7 = y0 * (((y5 * t_2) + (c * t_1)) + (b * ((z * k) - (x * j))));
	t_8 = (y1 * y4) - (y0 * y5);
	tmp = 0.0;
	if (y0 <= -3.6e+221)
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_1)) + (y4 * t_3));
	elseif (y0 <= -1.4e+104)
		tmp = t_7;
	elseif (y0 <= -5.8e+54)
		tmp = y1 * ((i * ((x * j) - (z * k))) - ((a * t_1) + (y4 * t_2)));
	elseif (y0 <= -2.35e-90)
		tmp = t_4;
	elseif (y0 <= -2.05e-206)
		tmp = t_5;
	elseif (y0 <= -4.6e-254)
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	elseif (y0 <= -6.2e-294)
		tmp = t_6;
	elseif (y0 <= 1.55e-214)
		tmp = k * (((y * ((i * y5) - (b * y4))) + (y2 * t_8)) + (z * ((b * y0) - (i * y1))));
	elseif (y0 <= 5.4e-144)
		tmp = y2 * ((k * t_8) + (t * ((a * y5) - (c * y4))));
	elseif (y0 <= 5.4e-76)
		tmp = t_6;
	elseif (y0 <= 1.25e-59)
		tmp = t_5;
	elseif (y0 <= 1.45e+69)
		tmp = t_4;
	elseif (y0 <= 1.42e+105)
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	else
		tmp = t_7;
	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[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y * N[(y5 * N[(N[(i * k), $MachinePrecision] - N[(a * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(a * N[(N[(N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(y0 * N[(N[(N[(y5 * t$95$2), $MachinePrecision] + N[(c * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -3.6e+221], N[(c * N[(N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1.4e+104], t$95$7, If[LessEqual[y0, -5.8e+54], N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(a * t$95$1), $MachinePrecision] + N[(y4 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -2.35e-90], t$95$4, If[LessEqual[y0, -2.05e-206], t$95$5, If[LessEqual[y0, -4.6e-254], N[(y1 * N[(y3 * N[(N[(z * a), $MachinePrecision] - N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -6.2e-294], t$95$6, If[LessEqual[y0, 1.55e-214], N[(k * N[(N[(N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$8), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 5.4e-144], N[(y2 * N[(N[(k * t$95$8), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 5.4e-76], t$95$6, If[LessEqual[y0, 1.25e-59], t$95$5, If[LessEqual[y0, 1.45e+69], t$95$4, If[LessEqual[y0, 1.42e+105], N[(y1 * N[(y2 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$7]]]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if y0 < -3.60000000000000009e221

   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 c around inf 65.0%

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

   if -3.60000000000000009e221 < y0 < -1.4e104 or 1.41999999999999991e105 < y0

   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 y0 around inf 61.4%

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

   if -1.4e104 < y0 < -5.7999999999999997e54

   1. Initial program 25.0%

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

   3. Taylor expanded in y1 around inf 63.4%

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

   if -5.7999999999999997e54 < y0 < -2.35e-90 or 1.25e-59 < y0 < 1.4499999999999999e69

   1. Initial program 37.2%

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

   3. Taylor expanded in y4 around inf 62.9%

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

   if -2.35e-90 < y0 < -2.05000000000000008e-206 or 5.4000000000000001e-76 < y0 < 1.25e-59

   1. Initial program 46.4%

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

   3. Taylor expanded in y5 around -inf 50.3%

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

      1. associate-*r* 50.3%

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

      2. neg-mul-1 50.3%

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

      3. fma-def 50.3%

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

      4. *-commutative 50.3%

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

      5. *-commutative 50.3%

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

      6. *-commutative 50.3%

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

   5. Simplified 50.3%

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

   6. Taylor expanded in y around -inf 68.2%

      \[\leadsto \color{blue}{y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 68.2%

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

   8. Simplified 68.2%

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

   if -2.05000000000000008e-206 < y0 < -4.5999999999999997e-254

   1. Initial program 8.3%

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

   3. Taylor expanded in y1 around inf 33.9%

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

   4. Taylor expanded in y3 around inf 75.4%

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

      1. +-commutative 75.4%

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

      2. mul-1-neg 75.4%

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

      3. unsub-neg 75.4%

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

      4. *-commutative 75.4%

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

      5. *-commutative 75.4%

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

   6. Simplified 75.4%

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

   if -4.5999999999999997e-254 < y0 < -6.20000000000000007e-294 or 5.3999999999999995e-144 < y0 < 5.4000000000000001e-76

   1. Initial program 33.6%

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

   3. Simplified 33.6%

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

   5. Taylor expanded in a around inf 67.0%

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

   if -6.20000000000000007e-294 < y0 < 1.55000000000000002e-214

   1. Initial program 27.6%

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

   3. Taylor expanded in k around inf 46.8%

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

   if 1.55000000000000002e-214 < y0 < 5.3999999999999995e-144

   1. Initial program 27.9%

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

   3. Taylor expanded in y2 around inf 52.6%

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

   4. Taylor expanded in x around 0 62.3%

      \[\leadsto \color{blue}{y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   5. Step-by-step derivation

      1. sub-neg 62.3%

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

      2. *-commutative 62.3%

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

      3. sub-neg 62.3%

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

      4. *-commutative 62.3%

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

      5. *-commutative 62.3%

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

   6. Simplified 62.3%

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

   if 1.4499999999999999e69 < y0 < 1.41999999999999991e105

   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 y2 around inf 41.0%

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

   4. Taylor expanded in y1 around inf 72.2%

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

      1. associate-*r* 72.2%

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

      2. *-commutative 72.2%

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

      3. +-commutative 72.2%

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

      4. mul-1-neg 72.2%

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

      5. unsub-neg 72.2%

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

   6. Simplified 72.2%

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

   7. Taylor expanded in y2 around 0 72.2%

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

      1. *-commutative 72.2%

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

      2. *-commutative 72.2%

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

   9. Simplified 72.2%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -3.6 \cdot 10^{+221}:\\ \;\;\;\;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}\;y0 \leq -1.4 \cdot 10^{+104}:\\ \;\;\;\;y0 \cdot \left(\left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -5.8 \cdot 10^{+54}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) - \left(a \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y0 \leq -2.35 \cdot 10^{-90}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq -2.05 \cdot 10^{-206}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq -4.6 \cdot 10^{-254}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq -6.2 \cdot 10^{-294}:\\ \;\;\;\;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}\;y0 \leq 1.55 \cdot 10^{-214}:\\ \;\;\;\;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}\;y0 \leq 5.4 \cdot 10^{-144}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 5.4 \cdot 10^{-76}:\\ \;\;\;\;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}\;y0 \leq 1.25 \cdot 10^{-59}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq 1.45 \cdot 10^{+69}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq 1.42 \cdot 10^{+105}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(\left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 38.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot j - y \cdot k\right)\\ t_2 := x \cdot y2 - z \cdot y3\\ t_3 := j \cdot y3 - k \cdot y2\\ t_4 := y \cdot y3 - t \cdot y2\\ t_5 := y1 \cdot y4 - y0 \cdot y5\\ t_6 := y4 \cdot \left(\left(t_1 + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot t_4\right)\\ t_7 := y0 \cdot \left(\left(y5 \cdot t_3 + c \cdot t_2\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{if}\;y0 \leq -5 \cdot 10^{+222}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot t_2\right) + y4 \cdot t_4\right)\\ \mathbf{elif}\;y0 \leq -1.9 \cdot 10^{+104}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;y0 \leq -7.5 \cdot 10^{+54}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) - \left(a \cdot t_2 + y4 \cdot t_3\right)\right)\\ \mathbf{elif}\;y0 \leq -5 \cdot 10^{-98}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y0 \leq -6 \cdot 10^{-206}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq -3.5 \cdot 10^{-254}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq -4.8 \cdot 10^{-290}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 3.1 \cdot 10^{-226}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(j \cdot t_5 + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 2 \cdot 10^{-111}:\\ \;\;\;\;y2 \cdot \left(k \cdot t_5 + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 1.12 \cdot 10^{+67}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y0 \leq 3.65 \cdot 10^{+84}:\\ \;\;\;\;k \cdot \left(\left(y \cdot \left(i \cdot y5 - b \cdot y4\right) + y2 \cdot t_5\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y0 \leq 5.6 \cdot 10^{+153}:\\ \;\;\;\;y4 \cdot t_1\\ \mathbf{else}:\\ \;\;\;\;t_7\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (- (* t j) (* y k))))
        (t_2 (- (* x y2) (* z y3)))
        (t_3 (- (* j y3) (* k y2)))
        (t_4 (- (* y y3) (* t y2)))
        (t_5 (- (* y1 y4) (* y0 y5)))
        (t_6 (* y4 (+ (+ t_1 (* y1 (- (* k y2) (* j y3)))) (* c t_4))))
        (t_7 (* y0 (+ (+ (* y5 t_3) (* c t_2)) (* b (- (* z k) (* x j)))))))
   (if (<= y0 -5e+222)
     (* c (+ (+ (* i (- (* z t) (* x y))) (* y0 t_2)) (* y4 t_4)))
     (if (<= y0 -1.9e+104)
       t_7
       (if (<= y0 -7.5e+54)
         (* y1 (- (* i (- (* x j) (* z k))) (+ (* a t_2) (* y4 t_3))))
         (if (<= y0 -5e-98)
           t_6
           (if (<= y0 -6e-206)
             (* y (* y5 (- (* i k) (* a y3))))
             (if (<= y0 -3.5e-254)
               (* y1 (* y3 (- (* z a) (* j y4))))
               (if (<= y0 -4.8e-290)
                 (* a (* y (- (* x b) (* y3 y5))))
                 (if (<= y0 3.1e-226)
                   (*
                    y3
                    (-
                     (* y (- (* c y4) (* a y5)))
                     (+ (* j t_5) (* z (- (* c y0) (* a y1))))))
                   (if (<= y0 2e-111)
                     (* y2 (+ (* k t_5) (* t (- (* a y5) (* c y4)))))
                     (if (<= y0 1.12e+67)
                       t_6
                       (if (<= y0 3.65e+84)
                         (*
                          k
                          (+
                           (+ (* y (- (* i y5) (* b y4))) (* y2 t_5))
                           (* z (- (* b y0) (* i y1)))))
                         (if (<= y0 5.6e+153) (* y4 t_1) t_7))))))))))))))

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 * ((t * j) - (y * k));
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (j * y3) - (k * y2);
	double t_4 = (y * y3) - (t * y2);
	double t_5 = (y1 * y4) - (y0 * y5);
	double t_6 = y4 * ((t_1 + (y1 * ((k * y2) - (j * y3)))) + (c * t_4));
	double t_7 = y0 * (((y5 * t_3) + (c * t_2)) + (b * ((z * k) - (x * j))));
	double tmp;
	if (y0 <= -5e+222) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_2)) + (y4 * t_4));
	} else if (y0 <= -1.9e+104) {
		tmp = t_7;
	} else if (y0 <= -7.5e+54) {
		tmp = y1 * ((i * ((x * j) - (z * k))) - ((a * t_2) + (y4 * t_3)));
	} else if (y0 <= -5e-98) {
		tmp = t_6;
	} else if (y0 <= -6e-206) {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	} else if (y0 <= -3.5e-254) {
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	} else if (y0 <= -4.8e-290) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (y0 <= 3.1e-226) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) - ((j * t_5) + (z * ((c * y0) - (a * y1)))));
	} else if (y0 <= 2e-111) {
		tmp = y2 * ((k * t_5) + (t * ((a * y5) - (c * y4))));
	} else if (y0 <= 1.12e+67) {
		tmp = t_6;
	} else if (y0 <= 3.65e+84) {
		tmp = k * (((y * ((i * y5) - (b * y4))) + (y2 * t_5)) + (z * ((b * y0) - (i * y1))));
	} else if (y0 <= 5.6e+153) {
		tmp = y4 * t_1;
	} else {
		tmp = t_7;
	}
	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 = b * ((t * j) - (y * k))
    t_2 = (x * y2) - (z * y3)
    t_3 = (j * y3) - (k * y2)
    t_4 = (y * y3) - (t * y2)
    t_5 = (y1 * y4) - (y0 * y5)
    t_6 = y4 * ((t_1 + (y1 * ((k * y2) - (j * y3)))) + (c * t_4))
    t_7 = y0 * (((y5 * t_3) + (c * t_2)) + (b * ((z * k) - (x * j))))
    if (y0 <= (-5d+222)) then
        tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_2)) + (y4 * t_4))
    else if (y0 <= (-1.9d+104)) then
        tmp = t_7
    else if (y0 <= (-7.5d+54)) then
        tmp = y1 * ((i * ((x * j) - (z * k))) - ((a * t_2) + (y4 * t_3)))
    else if (y0 <= (-5d-98)) then
        tmp = t_6
    else if (y0 <= (-6d-206)) then
        tmp = y * (y5 * ((i * k) - (a * y3)))
    else if (y0 <= (-3.5d-254)) then
        tmp = y1 * (y3 * ((z * a) - (j * y4)))
    else if (y0 <= (-4.8d-290)) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (y0 <= 3.1d-226) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) - ((j * t_5) + (z * ((c * y0) - (a * y1)))))
    else if (y0 <= 2d-111) then
        tmp = y2 * ((k * t_5) + (t * ((a * y5) - (c * y4))))
    else if (y0 <= 1.12d+67) then
        tmp = t_6
    else if (y0 <= 3.65d+84) then
        tmp = k * (((y * ((i * y5) - (b * y4))) + (y2 * t_5)) + (z * ((b * y0) - (i * y1))))
    else if (y0 <= 5.6d+153) then
        tmp = y4 * t_1
    else
        tmp = t_7
    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 * ((t * j) - (y * k));
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (j * y3) - (k * y2);
	double t_4 = (y * y3) - (t * y2);
	double t_5 = (y1 * y4) - (y0 * y5);
	double t_6 = y4 * ((t_1 + (y1 * ((k * y2) - (j * y3)))) + (c * t_4));
	double t_7 = y0 * (((y5 * t_3) + (c * t_2)) + (b * ((z * k) - (x * j))));
	double tmp;
	if (y0 <= -5e+222) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_2)) + (y4 * t_4));
	} else if (y0 <= -1.9e+104) {
		tmp = t_7;
	} else if (y0 <= -7.5e+54) {
		tmp = y1 * ((i * ((x * j) - (z * k))) - ((a * t_2) + (y4 * t_3)));
	} else if (y0 <= -5e-98) {
		tmp = t_6;
	} else if (y0 <= -6e-206) {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	} else if (y0 <= -3.5e-254) {
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	} else if (y0 <= -4.8e-290) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (y0 <= 3.1e-226) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) - ((j * t_5) + (z * ((c * y0) - (a * y1)))));
	} else if (y0 <= 2e-111) {
		tmp = y2 * ((k * t_5) + (t * ((a * y5) - (c * y4))));
	} else if (y0 <= 1.12e+67) {
		tmp = t_6;
	} else if (y0 <= 3.65e+84) {
		tmp = k * (((y * ((i * y5) - (b * y4))) + (y2 * t_5)) + (z * ((b * y0) - (i * y1))));
	} else if (y0 <= 5.6e+153) {
		tmp = y4 * t_1;
	} else {
		tmp = t_7;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * ((t * j) - (y * k))
	t_2 = (x * y2) - (z * y3)
	t_3 = (j * y3) - (k * y2)
	t_4 = (y * y3) - (t * y2)
	t_5 = (y1 * y4) - (y0 * y5)
	t_6 = y4 * ((t_1 + (y1 * ((k * y2) - (j * y3)))) + (c * t_4))
	t_7 = y0 * (((y5 * t_3) + (c * t_2)) + (b * ((z * k) - (x * j))))
	tmp = 0
	if y0 <= -5e+222:
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_2)) + (y4 * t_4))
	elif y0 <= -1.9e+104:
		tmp = t_7
	elif y0 <= -7.5e+54:
		tmp = y1 * ((i * ((x * j) - (z * k))) - ((a * t_2) + (y4 * t_3)))
	elif y0 <= -5e-98:
		tmp = t_6
	elif y0 <= -6e-206:
		tmp = y * (y5 * ((i * k) - (a * y3)))
	elif y0 <= -3.5e-254:
		tmp = y1 * (y3 * ((z * a) - (j * y4)))
	elif y0 <= -4.8e-290:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif y0 <= 3.1e-226:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) - ((j * t_5) + (z * ((c * y0) - (a * y1)))))
	elif y0 <= 2e-111:
		tmp = y2 * ((k * t_5) + (t * ((a * y5) - (c * y4))))
	elif y0 <= 1.12e+67:
		tmp = t_6
	elif y0 <= 3.65e+84:
		tmp = k * (((y * ((i * y5) - (b * y4))) + (y2 * t_5)) + (z * ((b * y0) - (i * y1))))
	elif y0 <= 5.6e+153:
		tmp = y4 * t_1
	else:
		tmp = t_7
	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(t * j) - Float64(y * k)))
	t_2 = Float64(Float64(x * y2) - Float64(z * y3))
	t_3 = Float64(Float64(j * y3) - Float64(k * y2))
	t_4 = Float64(Float64(y * y3) - Float64(t * y2))
	t_5 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_6 = Float64(y4 * Float64(Float64(t_1 + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * t_4)))
	t_7 = Float64(y0 * Float64(Float64(Float64(y5 * t_3) + Float64(c * t_2)) + Float64(b * Float64(Float64(z * k) - Float64(x * j)))))
	tmp = 0.0
	if (y0 <= -5e+222)
		tmp = Float64(c * Float64(Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(y0 * t_2)) + Float64(y4 * t_4)));
	elseif (y0 <= -1.9e+104)
		tmp = t_7;
	elseif (y0 <= -7.5e+54)
		tmp = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) - Float64(Float64(a * t_2) + Float64(y4 * t_3))));
	elseif (y0 <= -5e-98)
		tmp = t_6;
	elseif (y0 <= -6e-206)
		tmp = Float64(y * Float64(y5 * Float64(Float64(i * k) - Float64(a * y3))));
	elseif (y0 <= -3.5e-254)
		tmp = Float64(y1 * Float64(y3 * Float64(Float64(z * a) - Float64(j * y4))));
	elseif (y0 <= -4.8e-290)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (y0 <= 3.1e-226)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) - Float64(Float64(j * t_5) + Float64(z * Float64(Float64(c * y0) - Float64(a * y1))))));
	elseif (y0 <= 2e-111)
		tmp = Float64(y2 * Float64(Float64(k * t_5) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y0 <= 1.12e+67)
		tmp = t_6;
	elseif (y0 <= 3.65e+84)
		tmp = 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)))));
	elseif (y0 <= 5.6e+153)
		tmp = Float64(y4 * t_1);
	else
		tmp = t_7;
	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 * ((t * j) - (y * k));
	t_2 = (x * y2) - (z * y3);
	t_3 = (j * y3) - (k * y2);
	t_4 = (y * y3) - (t * y2);
	t_5 = (y1 * y4) - (y0 * y5);
	t_6 = y4 * ((t_1 + (y1 * ((k * y2) - (j * y3)))) + (c * t_4));
	t_7 = y0 * (((y5 * t_3) + (c * t_2)) + (b * ((z * k) - (x * j))));
	tmp = 0.0;
	if (y0 <= -5e+222)
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_2)) + (y4 * t_4));
	elseif (y0 <= -1.9e+104)
		tmp = t_7;
	elseif (y0 <= -7.5e+54)
		tmp = y1 * ((i * ((x * j) - (z * k))) - ((a * t_2) + (y4 * t_3)));
	elseif (y0 <= -5e-98)
		tmp = t_6;
	elseif (y0 <= -6e-206)
		tmp = y * (y5 * ((i * k) - (a * y3)));
	elseif (y0 <= -3.5e-254)
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	elseif (y0 <= -4.8e-290)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (y0 <= 3.1e-226)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) - ((j * t_5) + (z * ((c * y0) - (a * y1)))));
	elseif (y0 <= 2e-111)
		tmp = y2 * ((k * t_5) + (t * ((a * y5) - (c * y4))));
	elseif (y0 <= 1.12e+67)
		tmp = t_6;
	elseif (y0 <= 3.65e+84)
		tmp = k * (((y * ((i * y5) - (b * y4))) + (y2 * t_5)) + (z * ((b * y0) - (i * y1))));
	elseif (y0 <= 5.6e+153)
		tmp = y4 * t_1;
	else
		tmp = t_7;
	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[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(y4 * N[(N[(t$95$1 + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(y0 * N[(N[(N[(y5 * t$95$3), $MachinePrecision] + N[(c * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -5e+222], N[(c * N[(N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1.9e+104], t$95$7, If[LessEqual[y0, -7.5e+54], N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(a * t$95$2), $MachinePrecision] + N[(y4 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -5e-98], t$95$6, If[LessEqual[y0, -6e-206], N[(y * N[(y5 * N[(N[(i * k), $MachinePrecision] - N[(a * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -3.5e-254], N[(y1 * N[(y3 * N[(N[(z * a), $MachinePrecision] - N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -4.8e-290], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 3.1e-226], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * t$95$5), $MachinePrecision] + N[(z * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 2e-111], N[(y2 * N[(N[(k * t$95$5), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.12e+67], t$95$6, If[LessEqual[y0, 3.65e+84], 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[y0, 5.6e+153], N[(y4 * t$95$1), $MachinePrecision], t$95$7]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 11 regimes

2. if y0 < -5.00000000000000023e222

   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 c around inf 65.0%

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

   if -5.00000000000000023e222 < y0 < -1.89999999999999984e104 or 5.5999999999999997e153 < y0

   1. Initial program 29.3%

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

   3. Taylor expanded in y0 around inf 66.6%

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

   if -1.89999999999999984e104 < y0 < -7.50000000000000042e54

   1. Initial program 25.0%

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

   3. Taylor expanded in y1 around inf 63.4%

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

   if -7.50000000000000042e54 < y0 < -5.00000000000000018e-98 or 2.00000000000000018e-111 < y0 < 1.12e67

   1. Initial program 39.0%

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

   3. Taylor expanded in y4 around inf 59.7%

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

   if -5.00000000000000018e-98 < y0 < -6.0000000000000004e-206

   1. Initial program 41.6%

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

   3. Taylor expanded in y5 around -inf 50.2%

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

      1. associate-*r* 50.2%

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

      2. neg-mul-1 50.2%

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

      3. fma-def 50.2%

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

      4. *-commutative 50.2%

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

      5. *-commutative 50.2%

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

      6. *-commutative 50.2%

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

   5. Simplified 50.2%

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

   6. Taylor expanded in y around -inf 67.0%

      \[\leadsto \color{blue}{y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 67.0%

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

   8. Simplified 67.0%

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

   if -6.0000000000000004e-206 < y0 < -3.50000000000000007e-254

   1. Initial program 8.3%

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

   3. Taylor expanded in y1 around inf 33.9%

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

   4. Taylor expanded in y3 around inf 75.4%

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

      1. +-commutative 75.4%

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

      2. mul-1-neg 75.4%

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

      3. unsub-neg 75.4%

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

      4. *-commutative 75.4%

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

      5. *-commutative 75.4%

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

   6. Simplified 75.4%

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

   if -3.50000000000000007e-254 < y0 < -4.8000000000000001e-290

   1. Initial program 50.8%

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

   3. Simplified 50.8%

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

   5. Taylor expanded in a around inf 67.7%

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

   6. Taylor expanded in y around inf 53.1%

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

      1. *-commutative 53.1%

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

      2. *-commutative 53.1%

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

   8. Simplified 53.1%

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

   if -4.8000000000000001e-290 < y0 < 3.09999999999999989e-226

   1. Initial program 30.3%

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

   3. Taylor expanded in y3 around -inf 55.3%

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

   if 3.09999999999999989e-226 < y0 < 2.00000000000000018e-111

   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 y2 around inf 44.2%

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

   4. Taylor expanded in x around 0 50.6%

      \[\leadsto \color{blue}{y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   5. Step-by-step derivation

      1. sub-neg 50.6%

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

      2. *-commutative 50.6%

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

      3. sub-neg 50.6%

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

      4. *-commutative 50.6%

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

      5. *-commutative 50.6%

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

   6. Simplified 50.6%

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

   if 1.12e67 < y0 < 3.65e84

   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 k around inf 67.7%

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

   if 3.65e84 < y0 < 5.5999999999999997e153

   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 60.4%

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

   4. Taylor expanded in b around inf 67.4%

      \[\leadsto y4 \cdot \color{blue}{\left(b \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
3. Recombined 11 regimes into one program.

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -5 \cdot 10^{+222}:\\ \;\;\;\;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}\;y0 \leq -1.9 \cdot 10^{+104}:\\ \;\;\;\;y0 \cdot \left(\left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -7.5 \cdot 10^{+54}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) - \left(a \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y0 \leq -5 \cdot 10^{-98}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq -6 \cdot 10^{-206}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq -3.5 \cdot 10^{-254}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq -4.8 \cdot 10^{-290}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 3.1 \cdot 10^{-226}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 2 \cdot 10^{-111}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 1.12 \cdot 10^{+67}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq 3.65 \cdot 10^{+84}:\\ \;\;\;\;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}\;y0 \leq 5.6 \cdot 10^{+153}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(\left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 38.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot y4 - y0 \cdot y5\\ t_2 := b \cdot \left(t \cdot j - y \cdot k\right)\\ t_3 := y \cdot y3 - t \cdot y2\\ t_4 := x \cdot y2 - z \cdot y3\\ t_5 := y0 \cdot \left(\left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot t_4\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ t_6 := y4 \cdot \left(\left(t_2 + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot t_3\right)\\ \mathbf{if}\;y0 \leq -2 \cdot 10^{+220}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot t_4\right) + y4 \cdot t_3\right)\\ \mathbf{elif}\;y0 \leq -7.8 \cdot 10^{+54}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y0 \leq -5 \cdot 10^{-91}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y0 \leq -1.55 \cdot 10^{-206}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq -4.5 \cdot 10^{-253}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq -4.2 \cdot 10^{-290}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 2.05 \cdot 10^{-225}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(j \cdot t_1 + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 3.5 \cdot 10^{-110}:\\ \;\;\;\;y2 \cdot \left(k \cdot t_1 + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 6.5 \cdot 10^{+66}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y0 \leq 3.65 \cdot 10^{+84}:\\ \;\;\;\;k \cdot \left(\left(y \cdot \left(i \cdot y5 - b \cdot y4\right) + y2 \cdot t_1\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y0 \leq 2.2 \cdot 10^{+155}:\\ \;\;\;\;y4 \cdot t_2\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y1 y4) (* y0 y5)))
        (t_2 (* b (- (* t j) (* y k))))
        (t_3 (- (* y y3) (* t y2)))
        (t_4 (- (* x y2) (* z y3)))
        (t_5
         (*
          y0
          (+
           (+ (* y5 (- (* j y3) (* k y2))) (* c t_4))
           (* b (- (* z k) (* x j))))))
        (t_6 (* y4 (+ (+ t_2 (* y1 (- (* k y2) (* j y3)))) (* c t_3)))))
   (if (<= y0 -2e+220)
     (* c (+ (+ (* i (- (* z t) (* x y))) (* y0 t_4)) (* y4 t_3)))
     (if (<= y0 -7.8e+54)
       t_5
       (if (<= y0 -5e-91)
         t_6
         (if (<= y0 -1.55e-206)
           (* y (* y5 (- (* i k) (* a y3))))
           (if (<= y0 -4.5e-253)
             (* y1 (* y3 (- (* z a) (* j y4))))
             (if (<= y0 -4.2e-290)
               (* a (* y (- (* x b) (* y3 y5))))
               (if (<= y0 2.05e-225)
                 (*
                  y3
                  (-
                   (* y (- (* c y4) (* a y5)))
                   (+ (* j t_1) (* z (- (* c y0) (* a y1))))))
                 (if (<= y0 3.5e-110)
                   (* y2 (+ (* k t_1) (* t (- (* a y5) (* c y4)))))
                   (if (<= y0 6.5e+66)
                     t_6
                     (if (<= y0 3.65e+84)
                       (*
                        k
                        (+
                         (+ (* y (- (* i y5) (* b y4))) (* y2 t_1))
                         (* z (- (* b y0) (* i y1)))))
                       (if (<= y0 2.2e+155) (* y4 t_2) t_5)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y1 * y4) - (y0 * y5);
	double t_2 = b * ((t * j) - (y * k));
	double t_3 = (y * y3) - (t * y2);
	double t_4 = (x * y2) - (z * y3);
	double t_5 = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * t_4)) + (b * ((z * k) - (x * j))));
	double t_6 = y4 * ((t_2 + (y1 * ((k * y2) - (j * y3)))) + (c * t_3));
	double tmp;
	if (y0 <= -2e+220) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_4)) + (y4 * t_3));
	} else if (y0 <= -7.8e+54) {
		tmp = t_5;
	} else if (y0 <= -5e-91) {
		tmp = t_6;
	} else if (y0 <= -1.55e-206) {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	} else if (y0 <= -4.5e-253) {
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	} else if (y0 <= -4.2e-290) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (y0 <= 2.05e-225) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) - ((j * t_1) + (z * ((c * y0) - (a * y1)))));
	} else if (y0 <= 3.5e-110) {
		tmp = y2 * ((k * t_1) + (t * ((a * y5) - (c * y4))));
	} else if (y0 <= 6.5e+66) {
		tmp = t_6;
	} else if (y0 <= 3.65e+84) {
		tmp = k * (((y * ((i * y5) - (b * y4))) + (y2 * t_1)) + (z * ((b * y0) - (i * y1))));
	} else if (y0 <= 2.2e+155) {
		tmp = y4 * t_2;
	} else {
		tmp = t_5;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = (y1 * y4) - (y0 * y5)
    t_2 = b * ((t * j) - (y * k))
    t_3 = (y * y3) - (t * y2)
    t_4 = (x * y2) - (z * y3)
    t_5 = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * t_4)) + (b * ((z * k) - (x * j))))
    t_6 = y4 * ((t_2 + (y1 * ((k * y2) - (j * y3)))) + (c * t_3))
    if (y0 <= (-2d+220)) then
        tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_4)) + (y4 * t_3))
    else if (y0 <= (-7.8d+54)) then
        tmp = t_5
    else if (y0 <= (-5d-91)) then
        tmp = t_6
    else if (y0 <= (-1.55d-206)) then
        tmp = y * (y5 * ((i * k) - (a * y3)))
    else if (y0 <= (-4.5d-253)) then
        tmp = y1 * (y3 * ((z * a) - (j * y4)))
    else if (y0 <= (-4.2d-290)) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (y0 <= 2.05d-225) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) - ((j * t_1) + (z * ((c * y0) - (a * y1)))))
    else if (y0 <= 3.5d-110) then
        tmp = y2 * ((k * t_1) + (t * ((a * y5) - (c * y4))))
    else if (y0 <= 6.5d+66) then
        tmp = t_6
    else if (y0 <= 3.65d+84) then
        tmp = k * (((y * ((i * y5) - (b * y4))) + (y2 * t_1)) + (z * ((b * y0) - (i * y1))))
    else if (y0 <= 2.2d+155) then
        tmp = y4 * t_2
    else
        tmp = t_5
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y1 * y4) - (y0 * y5);
	double t_2 = b * ((t * j) - (y * k));
	double t_3 = (y * y3) - (t * y2);
	double t_4 = (x * y2) - (z * y3);
	double t_5 = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * t_4)) + (b * ((z * k) - (x * j))));
	double t_6 = y4 * ((t_2 + (y1 * ((k * y2) - (j * y3)))) + (c * t_3));
	double tmp;
	if (y0 <= -2e+220) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_4)) + (y4 * t_3));
	} else if (y0 <= -7.8e+54) {
		tmp = t_5;
	} else if (y0 <= -5e-91) {
		tmp = t_6;
	} else if (y0 <= -1.55e-206) {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	} else if (y0 <= -4.5e-253) {
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	} else if (y0 <= -4.2e-290) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (y0 <= 2.05e-225) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) - ((j * t_1) + (z * ((c * y0) - (a * y1)))));
	} else if (y0 <= 3.5e-110) {
		tmp = y2 * ((k * t_1) + (t * ((a * y5) - (c * y4))));
	} else if (y0 <= 6.5e+66) {
		tmp = t_6;
	} else if (y0 <= 3.65e+84) {
		tmp = k * (((y * ((i * y5) - (b * y4))) + (y2 * t_1)) + (z * ((b * y0) - (i * y1))));
	} else if (y0 <= 2.2e+155) {
		tmp = y4 * t_2;
	} else {
		tmp = t_5;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y1 * y4) - (y0 * y5)
	t_2 = b * ((t * j) - (y * k))
	t_3 = (y * y3) - (t * y2)
	t_4 = (x * y2) - (z * y3)
	t_5 = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * t_4)) + (b * ((z * k) - (x * j))))
	t_6 = y4 * ((t_2 + (y1 * ((k * y2) - (j * y3)))) + (c * t_3))
	tmp = 0
	if y0 <= -2e+220:
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_4)) + (y4 * t_3))
	elif y0 <= -7.8e+54:
		tmp = t_5
	elif y0 <= -5e-91:
		tmp = t_6
	elif y0 <= -1.55e-206:
		tmp = y * (y5 * ((i * k) - (a * y3)))
	elif y0 <= -4.5e-253:
		tmp = y1 * (y3 * ((z * a) - (j * y4)))
	elif y0 <= -4.2e-290:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif y0 <= 2.05e-225:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) - ((j * t_1) + (z * ((c * y0) - (a * y1)))))
	elif y0 <= 3.5e-110:
		tmp = y2 * ((k * t_1) + (t * ((a * y5) - (c * y4))))
	elif y0 <= 6.5e+66:
		tmp = t_6
	elif y0 <= 3.65e+84:
		tmp = k * (((y * ((i * y5) - (b * y4))) + (y2 * t_1)) + (z * ((b * y0) - (i * y1))))
	elif y0 <= 2.2e+155:
		tmp = y4 * t_2
	else:
		tmp = t_5
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_2 = Float64(b * Float64(Float64(t * j) - Float64(y * k)))
	t_3 = Float64(Float64(y * y3) - Float64(t * y2))
	t_4 = Float64(Float64(x * y2) - Float64(z * y3))
	t_5 = Float64(y0 * Float64(Float64(Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))) + Float64(c * t_4)) + Float64(b * Float64(Float64(z * k) - Float64(x * j)))))
	t_6 = Float64(y4 * Float64(Float64(t_2 + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * t_3)))
	tmp = 0.0
	if (y0 <= -2e+220)
		tmp = Float64(c * Float64(Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(y0 * t_4)) + Float64(y4 * t_3)));
	elseif (y0 <= -7.8e+54)
		tmp = t_5;
	elseif (y0 <= -5e-91)
		tmp = t_6;
	elseif (y0 <= -1.55e-206)
		tmp = Float64(y * Float64(y5 * Float64(Float64(i * k) - Float64(a * y3))));
	elseif (y0 <= -4.5e-253)
		tmp = Float64(y1 * Float64(y3 * Float64(Float64(z * a) - Float64(j * y4))));
	elseif (y0 <= -4.2e-290)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (y0 <= 2.05e-225)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) - Float64(Float64(j * t_1) + Float64(z * Float64(Float64(c * y0) - Float64(a * y1))))));
	elseif (y0 <= 3.5e-110)
		tmp = Float64(y2 * Float64(Float64(k * t_1) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y0 <= 6.5e+66)
		tmp = t_6;
	elseif (y0 <= 3.65e+84)
		tmp = Float64(k * Float64(Float64(Float64(y * Float64(Float64(i * y5) - Float64(b * y4))) + Float64(y2 * t_1)) + Float64(z * Float64(Float64(b * y0) - Float64(i * y1)))));
	elseif (y0 <= 2.2e+155)
		tmp = Float64(y4 * t_2);
	else
		tmp = t_5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y1 * y4) - (y0 * y5);
	t_2 = b * ((t * j) - (y * k));
	t_3 = (y * y3) - (t * y2);
	t_4 = (x * y2) - (z * y3);
	t_5 = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * t_4)) + (b * ((z * k) - (x * j))));
	t_6 = y4 * ((t_2 + (y1 * ((k * y2) - (j * y3)))) + (c * t_3));
	tmp = 0.0;
	if (y0 <= -2e+220)
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_4)) + (y4 * t_3));
	elseif (y0 <= -7.8e+54)
		tmp = t_5;
	elseif (y0 <= -5e-91)
		tmp = t_6;
	elseif (y0 <= -1.55e-206)
		tmp = y * (y5 * ((i * k) - (a * y3)));
	elseif (y0 <= -4.5e-253)
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	elseif (y0 <= -4.2e-290)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (y0 <= 2.05e-225)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) - ((j * t_1) + (z * ((c * y0) - (a * y1)))));
	elseif (y0 <= 3.5e-110)
		tmp = y2 * ((k * t_1) + (t * ((a * y5) - (c * y4))));
	elseif (y0 <= 6.5e+66)
		tmp = t_6;
	elseif (y0 <= 3.65e+84)
		tmp = k * (((y * ((i * y5) - (b * y4))) + (y2 * t_1)) + (z * ((b * y0) - (i * y1))));
	elseif (y0 <= 2.2e+155)
		tmp = y4 * t_2;
	else
		tmp = t_5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y0 * N[(N[(N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$4), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(y4 * N[(N[(t$95$2 + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -2e+220], N[(c * N[(N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$4), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -7.8e+54], t$95$5, If[LessEqual[y0, -5e-91], t$95$6, If[LessEqual[y0, -1.55e-206], N[(y * N[(y5 * N[(N[(i * k), $MachinePrecision] - N[(a * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -4.5e-253], N[(y1 * N[(y3 * N[(N[(z * a), $MachinePrecision] - N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -4.2e-290], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 2.05e-225], 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[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 3.5e-110], N[(y2 * N[(N[(k * t$95$1), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 6.5e+66], t$95$6, If[LessEqual[y0, 3.65e+84], N[(k * N[(N[(N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 2.2e+155], N[(y4 * t$95$2), $MachinePrecision], t$95$5]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if y0 < -2e220

   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 c around inf 65.0%

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

   if -2e220 < y0 < -7.8000000000000005e54 or 2.2000000000000002e155 < y0

   1. Initial program 28.1%

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

   3. Taylor expanded in y0 around inf 57.1%

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

   if -7.8000000000000005e54 < y0 < -4.99999999999999997e-91 or 3.49999999999999974e-110 < y0 < 6.5000000000000001e66

   1. Initial program 39.0%

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

   3. Taylor expanded in y4 around inf 59.7%

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

   if -4.99999999999999997e-91 < y0 < -1.5500000000000001e-206

   1. Initial program 41.6%

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

   3. Taylor expanded in y5 around -inf 50.2%

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

      1. associate-*r* 50.2%

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

      2. neg-mul-1 50.2%

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

      3. fma-def 50.2%

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

      4. *-commutative 50.2%

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

      5. *-commutative 50.2%

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

      6. *-commutative 50.2%

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

   5. Simplified 50.2%

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

   6. Taylor expanded in y around -inf 67.0%

      \[\leadsto \color{blue}{y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 67.0%

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

   8. Simplified 67.0%

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

   if -1.5500000000000001e-206 < y0 < -4.50000000000000029e-253

   1. Initial program 8.3%

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

   3. Taylor expanded in y1 around inf 33.9%

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

   4. Taylor expanded in y3 around inf 75.4%

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

      1. +-commutative 75.4%

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

      2. mul-1-neg 75.4%

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

      3. unsub-neg 75.4%

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

      4. *-commutative 75.4%

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

      5. *-commutative 75.4%

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

   6. Simplified 75.4%

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

   if -4.50000000000000029e-253 < y0 < -4.2000000000000002e-290

   1. Initial program 50.8%

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

   3. Simplified 50.8%

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

   5. Taylor expanded in a around inf 67.7%

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

   6. Taylor expanded in y around inf 53.1%

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

      1. *-commutative 53.1%

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

      2. *-commutative 53.1%

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

   8. Simplified 53.1%

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

   if -4.2000000000000002e-290 < y0 < 2.05000000000000011e-225

   1. Initial program 30.3%

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

   3. Taylor expanded in y3 around -inf 55.3%

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

   if 2.05000000000000011e-225 < y0 < 3.49999999999999974e-110

   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 y2 around inf 44.2%

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

   4. Taylor expanded in x around 0 50.6%

      \[\leadsto \color{blue}{y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   5. Step-by-step derivation

      1. sub-neg 50.6%

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

      2. *-commutative 50.6%

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

      3. sub-neg 50.6%

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

      4. *-commutative 50.6%

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

      5. *-commutative 50.6%

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

   6. Simplified 50.6%

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

   if 6.5000000000000001e66 < y0 < 3.65e84

   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 k around inf 67.7%

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

   if 3.65e84 < y0 < 2.2000000000000002e155

   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 60.4%

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

   4. Taylor expanded in b around inf 67.4%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -2 \cdot 10^{+220}:\\ \;\;\;\;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}\;y0 \leq -7.8 \cdot 10^{+54}:\\ \;\;\;\;y0 \cdot \left(\left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -5 \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}\;y0 \leq -1.55 \cdot 10^{-206}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq -4.5 \cdot 10^{-253}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq -4.2 \cdot 10^{-290}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 2.05 \cdot 10^{-225}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 3.5 \cdot 10^{-110}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 6.5 \cdot 10^{+66}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq 3.65 \cdot 10^{+84}:\\ \;\;\;\;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}\;y0 \leq 2.2 \cdot 10^{+155}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(\left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 39.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot y4 - y0 \cdot y5\\ t_2 := y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ t_3 := x \cdot y2 - z \cdot y3\\ t_4 := y0 \cdot \left(\left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot t_3\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ t_5 := a \cdot y5 - c \cdot y4\\ \mathbf{if}\;y0 \leq -6.2 \cdot 10^{+223}:\\ \;\;\;\;c \cdot \left(y0 \cdot t_3\right)\\ \mathbf{elif}\;y0 \leq -4 \cdot 10^{+80}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y0 \leq -8 \cdot 10^{+23}:\\ \;\;\;\;t \cdot \left(y2 \cdot t_5\right)\\ \mathbf{elif}\;y0 \leq -9.8 \cdot 10^{-89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y0 \leq -4.1 \cdot 10^{-206}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq -1.65 \cdot 10^{-254}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq -9.8 \cdot 10^{-284}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 8.3 \cdot 10^{-221}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(j \cdot t_1 + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 2.15 \cdot 10^{-110}:\\ \;\;\;\;y2 \cdot \left(k \cdot t_1 + t \cdot t_5\right)\\ \mathbf{elif}\;y0 \leq 8 \cdot 10^{+156}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y1 y4) (* y0 y5)))
        (t_2
         (*
          y4
          (+
           (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
           (* c (- (* y y3) (* t y2))))))
        (t_3 (- (* x y2) (* z y3)))
        (t_4
         (*
          y0
          (+
           (+ (* y5 (- (* j y3) (* k y2))) (* c t_3))
           (* b (- (* z k) (* x j))))))
        (t_5 (- (* a y5) (* c y4))))
   (if (<= y0 -6.2e+223)
     (* c (* y0 t_3))
     (if (<= y0 -4e+80)
       t_4
       (if (<= y0 -8e+23)
         (* t (* y2 t_5))
         (if (<= y0 -9.8e-89)
           t_2
           (if (<= y0 -4.1e-206)
             (* y (* y5 (- (* i k) (* a y3))))
             (if (<= y0 -1.65e-254)
               (* y1 (* y3 (- (* z a) (* j y4))))
               (if (<= y0 -9.8e-284)
                 (* a (* y (- (* x b) (* y3 y5))))
                 (if (<= y0 8.3e-221)
                   (*
                    y3
                    (-
                     (* y (- (* c y4) (* a y5)))
                     (+ (* j t_1) (* z (- (* c y0) (* a y1))))))
                   (if (<= y0 2.15e-110)
                     (* y2 (+ (* k t_1) (* t t_5)))
                     (if (<= y0 8e+156) 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 = (y1 * y4) - (y0 * y5);
	double t_2 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double t_3 = (x * y2) - (z * y3);
	double t_4 = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * t_3)) + (b * ((z * k) - (x * j))));
	double t_5 = (a * y5) - (c * y4);
	double tmp;
	if (y0 <= -6.2e+223) {
		tmp = c * (y0 * t_3);
	} else if (y0 <= -4e+80) {
		tmp = t_4;
	} else if (y0 <= -8e+23) {
		tmp = t * (y2 * t_5);
	} else if (y0 <= -9.8e-89) {
		tmp = t_2;
	} else if (y0 <= -4.1e-206) {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	} else if (y0 <= -1.65e-254) {
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	} else if (y0 <= -9.8e-284) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (y0 <= 8.3e-221) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) - ((j * t_1) + (z * ((c * y0) - (a * y1)))));
	} else if (y0 <= 2.15e-110) {
		tmp = y2 * ((k * t_1) + (t * t_5));
	} else if (y0 <= 8e+156) {
		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) :: tmp
    t_1 = (y1 * y4) - (y0 * y5)
    t_2 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    t_3 = (x * y2) - (z * y3)
    t_4 = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * t_3)) + (b * ((z * k) - (x * j))))
    t_5 = (a * y5) - (c * y4)
    if (y0 <= (-6.2d+223)) then
        tmp = c * (y0 * t_3)
    else if (y0 <= (-4d+80)) then
        tmp = t_4
    else if (y0 <= (-8d+23)) then
        tmp = t * (y2 * t_5)
    else if (y0 <= (-9.8d-89)) then
        tmp = t_2
    else if (y0 <= (-4.1d-206)) then
        tmp = y * (y5 * ((i * k) - (a * y3)))
    else if (y0 <= (-1.65d-254)) then
        tmp = y1 * (y3 * ((z * a) - (j * y4)))
    else if (y0 <= (-9.8d-284)) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (y0 <= 8.3d-221) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) - ((j * t_1) + (z * ((c * y0) - (a * y1)))))
    else if (y0 <= 2.15d-110) then
        tmp = y2 * ((k * t_1) + (t * t_5))
    else if (y0 <= 8d+156) 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 = (y1 * y4) - (y0 * y5);
	double t_2 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double t_3 = (x * y2) - (z * y3);
	double t_4 = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * t_3)) + (b * ((z * k) - (x * j))));
	double t_5 = (a * y5) - (c * y4);
	double tmp;
	if (y0 <= -6.2e+223) {
		tmp = c * (y0 * t_3);
	} else if (y0 <= -4e+80) {
		tmp = t_4;
	} else if (y0 <= -8e+23) {
		tmp = t * (y2 * t_5);
	} else if (y0 <= -9.8e-89) {
		tmp = t_2;
	} else if (y0 <= -4.1e-206) {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	} else if (y0 <= -1.65e-254) {
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	} else if (y0 <= -9.8e-284) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (y0 <= 8.3e-221) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) - ((j * t_1) + (z * ((c * y0) - (a * y1)))));
	} else if (y0 <= 2.15e-110) {
		tmp = y2 * ((k * t_1) + (t * t_5));
	} else if (y0 <= 8e+156) {
		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 = (y1 * y4) - (y0 * y5)
	t_2 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	t_3 = (x * y2) - (z * y3)
	t_4 = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * t_3)) + (b * ((z * k) - (x * j))))
	t_5 = (a * y5) - (c * y4)
	tmp = 0
	if y0 <= -6.2e+223:
		tmp = c * (y0 * t_3)
	elif y0 <= -4e+80:
		tmp = t_4
	elif y0 <= -8e+23:
		tmp = t * (y2 * t_5)
	elif y0 <= -9.8e-89:
		tmp = t_2
	elif y0 <= -4.1e-206:
		tmp = y * (y5 * ((i * k) - (a * y3)))
	elif y0 <= -1.65e-254:
		tmp = y1 * (y3 * ((z * a) - (j * y4)))
	elif y0 <= -9.8e-284:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif y0 <= 8.3e-221:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) - ((j * t_1) + (z * ((c * y0) - (a * y1)))))
	elif y0 <= 2.15e-110:
		tmp = y2 * ((k * t_1) + (t * t_5))
	elif y0 <= 8e+156:
		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(y1 * y4) - Float64(y0 * y5))
	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)))))
	t_3 = Float64(Float64(x * y2) - Float64(z * y3))
	t_4 = Float64(y0 * Float64(Float64(Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))) + Float64(c * t_3)) + Float64(b * Float64(Float64(z * k) - Float64(x * j)))))
	t_5 = Float64(Float64(a * y5) - Float64(c * y4))
	tmp = 0.0
	if (y0 <= -6.2e+223)
		tmp = Float64(c * Float64(y0 * t_3));
	elseif (y0 <= -4e+80)
		tmp = t_4;
	elseif (y0 <= -8e+23)
		tmp = Float64(t * Float64(y2 * t_5));
	elseif (y0 <= -9.8e-89)
		tmp = t_2;
	elseif (y0 <= -4.1e-206)
		tmp = Float64(y * Float64(y5 * Float64(Float64(i * k) - Float64(a * y3))));
	elseif (y0 <= -1.65e-254)
		tmp = Float64(y1 * Float64(y3 * Float64(Float64(z * a) - Float64(j * y4))));
	elseif (y0 <= -9.8e-284)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (y0 <= 8.3e-221)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) - Float64(Float64(j * t_1) + Float64(z * Float64(Float64(c * y0) - Float64(a * y1))))));
	elseif (y0 <= 2.15e-110)
		tmp = Float64(y2 * Float64(Float64(k * t_1) + Float64(t * t_5)));
	elseif (y0 <= 8e+156)
		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 = (y1 * y4) - (y0 * y5);
	t_2 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	t_3 = (x * y2) - (z * y3);
	t_4 = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * t_3)) + (b * ((z * k) - (x * j))));
	t_5 = (a * y5) - (c * y4);
	tmp = 0.0;
	if (y0 <= -6.2e+223)
		tmp = c * (y0 * t_3);
	elseif (y0 <= -4e+80)
		tmp = t_4;
	elseif (y0 <= -8e+23)
		tmp = t * (y2 * t_5);
	elseif (y0 <= -9.8e-89)
		tmp = t_2;
	elseif (y0 <= -4.1e-206)
		tmp = y * (y5 * ((i * k) - (a * y3)));
	elseif (y0 <= -1.65e-254)
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	elseif (y0 <= -9.8e-284)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (y0 <= 8.3e-221)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) - ((j * t_1) + (z * ((c * y0) - (a * y1)))));
	elseif (y0 <= 2.15e-110)
		tmp = y2 * ((k * t_1) + (t * t_5));
	elseif (y0 <= 8e+156)
		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[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $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]}, Block[{t$95$3 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y0 * N[(N[(N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -6.2e+223], N[(c * N[(y0 * t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -4e+80], t$95$4, If[LessEqual[y0, -8e+23], N[(t * N[(y2 * t$95$5), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -9.8e-89], t$95$2, If[LessEqual[y0, -4.1e-206], N[(y * N[(y5 * N[(N[(i * k), $MachinePrecision] - N[(a * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1.65e-254], N[(y1 * N[(y3 * N[(N[(z * a), $MachinePrecision] - N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -9.8e-284], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 8.3e-221], 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[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 2.15e-110], N[(y2 * N[(N[(k * t$95$1), $MachinePrecision] + N[(t * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 8e+156], t$95$2, t$95$4]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y0 < -6.19999999999999965e223

   1. Initial program 15.8%

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

   3. Simplified 15.8%

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

   5. Taylor expanded in c around inf 63.2%

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

   6. Taylor expanded in y0 around inf 58.1%

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

   if -6.19999999999999965e223 < y0 < -4e80 or 7.9999999999999999e156 < y0

   1. Initial program 30.6%

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

   3. Taylor expanded in y0 around inf 62.0%

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

   if -4e80 < y0 < -7.9999999999999993e23

   1. Initial program 23.5%

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

   3. Taylor expanded in y2 around inf 47.1%

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

   4. Taylor expanded in t around inf 59.0%

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

      1. *-commutative 59.0%

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

      2. *-commutative 59.0%

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

   6. Simplified 59.0%

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

   if -7.9999999999999993e23 < y0 < -9.8e-89 or 2.15000000000000012e-110 < y0 < 7.9999999999999999e156

   1. Initial program 36.1%

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

   3. Taylor expanded in y4 around inf 56.0%

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

   if -9.8e-89 < y0 < -4.10000000000000016e-206

   1. Initial program 41.6%

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

   3. Taylor expanded in y5 around -inf 50.2%

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

      1. associate-*r* 50.2%

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

      2. neg-mul-1 50.2%

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

      3. fma-def 50.2%

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

      4. *-commutative 50.2%

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

      5. *-commutative 50.2%

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

      6. *-commutative 50.2%

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

   5. Simplified 50.2%

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

   6. Taylor expanded in y around -inf 67.0%

      \[\leadsto \color{blue}{y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 67.0%

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

   8. Simplified 67.0%

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

   if -4.10000000000000016e-206 < y0 < -1.65000000000000008e-254

   1. Initial program 8.3%

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

   3. Taylor expanded in y1 around inf 33.9%

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

   4. Taylor expanded in y3 around inf 75.4%

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

      1. +-commutative 75.4%

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

      2. mul-1-neg 75.4%

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

      3. unsub-neg 75.4%

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

      4. *-commutative 75.4%

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

      5. *-commutative 75.4%

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

   6. Simplified 75.4%

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

   if -1.65000000000000008e-254 < y0 < -9.79999999999999979e-284

   1. Initial program 50.8%

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

   3. Simplified 50.8%

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

   5. Taylor expanded in a around inf 67.7%

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

   6. Taylor expanded in y around inf 53.1%

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

      1. *-commutative 53.1%

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

      2. *-commutative 53.1%

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

   8. Simplified 53.1%

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

   if -9.79999999999999979e-284 < y0 < 8.30000000000000035e-221

   1. Initial program 30.3%

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

   3. Taylor expanded in y3 around -inf 55.3%

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

   if 8.30000000000000035e-221 < y0 < 2.15000000000000012e-110

   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 y2 around inf 44.2%

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

   4. Taylor expanded in x around 0 50.6%

      \[\leadsto \color{blue}{y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   5. Step-by-step derivation

      1. sub-neg 50.6%

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

      2. *-commutative 50.6%

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

      3. sub-neg 50.6%

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

      4. *-commutative 50.6%

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

      5. *-commutative 50.6%

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

   6. Simplified 50.6%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -6.2 \cdot 10^{+223}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq -4 \cdot 10^{+80}:\\ \;\;\;\;y0 \cdot \left(\left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -8 \cdot 10^{+23}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq -9.8 \cdot 10^{-89}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq -4.1 \cdot 10^{-206}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq -1.65 \cdot 10^{-254}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq -9.8 \cdot 10^{-284}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 8.3 \cdot 10^{-221}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 2.15 \cdot 10^{-110}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 8 \cdot 10^{+156}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(\left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 39.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot y4 - y0 \cdot y5\\ t_2 := y \cdot y3 - t \cdot y2\\ t_3 := x \cdot y2 - z \cdot y3\\ t_4 := y0 \cdot \left(\left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot t_3\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ t_5 := y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot t_2\right)\\ \mathbf{if}\;y0 \leq -3.6 \cdot 10^{+222}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot t_3\right) + y4 \cdot t_2\right)\\ \mathbf{elif}\;y0 \leq -8 \cdot 10^{+54}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y0 \leq -7.4 \cdot 10^{-94}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y0 \leq -9.2 \cdot 10^{-206}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq -9.2 \cdot 10^{-254}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq -1.5 \cdot 10^{-283}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 2.7 \cdot 10^{-221}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(j \cdot t_1 + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 5.4 \cdot 10^{-111}:\\ \;\;\;\;y2 \cdot \left(k \cdot t_1 + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 7.8 \cdot 10^{+156}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y1 y4) (* y0 y5)))
        (t_2 (- (* y y3) (* t y2)))
        (t_3 (- (* x y2) (* z y3)))
        (t_4
         (*
          y0
          (+
           (+ (* y5 (- (* j y3) (* k y2))) (* c t_3))
           (* b (- (* z k) (* x j))))))
        (t_5
         (*
          y4
          (+
           (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
           (* c t_2)))))
   (if (<= y0 -3.6e+222)
     (* c (+ (+ (* i (- (* z t) (* x y))) (* y0 t_3)) (* y4 t_2)))
     (if (<= y0 -8e+54)
       t_4
       (if (<= y0 -7.4e-94)
         t_5
         (if (<= y0 -9.2e-206)
           (* y (* y5 (- (* i k) (* a y3))))
           (if (<= y0 -9.2e-254)
             (* y1 (* y3 (- (* z a) (* j y4))))
             (if (<= y0 -1.5e-283)
               (* a (* y (- (* x b) (* y3 y5))))
               (if (<= y0 2.7e-221)
                 (*
                  y3
                  (-
                   (* y (- (* c y4) (* a y5)))
                   (+ (* j t_1) (* z (- (* c y0) (* a y1))))))
                 (if (<= y0 5.4e-111)
                   (* y2 (+ (* k t_1) (* t (- (* a y5) (* c y4)))))
                   (if (<= y0 7.8e+156) t_5 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 = (y1 * y4) - (y0 * y5);
	double t_2 = (y * y3) - (t * y2);
	double t_3 = (x * y2) - (z * y3);
	double t_4 = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * t_3)) + (b * ((z * k) - (x * j))));
	double t_5 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_2));
	double tmp;
	if (y0 <= -3.6e+222) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_3)) + (y4 * t_2));
	} else if (y0 <= -8e+54) {
		tmp = t_4;
	} else if (y0 <= -7.4e-94) {
		tmp = t_5;
	} else if (y0 <= -9.2e-206) {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	} else if (y0 <= -9.2e-254) {
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	} else if (y0 <= -1.5e-283) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (y0 <= 2.7e-221) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) - ((j * t_1) + (z * ((c * y0) - (a * y1)))));
	} else if (y0 <= 5.4e-111) {
		tmp = y2 * ((k * t_1) + (t * ((a * y5) - (c * y4))));
	} else if (y0 <= 7.8e+156) {
		tmp = t_5;
	} 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 = (y1 * y4) - (y0 * y5)
    t_2 = (y * y3) - (t * y2)
    t_3 = (x * y2) - (z * y3)
    t_4 = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * t_3)) + (b * ((z * k) - (x * j))))
    t_5 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_2))
    if (y0 <= (-3.6d+222)) then
        tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_3)) + (y4 * t_2))
    else if (y0 <= (-8d+54)) then
        tmp = t_4
    else if (y0 <= (-7.4d-94)) then
        tmp = t_5
    else if (y0 <= (-9.2d-206)) then
        tmp = y * (y5 * ((i * k) - (a * y3)))
    else if (y0 <= (-9.2d-254)) then
        tmp = y1 * (y3 * ((z * a) - (j * y4)))
    else if (y0 <= (-1.5d-283)) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (y0 <= 2.7d-221) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) - ((j * t_1) + (z * ((c * y0) - (a * y1)))))
    else if (y0 <= 5.4d-111) then
        tmp = y2 * ((k * t_1) + (t * ((a * y5) - (c * y4))))
    else if (y0 <= 7.8d+156) then
        tmp = t_5
    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 = (y1 * y4) - (y0 * y5);
	double t_2 = (y * y3) - (t * y2);
	double t_3 = (x * y2) - (z * y3);
	double t_4 = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * t_3)) + (b * ((z * k) - (x * j))));
	double t_5 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_2));
	double tmp;
	if (y0 <= -3.6e+222) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_3)) + (y4 * t_2));
	} else if (y0 <= -8e+54) {
		tmp = t_4;
	} else if (y0 <= -7.4e-94) {
		tmp = t_5;
	} else if (y0 <= -9.2e-206) {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	} else if (y0 <= -9.2e-254) {
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	} else if (y0 <= -1.5e-283) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (y0 <= 2.7e-221) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) - ((j * t_1) + (z * ((c * y0) - (a * y1)))));
	} else if (y0 <= 5.4e-111) {
		tmp = y2 * ((k * t_1) + (t * ((a * y5) - (c * y4))));
	} else if (y0 <= 7.8e+156) {
		tmp = t_5;
	} 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 = (y1 * y4) - (y0 * y5)
	t_2 = (y * y3) - (t * y2)
	t_3 = (x * y2) - (z * y3)
	t_4 = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * t_3)) + (b * ((z * k) - (x * j))))
	t_5 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_2))
	tmp = 0
	if y0 <= -3.6e+222:
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_3)) + (y4 * t_2))
	elif y0 <= -8e+54:
		tmp = t_4
	elif y0 <= -7.4e-94:
		tmp = t_5
	elif y0 <= -9.2e-206:
		tmp = y * (y5 * ((i * k) - (a * y3)))
	elif y0 <= -9.2e-254:
		tmp = y1 * (y3 * ((z * a) - (j * y4)))
	elif y0 <= -1.5e-283:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif y0 <= 2.7e-221:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) - ((j * t_1) + (z * ((c * y0) - (a * y1)))))
	elif y0 <= 5.4e-111:
		tmp = y2 * ((k * t_1) + (t * ((a * y5) - (c * y4))))
	elif y0 <= 7.8e+156:
		tmp = t_5
	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(y1 * y4) - Float64(y0 * y5))
	t_2 = Float64(Float64(y * y3) - Float64(t * y2))
	t_3 = Float64(Float64(x * y2) - Float64(z * y3))
	t_4 = Float64(y0 * Float64(Float64(Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))) + Float64(c * t_3)) + Float64(b * Float64(Float64(z * k) - Float64(x * j)))))
	t_5 = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * t_2)))
	tmp = 0.0
	if (y0 <= -3.6e+222)
		tmp = Float64(c * Float64(Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(y0 * t_3)) + Float64(y4 * t_2)));
	elseif (y0 <= -8e+54)
		tmp = t_4;
	elseif (y0 <= -7.4e-94)
		tmp = t_5;
	elseif (y0 <= -9.2e-206)
		tmp = Float64(y * Float64(y5 * Float64(Float64(i * k) - Float64(a * y3))));
	elseif (y0 <= -9.2e-254)
		tmp = Float64(y1 * Float64(y3 * Float64(Float64(z * a) - Float64(j * y4))));
	elseif (y0 <= -1.5e-283)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (y0 <= 2.7e-221)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) - Float64(Float64(j * t_1) + Float64(z * Float64(Float64(c * y0) - Float64(a * y1))))));
	elseif (y0 <= 5.4e-111)
		tmp = Float64(y2 * Float64(Float64(k * t_1) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y0 <= 7.8e+156)
		tmp = t_5;
	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 = (y1 * y4) - (y0 * y5);
	t_2 = (y * y3) - (t * y2);
	t_3 = (x * y2) - (z * y3);
	t_4 = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * t_3)) + (b * ((z * k) - (x * j))));
	t_5 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_2));
	tmp = 0.0;
	if (y0 <= -3.6e+222)
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_3)) + (y4 * t_2));
	elseif (y0 <= -8e+54)
		tmp = t_4;
	elseif (y0 <= -7.4e-94)
		tmp = t_5;
	elseif (y0 <= -9.2e-206)
		tmp = y * (y5 * ((i * k) - (a * y3)));
	elseif (y0 <= -9.2e-254)
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	elseif (y0 <= -1.5e-283)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (y0 <= 2.7e-221)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) - ((j * t_1) + (z * ((c * y0) - (a * y1)))));
	elseif (y0 <= 5.4e-111)
		tmp = y2 * ((k * t_1) + (t * ((a * y5) - (c * y4))));
	elseif (y0 <= 7.8e+156)
		tmp = t_5;
	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[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y0 * N[(N[(N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = 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 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -3.6e+222], N[(c * N[(N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -8e+54], t$95$4, If[LessEqual[y0, -7.4e-94], t$95$5, If[LessEqual[y0, -9.2e-206], N[(y * N[(y5 * N[(N[(i * k), $MachinePrecision] - N[(a * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -9.2e-254], N[(y1 * N[(y3 * N[(N[(z * a), $MachinePrecision] - N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1.5e-283], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 2.7e-221], 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[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 5.4e-111], N[(y2 * N[(N[(k * t$95$1), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 7.8e+156], t$95$5, t$95$4]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y0 < -3.6000000000000002e222

   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 c around inf 65.0%

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

   if -3.6000000000000002e222 < y0 < -8.0000000000000006e54 or 7.7999999999999994e156 < y0

   1. Initial program 28.1%

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

   3. Taylor expanded in y0 around inf 57.1%

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

   if -8.0000000000000006e54 < y0 < -7.3999999999999996e-94 or 5.39999999999999977e-111 < y0 < 7.7999999999999994e156

   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 y4 around inf 56.7%

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

   if -7.3999999999999996e-94 < y0 < -9.2e-206

   1. Initial program 41.6%

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

   3. Taylor expanded in y5 around -inf 50.2%

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

      1. associate-*r* 50.2%

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

      2. neg-mul-1 50.2%

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

      3. fma-def 50.2%

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

      4. *-commutative 50.2%

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

      5. *-commutative 50.2%

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

      6. *-commutative 50.2%

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

   5. Simplified 50.2%

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

   6. Taylor expanded in y around -inf 67.0%

      \[\leadsto \color{blue}{y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 67.0%

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

   8. Simplified 67.0%

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

   if -9.2e-206 < y0 < -9.1999999999999995e-254

   1. Initial program 8.3%

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

   3. Taylor expanded in y1 around inf 33.9%

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

   4. Taylor expanded in y3 around inf 75.4%

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

      1. +-commutative 75.4%

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

      2. mul-1-neg 75.4%

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

      3. unsub-neg 75.4%

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

      4. *-commutative 75.4%

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

      5. *-commutative 75.4%

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

   6. Simplified 75.4%

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

   if -9.1999999999999995e-254 < y0 < -1.49999999999999998e-283

   1. Initial program 50.8%

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

   3. Simplified 50.8%

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

   5. Taylor expanded in a around inf 67.7%

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

   6. Taylor expanded in y around inf 53.1%

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

      1. *-commutative 53.1%

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

      2. *-commutative 53.1%

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

   8. Simplified 53.1%

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

   if -1.49999999999999998e-283 < y0 < 2.7e-221

   1. Initial program 30.3%

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

   3. Taylor expanded in y3 around -inf 55.3%

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

   if 2.7e-221 < y0 < 5.39999999999999977e-111

   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 y2 around inf 44.2%

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

   4. Taylor expanded in x around 0 50.6%

      \[\leadsto \color{blue}{y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   5. Step-by-step derivation

      1. sub-neg 50.6%

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

      2. *-commutative 50.6%

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

      3. sub-neg 50.6%

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

      4. *-commutative 50.6%

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

      5. *-commutative 50.6%

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

   6. Simplified 50.6%

      \[\leadsto \color{blue}{y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y5 \cdot y0\right) - t \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -3.6 \cdot 10^{+222}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq -8 \cdot 10^{+54}:\\ \;\;\;\;y0 \cdot \left(\left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -7.4 \cdot 10^{-94}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq -9.2 \cdot 10^{-206}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq -9.2 \cdot 10^{-254}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq -1.5 \cdot 10^{-283}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 2.7 \cdot 10^{-221}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 5.4 \cdot 10^{-111}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 7.8 \cdot 10^{+156}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(\left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 28.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ t_2 := c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;a \leq -3.4 \cdot 10^{+123}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3 \cdot 10^{+45}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-99}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(z \cdot t - x \cdot y\right)\\ \mathbf{elif}\;a \leq -3.3 \cdot 10^{-139}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-163}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-191}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-278}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-156}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{+22}:\\ \;\;\;\;\left(j \cdot y5\right) \cdot \left(y0 \cdot y3 - t \cdot i\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+151}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* z (- (* y1 y3) (* t b)))))
        (t_2 (* c (* y4 (- (* y y3) (* t y2))))))
   (if (<= a -3.4e+123)
     t_1
     (if (<= a -3e+45)
       (* y4 (* y1 (- (* k y2) (* j y3))))
       (if (<= a -1.4e-46)
         t_1
         (if (<= a -3.1e-99)
           (* (* c i) (- (* z t) (* x y)))
           (if (<= a -3.3e-139)
             (* k (* y2 (- (* y1 y4) (* y0 y5))))
             (if (<= a -3.7e-163)
               (* c (* y4 (* y y3)))
               (if (<= a -1e-191)
                 (* y1 (* i (- (* x j) (* z k))))
                 (if (<= a -5.2e-278)
                   t_2
                   (if (<= a 2.7e-156)
                     (* j (* y3 (* y0 y5)))
                     (if (<= a 3.9e-51)
                       t_2
                       (if (<= a 2.35e+22)
                         (* (* j y5) (- (* y0 y3) (* t i)))
                         (if (<= a 8e+151)
                           (* t (* y2 (- (* a y5) (* c y4))))
                           (* y1 (* y3 (- (* z a) (* j 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 * (z * ((y1 * y3) - (t * b)));
	double t_2 = c * (y4 * ((y * y3) - (t * y2)));
	double tmp;
	if (a <= -3.4e+123) {
		tmp = t_1;
	} else if (a <= -3e+45) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (a <= -1.4e-46) {
		tmp = t_1;
	} else if (a <= -3.1e-99) {
		tmp = (c * i) * ((z * t) - (x * y));
	} else if (a <= -3.3e-139) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (a <= -3.7e-163) {
		tmp = c * (y4 * (y * y3));
	} else if (a <= -1e-191) {
		tmp = y1 * (i * ((x * j) - (z * k)));
	} else if (a <= -5.2e-278) {
		tmp = t_2;
	} else if (a <= 2.7e-156) {
		tmp = j * (y3 * (y0 * y5));
	} else if (a <= 3.9e-51) {
		tmp = t_2;
	} else if (a <= 2.35e+22) {
		tmp = (j * y5) * ((y0 * y3) - (t * i));
	} else if (a <= 8e+151) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else {
		tmp = y1 * (y3 * ((z * a) - (j * 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) :: t_2
    real(8) :: tmp
    t_1 = a * (z * ((y1 * y3) - (t * b)))
    t_2 = c * (y4 * ((y * y3) - (t * y2)))
    if (a <= (-3.4d+123)) then
        tmp = t_1
    else if (a <= (-3d+45)) then
        tmp = y4 * (y1 * ((k * y2) - (j * y3)))
    else if (a <= (-1.4d-46)) then
        tmp = t_1
    else if (a <= (-3.1d-99)) then
        tmp = (c * i) * ((z * t) - (x * y))
    else if (a <= (-3.3d-139)) then
        tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
    else if (a <= (-3.7d-163)) then
        tmp = c * (y4 * (y * y3))
    else if (a <= (-1d-191)) then
        tmp = y1 * (i * ((x * j) - (z * k)))
    else if (a <= (-5.2d-278)) then
        tmp = t_2
    else if (a <= 2.7d-156) then
        tmp = j * (y3 * (y0 * y5))
    else if (a <= 3.9d-51) then
        tmp = t_2
    else if (a <= 2.35d+22) then
        tmp = (j * y5) * ((y0 * y3) - (t * i))
    else if (a <= 8d+151) then
        tmp = t * (y2 * ((a * y5) - (c * y4)))
    else
        tmp = y1 * (y3 * ((z * a) - (j * 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 * (z * ((y1 * y3) - (t * b)));
	double t_2 = c * (y4 * ((y * y3) - (t * y2)));
	double tmp;
	if (a <= -3.4e+123) {
		tmp = t_1;
	} else if (a <= -3e+45) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (a <= -1.4e-46) {
		tmp = t_1;
	} else if (a <= -3.1e-99) {
		tmp = (c * i) * ((z * t) - (x * y));
	} else if (a <= -3.3e-139) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (a <= -3.7e-163) {
		tmp = c * (y4 * (y * y3));
	} else if (a <= -1e-191) {
		tmp = y1 * (i * ((x * j) - (z * k)));
	} else if (a <= -5.2e-278) {
		tmp = t_2;
	} else if (a <= 2.7e-156) {
		tmp = j * (y3 * (y0 * y5));
	} else if (a <= 3.9e-51) {
		tmp = t_2;
	} else if (a <= 2.35e+22) {
		tmp = (j * y5) * ((y0 * y3) - (t * i));
	} else if (a <= 8e+151) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else {
		tmp = y1 * (y3 * ((z * a) - (j * 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 * (z * ((y1 * y3) - (t * b)))
	t_2 = c * (y4 * ((y * y3) - (t * y2)))
	tmp = 0
	if a <= -3.4e+123:
		tmp = t_1
	elif a <= -3e+45:
		tmp = y4 * (y1 * ((k * y2) - (j * y3)))
	elif a <= -1.4e-46:
		tmp = t_1
	elif a <= -3.1e-99:
		tmp = (c * i) * ((z * t) - (x * y))
	elif a <= -3.3e-139:
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
	elif a <= -3.7e-163:
		tmp = c * (y4 * (y * y3))
	elif a <= -1e-191:
		tmp = y1 * (i * ((x * j) - (z * k)))
	elif a <= -5.2e-278:
		tmp = t_2
	elif a <= 2.7e-156:
		tmp = j * (y3 * (y0 * y5))
	elif a <= 3.9e-51:
		tmp = t_2
	elif a <= 2.35e+22:
		tmp = (j * y5) * ((y0 * y3) - (t * i))
	elif a <= 8e+151:
		tmp = t * (y2 * ((a * y5) - (c * y4)))
	else:
		tmp = y1 * (y3 * ((z * a) - (j * 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(z * Float64(Float64(y1 * y3) - Float64(t * b))))
	t_2 = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))))
	tmp = 0.0
	if (a <= -3.4e+123)
		tmp = t_1;
	elseif (a <= -3e+45)
		tmp = Float64(y4 * Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif (a <= -1.4e-46)
		tmp = t_1;
	elseif (a <= -3.1e-99)
		tmp = Float64(Float64(c * i) * Float64(Float64(z * t) - Float64(x * y)));
	elseif (a <= -3.3e-139)
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	elseif (a <= -3.7e-163)
		tmp = Float64(c * Float64(y4 * Float64(y * y3)));
	elseif (a <= -1e-191)
		tmp = Float64(y1 * Float64(i * Float64(Float64(x * j) - Float64(z * k))));
	elseif (a <= -5.2e-278)
		tmp = t_2;
	elseif (a <= 2.7e-156)
		tmp = Float64(j * Float64(y3 * Float64(y0 * y5)));
	elseif (a <= 3.9e-51)
		tmp = t_2;
	elseif (a <= 2.35e+22)
		tmp = Float64(Float64(j * y5) * Float64(Float64(y0 * y3) - Float64(t * i)));
	elseif (a <= 8e+151)
		tmp = Float64(t * Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))));
	else
		tmp = Float64(y1 * Float64(y3 * Float64(Float64(z * a) - Float64(j * 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 * (z * ((y1 * y3) - (t * b)));
	t_2 = c * (y4 * ((y * y3) - (t * y2)));
	tmp = 0.0;
	if (a <= -3.4e+123)
		tmp = t_1;
	elseif (a <= -3e+45)
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	elseif (a <= -1.4e-46)
		tmp = t_1;
	elseif (a <= -3.1e-99)
		tmp = (c * i) * ((z * t) - (x * y));
	elseif (a <= -3.3e-139)
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	elseif (a <= -3.7e-163)
		tmp = c * (y4 * (y * y3));
	elseif (a <= -1e-191)
		tmp = y1 * (i * ((x * j) - (z * k)));
	elseif (a <= -5.2e-278)
		tmp = t_2;
	elseif (a <= 2.7e-156)
		tmp = j * (y3 * (y0 * y5));
	elseif (a <= 3.9e-51)
		tmp = t_2;
	elseif (a <= 2.35e+22)
		tmp = (j * y5) * ((y0 * y3) - (t * i));
	elseif (a <= 8e+151)
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	else
		tmp = y1 * (y3 * ((z * a) - (j * 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[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.4e+123], t$95$1, If[LessEqual[a, -3e+45], N[(y4 * N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.4e-46], t$95$1, If[LessEqual[a, -3.1e-99], N[(N[(c * i), $MachinePrecision] * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.3e-139], N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.7e-163], N[(c * N[(y4 * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1e-191], N[(y1 * N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5.2e-278], t$95$2, If[LessEqual[a, 2.7e-156], N[(j * N[(y3 * N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.9e-51], t$95$2, If[LessEqual[a, 2.35e+22], N[(N[(j * y5), $MachinePrecision] * N[(N[(y0 * y3), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8e+151], N[(t * N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(y3 * N[(N[(z * a), $MachinePrecision] - N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]

Derivation

1. Split input into 11 regimes

2. if a < -3.40000000000000001e123 or -3.00000000000000011e45 < a < -1.3999999999999999e-46

   1. Initial program 19.5%

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

   3. Simplified 19.5%

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

   5. Taylor expanded in a around inf 57.6%

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

   6. Taylor expanded in z around inf 55.3%

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

      1. +-commutative 55.3%

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

      2. mul-1-neg 55.3%

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

      3. unsub-neg 55.3%

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

      4. *-commutative 55.3%

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

      5. *-commutative 55.3%

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

   8. Simplified 55.3%

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

   if -3.40000000000000001e123 < a < -3.00000000000000011e45

   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 55.3%

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

   4. Taylor expanded in y1 around inf 50.8%

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

   if -1.3999999999999999e-46 < a < -3.0999999999999999e-99

   1. Initial program 23.1%

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

   3. Simplified 23.1%

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

   5. Taylor expanded in c around inf 38.5%

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

   6. Taylor expanded in i around inf 78.0%

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

      1. mul-1-neg 78.0%

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

      2. associate-*r* 70.9%

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

      3. neg-mul-1 70.9%

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

      4. +-commutative 70.9%

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

      5. *-commutative 70.9%

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

      6. fma-udef 70.9%

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

      7. distribute-lft-neg-in 70.9%

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

      8. fma-udef 70.9%

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

      9. *-commutative 70.9%

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

      10. unsub-neg 70.9%

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

      11. *-commutative 70.9%

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

   8. Simplified 70.9%

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

   if -3.0999999999999999e-99 < a < -3.3e-139

   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 46.3%

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

   4. Taylor expanded in k around inf 50.0%

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

      1. *-commutative 50.0%

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

   6. Simplified 50.0%

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

   if -3.3e-139 < a < -3.6999999999999999e-163

   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 c around inf 81.4%

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

   6. Taylor expanded in y3 around inf 60.7%

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

      1. distribute-lft-out-- 60.7%

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

   8. Simplified 60.7%

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

   9. Taylor expanded in y0 around 0 80.7%

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

       1. mul-1-neg 80.7%

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

       2. distribute-lft-neg-out 80.7%

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

       3. *-commutative 80.7%

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

   11. Simplified 80.7%

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

   12. Taylor expanded in y3 around 0 62.1%

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

       1. *-commutative 62.1%

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

       2. *-commutative 62.1%

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

       3. associate-*l* 81.4%

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

   14. Simplified 81.4%

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

   if -3.6999999999999999e-163 < a < -1e-191

   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 y1 around inf 100.0%

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

   4. Taylor expanded in i around inf 80.6%

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

   if -1e-191 < a < -5.1999999999999997e-278 or 2.70000000000000012e-156 < a < 3.8999999999999997e-51

   1. Initial program 46.9%

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

   3. Simplified 46.9%

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

   5. Taylor expanded in c around inf 41.4%

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

   6. Taylor expanded in y4 around inf 47.9%

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

   if -5.1999999999999997e-278 < a < 2.70000000000000012e-156

   1. Initial program 48.1%

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

   3. Taylor expanded in y5 around -inf 41.7%

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

      1. associate-*r* 41.7%

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

      2. neg-mul-1 41.7%

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

      3. fma-def 45.4%

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

      4. *-commutative 45.4%

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

      5. *-commutative 45.4%

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

      6. *-commutative 45.4%

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

   5. Simplified 45.4%

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

   6. Taylor expanded in j around -inf 49.2%

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

      1. associate-*r* 42.1%

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

      2. +-commutative 42.1%

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

      3. mul-1-neg 42.1%

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

      4. unsub-neg 42.1%

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

   8. Simplified 42.1%

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

   9. Taylor expanded in y0 around inf 48.8%

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

       1. associate-*r* 45.3%

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

       2. *-commutative 45.3%

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

       3. associate-*l* 48.9%

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

   11. Simplified 48.9%

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

   if 3.8999999999999997e-51 < a < 2.3500000000000001e22

   1. Initial program 50.0%

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

   3. Taylor expanded in y5 around -inf 40.3%

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

      1. associate-*r* 40.3%

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

      2. neg-mul-1 40.3%

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

      3. fma-def 40.3%

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

      4. *-commutative 40.3%

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

      5. *-commutative 40.3%

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

      6. *-commutative 40.3%

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

   5. Simplified 40.3%

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

   6. Taylor expanded in j around -inf 42.4%

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

      1. associate-*r* 51.6%

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

      2. +-commutative 51.6%

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

      3. mul-1-neg 51.6%

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

      4. unsub-neg 51.6%

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

   8. Simplified 51.6%

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

   if 2.3500000000000001e22 < a < 8.00000000000000014e151

   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 y2 around inf 46.5%

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

   4. Taylor expanded in t around inf 49.4%

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

      1. *-commutative 49.4%

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

      2. *-commutative 49.4%

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

   6. Simplified 49.4%

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

   if 8.00000000000000014e151 < a

   1. Initial program 26.5%

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

   3. Taylor expanded in y1 around inf 53.5%

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

   4. Taylor expanded in y3 around inf 59.2%

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

      1. +-commutative 59.2%

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

      2. mul-1-neg 59.2%

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

      3. unsub-neg 59.2%

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

      4. *-commutative 59.2%

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

      5. *-commutative 59.2%

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

   6. Simplified 59.2%

      \[\leadsto y1 \cdot \color{blue}{\left(y3 \cdot \left(z \cdot a - y4 \cdot j\right)\right)} \]
3. Recombined 11 regimes into one program.

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+123}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;a \leq -3 \cdot 10^{+45}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-46}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-99}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(z \cdot t - x \cdot y\right)\\ \mathbf{elif}\;a \leq -3.3 \cdot 10^{-139}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-163}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-191}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-278}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-156}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-51}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{+22}:\\ \;\;\;\;\left(j \cdot y5\right) \cdot \left(y0 \cdot y3 - t \cdot i\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+151}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 36.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ t_2 := c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{if}\;y0 \leq -2.5 \cdot 10^{+131}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y0 \leq -7.6 \cdot 10^{-98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y0 \leq -1.15 \cdot 10^{-206}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq -5 \cdot 10^{-254}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq -6.4 \cdot 10^{-288}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 1.55 \cdot 10^{-214}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y0 \leq 1.5 \cdot 10^{-109}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 4.3 \cdot 10^{+158}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          y4
          (+
           (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
           (* c (- (* y y3) (* t y2))))))
        (t_2 (* c (* y0 (- (* x y2) (* z y3))))))
   (if (<= y0 -2.5e+131)
     t_2
     (if (<= y0 -7.6e-98)
       t_1
       (if (<= y0 -1.15e-206)
         (* y (* y5 (- (* i k) (* a y3))))
         (if (<= y0 -5e-254)
           (* y1 (* y3 (- (* z a) (* j y4))))
           (if (<= y0 -6.4e-288)
             (* a (* y (- (* x b) (* y3 y5))))
             (if (<= y0 1.55e-214)
               (* y1 (* i (- (* x j) (* z k))))
               (if (<= y0 1.5e-109)
                 (*
                  y2
                  (+
                   (* k (- (* y1 y4) (* y0 y5)))
                   (* t (- (* a y5) (* c y4)))))
                 (if (<= y0 4.3e+158) 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 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double t_2 = c * (y0 * ((x * y2) - (z * y3)));
	double tmp;
	if (y0 <= -2.5e+131) {
		tmp = t_2;
	} else if (y0 <= -7.6e-98) {
		tmp = t_1;
	} else if (y0 <= -1.15e-206) {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	} else if (y0 <= -5e-254) {
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	} else if (y0 <= -6.4e-288) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (y0 <= 1.55e-214) {
		tmp = y1 * (i * ((x * j) - (z * k)));
	} else if (y0 <= 1.5e-109) {
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + (t * ((a * y5) - (c * y4))));
	} else if (y0 <= 4.3e+158) {
		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 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    t_2 = c * (y0 * ((x * y2) - (z * y3)))
    if (y0 <= (-2.5d+131)) then
        tmp = t_2
    else if (y0 <= (-7.6d-98)) then
        tmp = t_1
    else if (y0 <= (-1.15d-206)) then
        tmp = y * (y5 * ((i * k) - (a * y3)))
    else if (y0 <= (-5d-254)) then
        tmp = y1 * (y3 * ((z * a) - (j * y4)))
    else if (y0 <= (-6.4d-288)) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (y0 <= 1.55d-214) then
        tmp = y1 * (i * ((x * j) - (z * k)))
    else if (y0 <= 1.5d-109) then
        tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + (t * ((a * y5) - (c * y4))))
    else if (y0 <= 4.3d+158) 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 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double t_2 = c * (y0 * ((x * y2) - (z * y3)));
	double tmp;
	if (y0 <= -2.5e+131) {
		tmp = t_2;
	} else if (y0 <= -7.6e-98) {
		tmp = t_1;
	} else if (y0 <= -1.15e-206) {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	} else if (y0 <= -5e-254) {
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	} else if (y0 <= -6.4e-288) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (y0 <= 1.55e-214) {
		tmp = y1 * (i * ((x * j) - (z * k)));
	} else if (y0 <= 1.5e-109) {
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + (t * ((a * y5) - (c * y4))));
	} else if (y0 <= 4.3e+158) {
		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 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	t_2 = c * (y0 * ((x * y2) - (z * y3)))
	tmp = 0
	if y0 <= -2.5e+131:
		tmp = t_2
	elif y0 <= -7.6e-98:
		tmp = t_1
	elif y0 <= -1.15e-206:
		tmp = y * (y5 * ((i * k) - (a * y3)))
	elif y0 <= -5e-254:
		tmp = y1 * (y3 * ((z * a) - (j * y4)))
	elif y0 <= -6.4e-288:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif y0 <= 1.55e-214:
		tmp = y1 * (i * ((x * j) - (z * k)))
	elif y0 <= 1.5e-109:
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + (t * ((a * y5) - (c * y4))))
	elif y0 <= 4.3e+158:
		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(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))))
	t_2 = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))))
	tmp = 0.0
	if (y0 <= -2.5e+131)
		tmp = t_2;
	elseif (y0 <= -7.6e-98)
		tmp = t_1;
	elseif (y0 <= -1.15e-206)
		tmp = Float64(y * Float64(y5 * Float64(Float64(i * k) - Float64(a * y3))));
	elseif (y0 <= -5e-254)
		tmp = Float64(y1 * Float64(y3 * Float64(Float64(z * a) - Float64(j * y4))));
	elseif (y0 <= -6.4e-288)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (y0 <= 1.55e-214)
		tmp = Float64(y1 * Float64(i * Float64(Float64(x * j) - Float64(z * k))));
	elseif (y0 <= 1.5e-109)
		tmp = Float64(y2 * Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y0 <= 4.3e+158)
		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 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	t_2 = c * (y0 * ((x * y2) - (z * y3)));
	tmp = 0.0;
	if (y0 <= -2.5e+131)
		tmp = t_2;
	elseif (y0 <= -7.6e-98)
		tmp = t_1;
	elseif (y0 <= -1.15e-206)
		tmp = y * (y5 * ((i * k) - (a * y3)));
	elseif (y0 <= -5e-254)
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	elseif (y0 <= -6.4e-288)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (y0 <= 1.55e-214)
		tmp = y1 * (i * ((x * j) - (z * k)));
	elseif (y0 <= 1.5e-109)
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + (t * ((a * y5) - (c * y4))));
	elseif (y0 <= 4.3e+158)
		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[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -2.5e+131], t$95$2, If[LessEqual[y0, -7.6e-98], t$95$1, If[LessEqual[y0, -1.15e-206], N[(y * N[(y5 * N[(N[(i * k), $MachinePrecision] - N[(a * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -5e-254], N[(y1 * N[(y3 * N[(N[(z * a), $MachinePrecision] - N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -6.4e-288], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.55e-214], N[(y1 * N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.5e-109], N[(y2 * N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 4.3e+158], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y0 < -2.49999999999999998e131 or 4.3e158 < y0

   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 23.6%

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

   5. Taylor expanded in c around inf 42.0%

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

   6. Taylor expanded in y0 around inf 53.0%

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

   if -2.49999999999999998e131 < y0 < -7.6000000000000006e-98 or 1.50000000000000011e-109 < y0 < 4.3e158

   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 y4 around inf 52.3%

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

   if -7.6000000000000006e-98 < y0 < -1.15e-206

   1. Initial program 41.6%

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

   3. Taylor expanded in y5 around -inf 50.2%

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

      1. associate-*r* 50.2%

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

      2. neg-mul-1 50.2%

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

      3. fma-def 50.2%

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

      4. *-commutative 50.2%

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

      5. *-commutative 50.2%

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

      6. *-commutative 50.2%

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

   5. Simplified 50.2%

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

   6. Taylor expanded in y around -inf 67.0%

      \[\leadsto \color{blue}{y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 67.0%

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

   8. Simplified 67.0%

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

   if -1.15e-206 < y0 < -5.0000000000000003e-254

   1. Initial program 8.3%

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

   3. Taylor expanded in y1 around inf 33.9%

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

   4. Taylor expanded in y3 around inf 75.4%

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

      1. +-commutative 75.4%

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

      2. mul-1-neg 75.4%

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

      3. unsub-neg 75.4%

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

      4. *-commutative 75.4%

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

      5. *-commutative 75.4%

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

   6. Simplified 75.4%

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

   if -5.0000000000000003e-254 < y0 < -6.4000000000000001e-288

   1. Initial program 50.8%

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

   3. Simplified 50.8%

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

   5. Taylor expanded in a around inf 67.7%

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

   6. Taylor expanded in y around inf 53.1%

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

      1. *-commutative 53.1%

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

      2. *-commutative 53.1%

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

   8. Simplified 53.1%

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

   if -6.4000000000000001e-288 < y0 < 1.55000000000000002e-214

   1. Initial program 30.7%

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

   3. Taylor expanded in y1 around inf 39.6%

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

   4. Taylor expanded in i around inf 39.9%

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

   if 1.55000000000000002e-214 < y0 < 1.50000000000000011e-109

   1. Initial program 26.4%

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

   3. Taylor expanded in y2 around inf 47.9%

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

   4. Taylor expanded in x around 0 54.8%

      \[\leadsto \color{blue}{y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   5. Step-by-step derivation

      1. sub-neg 54.8%

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

      2. *-commutative 54.8%

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

      3. sub-neg 54.8%

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

      4. *-commutative 54.8%

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

      5. *-commutative 54.8%

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

   6. Simplified 54.8%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -2.5 \cdot 10^{+131}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq -7.6 \cdot 10^{-98}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq -1.15 \cdot 10^{-206}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq -5 \cdot 10^{-254}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq -6.4 \cdot 10^{-288}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 1.55 \cdot 10^{-214}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y0 \leq 1.5 \cdot 10^{-109}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 4.3 \cdot 10^{+158}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 37.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ t_2 := c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ t_3 := y1 \cdot y4 - y0 \cdot y5\\ \mathbf{if}\;y0 \leq -8 \cdot 10^{+130}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y0 \leq -5 \cdot 10^{-98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y0 \leq -1.45 \cdot 10^{-206}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq -1.65 \cdot 10^{-254}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq -7 \cdot 10^{-290}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 2.1 \cdot 10^{-223}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(j \cdot t_3 + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 9.6 \cdot 10^{-111}:\\ \;\;\;\;y2 \cdot \left(k \cdot t_3 + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 2.15 \cdot 10^{+156}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          y4
          (+
           (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
           (* c (- (* y y3) (* t y2))))))
        (t_2 (* c (* y0 (- (* x y2) (* z y3)))))
        (t_3 (- (* y1 y4) (* y0 y5))))
   (if (<= y0 -8e+130)
     t_2
     (if (<= y0 -5e-98)
       t_1
       (if (<= y0 -1.45e-206)
         (* y (* y5 (- (* i k) (* a y3))))
         (if (<= y0 -1.65e-254)
           (* y1 (* y3 (- (* z a) (* j y4))))
           (if (<= y0 -7e-290)
             (* a (* y (- (* x b) (* y3 y5))))
             (if (<= y0 2.1e-223)
               (*
                y3
                (-
                 (* y (- (* c y4) (* a y5)))
                 (+ (* j t_3) (* z (- (* c y0) (* a y1))))))
               (if (<= y0 9.6e-111)
                 (* y2 (+ (* k t_3) (* t (- (* a y5) (* c y4)))))
                 (if (<= y0 2.15e+156) 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 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double t_2 = c * (y0 * ((x * y2) - (z * y3)));
	double t_3 = (y1 * y4) - (y0 * y5);
	double tmp;
	if (y0 <= -8e+130) {
		tmp = t_2;
	} else if (y0 <= -5e-98) {
		tmp = t_1;
	} else if (y0 <= -1.45e-206) {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	} else if (y0 <= -1.65e-254) {
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	} else if (y0 <= -7e-290) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (y0 <= 2.1e-223) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) - ((j * t_3) + (z * ((c * y0) - (a * y1)))));
	} else if (y0 <= 9.6e-111) {
		tmp = y2 * ((k * t_3) + (t * ((a * y5) - (c * y4))));
	} else if (y0 <= 2.15e+156) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    t_2 = c * (y0 * ((x * y2) - (z * y3)))
    t_3 = (y1 * y4) - (y0 * y5)
    if (y0 <= (-8d+130)) then
        tmp = t_2
    else if (y0 <= (-5d-98)) then
        tmp = t_1
    else if (y0 <= (-1.45d-206)) then
        tmp = y * (y5 * ((i * k) - (a * y3)))
    else if (y0 <= (-1.65d-254)) then
        tmp = y1 * (y3 * ((z * a) - (j * y4)))
    else if (y0 <= (-7d-290)) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (y0 <= 2.1d-223) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) - ((j * t_3) + (z * ((c * y0) - (a * y1)))))
    else if (y0 <= 9.6d-111) then
        tmp = y2 * ((k * t_3) + (t * ((a * y5) - (c * y4))))
    else if (y0 <= 2.15d+156) 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 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double t_2 = c * (y0 * ((x * y2) - (z * y3)));
	double t_3 = (y1 * y4) - (y0 * y5);
	double tmp;
	if (y0 <= -8e+130) {
		tmp = t_2;
	} else if (y0 <= -5e-98) {
		tmp = t_1;
	} else if (y0 <= -1.45e-206) {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	} else if (y0 <= -1.65e-254) {
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	} else if (y0 <= -7e-290) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (y0 <= 2.1e-223) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) - ((j * t_3) + (z * ((c * y0) - (a * y1)))));
	} else if (y0 <= 9.6e-111) {
		tmp = y2 * ((k * t_3) + (t * ((a * y5) - (c * y4))));
	} else if (y0 <= 2.15e+156) {
		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 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	t_2 = c * (y0 * ((x * y2) - (z * y3)))
	t_3 = (y1 * y4) - (y0 * y5)
	tmp = 0
	if y0 <= -8e+130:
		tmp = t_2
	elif y0 <= -5e-98:
		tmp = t_1
	elif y0 <= -1.45e-206:
		tmp = y * (y5 * ((i * k) - (a * y3)))
	elif y0 <= -1.65e-254:
		tmp = y1 * (y3 * ((z * a) - (j * y4)))
	elif y0 <= -7e-290:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif y0 <= 2.1e-223:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) - ((j * t_3) + (z * ((c * y0) - (a * y1)))))
	elif y0 <= 9.6e-111:
		tmp = y2 * ((k * t_3) + (t * ((a * y5) - (c * y4))))
	elif y0 <= 2.15e+156:
		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(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))))
	t_2 = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))))
	t_3 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	tmp = 0.0
	if (y0 <= -8e+130)
		tmp = t_2;
	elseif (y0 <= -5e-98)
		tmp = t_1;
	elseif (y0 <= -1.45e-206)
		tmp = Float64(y * Float64(y5 * Float64(Float64(i * k) - Float64(a * y3))));
	elseif (y0 <= -1.65e-254)
		tmp = Float64(y1 * Float64(y3 * Float64(Float64(z * a) - Float64(j * y4))));
	elseif (y0 <= -7e-290)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (y0 <= 2.1e-223)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) - Float64(Float64(j * t_3) + Float64(z * Float64(Float64(c * y0) - Float64(a * y1))))));
	elseif (y0 <= 9.6e-111)
		tmp = Float64(y2 * Float64(Float64(k * t_3) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y0 <= 2.15e+156)
		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 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	t_2 = c * (y0 * ((x * y2) - (z * y3)));
	t_3 = (y1 * y4) - (y0 * y5);
	tmp = 0.0;
	if (y0 <= -8e+130)
		tmp = t_2;
	elseif (y0 <= -5e-98)
		tmp = t_1;
	elseif (y0 <= -1.45e-206)
		tmp = y * (y5 * ((i * k) - (a * y3)));
	elseif (y0 <= -1.65e-254)
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	elseif (y0 <= -7e-290)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (y0 <= 2.1e-223)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) - ((j * t_3) + (z * ((c * y0) - (a * y1)))));
	elseif (y0 <= 9.6e-111)
		tmp = y2 * ((k * t_3) + (t * ((a * y5) - (c * y4))));
	elseif (y0 <= 2.15e+156)
		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[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -8e+130], t$95$2, If[LessEqual[y0, -5e-98], t$95$1, If[LessEqual[y0, -1.45e-206], N[(y * N[(y5 * N[(N[(i * k), $MachinePrecision] - N[(a * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1.65e-254], N[(y1 * N[(y3 * N[(N[(z * a), $MachinePrecision] - N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -7e-290], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 2.1e-223], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * t$95$3), $MachinePrecision] + N[(z * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 9.6e-111], N[(y2 * N[(N[(k * t$95$3), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 2.15e+156], t$95$1, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y0 < -8.0000000000000005e130 or 2.14999999999999993e156 < y0

   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 23.6%

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

   5. Taylor expanded in c around inf 42.0%

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

   6. Taylor expanded in y0 around inf 53.0%

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

   if -8.0000000000000005e130 < y0 < -5.00000000000000018e-98 or 9.6000000000000003e-111 < y0 < 2.14999999999999993e156

   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 y4 around inf 52.3%

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

   if -5.00000000000000018e-98 < y0 < -1.4500000000000001e-206

   1. Initial program 41.6%

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

   3. Taylor expanded in y5 around -inf 50.2%

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

      1. associate-*r* 50.2%

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

      2. neg-mul-1 50.2%

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

      3. fma-def 50.2%

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

      4. *-commutative 50.2%

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

      5. *-commutative 50.2%

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

      6. *-commutative 50.2%

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

   5. Simplified 50.2%

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

   6. Taylor expanded in y around -inf 67.0%

      \[\leadsto \color{blue}{y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 67.0%

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

   8. Simplified 67.0%

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

   if -1.4500000000000001e-206 < y0 < -1.65000000000000008e-254

   1. Initial program 8.3%

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

   3. Taylor expanded in y1 around inf 33.9%

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

   4. Taylor expanded in y3 around inf 75.4%

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

      1. +-commutative 75.4%

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

      2. mul-1-neg 75.4%

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

      3. unsub-neg 75.4%

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

      4. *-commutative 75.4%

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

      5. *-commutative 75.4%

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

   6. Simplified 75.4%

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

   if -1.65000000000000008e-254 < y0 < -6.99999999999999963e-290

   1. Initial program 50.8%

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

   3. Simplified 50.8%

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

   5. Taylor expanded in a around inf 67.7%

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

   6. Taylor expanded in y around inf 53.1%

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

      1. *-commutative 53.1%

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

      2. *-commutative 53.1%

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

   8. Simplified 53.1%

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

   if -6.99999999999999963e-290 < y0 < 2.09999999999999982e-223

   1. Initial program 30.3%

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

   3. Taylor expanded in y3 around -inf 55.3%

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

   if 2.09999999999999982e-223 < y0 < 9.6000000000000003e-111

   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 y2 around inf 44.2%

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

   4. Taylor expanded in x around 0 50.6%

      \[\leadsto \color{blue}{y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   5. Step-by-step derivation

      1. sub-neg 50.6%

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

      2. *-commutative 50.6%

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

      3. sub-neg 50.6%

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

      4. *-commutative 50.6%

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

      5. *-commutative 50.6%

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

   6. Simplified 50.6%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -8 \cdot 10^{+130}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq -5 \cdot 10^{-98}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq -1.45 \cdot 10^{-206}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq -1.65 \cdot 10^{-254}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq -7 \cdot 10^{-290}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 2.1 \cdot 10^{-223}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 9.6 \cdot 10^{-111}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 2.15 \cdot 10^{+156}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 28.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ t_2 := c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;a \leq -5.3 \cdot 10^{+125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.02 \cdot 10^{+49}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.4 \cdot 10^{-108}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;a \leq -5.7 \cdot 10^{-277}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.16 \cdot 10^{-156}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-50}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+15}:\\ \;\;\;\;\left(j \cdot y5\right) \cdot \left(y0 \cdot y3 - t \cdot i\right)\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+56}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{+106}:\\ \;\;\;\;\left(k \cdot y5\right) \cdot \left(y \cdot i - y0 \cdot y2\right)\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{+148}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* z (- (* y1 y3) (* t b)))))
        (t_2 (* c (* y4 (- (* y y3) (* t y2))))))
   (if (<= a -5.3e+125)
     t_1
     (if (<= a -1.02e+49)
       (* y4 (* y1 (- (* k y2) (* j y3))))
       (if (<= a -3.5e-40)
         t_1
         (if (<= a -6.4e-108)
           (* y4 (* b (- (* t j) (* y k))))
           (if (<= a -5.7e-277)
             t_2
             (if (<= a 1.16e-156)
               (* j (* y3 (* y0 y5)))
               (if (<= a 3.9e-50)
                 t_2
                 (if (<= a 1.05e+15)
                   (* (* j y5) (- (* y0 y3) (* t i)))
                   (if (<= a 4.5e+56)
                     (* c (* y2 (- (* x y0) (* t y4))))
                     (if (<= a 1.22e+106)
                       (* (* k y5) (- (* y i) (* y0 y2)))
                       (if (<= a 3.7e+148)
                         (* t (* y2 (- (* a y5) (* c y4))))
                         (* y1 (* y3 (- (* z a) (* j 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 * (z * ((y1 * y3) - (t * b)));
	double t_2 = c * (y4 * ((y * y3) - (t * y2)));
	double tmp;
	if (a <= -5.3e+125) {
		tmp = t_1;
	} else if (a <= -1.02e+49) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (a <= -3.5e-40) {
		tmp = t_1;
	} else if (a <= -6.4e-108) {
		tmp = y4 * (b * ((t * j) - (y * k)));
	} else if (a <= -5.7e-277) {
		tmp = t_2;
	} else if (a <= 1.16e-156) {
		tmp = j * (y3 * (y0 * y5));
	} else if (a <= 3.9e-50) {
		tmp = t_2;
	} else if (a <= 1.05e+15) {
		tmp = (j * y5) * ((y0 * y3) - (t * i));
	} else if (a <= 4.5e+56) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (a <= 1.22e+106) {
		tmp = (k * y5) * ((y * i) - (y0 * y2));
	} else if (a <= 3.7e+148) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else {
		tmp = y1 * (y3 * ((z * a) - (j * 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) :: t_2
    real(8) :: tmp
    t_1 = a * (z * ((y1 * y3) - (t * b)))
    t_2 = c * (y4 * ((y * y3) - (t * y2)))
    if (a <= (-5.3d+125)) then
        tmp = t_1
    else if (a <= (-1.02d+49)) then
        tmp = y4 * (y1 * ((k * y2) - (j * y3)))
    else if (a <= (-3.5d-40)) then
        tmp = t_1
    else if (a <= (-6.4d-108)) then
        tmp = y4 * (b * ((t * j) - (y * k)))
    else if (a <= (-5.7d-277)) then
        tmp = t_2
    else if (a <= 1.16d-156) then
        tmp = j * (y3 * (y0 * y5))
    else if (a <= 3.9d-50) then
        tmp = t_2
    else if (a <= 1.05d+15) then
        tmp = (j * y5) * ((y0 * y3) - (t * i))
    else if (a <= 4.5d+56) then
        tmp = c * (y2 * ((x * y0) - (t * y4)))
    else if (a <= 1.22d+106) then
        tmp = (k * y5) * ((y * i) - (y0 * y2))
    else if (a <= 3.7d+148) then
        tmp = t * (y2 * ((a * y5) - (c * y4)))
    else
        tmp = y1 * (y3 * ((z * a) - (j * 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 * (z * ((y1 * y3) - (t * b)));
	double t_2 = c * (y4 * ((y * y3) - (t * y2)));
	double tmp;
	if (a <= -5.3e+125) {
		tmp = t_1;
	} else if (a <= -1.02e+49) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (a <= -3.5e-40) {
		tmp = t_1;
	} else if (a <= -6.4e-108) {
		tmp = y4 * (b * ((t * j) - (y * k)));
	} else if (a <= -5.7e-277) {
		tmp = t_2;
	} else if (a <= 1.16e-156) {
		tmp = j * (y3 * (y0 * y5));
	} else if (a <= 3.9e-50) {
		tmp = t_2;
	} else if (a <= 1.05e+15) {
		tmp = (j * y5) * ((y0 * y3) - (t * i));
	} else if (a <= 4.5e+56) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (a <= 1.22e+106) {
		tmp = (k * y5) * ((y * i) - (y0 * y2));
	} else if (a <= 3.7e+148) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else {
		tmp = y1 * (y3 * ((z * a) - (j * 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 * (z * ((y1 * y3) - (t * b)))
	t_2 = c * (y4 * ((y * y3) - (t * y2)))
	tmp = 0
	if a <= -5.3e+125:
		tmp = t_1
	elif a <= -1.02e+49:
		tmp = y4 * (y1 * ((k * y2) - (j * y3)))
	elif a <= -3.5e-40:
		tmp = t_1
	elif a <= -6.4e-108:
		tmp = y4 * (b * ((t * j) - (y * k)))
	elif a <= -5.7e-277:
		tmp = t_2
	elif a <= 1.16e-156:
		tmp = j * (y3 * (y0 * y5))
	elif a <= 3.9e-50:
		tmp = t_2
	elif a <= 1.05e+15:
		tmp = (j * y5) * ((y0 * y3) - (t * i))
	elif a <= 4.5e+56:
		tmp = c * (y2 * ((x * y0) - (t * y4)))
	elif a <= 1.22e+106:
		tmp = (k * y5) * ((y * i) - (y0 * y2))
	elif a <= 3.7e+148:
		tmp = t * (y2 * ((a * y5) - (c * y4)))
	else:
		tmp = y1 * (y3 * ((z * a) - (j * 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(z * Float64(Float64(y1 * y3) - Float64(t * b))))
	t_2 = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))))
	tmp = 0.0
	if (a <= -5.3e+125)
		tmp = t_1;
	elseif (a <= -1.02e+49)
		tmp = Float64(y4 * Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif (a <= -3.5e-40)
		tmp = t_1;
	elseif (a <= -6.4e-108)
		tmp = Float64(y4 * Float64(b * Float64(Float64(t * j) - Float64(y * k))));
	elseif (a <= -5.7e-277)
		tmp = t_2;
	elseif (a <= 1.16e-156)
		tmp = Float64(j * Float64(y3 * Float64(y0 * y5)));
	elseif (a <= 3.9e-50)
		tmp = t_2;
	elseif (a <= 1.05e+15)
		tmp = Float64(Float64(j * y5) * Float64(Float64(y0 * y3) - Float64(t * i)));
	elseif (a <= 4.5e+56)
		tmp = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))));
	elseif (a <= 1.22e+106)
		tmp = Float64(Float64(k * y5) * Float64(Float64(y * i) - Float64(y0 * y2)));
	elseif (a <= 3.7e+148)
		tmp = Float64(t * Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))));
	else
		tmp = Float64(y1 * Float64(y3 * Float64(Float64(z * a) - Float64(j * 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 * (z * ((y1 * y3) - (t * b)));
	t_2 = c * (y4 * ((y * y3) - (t * y2)));
	tmp = 0.0;
	if (a <= -5.3e+125)
		tmp = t_1;
	elseif (a <= -1.02e+49)
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	elseif (a <= -3.5e-40)
		tmp = t_1;
	elseif (a <= -6.4e-108)
		tmp = y4 * (b * ((t * j) - (y * k)));
	elseif (a <= -5.7e-277)
		tmp = t_2;
	elseif (a <= 1.16e-156)
		tmp = j * (y3 * (y0 * y5));
	elseif (a <= 3.9e-50)
		tmp = t_2;
	elseif (a <= 1.05e+15)
		tmp = (j * y5) * ((y0 * y3) - (t * i));
	elseif (a <= 4.5e+56)
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	elseif (a <= 1.22e+106)
		tmp = (k * y5) * ((y * i) - (y0 * y2));
	elseif (a <= 3.7e+148)
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	else
		tmp = y1 * (y3 * ((z * a) - (j * 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[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.3e+125], t$95$1, If[LessEqual[a, -1.02e+49], N[(y4 * N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.5e-40], t$95$1, If[LessEqual[a, -6.4e-108], N[(y4 * N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5.7e-277], t$95$2, If[LessEqual[a, 1.16e-156], N[(j * N[(y3 * N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.9e-50], t$95$2, If[LessEqual[a, 1.05e+15], N[(N[(j * y5), $MachinePrecision] * N[(N[(y0 * y3), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.5e+56], N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.22e+106], N[(N[(k * y5), $MachinePrecision] * N[(N[(y * i), $MachinePrecision] - N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.7e+148], N[(t * N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(y3 * N[(N[(z * a), $MachinePrecision] - N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if a < -5.3000000000000003e125 or -1.02e49 < a < -3.5000000000000002e-40

   1. Initial program 18.7%

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

   3. Simplified 18.7%

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

   5. Taylor expanded in a around inf 57.1%

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

   6. Taylor expanded in z around inf 54.7%

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

      1. +-commutative 54.7%

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

      2. mul-1-neg 54.7%

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

      3. unsub-neg 54.7%

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

      4. *-commutative 54.7%

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

      5. *-commutative 54.7%

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

   8. Simplified 54.7%

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

   if -5.3000000000000003e125 < a < -1.02e49

   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 55.3%

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

   4. Taylor expanded in y1 around inf 50.8%

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

   if -3.5000000000000002e-40 < a < -6.3999999999999999e-108

   1. Initial program 31.6%

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

   3. Taylor expanded in y4 around inf 52.8%

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

   4. Taylor expanded in b around inf 63.7%

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

   if -6.3999999999999999e-108 < a < -5.69999999999999954e-277 or 1.15999999999999995e-156 < a < 3.90000000000000021e-50

   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 c around inf 44.6%

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

   6. Taylor expanded in y4 around inf 47.0%

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

   if -5.69999999999999954e-277 < a < 1.15999999999999995e-156

   1. Initial program 48.1%

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

   3. Taylor expanded in y5 around -inf 41.7%

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

      1. associate-*r* 41.7%

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

      2. neg-mul-1 41.7%

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

      3. fma-def 45.4%

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

      4. *-commutative 45.4%

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

      5. *-commutative 45.4%

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

      6. *-commutative 45.4%

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

   5. Simplified 45.4%

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

   6. Taylor expanded in j around -inf 49.2%

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

      1. associate-*r* 42.1%

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

      2. +-commutative 42.1%

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

      3. mul-1-neg 42.1%

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

      4. unsub-neg 42.1%

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

   8. Simplified 42.1%

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

   9. Taylor expanded in y0 around inf 48.8%

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

       1. associate-*r* 45.3%

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

       2. *-commutative 45.3%

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

       3. associate-*l* 48.9%

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

   11. Simplified 48.9%

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

   if 3.90000000000000021e-50 < a < 1.05e15

   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 y5 around -inf 37.7%

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

      1. associate-*r* 37.7%

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

      2. neg-mul-1 37.7%

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

      3. fma-def 37.7%

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

      4. *-commutative 37.7%

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

      5. *-commutative 37.7%

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

      6. *-commutative 37.7%

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

   5. Simplified 37.7%

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

   6. Taylor expanded in j around -inf 51.9%

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

      1. associate-*r* 63.5%

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

      2. +-commutative 63.5%

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

      3. mul-1-neg 63.5%

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

      4. unsub-neg 63.5%

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

   8. Simplified 63.5%

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

   if 1.05e15 < a < 4.5000000000000003e56

   1. Initial program 50.0%

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

   3. Taylor expanded in y2 around inf 78.3%

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

   4. Taylor expanded in c around inf 67.8%

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

      1. *-commutative 67.8%

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

   6. Simplified 67.8%

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

   if 4.5000000000000003e56 < a < 1.2199999999999999e106

   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 y5 around -inf 55.3%

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

      1. associate-*r* 55.3%

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

      2. neg-mul-1 55.3%

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

      3. fma-def 55.3%

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

      4. *-commutative 55.3%

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

      5. *-commutative 55.3%

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

      6. *-commutative 55.3%

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

   5. Simplified 55.3%

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

   6. Taylor expanded in k around -inf 51.6%

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

      1. associate-*r* 51.7%

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

      2. *-commutative 51.7%

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

      3. +-commutative 51.7%

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

      4. mul-1-neg 51.7%

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

      5. unsub-neg 51.7%

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

   8. Simplified 51.7%

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

   if 1.2199999999999999e106 < a < 3.7000000000000002e148

   1. Initial program 15.4%

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

   3. Taylor expanded in y2 around inf 46.2%

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

   4. Taylor expanded in t around inf 69.6%

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

      1. *-commutative 69.6%

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

      2. *-commutative 69.6%

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

   6. Simplified 69.6%

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

   if 3.7000000000000002e148 < a

   1. Initial program 26.5%

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

   3. Taylor expanded in y1 around inf 53.5%

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

   4. Taylor expanded in y3 around inf 59.2%

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

      1. +-commutative 59.2%

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

      2. mul-1-neg 59.2%

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

      3. unsub-neg 59.2%

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

      4. *-commutative 59.2%

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

      5. *-commutative 59.2%

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

   6. Simplified 59.2%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.3 \cdot 10^{+125}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;a \leq -1.02 \cdot 10^{+49}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-40}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;a \leq -6.4 \cdot 10^{-108}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;a \leq -5.7 \cdot 10^{-277}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 1.16 \cdot 10^{-156}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-50}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+15}:\\ \;\;\;\;\left(j \cdot y5\right) \cdot \left(y0 \cdot y3 - t \cdot i\right)\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+56}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{+106}:\\ \;\;\;\;\left(k \cdot y5\right) \cdot \left(y \cdot i - y0 \cdot y2\right)\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{+148}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 33.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ t_2 := y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ t_3 := a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{if}\;y0 \leq -2.9 \cdot 10^{+107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y0 \leq -1.2 \cdot 10^{+84}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;y0 \leq -4.8 \cdot 10^{+65}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;y0 \leq -9.5 \cdot 10^{-84}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y0 \leq -2.9 \cdot 10^{-207}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq -1.1 \cdot 10^{-254}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq -3.5 \cdot 10^{-284}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y0 \leq 1.1 \cdot 10^{-210}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y0 \leq 7.2 \cdot 10^{-55}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y0 \leq 7 \cdot 10^{+174}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y0 (- (* x y2) (* z y3)))))
        (t_2
         (* y2 (+ (* k (- (* y1 y4) (* y0 y5))) (* t (- (* a y5) (* c y4))))))
        (t_3 (* a (* y (- (* x b) (* y3 y5))))))
   (if (<= y0 -2.9e+107)
     t_1
     (if (<= y0 -1.2e+84)
       (* a (* z (- (* y1 y3) (* t b))))
       (if (<= y0 -4.8e+65)
         (* y1 (* y2 (- (* k y4) (* x a))))
         (if (<= y0 -9.5e-84)
           t_2
           (if (<= y0 -2.9e-207)
             (* y (* y5 (- (* i k) (* a y3))))
             (if (<= y0 -1.1e-254)
               (* y1 (* y3 (- (* z a) (* j y4))))
               (if (<= y0 -3.5e-284)
                 t_3
                 (if (<= y0 1.1e-210)
                   (* y1 (* i (- (* x j) (* z k))))
                   (if (<= y0 7.2e-55)
                     t_2
                     (if (<= y0 7e+174) 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 = c * (y0 * ((x * y2) - (z * y3)));
	double t_2 = y2 * ((k * ((y1 * y4) - (y0 * y5))) + (t * ((a * y5) - (c * y4))));
	double t_3 = a * (y * ((x * b) - (y3 * y5)));
	double tmp;
	if (y0 <= -2.9e+107) {
		tmp = t_1;
	} else if (y0 <= -1.2e+84) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (y0 <= -4.8e+65) {
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	} else if (y0 <= -9.5e-84) {
		tmp = t_2;
	} else if (y0 <= -2.9e-207) {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	} else if (y0 <= -1.1e-254) {
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	} else if (y0 <= -3.5e-284) {
		tmp = t_3;
	} else if (y0 <= 1.1e-210) {
		tmp = y1 * (i * ((x * j) - (z * k)));
	} else if (y0 <= 7.2e-55) {
		tmp = t_2;
	} else if (y0 <= 7e+174) {
		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 = c * (y0 * ((x * y2) - (z * y3)))
    t_2 = y2 * ((k * ((y1 * y4) - (y0 * y5))) + (t * ((a * y5) - (c * y4))))
    t_3 = a * (y * ((x * b) - (y3 * y5)))
    if (y0 <= (-2.9d+107)) then
        tmp = t_1
    else if (y0 <= (-1.2d+84)) then
        tmp = a * (z * ((y1 * y3) - (t * b)))
    else if (y0 <= (-4.8d+65)) then
        tmp = y1 * (y2 * ((k * y4) - (x * a)))
    else if (y0 <= (-9.5d-84)) then
        tmp = t_2
    else if (y0 <= (-2.9d-207)) then
        tmp = y * (y5 * ((i * k) - (a * y3)))
    else if (y0 <= (-1.1d-254)) then
        tmp = y1 * (y3 * ((z * a) - (j * y4)))
    else if (y0 <= (-3.5d-284)) then
        tmp = t_3
    else if (y0 <= 1.1d-210) then
        tmp = y1 * (i * ((x * j) - (z * k)))
    else if (y0 <= 7.2d-55) then
        tmp = t_2
    else if (y0 <= 7d+174) 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 = c * (y0 * ((x * y2) - (z * y3)));
	double t_2 = y2 * ((k * ((y1 * y4) - (y0 * y5))) + (t * ((a * y5) - (c * y4))));
	double t_3 = a * (y * ((x * b) - (y3 * y5)));
	double tmp;
	if (y0 <= -2.9e+107) {
		tmp = t_1;
	} else if (y0 <= -1.2e+84) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (y0 <= -4.8e+65) {
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	} else if (y0 <= -9.5e-84) {
		tmp = t_2;
	} else if (y0 <= -2.9e-207) {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	} else if (y0 <= -1.1e-254) {
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	} else if (y0 <= -3.5e-284) {
		tmp = t_3;
	} else if (y0 <= 1.1e-210) {
		tmp = y1 * (i * ((x * j) - (z * k)));
	} else if (y0 <= 7.2e-55) {
		tmp = t_2;
	} else if (y0 <= 7e+174) {
		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 = c * (y0 * ((x * y2) - (z * y3)))
	t_2 = y2 * ((k * ((y1 * y4) - (y0 * y5))) + (t * ((a * y5) - (c * y4))))
	t_3 = a * (y * ((x * b) - (y3 * y5)))
	tmp = 0
	if y0 <= -2.9e+107:
		tmp = t_1
	elif y0 <= -1.2e+84:
		tmp = a * (z * ((y1 * y3) - (t * b)))
	elif y0 <= -4.8e+65:
		tmp = y1 * (y2 * ((k * y4) - (x * a)))
	elif y0 <= -9.5e-84:
		tmp = t_2
	elif y0 <= -2.9e-207:
		tmp = y * (y5 * ((i * k) - (a * y3)))
	elif y0 <= -1.1e-254:
		tmp = y1 * (y3 * ((z * a) - (j * y4)))
	elif y0 <= -3.5e-284:
		tmp = t_3
	elif y0 <= 1.1e-210:
		tmp = y1 * (i * ((x * j) - (z * k)))
	elif y0 <= 7.2e-55:
		tmp = t_2
	elif y0 <= 7e+174:
		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(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))))
	t_2 = Float64(y2 * Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))))
	t_3 = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))))
	tmp = 0.0
	if (y0 <= -2.9e+107)
		tmp = t_1;
	elseif (y0 <= -1.2e+84)
		tmp = Float64(a * Float64(z * Float64(Float64(y1 * y3) - Float64(t * b))));
	elseif (y0 <= -4.8e+65)
		tmp = Float64(y1 * Float64(y2 * Float64(Float64(k * y4) - Float64(x * a))));
	elseif (y0 <= -9.5e-84)
		tmp = t_2;
	elseif (y0 <= -2.9e-207)
		tmp = Float64(y * Float64(y5 * Float64(Float64(i * k) - Float64(a * y3))));
	elseif (y0 <= -1.1e-254)
		tmp = Float64(y1 * Float64(y3 * Float64(Float64(z * a) - Float64(j * y4))));
	elseif (y0 <= -3.5e-284)
		tmp = t_3;
	elseif (y0 <= 1.1e-210)
		tmp = Float64(y1 * Float64(i * Float64(Float64(x * j) - Float64(z * k))));
	elseif (y0 <= 7.2e-55)
		tmp = t_2;
	elseif (y0 <= 7e+174)
		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 = c * (y0 * ((x * y2) - (z * y3)));
	t_2 = y2 * ((k * ((y1 * y4) - (y0 * y5))) + (t * ((a * y5) - (c * y4))));
	t_3 = a * (y * ((x * b) - (y3 * y5)));
	tmp = 0.0;
	if (y0 <= -2.9e+107)
		tmp = t_1;
	elseif (y0 <= -1.2e+84)
		tmp = a * (z * ((y1 * y3) - (t * b)));
	elseif (y0 <= -4.8e+65)
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	elseif (y0 <= -9.5e-84)
		tmp = t_2;
	elseif (y0 <= -2.9e-207)
		tmp = y * (y5 * ((i * k) - (a * y3)));
	elseif (y0 <= -1.1e-254)
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	elseif (y0 <= -3.5e-284)
		tmp = t_3;
	elseif (y0 <= 1.1e-210)
		tmp = y1 * (i * ((x * j) - (z * k)));
	elseif (y0 <= 7.2e-55)
		tmp = t_2;
	elseif (y0 <= 7e+174)
		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[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y2 * N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -2.9e+107], t$95$1, If[LessEqual[y0, -1.2e+84], N[(a * N[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -4.8e+65], N[(y1 * N[(y2 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -9.5e-84], t$95$2, If[LessEqual[y0, -2.9e-207], N[(y * N[(y5 * N[(N[(i * k), $MachinePrecision] - N[(a * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1.1e-254], N[(y1 * N[(y3 * N[(N[(z * a), $MachinePrecision] - N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -3.5e-284], t$95$3, If[LessEqual[y0, 1.1e-210], N[(y1 * N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 7.2e-55], t$95$2, If[LessEqual[y0, 7e+174], t$95$3, t$95$1]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y0 < -2.89999999999999988e107 or 7.0000000000000003e174 < y0

   1. Initial program 25.0%

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

   3. Simplified 25.0%

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

   5. Taylor expanded in c around inf 44.8%

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

   6. Taylor expanded in y0 around inf 53.9%

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

   if -2.89999999999999988e107 < y0 < -1.2e84

   1. Initial program 25.0%

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

   3. Simplified 25.0%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   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 z around inf 63.3%

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

      1. +-commutative 63.3%

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

      2. mul-1-neg 63.3%

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

      3. unsub-neg 63.3%

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

      4. *-commutative 63.3%

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

      5. *-commutative 63.3%

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

   8. Simplified 63.3%

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

   if -1.2e84 < y0 < -4.8000000000000003e65

   1. Initial program 33.3%

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

   3. Taylor expanded in y2 around inf 33.3%

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

   4. Taylor expanded in y1 around inf 68.1%

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

      1. associate-*r* 36.0%

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

      2. *-commutative 36.0%

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

      3. +-commutative 36.0%

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

      4. mul-1-neg 36.0%

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

      5. unsub-neg 36.0%

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

   6. Simplified 36.0%

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

   7. Taylor expanded in y2 around 0 68.1%

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

      1. *-commutative 68.1%

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

      2. *-commutative 68.1%

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

   9. Simplified 68.1%

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

   if -4.8000000000000003e65 < y0 < -9.49999999999999941e-84 or 1.09999999999999995e-210 < y0 < 7.2000000000000001e-55

   1. Initial program 35.9%

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

   3. Taylor expanded in y2 around inf 44.2%

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

   4. Taylor expanded in x around 0 51.0%

      \[\leadsto \color{blue}{y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   5. Step-by-step derivation

      1. sub-neg 51.0%

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

      2. *-commutative 51.0%

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

      3. sub-neg 51.0%

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

      4. *-commutative 51.0%

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

      5. *-commutative 51.0%

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

   6. Simplified 51.0%

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

   if -9.49999999999999941e-84 < y0 < -2.90000000000000011e-207

   1. Initial program 39.9%

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

   3. Taylor expanded in y5 around -inf 48.2%

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

      1. associate-*r* 48.2%

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

      2. neg-mul-1 48.2%

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

      3. fma-def 48.2%

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

      4. *-commutative 48.2%

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

      5. *-commutative 48.2%

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

      6. *-commutative 48.2%

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

   5. Simplified 48.2%

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

   6. Taylor expanded in y around -inf 64.3%

      \[\leadsto \color{blue}{y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 64.3%

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

   8. Simplified 64.3%

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

   if -2.90000000000000011e-207 < y0 < -1.1000000000000001e-254

   1. Initial program 8.3%

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

   3. Taylor expanded in y1 around inf 33.9%

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

   4. Taylor expanded in y3 around inf 75.4%

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

      1. +-commutative 75.4%

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

      2. mul-1-neg 75.4%

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

      3. unsub-neg 75.4%

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

      4. *-commutative 75.4%

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

      5. *-commutative 75.4%

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

   6. Simplified 75.4%

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

   if -1.1000000000000001e-254 < y0 < -3.49999999999999975e-284 or 7.2000000000000001e-55 < y0 < 7.0000000000000003e174

   1. Initial program 31.3%

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

   3. Simplified 33.4%

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

   5. Taylor expanded in a around inf 43.8%

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

   6. Taylor expanded in y around inf 48.9%

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

      1. *-commutative 48.9%

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

      2. *-commutative 48.9%

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

   8. Simplified 48.9%

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

   if -3.49999999999999975e-284 < y0 < 1.09999999999999995e-210

   1. Initial program 27.2%

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

   3. Taylor expanded in y1 around inf 42.7%

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

   4. Taylor expanded in i around inf 43.0%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -2.9 \cdot 10^{+107}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq -1.2 \cdot 10^{+84}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;y0 \leq -4.8 \cdot 10^{+65}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;y0 \leq -9.5 \cdot 10^{-84}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq -2.9 \cdot 10^{-207}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq -1.1 \cdot 10^{-254}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq -3.5 \cdot 10^{-284}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 1.1 \cdot 10^{-210}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y0 \leq 7.2 \cdot 10^{-55}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 7 \cdot 10^{+174}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 34.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ t_2 := a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ t_3 := t \cdot \left(a \cdot y5 - c \cdot y4\right)\\ t_4 := y2 \cdot \left(\left(t_1 + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t_3\right)\\ \mathbf{if}\;z \leq -9.8 \cdot 10^{+179}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+70}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-25}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-97}:\\ \;\;\;\;\left(x \cdot c\right) \cdot \left(y0 \cdot y2 - y \cdot i\right)\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-125}:\\ \;\;\;\;y2 \cdot \left(t_1 + t_3\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-251}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;z \leq 3.75 \cdot 10^{-47}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+50}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(z \cdot t - x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (- (* y1 y4) (* y0 y5))))
        (t_2 (* a (* z (- (* y1 y3) (* t b)))))
        (t_3 (* t (- (* a y5) (* c y4))))
        (t_4 (* y2 (+ (+ t_1 (* x (- (* c y0) (* a y1)))) t_3))))
   (if (<= z -9.8e+179)
     t_2
     (if (<= z -6e+70)
       (* y1 (* i (- (* x j) (* z k))))
       (if (<= z -3.6e-25)
         t_4
         (if (<= z -1.55e-97)
           (* (* x c) (- (* y0 y2) (* y i)))
           (if (<= z -3.4e-125)
             (* y2 (+ t_1 t_3))
             (if (<= z 2.5e-251)
               (* i (* y5 (- (* y k) (* t j))))
               (if (<= z 3.75e-47)
                 t_4
                 (if (<= z 1.55e+50)
                   (* (* c i) (- (* z t) (* x y)))
                   t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * ((y1 * y4) - (y0 * y5));
	double t_2 = a * (z * ((y1 * y3) - (t * b)));
	double t_3 = t * ((a * y5) - (c * y4));
	double t_4 = y2 * ((t_1 + (x * ((c * y0) - (a * y1)))) + t_3);
	double tmp;
	if (z <= -9.8e+179) {
		tmp = t_2;
	} else if (z <= -6e+70) {
		tmp = y1 * (i * ((x * j) - (z * k)));
	} else if (z <= -3.6e-25) {
		tmp = t_4;
	} else if (z <= -1.55e-97) {
		tmp = (x * c) * ((y0 * y2) - (y * i));
	} else if (z <= -3.4e-125) {
		tmp = y2 * (t_1 + t_3);
	} else if (z <= 2.5e-251) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (z <= 3.75e-47) {
		tmp = t_4;
	} else if (z <= 1.55e+50) {
		tmp = (c * i) * ((z * t) - (x * y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = k * ((y1 * y4) - (y0 * y5))
    t_2 = a * (z * ((y1 * y3) - (t * b)))
    t_3 = t * ((a * y5) - (c * y4))
    t_4 = y2 * ((t_1 + (x * ((c * y0) - (a * y1)))) + t_3)
    if (z <= (-9.8d+179)) then
        tmp = t_2
    else if (z <= (-6d+70)) then
        tmp = y1 * (i * ((x * j) - (z * k)))
    else if (z <= (-3.6d-25)) then
        tmp = t_4
    else if (z <= (-1.55d-97)) then
        tmp = (x * c) * ((y0 * y2) - (y * i))
    else if (z <= (-3.4d-125)) then
        tmp = y2 * (t_1 + t_3)
    else if (z <= 2.5d-251) then
        tmp = i * (y5 * ((y * k) - (t * j)))
    else if (z <= 3.75d-47) then
        tmp = t_4
    else if (z <= 1.55d+50) then
        tmp = (c * i) * ((z * t) - (x * y))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * ((y1 * y4) - (y0 * y5));
	double t_2 = a * (z * ((y1 * y3) - (t * b)));
	double t_3 = t * ((a * y5) - (c * y4));
	double t_4 = y2 * ((t_1 + (x * ((c * y0) - (a * y1)))) + t_3);
	double tmp;
	if (z <= -9.8e+179) {
		tmp = t_2;
	} else if (z <= -6e+70) {
		tmp = y1 * (i * ((x * j) - (z * k)));
	} else if (z <= -3.6e-25) {
		tmp = t_4;
	} else if (z <= -1.55e-97) {
		tmp = (x * c) * ((y0 * y2) - (y * i));
	} else if (z <= -3.4e-125) {
		tmp = y2 * (t_1 + t_3);
	} else if (z <= 2.5e-251) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (z <= 3.75e-47) {
		tmp = t_4;
	} else if (z <= 1.55e+50) {
		tmp = (c * i) * ((z * t) - (x * y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = k * ((y1 * y4) - (y0 * y5))
	t_2 = a * (z * ((y1 * y3) - (t * b)))
	t_3 = t * ((a * y5) - (c * y4))
	t_4 = y2 * ((t_1 + (x * ((c * y0) - (a * y1)))) + t_3)
	tmp = 0
	if z <= -9.8e+179:
		tmp = t_2
	elif z <= -6e+70:
		tmp = y1 * (i * ((x * j) - (z * k)))
	elif z <= -3.6e-25:
		tmp = t_4
	elif z <= -1.55e-97:
		tmp = (x * c) * ((y0 * y2) - (y * i))
	elif z <= -3.4e-125:
		tmp = y2 * (t_1 + t_3)
	elif z <= 2.5e-251:
		tmp = i * (y5 * ((y * k) - (t * j)))
	elif z <= 3.75e-47:
		tmp = t_4
	elif z <= 1.55e+50:
		tmp = (c * i) * ((z * t) - (x * y))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))
	t_2 = Float64(a * Float64(z * Float64(Float64(y1 * y3) - Float64(t * b))))
	t_3 = Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))
	t_4 = Float64(y2 * Float64(Float64(t_1 + Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))) + t_3))
	tmp = 0.0
	if (z <= -9.8e+179)
		tmp = t_2;
	elseif (z <= -6e+70)
		tmp = Float64(y1 * Float64(i * Float64(Float64(x * j) - Float64(z * k))));
	elseif (z <= -3.6e-25)
		tmp = t_4;
	elseif (z <= -1.55e-97)
		tmp = Float64(Float64(x * c) * Float64(Float64(y0 * y2) - Float64(y * i)));
	elseif (z <= -3.4e-125)
		tmp = Float64(y2 * Float64(t_1 + t_3));
	elseif (z <= 2.5e-251)
		tmp = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))));
	elseif (z <= 3.75e-47)
		tmp = t_4;
	elseif (z <= 1.55e+50)
		tmp = Float64(Float64(c * i) * Float64(Float64(z * t) - Float64(x * y)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = k * ((y1 * y4) - (y0 * y5));
	t_2 = a * (z * ((y1 * y3) - (t * b)));
	t_3 = t * ((a * y5) - (c * y4));
	t_4 = y2 * ((t_1 + (x * ((c * y0) - (a * y1)))) + t_3);
	tmp = 0.0;
	if (z <= -9.8e+179)
		tmp = t_2;
	elseif (z <= -6e+70)
		tmp = y1 * (i * ((x * j) - (z * k)));
	elseif (z <= -3.6e-25)
		tmp = t_4;
	elseif (z <= -1.55e-97)
		tmp = (x * c) * ((y0 * y2) - (y * i));
	elseif (z <= -3.4e-125)
		tmp = y2 * (t_1 + t_3);
	elseif (z <= 2.5e-251)
		tmp = i * (y5 * ((y * k) - (t * j)));
	elseif (z <= 3.75e-47)
		tmp = t_4;
	elseif (z <= 1.55e+50)
		tmp = (c * i) * ((z * t) - (x * y));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y2 * N[(N[(t$95$1 + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.8e+179], t$95$2, If[LessEqual[z, -6e+70], N[(y1 * N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.6e-25], t$95$4, If[LessEqual[z, -1.55e-97], N[(N[(x * c), $MachinePrecision] * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.4e-125], N[(y2 * N[(t$95$1 + t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e-251], N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.75e-47], t$95$4, If[LessEqual[z, 1.55e+50], N[(N[(c * i), $MachinePrecision] * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -9.7999999999999997e179 or 1.55000000000000001e50 < z

   1. Initial program 18.9%

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

   3. Simplified 20.1%

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

   5. Taylor expanded in a around inf 39.8%

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

   6. Taylor expanded in z around inf 52.3%

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

      1. +-commutative 52.3%

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

      2. mul-1-neg 52.3%

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

      3. unsub-neg 52.3%

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

      4. *-commutative 52.3%

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

      5. *-commutative 52.3%

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

   8. Simplified 52.3%

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

   if -9.7999999999999997e179 < z < -5.99999999999999952e70

   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 y1 around inf 66.8%

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

   4. Taylor expanded in i around inf 62.2%

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

   if -5.99999999999999952e70 < z < -3.5999999999999999e-25 or 2.5000000000000001e-251 < z < 3.74999999999999984e-47

   1. Initial program 42.4%

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

   3. Taylor expanded in y2 around inf 56.8%

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

   if -3.5999999999999999e-25 < z < -1.55000000000000001e-97

   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 c around inf 54.1%

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

   6. Taylor expanded in x around inf 47.7%

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

      1. associate-*r* 47.7%

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

      2. *-commutative 47.7%

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

      3. +-commutative 47.7%

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

      4. mul-1-neg 47.7%

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

      5. unsub-neg 47.7%

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

   8. Simplified 47.7%

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

   if -1.55000000000000001e-97 < z < -3.39999999999999975e-125

   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 70.1%

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

   4. Taylor expanded in x around 0 70.6%

      \[\leadsto \color{blue}{y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   5. Step-by-step derivation

      1. sub-neg 70.6%

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

      2. *-commutative 70.6%

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

      3. sub-neg 70.6%

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

      4. *-commutative 70.6%

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

      5. *-commutative 70.6%

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

   6. Simplified 70.6%

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

   if -3.39999999999999975e-125 < z < 2.5000000000000001e-251

   1. Initial program 37.1%

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

   3. Taylor expanded in y5 around -inf 39.7%

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

      1. associate-*r* 39.7%

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

      2. neg-mul-1 39.7%

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

      3. fma-def 41.9%

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

      4. *-commutative 41.9%

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

      5. *-commutative 41.9%

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

      6. *-commutative 41.9%

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

   5. Simplified 41.9%

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

   6. Taylor expanded in i around inf 38.2%

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

      1. mul-1-neg 38.2%

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

      2. *-commutative 38.2%

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

      3. distribute-rgt-neg-in 38.2%

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

   8. Simplified 38.2%

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

   if 3.74999999999999984e-47 < z < 1.55000000000000001e50

   1. Initial program 25.0%

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

   3. Simplified 25.0%

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

   5. Taylor expanded in c around inf 43.9%

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

   6. Taylor expanded in i around inf 56.9%

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

      1. mul-1-neg 56.9%

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

      2. associate-*r* 56.9%

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

      3. neg-mul-1 56.9%

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

      4. +-commutative 56.9%

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

      5. *-commutative 56.9%

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

      6. fma-udef 56.9%

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

      7. distribute-lft-neg-in 56.9%

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

      8. fma-udef 56.9%

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

      9. *-commutative 56.9%

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

      10. unsub-neg 56.9%

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

      11. *-commutative 56.9%

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

   8. Simplified 56.9%

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

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+179}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+70}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-25}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-97}:\\ \;\;\;\;\left(x \cdot c\right) \cdot \left(y0 \cdot y2 - y \cdot i\right)\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-125}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-251}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;z \leq 3.75 \cdot 10^{-47}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+50}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(z \cdot t - x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 29.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ t_2 := c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;a \leq -7.8 \cdot 10^{+124}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{+45}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-108}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;a \leq -5.3 \cdot 10^{-278}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-155}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-48}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{+22}:\\ \;\;\;\;\left(j \cdot y5\right) \cdot \left(y0 \cdot y3 - t \cdot i\right)\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+146}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* z (- (* y1 y3) (* t b)))))
        (t_2 (* c (* y4 (- (* y y3) (* t y2))))))
   (if (<= a -7.8e+124)
     t_1
     (if (<= a -2.2e+45)
       (* y4 (* y1 (- (* k y2) (* j y3))))
       (if (<= a -2.1e-40)
         t_1
         (if (<= a -6e-108)
           (* y4 (* b (- (* t j) (* y k))))
           (if (<= a -5.3e-278)
             t_2
             (if (<= a 1.05e-155)
               (* j (* y3 (* y0 y5)))
               (if (<= a 3.6e-48)
                 t_2
                 (if (<= a 8.8e+22)
                   (* (* j y5) (- (* y0 y3) (* t i)))
                   (if (<= a 2.7e+146)
                     (* t (* y2 (- (* a y5) (* c y4))))
                     (* y1 (* y3 (- (* z a) (* j 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 * (z * ((y1 * y3) - (t * b)));
	double t_2 = c * (y4 * ((y * y3) - (t * y2)));
	double tmp;
	if (a <= -7.8e+124) {
		tmp = t_1;
	} else if (a <= -2.2e+45) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (a <= -2.1e-40) {
		tmp = t_1;
	} else if (a <= -6e-108) {
		tmp = y4 * (b * ((t * j) - (y * k)));
	} else if (a <= -5.3e-278) {
		tmp = t_2;
	} else if (a <= 1.05e-155) {
		tmp = j * (y3 * (y0 * y5));
	} else if (a <= 3.6e-48) {
		tmp = t_2;
	} else if (a <= 8.8e+22) {
		tmp = (j * y5) * ((y0 * y3) - (t * i));
	} else if (a <= 2.7e+146) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else {
		tmp = y1 * (y3 * ((z * a) - (j * 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) :: t_2
    real(8) :: tmp
    t_1 = a * (z * ((y1 * y3) - (t * b)))
    t_2 = c * (y4 * ((y * y3) - (t * y2)))
    if (a <= (-7.8d+124)) then
        tmp = t_1
    else if (a <= (-2.2d+45)) then
        tmp = y4 * (y1 * ((k * y2) - (j * y3)))
    else if (a <= (-2.1d-40)) then
        tmp = t_1
    else if (a <= (-6d-108)) then
        tmp = y4 * (b * ((t * j) - (y * k)))
    else if (a <= (-5.3d-278)) then
        tmp = t_2
    else if (a <= 1.05d-155) then
        tmp = j * (y3 * (y0 * y5))
    else if (a <= 3.6d-48) then
        tmp = t_2
    else if (a <= 8.8d+22) then
        tmp = (j * y5) * ((y0 * y3) - (t * i))
    else if (a <= 2.7d+146) then
        tmp = t * (y2 * ((a * y5) - (c * y4)))
    else
        tmp = y1 * (y3 * ((z * a) - (j * 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 * (z * ((y1 * y3) - (t * b)));
	double t_2 = c * (y4 * ((y * y3) - (t * y2)));
	double tmp;
	if (a <= -7.8e+124) {
		tmp = t_1;
	} else if (a <= -2.2e+45) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (a <= -2.1e-40) {
		tmp = t_1;
	} else if (a <= -6e-108) {
		tmp = y4 * (b * ((t * j) - (y * k)));
	} else if (a <= -5.3e-278) {
		tmp = t_2;
	} else if (a <= 1.05e-155) {
		tmp = j * (y3 * (y0 * y5));
	} else if (a <= 3.6e-48) {
		tmp = t_2;
	} else if (a <= 8.8e+22) {
		tmp = (j * y5) * ((y0 * y3) - (t * i));
	} else if (a <= 2.7e+146) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else {
		tmp = y1 * (y3 * ((z * a) - (j * 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 * (z * ((y1 * y3) - (t * b)))
	t_2 = c * (y4 * ((y * y3) - (t * y2)))
	tmp = 0
	if a <= -7.8e+124:
		tmp = t_1
	elif a <= -2.2e+45:
		tmp = y4 * (y1 * ((k * y2) - (j * y3)))
	elif a <= -2.1e-40:
		tmp = t_1
	elif a <= -6e-108:
		tmp = y4 * (b * ((t * j) - (y * k)))
	elif a <= -5.3e-278:
		tmp = t_2
	elif a <= 1.05e-155:
		tmp = j * (y3 * (y0 * y5))
	elif a <= 3.6e-48:
		tmp = t_2
	elif a <= 8.8e+22:
		tmp = (j * y5) * ((y0 * y3) - (t * i))
	elif a <= 2.7e+146:
		tmp = t * (y2 * ((a * y5) - (c * y4)))
	else:
		tmp = y1 * (y3 * ((z * a) - (j * 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(z * Float64(Float64(y1 * y3) - Float64(t * b))))
	t_2 = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))))
	tmp = 0.0
	if (a <= -7.8e+124)
		tmp = t_1;
	elseif (a <= -2.2e+45)
		tmp = Float64(y4 * Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif (a <= -2.1e-40)
		tmp = t_1;
	elseif (a <= -6e-108)
		tmp = Float64(y4 * Float64(b * Float64(Float64(t * j) - Float64(y * k))));
	elseif (a <= -5.3e-278)
		tmp = t_2;
	elseif (a <= 1.05e-155)
		tmp = Float64(j * Float64(y3 * Float64(y0 * y5)));
	elseif (a <= 3.6e-48)
		tmp = t_2;
	elseif (a <= 8.8e+22)
		tmp = Float64(Float64(j * y5) * Float64(Float64(y0 * y3) - Float64(t * i)));
	elseif (a <= 2.7e+146)
		tmp = Float64(t * Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))));
	else
		tmp = Float64(y1 * Float64(y3 * Float64(Float64(z * a) - Float64(j * 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 * (z * ((y1 * y3) - (t * b)));
	t_2 = c * (y4 * ((y * y3) - (t * y2)));
	tmp = 0.0;
	if (a <= -7.8e+124)
		tmp = t_1;
	elseif (a <= -2.2e+45)
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	elseif (a <= -2.1e-40)
		tmp = t_1;
	elseif (a <= -6e-108)
		tmp = y4 * (b * ((t * j) - (y * k)));
	elseif (a <= -5.3e-278)
		tmp = t_2;
	elseif (a <= 1.05e-155)
		tmp = j * (y3 * (y0 * y5));
	elseif (a <= 3.6e-48)
		tmp = t_2;
	elseif (a <= 8.8e+22)
		tmp = (j * y5) * ((y0 * y3) - (t * i));
	elseif (a <= 2.7e+146)
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	else
		tmp = y1 * (y3 * ((z * a) - (j * 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[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.8e+124], t$95$1, If[LessEqual[a, -2.2e+45], N[(y4 * N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.1e-40], t$95$1, If[LessEqual[a, -6e-108], N[(y4 * N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5.3e-278], t$95$2, If[LessEqual[a, 1.05e-155], N[(j * N[(y3 * N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.6e-48], t$95$2, If[LessEqual[a, 8.8e+22], N[(N[(j * y5), $MachinePrecision] * N[(N[(y0 * y3), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.7e+146], N[(t * N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(y3 * N[(N[(z * a), $MachinePrecision] - N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if a < -7.8000000000000001e124 or -2.2e45 < a < -2.10000000000000018e-40

   1. Initial program 18.7%

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

   3. Simplified 18.7%

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

   5. Taylor expanded in a around inf 57.1%

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

   6. Taylor expanded in z around inf 54.7%

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

      1. +-commutative 54.7%

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

      2. mul-1-neg 54.7%

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

      3. unsub-neg 54.7%

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

      4. *-commutative 54.7%

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

      5. *-commutative 54.7%

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

   8. Simplified 54.7%

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

   if -7.8000000000000001e124 < a < -2.2e45

   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 55.3%

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

   4. Taylor expanded in y1 around inf 50.8%

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

   if -2.10000000000000018e-40 < a < -5.99999999999999986e-108

   1. Initial program 31.6%

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

   3. Taylor expanded in y4 around inf 52.8%

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

   4. Taylor expanded in b around inf 63.7%

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

   if -5.99999999999999986e-108 < a < -5.3e-278 or 1.0500000000000001e-155 < a < 3.6000000000000002e-48

   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 c around inf 44.6%

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

   6. Taylor expanded in y4 around inf 47.0%

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

   if -5.3e-278 < a < 1.0500000000000001e-155

   1. Initial program 48.1%

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

   3. Taylor expanded in y5 around -inf 41.7%

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

      1. associate-*r* 41.7%

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

      2. neg-mul-1 41.7%

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

      3. fma-def 45.4%

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

      4. *-commutative 45.4%

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

      5. *-commutative 45.4%

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

      6. *-commutative 45.4%

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

   5. Simplified 45.4%

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

   6. Taylor expanded in j around -inf 49.2%

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

      1. associate-*r* 42.1%

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

      2. +-commutative 42.1%

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

      3. mul-1-neg 42.1%

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

      4. unsub-neg 42.1%

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

   8. Simplified 42.1%

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

   9. Taylor expanded in y0 around inf 48.8%

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

       1. associate-*r* 45.3%

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

       2. *-commutative 45.3%

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

       3. associate-*l* 48.9%

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

   11. Simplified 48.9%

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

   if 3.6000000000000002e-48 < a < 8.8e22

   1. Initial program 50.0%

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

   3. Taylor expanded in y5 around -inf 40.3%

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

      1. associate-*r* 40.3%

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

      2. neg-mul-1 40.3%

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

      3. fma-def 40.3%

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

      4. *-commutative 40.3%

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

      5. *-commutative 40.3%

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

      6. *-commutative 40.3%

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

   5. Simplified 40.3%

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

   6. Taylor expanded in j around -inf 42.4%

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

      1. associate-*r* 51.6%

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

      2. +-commutative 51.6%

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

      3. mul-1-neg 51.6%

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

      4. unsub-neg 51.6%

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

   8. Simplified 51.6%

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

   if 8.8e22 < a < 2.69999999999999989e146

   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 y2 around inf 46.5%

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

   4. Taylor expanded in t around inf 49.4%

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

      1. *-commutative 49.4%

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

      2. *-commutative 49.4%

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

   6. Simplified 49.4%

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

   if 2.69999999999999989e146 < a

   1. Initial program 26.5%

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

   3. Taylor expanded in y1 around inf 53.5%

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

   4. Taylor expanded in y3 around inf 59.2%

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

      1. +-commutative 59.2%

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

      2. mul-1-neg 59.2%

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

      3. unsub-neg 59.2%

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

      4. *-commutative 59.2%

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

      5. *-commutative 59.2%

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

   6. Simplified 59.2%

      \[\leadsto y1 \cdot \color{blue}{\left(y3 \cdot \left(z \cdot a - y4 \cdot j\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{+124}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{+45}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-40}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-108}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;a \leq -5.3 \cdot 10^{-278}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-155}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-48}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{+22}:\\ \;\;\;\;\left(j \cdot y5\right) \cdot \left(y0 \cdot y3 - t \cdot i\right)\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+146}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 29.0% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right)\right)\\ t_2 := a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{if}\;a \leq -9.8 \cdot 10^{+120}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-277}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-159}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{+151}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y4 (* b (- (* t j) (* y k)))))
        (t_2 (* a (* z (- (* y1 y3) (* t b))))))
   (if (<= a -9.8e+120)
     t_2
     (if (<= a -3.5e+47)
       t_1
       (if (<= a -3.8e-40)
         t_2
         (if (<= a -1.35e-107)
           t_1
           (if (<= a -1.75e-277)
             (* c (* y4 (- (* y y3) (* t y2))))
             (if (<= a 4.5e-159)
               (* j (* y3 (* y0 y5)))
               (if (<= a 8.8e+151)
                 (* t (* y2 (- (* a y5) (* c y4))))
                 (* y1 (* y3 (- (* z a) (* j 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 = y4 * (b * ((t * j) - (y * k)));
	double t_2 = a * (z * ((y1 * y3) - (t * b)));
	double tmp;
	if (a <= -9.8e+120) {
		tmp = t_2;
	} else if (a <= -3.5e+47) {
		tmp = t_1;
	} else if (a <= -3.8e-40) {
		tmp = t_2;
	} else if (a <= -1.35e-107) {
		tmp = t_1;
	} else if (a <= -1.75e-277) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (a <= 4.5e-159) {
		tmp = j * (y3 * (y0 * y5));
	} else if (a <= 8.8e+151) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else {
		tmp = y1 * (y3 * ((z * a) - (j * 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) :: t_2
    real(8) :: tmp
    t_1 = y4 * (b * ((t * j) - (y * k)))
    t_2 = a * (z * ((y1 * y3) - (t * b)))
    if (a <= (-9.8d+120)) then
        tmp = t_2
    else if (a <= (-3.5d+47)) then
        tmp = t_1
    else if (a <= (-3.8d-40)) then
        tmp = t_2
    else if (a <= (-1.35d-107)) then
        tmp = t_1
    else if (a <= (-1.75d-277)) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else if (a <= 4.5d-159) then
        tmp = j * (y3 * (y0 * y5))
    else if (a <= 8.8d+151) then
        tmp = t * (y2 * ((a * y5) - (c * y4)))
    else
        tmp = y1 * (y3 * ((z * a) - (j * 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 = y4 * (b * ((t * j) - (y * k)));
	double t_2 = a * (z * ((y1 * y3) - (t * b)));
	double tmp;
	if (a <= -9.8e+120) {
		tmp = t_2;
	} else if (a <= -3.5e+47) {
		tmp = t_1;
	} else if (a <= -3.8e-40) {
		tmp = t_2;
	} else if (a <= -1.35e-107) {
		tmp = t_1;
	} else if (a <= -1.75e-277) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (a <= 4.5e-159) {
		tmp = j * (y3 * (y0 * y5));
	} else if (a <= 8.8e+151) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else {
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y4 * (b * ((t * j) - (y * k)))
	t_2 = a * (z * ((y1 * y3) - (t * b)))
	tmp = 0
	if a <= -9.8e+120:
		tmp = t_2
	elif a <= -3.5e+47:
		tmp = t_1
	elif a <= -3.8e-40:
		tmp = t_2
	elif a <= -1.35e-107:
		tmp = t_1
	elif a <= -1.75e-277:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	elif a <= 4.5e-159:
		tmp = j * (y3 * (y0 * y5))
	elif a <= 8.8e+151:
		tmp = t * (y2 * ((a * y5) - (c * y4)))
	else:
		tmp = y1 * (y3 * ((z * a) - (j * 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(y4 * Float64(b * Float64(Float64(t * j) - Float64(y * k))))
	t_2 = Float64(a * Float64(z * Float64(Float64(y1 * y3) - Float64(t * b))))
	tmp = 0.0
	if (a <= -9.8e+120)
		tmp = t_2;
	elseif (a <= -3.5e+47)
		tmp = t_1;
	elseif (a <= -3.8e-40)
		tmp = t_2;
	elseif (a <= -1.35e-107)
		tmp = t_1;
	elseif (a <= -1.75e-277)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (a <= 4.5e-159)
		tmp = Float64(j * Float64(y3 * Float64(y0 * y5)));
	elseif (a <= 8.8e+151)
		tmp = Float64(t * Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))));
	else
		tmp = Float64(y1 * Float64(y3 * Float64(Float64(z * a) - Float64(j * 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 = y4 * (b * ((t * j) - (y * k)));
	t_2 = a * (z * ((y1 * y3) - (t * b)));
	tmp = 0.0;
	if (a <= -9.8e+120)
		tmp = t_2;
	elseif (a <= -3.5e+47)
		tmp = t_1;
	elseif (a <= -3.8e-40)
		tmp = t_2;
	elseif (a <= -1.35e-107)
		tmp = t_1;
	elseif (a <= -1.75e-277)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	elseif (a <= 4.5e-159)
		tmp = j * (y3 * (y0 * y5));
	elseif (a <= 8.8e+151)
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	else
		tmp = y1 * (y3 * ((z * a) - (j * 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[(y4 * N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9.8e+120], t$95$2, If[LessEqual[a, -3.5e+47], t$95$1, If[LessEqual[a, -3.8e-40], t$95$2, If[LessEqual[a, -1.35e-107], t$95$1, If[LessEqual[a, -1.75e-277], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.5e-159], N[(j * N[(y3 * N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.8e+151], N[(t * N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(y3 * N[(N[(z * a), $MachinePrecision] - N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -9.80000000000000021e120 or -3.50000000000000015e47 < a < -3.7999999999999999e-40

   1. Initial program 18.7%

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

   3. Simplified 18.7%

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

   5. Taylor expanded in a around inf 57.1%

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

   6. Taylor expanded in z around inf 54.7%

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

      1. +-commutative 54.7%

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

      2. mul-1-neg 54.7%

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

      3. unsub-neg 54.7%

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

      4. *-commutative 54.7%

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

      5. *-commutative 54.7%

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

   8. Simplified 54.7%

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

   if -9.80000000000000021e120 < a < -3.50000000000000015e47 or -3.7999999999999999e-40 < a < -1.35e-107

   1. Initial program 25.6%

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

   3. Taylor expanded in y4 around inf 54.1%

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

   4. Taylor expanded in b around inf 54.8%

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

   if -1.35e-107 < a < -1.74999999999999991e-277

   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 c around inf 45.7%

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

   6. Taylor expanded in y4 around inf 49.1%

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

   if -1.74999999999999991e-277 < a < 4.49999999999999989e-159

   1. Initial program 46.2%

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

   3. Taylor expanded in y5 around -inf 39.5%

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

      1. associate-*r* 39.5%

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

      2. neg-mul-1 39.5%

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

      3. fma-def 43.3%

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

      4. *-commutative 43.3%

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

      5. *-commutative 43.3%

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

      6. *-commutative 43.3%

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

   5. Simplified 43.3%

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

   6. Taylor expanded in j around -inf 47.3%

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

      1. associate-*r* 43.5%

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

      2. +-commutative 43.5%

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

      3. mul-1-neg 43.5%

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

      4. unsub-neg 43.5%

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

   8. Simplified 43.5%

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

   9. Taylor expanded in y0 around inf 46.9%

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

       1. associate-*r* 46.9%

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

       2. *-commutative 46.9%

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

       3. associate-*l* 50.6%

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

   11. Simplified 50.6%

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

   if 4.49999999999999989e-159 < a < 8.80000000000000027e151

   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 y2 around inf 43.2%

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

   4. Taylor expanded in t around inf 38.3%

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

      1. *-commutative 38.3%

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

      2. *-commutative 38.3%

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

   6. Simplified 38.3%

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

   if 8.80000000000000027e151 < a

   1. Initial program 26.5%

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

   3. Taylor expanded in y1 around inf 53.5%

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

   4. Taylor expanded in y3 around inf 59.2%

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

      1. +-commutative 59.2%

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

      2. mul-1-neg 59.2%

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

      3. unsub-neg 59.2%

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

      4. *-commutative 59.2%

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

      5. *-commutative 59.2%

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

   6. Simplified 59.2%

      \[\leadsto y1 \cdot \color{blue}{\left(y3 \cdot \left(z \cdot a - y4 \cdot j\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 49.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.8 \cdot 10^{+120}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{+47}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-40}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-107}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-277}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-159}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{+151}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 28.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{if}\;a \leq -9 \cdot 10^{+122}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{+45}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-107}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;a \leq -3.15 \cdot 10^{-276}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{-158}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{+147}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* z (- (* y1 y3) (* t b))))))
   (if (<= a -9e+122)
     t_1
     (if (<= a -8.5e+45)
       (* y4 (* y1 (- (* k y2) (* j y3))))
       (if (<= a -1.25e-40)
         t_1
         (if (<= a -1.15e-107)
           (* y4 (* b (- (* t j) (* y k))))
           (if (<= a -3.15e-276)
             (* c (* y4 (- (* y y3) (* t y2))))
             (if (<= a 7.8e-158)
               (* j (* y3 (* y0 y5)))
               (if (<= a 8.6e+147)
                 (* t (* y2 (- (* a y5) (* c y4))))
                 (* y1 (* y3 (- (* z a) (* j 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 * (z * ((y1 * y3) - (t * b)));
	double tmp;
	if (a <= -9e+122) {
		tmp = t_1;
	} else if (a <= -8.5e+45) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (a <= -1.25e-40) {
		tmp = t_1;
	} else if (a <= -1.15e-107) {
		tmp = y4 * (b * ((t * j) - (y * k)));
	} else if (a <= -3.15e-276) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (a <= 7.8e-158) {
		tmp = j * (y3 * (y0 * y5));
	} else if (a <= 8.6e+147) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else {
		tmp = y1 * (y3 * ((z * a) - (j * 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 * (z * ((y1 * y3) - (t * b)))
    if (a <= (-9d+122)) then
        tmp = t_1
    else if (a <= (-8.5d+45)) then
        tmp = y4 * (y1 * ((k * y2) - (j * y3)))
    else if (a <= (-1.25d-40)) then
        tmp = t_1
    else if (a <= (-1.15d-107)) then
        tmp = y4 * (b * ((t * j) - (y * k)))
    else if (a <= (-3.15d-276)) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else if (a <= 7.8d-158) then
        tmp = j * (y3 * (y0 * y5))
    else if (a <= 8.6d+147) then
        tmp = t * (y2 * ((a * y5) - (c * y4)))
    else
        tmp = y1 * (y3 * ((z * a) - (j * 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 * (z * ((y1 * y3) - (t * b)));
	double tmp;
	if (a <= -9e+122) {
		tmp = t_1;
	} else if (a <= -8.5e+45) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (a <= -1.25e-40) {
		tmp = t_1;
	} else if (a <= -1.15e-107) {
		tmp = y4 * (b * ((t * j) - (y * k)));
	} else if (a <= -3.15e-276) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (a <= 7.8e-158) {
		tmp = j * (y3 * (y0 * y5));
	} else if (a <= 8.6e+147) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else {
		tmp = y1 * (y3 * ((z * a) - (j * 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 * (z * ((y1 * y3) - (t * b)))
	tmp = 0
	if a <= -9e+122:
		tmp = t_1
	elif a <= -8.5e+45:
		tmp = y4 * (y1 * ((k * y2) - (j * y3)))
	elif a <= -1.25e-40:
		tmp = t_1
	elif a <= -1.15e-107:
		tmp = y4 * (b * ((t * j) - (y * k)))
	elif a <= -3.15e-276:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	elif a <= 7.8e-158:
		tmp = j * (y3 * (y0 * y5))
	elif a <= 8.6e+147:
		tmp = t * (y2 * ((a * y5) - (c * y4)))
	else:
		tmp = y1 * (y3 * ((z * a) - (j * 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(z * Float64(Float64(y1 * y3) - Float64(t * b))))
	tmp = 0.0
	if (a <= -9e+122)
		tmp = t_1;
	elseif (a <= -8.5e+45)
		tmp = Float64(y4 * Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif (a <= -1.25e-40)
		tmp = t_1;
	elseif (a <= -1.15e-107)
		tmp = Float64(y4 * Float64(b * Float64(Float64(t * j) - Float64(y * k))));
	elseif (a <= -3.15e-276)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (a <= 7.8e-158)
		tmp = Float64(j * Float64(y3 * Float64(y0 * y5)));
	elseif (a <= 8.6e+147)
		tmp = Float64(t * Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))));
	else
		tmp = Float64(y1 * Float64(y3 * Float64(Float64(z * a) - Float64(j * 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 * (z * ((y1 * y3) - (t * b)));
	tmp = 0.0;
	if (a <= -9e+122)
		tmp = t_1;
	elseif (a <= -8.5e+45)
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	elseif (a <= -1.25e-40)
		tmp = t_1;
	elseif (a <= -1.15e-107)
		tmp = y4 * (b * ((t * j) - (y * k)));
	elseif (a <= -3.15e-276)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	elseif (a <= 7.8e-158)
		tmp = j * (y3 * (y0 * y5));
	elseif (a <= 8.6e+147)
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	else
		tmp = y1 * (y3 * ((z * a) - (j * 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[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9e+122], t$95$1, If[LessEqual[a, -8.5e+45], N[(y4 * N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.25e-40], t$95$1, If[LessEqual[a, -1.15e-107], N[(y4 * N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.15e-276], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.8e-158], N[(j * N[(y3 * N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.6e+147], N[(t * N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(y3 * N[(N[(z * a), $MachinePrecision] - N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if a < -8.99999999999999995e122 or -8.4999999999999996e45 < a < -1.24999999999999991e-40

   1. Initial program 18.7%

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

   3. Simplified 18.7%

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

   5. Taylor expanded in a around inf 57.1%

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

   6. Taylor expanded in z around inf 54.7%

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

      1. +-commutative 54.7%

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

      2. mul-1-neg 54.7%

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

      3. unsub-neg 54.7%

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

      4. *-commutative 54.7%

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

      5. *-commutative 54.7%

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

   8. Simplified 54.7%

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

   if -8.99999999999999995e122 < a < -8.4999999999999996e45

   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 55.3%

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

   4. Taylor expanded in y1 around inf 50.8%

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

   if -1.24999999999999991e-40 < a < -1.15000000000000002e-107

   1. Initial program 31.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf 52.8%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in b around inf 63.7%

      \[\leadsto y4 \cdot \color{blue}{\left(b \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   if -1.15000000000000002e-107 < a < -3.1499999999999999e-276

   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 c around inf 45.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   6. Taylor expanded in y4 around inf 49.1%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   if -3.1499999999999999e-276 < a < 7.7999999999999993e-158

   1. Initial program 46.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around -inf 39.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 39.5%

         \[\leadsto \color{blue}{\left(-1 \cdot y5\right) \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. neg-mul-1 39.5%

         \[\leadsto \color{blue}{\left(-y5\right)} \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. fma-def 43.3%

         \[\leadsto \left(-y5\right) \cdot \left(\color{blue}{\mathsf{fma}\left(i, j \cdot t - k \cdot y, y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 43.3%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, \color{blue}{t \cdot j} - k \cdot y, y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 43.3%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 43.3%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   5. Simplified 43.3%

      \[\leadsto \color{blue}{\left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in j around -inf 47.3%

      \[\leadsto \color{blue}{j \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 43.5%

         \[\leadsto \color{blue}{\left(j \cdot y5\right) \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)} \]

      2. +-commutative 43.5%

         \[\leadsto \left(j \cdot y5\right) \cdot \color{blue}{\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)} \]

      3. mul-1-neg 43.5%

         \[\leadsto \left(j \cdot y5\right) \cdot \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right) \]

      4. unsub-neg 43.5%

         \[\leadsto \left(j \cdot y5\right) \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)} \]

   8. Simplified 43.5%

      \[\leadsto \color{blue}{\left(j \cdot y5\right) \cdot \left(y0 \cdot y3 - i \cdot t\right)} \]

   9. Taylor expanded in y0 around inf 46.9%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 46.9%

          \[\leadsto j \cdot \color{blue}{\left(\left(y0 \cdot y3\right) \cdot y5\right)} \]

       2. *-commutative 46.9%

          \[\leadsto j \cdot \left(\color{blue}{\left(y3 \cdot y0\right)} \cdot y5\right) \]

       3. associate-*l* 50.6%

          \[\leadsto j \cdot \color{blue}{\left(y3 \cdot \left(y0 \cdot y5\right)\right)} \]

   11. Simplified 50.6%

       \[\leadsto \color{blue}{j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)} \]

   if 7.7999999999999993e-158 < a < 8.5999999999999997e147

   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 y2 around inf 43.2%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 38.3%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 38.3%

         \[\leadsto t \cdot \left(y2 \cdot \left(\color{blue}{y5 \cdot a} - c \cdot y4\right)\right) \]

      2. *-commutative 38.3%

         \[\leadsto t \cdot \left(y2 \cdot \left(y5 \cdot a - \color{blue}{y4 \cdot c}\right)\right) \]

   6. Simplified 38.3%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(y5 \cdot a - y4 \cdot c\right)\right)} \]

   if 8.5999999999999997e147 < a

   1. Initial program 26.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 53.5%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in y3 around inf 59.2%

      \[\leadsto y1 \cdot \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(j \cdot y4\right) + a \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 59.2%

         \[\leadsto y1 \cdot \left(y3 \cdot \color{blue}{\left(a \cdot z + -1 \cdot \left(j \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 59.2%

         \[\leadsto y1 \cdot \left(y3 \cdot \left(a \cdot z + \color{blue}{\left(-j \cdot y4\right)}\right)\right) \]

      3. unsub-neg 59.2%

         \[\leadsto y1 \cdot \left(y3 \cdot \color{blue}{\left(a \cdot z - j \cdot y4\right)}\right) \]

      4. *-commutative 59.2%

         \[\leadsto y1 \cdot \left(y3 \cdot \left(\color{blue}{z \cdot a} - j \cdot y4\right)\right) \]

      5. *-commutative 59.2%

         \[\leadsto y1 \cdot \left(y3 \cdot \left(z \cdot a - \color{blue}{y4 \cdot j}\right)\right) \]

   6. Simplified 59.2%

      \[\leadsto y1 \cdot \color{blue}{\left(y3 \cdot \left(z \cdot a - y4 \cdot j\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 50.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+122}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{+45}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-40}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-107}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;a \leq -3.15 \cdot 10^{-276}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{-158}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{+147}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 29.4% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ t_2 := a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{if}\;a \leq -1.15 \cdot 10^{-55}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-276}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-153}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 3.75 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.65 \cdot 10^{+101}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+142}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y4 (- (* y y3) (* t y2)))))
        (t_2 (* a (* z (- (* y1 y3) (* t b))))))
   (if (<= a -1.15e-55)
     t_2
     (if (<= a -3e-276)
       t_1
       (if (<= a 1.45e-153)
         (* j (* y3 (* y0 y5)))
         (if (<= a 3.75e+56)
           t_1
           (if (<= a 2.65e+101)
             (* a (* y (- (* x b) (* y3 y5))))
             (if (<= a 6.2e+142) (* c (* y2 (- (* x y0) (* t y4)))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y4 * ((y * y3) - (t * y2)));
	double t_2 = a * (z * ((y1 * y3) - (t * b)));
	double tmp;
	if (a <= -1.15e-55) {
		tmp = t_2;
	} else if (a <= -3e-276) {
		tmp = t_1;
	} else if (a <= 1.45e-153) {
		tmp = j * (y3 * (y0 * y5));
	} else if (a <= 3.75e+56) {
		tmp = t_1;
	} else if (a <= 2.65e+101) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (a <= 6.2e+142) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * (y4 * ((y * y3) - (t * y2)))
    t_2 = a * (z * ((y1 * y3) - (t * b)))
    if (a <= (-1.15d-55)) then
        tmp = t_2
    else if (a <= (-3d-276)) then
        tmp = t_1
    else if (a <= 1.45d-153) then
        tmp = j * (y3 * (y0 * y5))
    else if (a <= 3.75d+56) then
        tmp = t_1
    else if (a <= 2.65d+101) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (a <= 6.2d+142) then
        tmp = c * (y2 * ((x * y0) - (t * y4)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y4 * ((y * y3) - (t * y2)));
	double t_2 = a * (z * ((y1 * y3) - (t * b)));
	double tmp;
	if (a <= -1.15e-55) {
		tmp = t_2;
	} else if (a <= -3e-276) {
		tmp = t_1;
	} else if (a <= 1.45e-153) {
		tmp = j * (y3 * (y0 * y5));
	} else if (a <= 3.75e+56) {
		tmp = t_1;
	} else if (a <= 2.65e+101) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (a <= 6.2e+142) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (y4 * ((y * y3) - (t * y2)))
	t_2 = a * (z * ((y1 * y3) - (t * b)))
	tmp = 0
	if a <= -1.15e-55:
		tmp = t_2
	elif a <= -3e-276:
		tmp = t_1
	elif a <= 1.45e-153:
		tmp = j * (y3 * (y0 * y5))
	elif a <= 3.75e+56:
		tmp = t_1
	elif a <= 2.65e+101:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif a <= 6.2e+142:
		tmp = c * (y2 * ((x * y0) - (t * y4)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))))
	t_2 = Float64(a * Float64(z * Float64(Float64(y1 * y3) - Float64(t * b))))
	tmp = 0.0
	if (a <= -1.15e-55)
		tmp = t_2;
	elseif (a <= -3e-276)
		tmp = t_1;
	elseif (a <= 1.45e-153)
		tmp = Float64(j * Float64(y3 * Float64(y0 * y5)));
	elseif (a <= 3.75e+56)
		tmp = t_1;
	elseif (a <= 2.65e+101)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (a <= 6.2e+142)
		tmp = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (y4 * ((y * y3) - (t * y2)));
	t_2 = a * (z * ((y1 * y3) - (t * b)));
	tmp = 0.0;
	if (a <= -1.15e-55)
		tmp = t_2;
	elseif (a <= -3e-276)
		tmp = t_1;
	elseif (a <= 1.45e-153)
		tmp = j * (y3 * (y0 * y5));
	elseif (a <= 3.75e+56)
		tmp = t_1;
	elseif (a <= 2.65e+101)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (a <= 6.2e+142)
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.15e-55], t$95$2, If[LessEqual[a, -3e-276], t$95$1, If[LessEqual[a, 1.45e-153], N[(j * N[(y3 * N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.75e+56], t$95$1, If[LessEqual[a, 2.65e+101], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.2e+142], N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.15000000000000006e-55 or 6.1999999999999998e142 < a

   1. Initial program 21.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 21.5%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   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 z around inf 47.1%

      \[\leadsto a \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 47.1%

         \[\leadsto a \cdot \left(z \cdot \color{blue}{\left(y1 \cdot y3 + -1 \cdot \left(b \cdot t\right)\right)}\right) \]

      2. mul-1-neg 47.1%

         \[\leadsto a \cdot \left(z \cdot \left(y1 \cdot y3 + \color{blue}{\left(-b \cdot t\right)}\right)\right) \]

      3. unsub-neg 47.1%

         \[\leadsto a \cdot \left(z \cdot \color{blue}{\left(y1 \cdot y3 - b \cdot t\right)}\right) \]

      4. *-commutative 47.1%

         \[\leadsto a \cdot \left(z \cdot \left(\color{blue}{y3 \cdot y1} - b \cdot t\right)\right) \]

      5. *-commutative 47.1%

         \[\leadsto a \cdot \left(z \cdot \left(y3 \cdot y1 - \color{blue}{t \cdot b}\right)\right) \]

   8. Simplified 47.1%

      \[\leadsto a \cdot \color{blue}{\left(z \cdot \left(y3 \cdot y1 - t \cdot b\right)\right)} \]

   if -1.15000000000000006e-55 < a < -2.99999999999999988e-276 or 1.45000000000000001e-153 < a < 3.75e56

   1. Initial program 39.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 39.5%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 45.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   6. Taylor expanded in y4 around inf 41.9%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   if -2.99999999999999988e-276 < a < 1.45000000000000001e-153

   1. Initial program 48.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around -inf 41.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 41.7%

         \[\leadsto \color{blue}{\left(-1 \cdot y5\right) \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. neg-mul-1 41.7%

         \[\leadsto \color{blue}{\left(-y5\right)} \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. fma-def 45.4%

         \[\leadsto \left(-y5\right) \cdot \left(\color{blue}{\mathsf{fma}\left(i, j \cdot t - k \cdot y, y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 45.4%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, \color{blue}{t \cdot j} - k \cdot y, y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 45.4%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 45.4%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   5. Simplified 45.4%

      \[\leadsto \color{blue}{\left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in j around -inf 49.2%

      \[\leadsto \color{blue}{j \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 42.1%

         \[\leadsto \color{blue}{\left(j \cdot y5\right) \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)} \]

      2. +-commutative 42.1%

         \[\leadsto \left(j \cdot y5\right) \cdot \color{blue}{\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)} \]

      3. mul-1-neg 42.1%

         \[\leadsto \left(j \cdot y5\right) \cdot \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right) \]

      4. unsub-neg 42.1%

         \[\leadsto \left(j \cdot y5\right) \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)} \]

   8. Simplified 42.1%

      \[\leadsto \color{blue}{\left(j \cdot y5\right) \cdot \left(y0 \cdot y3 - i \cdot t\right)} \]

   9. Taylor expanded in y0 around inf 48.8%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 45.3%

          \[\leadsto j \cdot \color{blue}{\left(\left(y0 \cdot y3\right) \cdot y5\right)} \]

       2. *-commutative 45.3%

          \[\leadsto j \cdot \left(\color{blue}{\left(y3 \cdot y0\right)} \cdot y5\right) \]

       3. associate-*l* 48.9%

          \[\leadsto j \cdot \color{blue}{\left(y3 \cdot \left(y0 \cdot y5\right)\right)} \]

   11. Simplified 48.9%

       \[\leadsto \color{blue}{j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)} \]

   if 3.75e56 < a < 2.65000000000000003e101

   1. Initial program 41.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 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 a around inf 59.5%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in y around inf 47.6%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 47.6%

         \[\leadsto a \cdot \left(y \cdot \left(\color{blue}{x \cdot b} - y3 \cdot y5\right)\right) \]

      2. *-commutative 47.6%

         \[\leadsto a \cdot \left(y \cdot \left(x \cdot b - \color{blue}{y5 \cdot y3}\right)\right) \]

   8. Simplified 47.6%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(x \cdot b - y5 \cdot y3\right)\right)} \]

   if 2.65000000000000003e101 < a < 6.1999999999999998e142

   1. Initial program 13.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 33.3%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 67.0%

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 67.0%

         \[\leadsto c \cdot \left(y2 \cdot \left(\color{blue}{y0 \cdot x} - t \cdot y4\right)\right) \]

   6. Simplified 67.0%

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(y0 \cdot x - t \cdot y4\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{-55}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-276}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-153}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 3.75 \cdot 10^{+56}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 2.65 \cdot 10^{+101}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+142}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 29.6% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ t_2 := a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{if}\;a \leq -3.8 \cdot 10^{-56}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-278}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-156}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+92}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+150}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y4 (- (* y y3) (* t y2)))))
        (t_2 (* a (* z (- (* y1 y3) (* t b))))))
   (if (<= a -3.8e-56)
     t_2
     (if (<= a -6.2e-278)
       t_1
       (if (<= a 1.6e-156)
         (* j (* y3 (* y0 y5)))
         (if (<= a 2.9e+56)
           t_1
           (if (<= a 5.2e+92)
             (* a (* y (- (* x b) (* y3 y5))))
             (if (<= a 1.8e+150) (* t (* y2 (- (* a y5) (* c y4)))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y4 * ((y * y3) - (t * y2)));
	double t_2 = a * (z * ((y1 * y3) - (t * b)));
	double tmp;
	if (a <= -3.8e-56) {
		tmp = t_2;
	} else if (a <= -6.2e-278) {
		tmp = t_1;
	} else if (a <= 1.6e-156) {
		tmp = j * (y3 * (y0 * y5));
	} else if (a <= 2.9e+56) {
		tmp = t_1;
	} else if (a <= 5.2e+92) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (a <= 1.8e+150) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * (y4 * ((y * y3) - (t * y2)))
    t_2 = a * (z * ((y1 * y3) - (t * b)))
    if (a <= (-3.8d-56)) then
        tmp = t_2
    else if (a <= (-6.2d-278)) then
        tmp = t_1
    else if (a <= 1.6d-156) then
        tmp = j * (y3 * (y0 * y5))
    else if (a <= 2.9d+56) then
        tmp = t_1
    else if (a <= 5.2d+92) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (a <= 1.8d+150) then
        tmp = t * (y2 * ((a * y5) - (c * y4)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y4 * ((y * y3) - (t * y2)));
	double t_2 = a * (z * ((y1 * y3) - (t * b)));
	double tmp;
	if (a <= -3.8e-56) {
		tmp = t_2;
	} else if (a <= -6.2e-278) {
		tmp = t_1;
	} else if (a <= 1.6e-156) {
		tmp = j * (y3 * (y0 * y5));
	} else if (a <= 2.9e+56) {
		tmp = t_1;
	} else if (a <= 5.2e+92) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (a <= 1.8e+150) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (y4 * ((y * y3) - (t * y2)))
	t_2 = a * (z * ((y1 * y3) - (t * b)))
	tmp = 0
	if a <= -3.8e-56:
		tmp = t_2
	elif a <= -6.2e-278:
		tmp = t_1
	elif a <= 1.6e-156:
		tmp = j * (y3 * (y0 * y5))
	elif a <= 2.9e+56:
		tmp = t_1
	elif a <= 5.2e+92:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif a <= 1.8e+150:
		tmp = t * (y2 * ((a * y5) - (c * y4)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))))
	t_2 = Float64(a * Float64(z * Float64(Float64(y1 * y3) - Float64(t * b))))
	tmp = 0.0
	if (a <= -3.8e-56)
		tmp = t_2;
	elseif (a <= -6.2e-278)
		tmp = t_1;
	elseif (a <= 1.6e-156)
		tmp = Float64(j * Float64(y3 * Float64(y0 * y5)));
	elseif (a <= 2.9e+56)
		tmp = t_1;
	elseif (a <= 5.2e+92)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (a <= 1.8e+150)
		tmp = Float64(t * Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (y4 * ((y * y3) - (t * y2)));
	t_2 = a * (z * ((y1 * y3) - (t * b)));
	tmp = 0.0;
	if (a <= -3.8e-56)
		tmp = t_2;
	elseif (a <= -6.2e-278)
		tmp = t_1;
	elseif (a <= 1.6e-156)
		tmp = j * (y3 * (y0 * y5));
	elseif (a <= 2.9e+56)
		tmp = t_1;
	elseif (a <= 5.2e+92)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (a <= 1.8e+150)
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.8e-56], t$95$2, If[LessEqual[a, -6.2e-278], t$95$1, If[LessEqual[a, 1.6e-156], N[(j * N[(y3 * N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.9e+56], t$95$1, If[LessEqual[a, 5.2e+92], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.8e+150], N[(t * N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.8000000000000002e-56 or 1.79999999999999993e150 < a

   1. Initial program 21.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 21.7%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 51.5%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in z around inf 47.5%

      \[\leadsto a \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 47.5%

         \[\leadsto a \cdot \left(z \cdot \color{blue}{\left(y1 \cdot y3 + -1 \cdot \left(b \cdot t\right)\right)}\right) \]

      2. mul-1-neg 47.5%

         \[\leadsto a \cdot \left(z \cdot \left(y1 \cdot y3 + \color{blue}{\left(-b \cdot t\right)}\right)\right) \]

      3. unsub-neg 47.5%

         \[\leadsto a \cdot \left(z \cdot \color{blue}{\left(y1 \cdot y3 - b \cdot t\right)}\right) \]

      4. *-commutative 47.5%

         \[\leadsto a \cdot \left(z \cdot \left(\color{blue}{y3 \cdot y1} - b \cdot t\right)\right) \]

      5. *-commutative 47.5%

         \[\leadsto a \cdot \left(z \cdot \left(y3 \cdot y1 - \color{blue}{t \cdot b}\right)\right) \]

   8. Simplified 47.5%

      \[\leadsto a \cdot \color{blue}{\left(z \cdot \left(y3 \cdot y1 - t \cdot b\right)\right)} \]

   if -3.8000000000000002e-56 < a < -6.19999999999999983e-278 or 1.59999999999999991e-156 < a < 2.90000000000000007e56

   1. Initial program 39.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 39.5%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 45.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   6. Taylor expanded in y4 around inf 41.9%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   if -6.19999999999999983e-278 < a < 1.59999999999999991e-156

   1. Initial program 48.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around -inf 41.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 41.7%

         \[\leadsto \color{blue}{\left(-1 \cdot y5\right) \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. neg-mul-1 41.7%

         \[\leadsto \color{blue}{\left(-y5\right)} \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. fma-def 45.4%

         \[\leadsto \left(-y5\right) \cdot \left(\color{blue}{\mathsf{fma}\left(i, j \cdot t - k \cdot y, y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 45.4%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, \color{blue}{t \cdot j} - k \cdot y, y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 45.4%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 45.4%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   5. Simplified 45.4%

      \[\leadsto \color{blue}{\left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in j around -inf 49.2%

      \[\leadsto \color{blue}{j \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 42.1%

         \[\leadsto \color{blue}{\left(j \cdot y5\right) \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)} \]

      2. +-commutative 42.1%

         \[\leadsto \left(j \cdot y5\right) \cdot \color{blue}{\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)} \]

      3. mul-1-neg 42.1%

         \[\leadsto \left(j \cdot y5\right) \cdot \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right) \]

      4. unsub-neg 42.1%

         \[\leadsto \left(j \cdot y5\right) \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)} \]

   8. Simplified 42.1%

      \[\leadsto \color{blue}{\left(j \cdot y5\right) \cdot \left(y0 \cdot y3 - i \cdot t\right)} \]

   9. Taylor expanded in y0 around inf 48.8%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 45.3%

          \[\leadsto j \cdot \color{blue}{\left(\left(y0 \cdot y3\right) \cdot y5\right)} \]

       2. *-commutative 45.3%

          \[\leadsto j \cdot \left(\color{blue}{\left(y3 \cdot y0\right)} \cdot y5\right) \]

       3. associate-*l* 48.9%

          \[\leadsto j \cdot \color{blue}{\left(y3 \cdot \left(y0 \cdot y5\right)\right)} \]

   11. Simplified 48.9%

       \[\leadsto \color{blue}{j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)} \]

   if 2.90000000000000007e56 < a < 5.1999999999999998e92

   1. Initial program 46.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 53.3%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 67.2%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in y around inf 53.7%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 53.7%

         \[\leadsto a \cdot \left(y \cdot \left(\color{blue}{x \cdot b} - y3 \cdot y5\right)\right) \]

      2. *-commutative 53.7%

         \[\leadsto a \cdot \left(y \cdot \left(x \cdot b - \color{blue}{y5 \cdot y3}\right)\right) \]

   8. Simplified 53.7%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(x \cdot b - y5 \cdot y3\right)\right)} \]

   if 5.1999999999999998e92 < a < 1.79999999999999993e150

   1. Initial program 11.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 38.9%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 61.4%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 61.4%

         \[\leadsto t \cdot \left(y2 \cdot \left(\color{blue}{y5 \cdot a} - c \cdot y4\right)\right) \]

      2. *-commutative 61.4%

         \[\leadsto t \cdot \left(y2 \cdot \left(y5 \cdot a - \color{blue}{y4 \cdot c}\right)\right) \]

   6. Simplified 61.4%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(y5 \cdot a - y4 \cdot c\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{-56}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-278}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-156}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+56}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+92}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+150}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 29.4% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;a \leq -3.8 \cdot 10^{-54}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-277}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-154}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+92}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+146}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y4 (- (* y y3) (* t y2))))))
   (if (<= a -3.8e-54)
     (* a (* z (- (* y1 y3) (* t b))))
     (if (<= a -1.2e-277)
       t_1
       (if (<= a 7.6e-154)
         (* j (* y3 (* y0 y5)))
         (if (<= a 4.8e+56)
           t_1
           (if (<= a 3.3e+92)
             (* a (* y (- (* x b) (* y3 y5))))
             (if (<= a 1.45e+146)
               (* t (* y2 (- (* a y5) (* c y4))))
               (* y1 (* y3 (- (* z a) (* j 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 = c * (y4 * ((y * y3) - (t * y2)));
	double tmp;
	if (a <= -3.8e-54) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (a <= -1.2e-277) {
		tmp = t_1;
	} else if (a <= 7.6e-154) {
		tmp = j * (y3 * (y0 * y5));
	} else if (a <= 4.8e+56) {
		tmp = t_1;
	} else if (a <= 3.3e+92) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (a <= 1.45e+146) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else {
		tmp = y1 * (y3 * ((z * a) - (j * 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 = c * (y4 * ((y * y3) - (t * y2)))
    if (a <= (-3.8d-54)) then
        tmp = a * (z * ((y1 * y3) - (t * b)))
    else if (a <= (-1.2d-277)) then
        tmp = t_1
    else if (a <= 7.6d-154) then
        tmp = j * (y3 * (y0 * y5))
    else if (a <= 4.8d+56) then
        tmp = t_1
    else if (a <= 3.3d+92) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (a <= 1.45d+146) then
        tmp = t * (y2 * ((a * y5) - (c * y4)))
    else
        tmp = y1 * (y3 * ((z * a) - (j * 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 = c * (y4 * ((y * y3) - (t * y2)));
	double tmp;
	if (a <= -3.8e-54) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (a <= -1.2e-277) {
		tmp = t_1;
	} else if (a <= 7.6e-154) {
		tmp = j * (y3 * (y0 * y5));
	} else if (a <= 4.8e+56) {
		tmp = t_1;
	} else if (a <= 3.3e+92) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (a <= 1.45e+146) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else {
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (y4 * ((y * y3) - (t * y2)))
	tmp = 0
	if a <= -3.8e-54:
		tmp = a * (z * ((y1 * y3) - (t * b)))
	elif a <= -1.2e-277:
		tmp = t_1
	elif a <= 7.6e-154:
		tmp = j * (y3 * (y0 * y5))
	elif a <= 4.8e+56:
		tmp = t_1
	elif a <= 3.3e+92:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif a <= 1.45e+146:
		tmp = t * (y2 * ((a * y5) - (c * y4)))
	else:
		tmp = y1 * (y3 * ((z * a) - (j * 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(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))))
	tmp = 0.0
	if (a <= -3.8e-54)
		tmp = Float64(a * Float64(z * Float64(Float64(y1 * y3) - Float64(t * b))));
	elseif (a <= -1.2e-277)
		tmp = t_1;
	elseif (a <= 7.6e-154)
		tmp = Float64(j * Float64(y3 * Float64(y0 * y5)));
	elseif (a <= 4.8e+56)
		tmp = t_1;
	elseif (a <= 3.3e+92)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (a <= 1.45e+146)
		tmp = Float64(t * Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))));
	else
		tmp = Float64(y1 * Float64(y3 * Float64(Float64(z * a) - Float64(j * 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 = c * (y4 * ((y * y3) - (t * y2)));
	tmp = 0.0;
	if (a <= -3.8e-54)
		tmp = a * (z * ((y1 * y3) - (t * b)));
	elseif (a <= -1.2e-277)
		tmp = t_1;
	elseif (a <= 7.6e-154)
		tmp = j * (y3 * (y0 * y5));
	elseif (a <= 4.8e+56)
		tmp = t_1;
	elseif (a <= 3.3e+92)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (a <= 1.45e+146)
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	else
		tmp = y1 * (y3 * ((z * a) - (j * 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[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.8e-54], N[(a * N[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.2e-277], t$95$1, If[LessEqual[a, 7.6e-154], N[(j * N[(y3 * N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.8e+56], t$95$1, If[LessEqual[a, 3.3e+92], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.45e+146], N[(t * N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(y3 * N[(N[(z * a), $MachinePrecision] - N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -3.8000000000000002e-54

   1. Initial program 19.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 19.8%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 49.7%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in z around inf 46.0%

      \[\leadsto a \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 46.0%

         \[\leadsto a \cdot \left(z \cdot \color{blue}{\left(y1 \cdot y3 + -1 \cdot \left(b \cdot t\right)\right)}\right) \]

      2. mul-1-neg 46.0%

         \[\leadsto a \cdot \left(z \cdot \left(y1 \cdot y3 + \color{blue}{\left(-b \cdot t\right)}\right)\right) \]

      3. unsub-neg 46.0%

         \[\leadsto a \cdot \left(z \cdot \color{blue}{\left(y1 \cdot y3 - b \cdot t\right)}\right) \]

      4. *-commutative 46.0%

         \[\leadsto a \cdot \left(z \cdot \left(\color{blue}{y3 \cdot y1} - b \cdot t\right)\right) \]

      5. *-commutative 46.0%

         \[\leadsto a \cdot \left(z \cdot \left(y3 \cdot y1 - \color{blue}{t \cdot b}\right)\right) \]

   8. Simplified 46.0%

      \[\leadsto a \cdot \color{blue}{\left(z \cdot \left(y3 \cdot y1 - t \cdot b\right)\right)} \]

   if -3.8000000000000002e-54 < a < -1.2e-277 or 7.60000000000000019e-154 < a < 4.80000000000000027e56

   1. Initial program 39.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 39.5%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 45.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   6. Taylor expanded in y4 around inf 41.9%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   if -1.2e-277 < a < 7.60000000000000019e-154

   1. Initial program 48.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around -inf 41.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 41.7%

         \[\leadsto \color{blue}{\left(-1 \cdot y5\right) \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. neg-mul-1 41.7%

         \[\leadsto \color{blue}{\left(-y5\right)} \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. fma-def 45.4%

         \[\leadsto \left(-y5\right) \cdot \left(\color{blue}{\mathsf{fma}\left(i, j \cdot t - k \cdot y, y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 45.4%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, \color{blue}{t \cdot j} - k \cdot y, y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 45.4%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 45.4%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   5. Simplified 45.4%

      \[\leadsto \color{blue}{\left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in j around -inf 49.2%

      \[\leadsto \color{blue}{j \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 42.1%

         \[\leadsto \color{blue}{\left(j \cdot y5\right) \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)} \]

      2. +-commutative 42.1%

         \[\leadsto \left(j \cdot y5\right) \cdot \color{blue}{\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)} \]

      3. mul-1-neg 42.1%

         \[\leadsto \left(j \cdot y5\right) \cdot \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right) \]

      4. unsub-neg 42.1%

         \[\leadsto \left(j \cdot y5\right) \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)} \]

   8. Simplified 42.1%

      \[\leadsto \color{blue}{\left(j \cdot y5\right) \cdot \left(y0 \cdot y3 - i \cdot t\right)} \]

   9. Taylor expanded in y0 around inf 48.8%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 45.3%

          \[\leadsto j \cdot \color{blue}{\left(\left(y0 \cdot y3\right) \cdot y5\right)} \]

       2. *-commutative 45.3%

          \[\leadsto j \cdot \left(\color{blue}{\left(y3 \cdot y0\right)} \cdot y5\right) \]

       3. associate-*l* 48.9%

          \[\leadsto j \cdot \color{blue}{\left(y3 \cdot \left(y0 \cdot y5\right)\right)} \]

   11. Simplified 48.9%

       \[\leadsto \color{blue}{j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)} \]

   if 4.80000000000000027e56 < a < 3.29999999999999974e92

   1. Initial program 46.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 53.3%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 67.2%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in y around inf 53.7%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 53.7%

         \[\leadsto a \cdot \left(y \cdot \left(\color{blue}{x \cdot b} - y3 \cdot y5\right)\right) \]

      2. *-commutative 53.7%

         \[\leadsto a \cdot \left(y \cdot \left(x \cdot b - \color{blue}{y5 \cdot y3}\right)\right) \]

   8. Simplified 53.7%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(x \cdot b - y5 \cdot y3\right)\right)} \]

   if 3.29999999999999974e92 < a < 1.4499999999999999e146

   1. Initial program 11.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 38.9%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 61.4%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 61.4%

         \[\leadsto t \cdot \left(y2 \cdot \left(\color{blue}{y5 \cdot a} - c \cdot y4\right)\right) \]

      2. *-commutative 61.4%

         \[\leadsto t \cdot \left(y2 \cdot \left(y5 \cdot a - \color{blue}{y4 \cdot c}\right)\right) \]

   6. Simplified 61.4%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(y5 \cdot a - y4 \cdot c\right)\right)} \]

   if 1.4499999999999999e146 < a

   1. Initial program 26.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 53.5%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in y3 around inf 59.2%

      \[\leadsto y1 \cdot \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(j \cdot y4\right) + a \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 59.2%

         \[\leadsto y1 \cdot \left(y3 \cdot \color{blue}{\left(a \cdot z + -1 \cdot \left(j \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 59.2%

         \[\leadsto y1 \cdot \left(y3 \cdot \left(a \cdot z + \color{blue}{\left(-j \cdot y4\right)}\right)\right) \]

      3. unsub-neg 59.2%

         \[\leadsto y1 \cdot \left(y3 \cdot \color{blue}{\left(a \cdot z - j \cdot y4\right)}\right) \]

      4. *-commutative 59.2%

         \[\leadsto y1 \cdot \left(y3 \cdot \left(\color{blue}{z \cdot a} - j \cdot y4\right)\right) \]

      5. *-commutative 59.2%

         \[\leadsto y1 \cdot \left(y3 \cdot \left(z \cdot a - \color{blue}{y4 \cdot j}\right)\right) \]

   6. Simplified 59.2%

      \[\leadsto y1 \cdot \color{blue}{\left(y3 \cdot \left(z \cdot a - y4 \cdot j\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{-54}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-277}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-154}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+56}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+92}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+146}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 27.5% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ t_2 := c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{if}\;a \leq -5.4 \cdot 10^{-52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-156}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+16}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 10^{+100}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{+138}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* z (- (* y1 y3) (* t b)))))
        (t_2 (* c (* t (- (* z i) (* y2 y4))))))
   (if (<= a -5.4e-52)
     t_1
     (if (<= a 2.1e-156)
       (* j (* y0 (* y3 y5)))
       (if (<= a 5.6e+16)
         t_2
         (if (<= a 1e+100)
           (* a (* y (- (* x b) (* y3 y5))))
           (if (<= a 5.4e+138) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (z * ((y1 * y3) - (t * b)));
	double t_2 = c * (t * ((z * i) - (y2 * y4)));
	double tmp;
	if (a <= -5.4e-52) {
		tmp = t_1;
	} else if (a <= 2.1e-156) {
		tmp = j * (y0 * (y3 * y5));
	} else if (a <= 5.6e+16) {
		tmp = t_2;
	} else if (a <= 1e+100) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (a <= 5.4e+138) {
		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 = a * (z * ((y1 * y3) - (t * b)))
    t_2 = c * (t * ((z * i) - (y2 * y4)))
    if (a <= (-5.4d-52)) then
        tmp = t_1
    else if (a <= 2.1d-156) then
        tmp = j * (y0 * (y3 * y5))
    else if (a <= 5.6d+16) then
        tmp = t_2
    else if (a <= 1d+100) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (a <= 5.4d+138) 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 = a * (z * ((y1 * y3) - (t * b)));
	double t_2 = c * (t * ((z * i) - (y2 * y4)));
	double tmp;
	if (a <= -5.4e-52) {
		tmp = t_1;
	} else if (a <= 2.1e-156) {
		tmp = j * (y0 * (y3 * y5));
	} else if (a <= 5.6e+16) {
		tmp = t_2;
	} else if (a <= 1e+100) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (a <= 5.4e+138) {
		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 = a * (z * ((y1 * y3) - (t * b)))
	t_2 = c * (t * ((z * i) - (y2 * y4)))
	tmp = 0
	if a <= -5.4e-52:
		tmp = t_1
	elif a <= 2.1e-156:
		tmp = j * (y0 * (y3 * y5))
	elif a <= 5.6e+16:
		tmp = t_2
	elif a <= 1e+100:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif a <= 5.4e+138:
		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(a * Float64(z * Float64(Float64(y1 * y3) - Float64(t * b))))
	t_2 = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))))
	tmp = 0.0
	if (a <= -5.4e-52)
		tmp = t_1;
	elseif (a <= 2.1e-156)
		tmp = Float64(j * Float64(y0 * Float64(y3 * y5)));
	elseif (a <= 5.6e+16)
		tmp = t_2;
	elseif (a <= 1e+100)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (a <= 5.4e+138)
		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 = a * (z * ((y1 * y3) - (t * b)));
	t_2 = c * (t * ((z * i) - (y2 * y4)));
	tmp = 0.0;
	if (a <= -5.4e-52)
		tmp = t_1;
	elseif (a <= 2.1e-156)
		tmp = j * (y0 * (y3 * y5));
	elseif (a <= 5.6e+16)
		tmp = t_2;
	elseif (a <= 1e+100)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (a <= 5.4e+138)
		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[(a * N[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.4e-52], t$95$1, If[LessEqual[a, 2.1e-156], N[(j * N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.6e+16], t$95$2, If[LessEqual[a, 1e+100], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.4e+138], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.40000000000000019e-52 or 5.40000000000000018e138 < a

   1. Initial program 20.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 20.9%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 51.5%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in z around inf 47.4%

      \[\leadsto a \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 47.4%

         \[\leadsto a \cdot \left(z \cdot \color{blue}{\left(y1 \cdot y3 + -1 \cdot \left(b \cdot t\right)\right)}\right) \]

      2. mul-1-neg 47.4%

         \[\leadsto a \cdot \left(z \cdot \left(y1 \cdot y3 + \color{blue}{\left(-b \cdot t\right)}\right)\right) \]

      3. unsub-neg 47.4%

         \[\leadsto a \cdot \left(z \cdot \color{blue}{\left(y1 \cdot y3 - b \cdot t\right)}\right) \]

      4. *-commutative 47.4%

         \[\leadsto a \cdot \left(z \cdot \left(\color{blue}{y3 \cdot y1} - b \cdot t\right)\right) \]

      5. *-commutative 47.4%

         \[\leadsto a \cdot \left(z \cdot \left(y3 \cdot y1 - \color{blue}{t \cdot b}\right)\right) \]

   8. Simplified 47.4%

      \[\leadsto a \cdot \color{blue}{\left(z \cdot \left(y3 \cdot y1 - t \cdot b\right)\right)} \]

   if -5.40000000000000019e-52 < a < 2.10000000000000012e-156

   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 34.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 34.5%

         \[\leadsto \color{blue}{\left(-1 \cdot y5\right) \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. neg-mul-1 34.5%

         \[\leadsto \color{blue}{\left(-y5\right)} \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. fma-def 38.7%

         \[\leadsto \left(-y5\right) \cdot \left(\color{blue}{\mathsf{fma}\left(i, j \cdot t - k \cdot y, y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 38.7%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, \color{blue}{t \cdot j} - k \cdot y, y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 38.7%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 38.7%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   5. Simplified 38.7%

      \[\leadsto \color{blue}{\left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in j around -inf 40.4%

      \[\leadsto \color{blue}{j \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 35.2%

         \[\leadsto \color{blue}{\left(j \cdot y5\right) \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)} \]

      2. +-commutative 35.2%

         \[\leadsto \left(j \cdot y5\right) \cdot \color{blue}{\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)} \]

      3. mul-1-neg 35.2%

         \[\leadsto \left(j \cdot y5\right) \cdot \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right) \]

      4. unsub-neg 35.2%

         \[\leadsto \left(j \cdot y5\right) \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)} \]

   8. Simplified 35.2%

      \[\leadsto \color{blue}{\left(j \cdot y5\right) \cdot \left(y0 \cdot y3 - i \cdot t\right)} \]

   9. Taylor expanded in y0 around inf 36.2%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]

   if 2.10000000000000012e-156 < a < 5.6e16 or 1.00000000000000002e100 < a < 5.40000000000000018e138

   1. Initial program 31.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.0%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 38.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   6. Taylor expanded in t around inf 46.1%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(i \cdot z - y2 \cdot y4\right)\right)} \]

   if 5.6e16 < a < 1.00000000000000002e100

   1. Initial program 43.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 47.8%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 56.7%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in y around inf 44.4%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 44.4%

         \[\leadsto a \cdot \left(y \cdot \left(\color{blue}{x \cdot b} - y3 \cdot y5\right)\right) \]

      2. *-commutative 44.4%

         \[\leadsto a \cdot \left(y \cdot \left(x \cdot b - \color{blue}{y5 \cdot y3}\right)\right) \]

   8. Simplified 44.4%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(x \cdot b - y5 \cdot y3\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.4 \cdot 10^{-52}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-156}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+16}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 10^{+100}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{+138}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 30.1% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ t_2 := a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{if}\;y2 \leq -8.5 \cdot 10^{+220}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq -6.8 \cdot 10^{-48}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 9.8 \cdot 10^{-231}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y2 \leq 1.1 \cdot 10^{-76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq 1.05 \cdot 10^{+93}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* z (- (* y1 y3) (* t b)))))
        (t_2 (* a (* y (- (* x b) (* y3 y5))))))
   (if (<= y2 -8.5e+220)
     t_1
     (if (<= y2 -6.8e-48)
       (* c (* t (- (* z i) (* y2 y4))))
       (if (<= y2 9.8e-231)
         t_2
         (if (<= y2 1.1e-76)
           t_1
           (if (<= y2 1.05e+93) t_2 (* c (* y2 (- (* x y0) (* t 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 * (z * ((y1 * y3) - (t * b)));
	double t_2 = a * (y * ((x * b) - (y3 * y5)));
	double tmp;
	if (y2 <= -8.5e+220) {
		tmp = t_1;
	} else if (y2 <= -6.8e-48) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (y2 <= 9.8e-231) {
		tmp = t_2;
	} else if (y2 <= 1.1e-76) {
		tmp = t_1;
	} else if (y2 <= 1.05e+93) {
		tmp = t_2;
	} else {
		tmp = c * (y2 * ((x * y0) - (t * 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) :: t_2
    real(8) :: tmp
    t_1 = a * (z * ((y1 * y3) - (t * b)))
    t_2 = a * (y * ((x * b) - (y3 * y5)))
    if (y2 <= (-8.5d+220)) then
        tmp = t_1
    else if (y2 <= (-6.8d-48)) then
        tmp = c * (t * ((z * i) - (y2 * y4)))
    else if (y2 <= 9.8d-231) then
        tmp = t_2
    else if (y2 <= 1.1d-76) then
        tmp = t_1
    else if (y2 <= 1.05d+93) then
        tmp = t_2
    else
        tmp = c * (y2 * ((x * y0) - (t * 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 * (z * ((y1 * y3) - (t * b)));
	double t_2 = a * (y * ((x * b) - (y3 * y5)));
	double tmp;
	if (y2 <= -8.5e+220) {
		tmp = t_1;
	} else if (y2 <= -6.8e-48) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (y2 <= 9.8e-231) {
		tmp = t_2;
	} else if (y2 <= 1.1e-76) {
		tmp = t_1;
	} else if (y2 <= 1.05e+93) {
		tmp = t_2;
	} else {
		tmp = c * (y2 * ((x * y0) - (t * 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 * (z * ((y1 * y3) - (t * b)))
	t_2 = a * (y * ((x * b) - (y3 * y5)))
	tmp = 0
	if y2 <= -8.5e+220:
		tmp = t_1
	elif y2 <= -6.8e-48:
		tmp = c * (t * ((z * i) - (y2 * y4)))
	elif y2 <= 9.8e-231:
		tmp = t_2
	elif y2 <= 1.1e-76:
		tmp = t_1
	elif y2 <= 1.05e+93:
		tmp = t_2
	else:
		tmp = c * (y2 * ((x * y0) - (t * 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(z * Float64(Float64(y1 * y3) - Float64(t * b))))
	t_2 = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))))
	tmp = 0.0
	if (y2 <= -8.5e+220)
		tmp = t_1;
	elseif (y2 <= -6.8e-48)
		tmp = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (y2 <= 9.8e-231)
		tmp = t_2;
	elseif (y2 <= 1.1e-76)
		tmp = t_1;
	elseif (y2 <= 1.05e+93)
		tmp = t_2;
	else
		tmp = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * 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 * (z * ((y1 * y3) - (t * b)));
	t_2 = a * (y * ((x * b) - (y3 * y5)));
	tmp = 0.0;
	if (y2 <= -8.5e+220)
		tmp = t_1;
	elseif (y2 <= -6.8e-48)
		tmp = c * (t * ((z * i) - (y2 * y4)));
	elseif (y2 <= 9.8e-231)
		tmp = t_2;
	elseif (y2 <= 1.1e-76)
		tmp = t_1;
	elseif (y2 <= 1.05e+93)
		tmp = t_2;
	else
		tmp = c * (y2 * ((x * y0) - (t * 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[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -8.5e+220], t$95$1, If[LessEqual[y2, -6.8e-48], N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 9.8e-231], t$95$2, If[LessEqual[y2, 1.1e-76], t$95$1, If[LessEqual[y2, 1.05e+93], t$95$2, N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y2 < -8.4999999999999996e220 or 9.80000000000000007e-231 < y2 < 1.1e-76

   1. Initial program 30.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.1%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 39.8%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in z around inf 52.4%

      \[\leadsto a \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 52.4%

         \[\leadsto a \cdot \left(z \cdot \color{blue}{\left(y1 \cdot y3 + -1 \cdot \left(b \cdot t\right)\right)}\right) \]

      2. mul-1-neg 52.4%

         \[\leadsto a \cdot \left(z \cdot \left(y1 \cdot y3 + \color{blue}{\left(-b \cdot t\right)}\right)\right) \]

      3. unsub-neg 52.4%

         \[\leadsto a \cdot \left(z \cdot \color{blue}{\left(y1 \cdot y3 - b \cdot t\right)}\right) \]

      4. *-commutative 52.4%

         \[\leadsto a \cdot \left(z \cdot \left(\color{blue}{y3 \cdot y1} - b \cdot t\right)\right) \]

      5. *-commutative 52.4%

         \[\leadsto a \cdot \left(z \cdot \left(y3 \cdot y1 - \color{blue}{t \cdot b}\right)\right) \]

   8. Simplified 52.4%

      \[\leadsto a \cdot \color{blue}{\left(z \cdot \left(y3 \cdot y1 - t \cdot b\right)\right)} \]

   if -8.4999999999999996e220 < y2 < -6.80000000000000056e-48

   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 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 c around inf 44.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   6. Taylor expanded in t around inf 40.9%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(i \cdot z - y2 \cdot y4\right)\right)} \]

   if -6.80000000000000056e-48 < y2 < 9.80000000000000007e-231 or 1.1e-76 < y2 < 1.0499999999999999e93

   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 a around inf 37.4%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in y around inf 36.3%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 36.3%

         \[\leadsto a \cdot \left(y \cdot \left(\color{blue}{x \cdot b} - y3 \cdot y5\right)\right) \]

      2. *-commutative 36.3%

         \[\leadsto a \cdot \left(y \cdot \left(x \cdot b - \color{blue}{y5 \cdot y3}\right)\right) \]

   8. Simplified 36.3%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(x \cdot b - y5 \cdot y3\right)\right)} \]

   if 1.0499999999999999e93 < y2

   1. Initial program 19.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 43.6%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 48.5%

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 48.5%

         \[\leadsto c \cdot \left(y2 \cdot \left(\color{blue}{y0 \cdot x} - t \cdot y4\right)\right) \]

   6. Simplified 48.5%

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(y0 \cdot x - t \cdot y4\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -8.5 \cdot 10^{+220}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq -6.8 \cdot 10^{-48}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 9.8 \cdot 10^{-231}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 1.1 \cdot 10^{-76}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 1.05 \cdot 10^{+93}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 21.0% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{if}\;y5 \leq -5.7 \cdot 10^{+74}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq -1.22 \cdot 10^{-203}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y5 \leq -5.9 \cdot 10^{-291}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq 8.6 \cdot 10^{-222}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y5 \leq 2.8 \cdot 10^{+74}:\\ \;\;\;\;\left(y \cdot c\right) \cdot \left(y3 \cdot y4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(k \cdot y0\right) \cdot \left(y2 \cdot \left(-y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y (* x b)))))
   (if (<= y5 -5.7e+74)
     (* j (* y0 (* y3 y5)))
     (if (<= y5 -1.22e-203)
       t_1
       (if (<= y5 -5.9e-291)
         (* y4 (* y (* c y3)))
         (if (<= y5 8.6e-222)
           t_1
           (if (<= y5 2.8e+74)
             (* (* y c) (* y3 y4))
             (* (* k y0) (* y2 (- y5))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y * (x * b));
	double tmp;
	if (y5 <= -5.7e+74) {
		tmp = j * (y0 * (y3 * y5));
	} else if (y5 <= -1.22e-203) {
		tmp = t_1;
	} else if (y5 <= -5.9e-291) {
		tmp = y4 * (y * (c * y3));
	} else if (y5 <= 8.6e-222) {
		tmp = t_1;
	} else if (y5 <= 2.8e+74) {
		tmp = (y * c) * (y3 * y4);
	} else {
		tmp = (k * y0) * (y2 * -y5);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (y * (x * b))
    if (y5 <= (-5.7d+74)) then
        tmp = j * (y0 * (y3 * y5))
    else if (y5 <= (-1.22d-203)) then
        tmp = t_1
    else if (y5 <= (-5.9d-291)) then
        tmp = y4 * (y * (c * y3))
    else if (y5 <= 8.6d-222) then
        tmp = t_1
    else if (y5 <= 2.8d+74) then
        tmp = (y * c) * (y3 * y4)
    else
        tmp = (k * y0) * (y2 * -y5)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y * (x * b));
	double tmp;
	if (y5 <= -5.7e+74) {
		tmp = j * (y0 * (y3 * y5));
	} else if (y5 <= -1.22e-203) {
		tmp = t_1;
	} else if (y5 <= -5.9e-291) {
		tmp = y4 * (y * (c * y3));
	} else if (y5 <= 8.6e-222) {
		tmp = t_1;
	} else if (y5 <= 2.8e+74) {
		tmp = (y * c) * (y3 * y4);
	} else {
		tmp = (k * y0) * (y2 * -y5);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y * (x * b))
	tmp = 0
	if y5 <= -5.7e+74:
		tmp = j * (y0 * (y3 * y5))
	elif y5 <= -1.22e-203:
		tmp = t_1
	elif y5 <= -5.9e-291:
		tmp = y4 * (y * (c * y3))
	elif y5 <= 8.6e-222:
		tmp = t_1
	elif y5 <= 2.8e+74:
		tmp = (y * c) * (y3 * y4)
	else:
		tmp = (k * y0) * (y2 * -y5)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y * Float64(x * b)))
	tmp = 0.0
	if (y5 <= -5.7e+74)
		tmp = Float64(j * Float64(y0 * Float64(y3 * y5)));
	elseif (y5 <= -1.22e-203)
		tmp = t_1;
	elseif (y5 <= -5.9e-291)
		tmp = Float64(y4 * Float64(y * Float64(c * y3)));
	elseif (y5 <= 8.6e-222)
		tmp = t_1;
	elseif (y5 <= 2.8e+74)
		tmp = Float64(Float64(y * c) * Float64(y3 * y4));
	else
		tmp = Float64(Float64(k * y0) * Float64(y2 * Float64(-y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y * (x * b));
	tmp = 0.0;
	if (y5 <= -5.7e+74)
		tmp = j * (y0 * (y3 * y5));
	elseif (y5 <= -1.22e-203)
		tmp = t_1;
	elseif (y5 <= -5.9e-291)
		tmp = y4 * (y * (c * y3));
	elseif (y5 <= 8.6e-222)
		tmp = t_1;
	elseif (y5 <= 2.8e+74)
		tmp = (y * c) * (y3 * y4);
	else
		tmp = (k * y0) * (y2 * -y5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -5.7e+74], N[(j * N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.22e-203], t$95$1, If[LessEqual[y5, -5.9e-291], N[(y4 * N[(y * N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 8.6e-222], t$95$1, If[LessEqual[y5, 2.8e+74], N[(N[(y * c), $MachinePrecision] * N[(y3 * y4), $MachinePrecision]), $MachinePrecision], N[(N[(k * y0), $MachinePrecision] * N[(y2 * (-y5)), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y5 < -5.69999999999999976e74

   1. Initial program 29.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around -inf 51.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 51.0%

         \[\leadsto \color{blue}{\left(-1 \cdot y5\right) \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. neg-mul-1 51.0%

         \[\leadsto \color{blue}{\left(-y5\right)} \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. fma-def 52.7%

         \[\leadsto \left(-y5\right) \cdot \left(\color{blue}{\mathsf{fma}\left(i, j \cdot t - k \cdot y, y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 52.7%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, \color{blue}{t \cdot j} - k \cdot y, y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 52.7%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 52.7%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   5. Simplified 52.7%

      \[\leadsto \color{blue}{\left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in j around -inf 54.9%

      \[\leadsto \color{blue}{j \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 48.4%

         \[\leadsto \color{blue}{\left(j \cdot y5\right) \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)} \]

      2. +-commutative 48.4%

         \[\leadsto \left(j \cdot y5\right) \cdot \color{blue}{\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)} \]

      3. mul-1-neg 48.4%

         \[\leadsto \left(j \cdot y5\right) \cdot \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right) \]

      4. unsub-neg 48.4%

         \[\leadsto \left(j \cdot y5\right) \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)} \]

   8. Simplified 48.4%

      \[\leadsto \color{blue}{\left(j \cdot y5\right) \cdot \left(y0 \cdot y3 - i \cdot t\right)} \]

   9. Taylor expanded in y0 around inf 41.2%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]

   if -5.69999999999999976e74 < y5 < -1.21999999999999995e-203 or -5.89999999999999972e-291 < y5 < 8.59999999999999983e-222

   1. Initial program 28.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.7%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 33.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in y around inf 34.9%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 34.9%

         \[\leadsto a \cdot \left(y \cdot \left(\color{blue}{x \cdot b} - y3 \cdot y5\right)\right) \]

      2. *-commutative 34.9%

         \[\leadsto a \cdot \left(y \cdot \left(x \cdot b - \color{blue}{y5 \cdot y3}\right)\right) \]

   8. Simplified 34.9%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(x \cdot b - y5 \cdot y3\right)\right)} \]

   9. Taylor expanded in x around inf 32.4%

      \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x\right)}\right) \]

   if -1.21999999999999995e-203 < y5 < -5.89999999999999972e-291

   1. Initial program 21.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 21.9%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 31.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   6. Taylor expanded in y3 around inf 19.1%

      \[\leadsto \color{blue}{c \cdot \left(y3 \cdot \left(-1 \cdot \left(y0 \cdot z\right) - -1 \cdot \left(y \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. distribute-lft-out-- 19.1%

         \[\leadsto c \cdot \left(y3 \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot z - y \cdot y4\right)\right)}\right) \]

   8. Simplified 19.1%

      \[\leadsto \color{blue}{c \cdot \left(y3 \cdot \left(-1 \cdot \left(y0 \cdot z - y \cdot y4\right)\right)\right)} \]

   9. Taylor expanded in y0 around 0 10.4%

      \[\leadsto c \cdot \left(y3 \cdot \left(-1 \cdot \color{blue}{\left(-1 \cdot \left(y \cdot y4\right)\right)}\right)\right) \]
   10. Step-by-step derivation

       1. mul-1-neg 10.4%

          \[\leadsto c \cdot \left(y3 \cdot \left(-1 \cdot \color{blue}{\left(-y \cdot y4\right)}\right)\right) \]

       2. distribute-lft-neg-out 10.4%

          \[\leadsto c \cdot \left(y3 \cdot \left(-1 \cdot \color{blue}{\left(\left(-y\right) \cdot y4\right)}\right)\right) \]

       3. *-commutative 10.4%

          \[\leadsto c \cdot \left(y3 \cdot \left(-1 \cdot \color{blue}{\left(y4 \cdot \left(-y\right)\right)}\right)\right) \]

   11. Simplified 10.4%

       \[\leadsto c \cdot \left(y3 \cdot \left(-1 \cdot \color{blue}{\left(y4 \cdot \left(-y\right)\right)}\right)\right) \]

   12. Taylor expanded in c around 0 14.7%

       \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)} \]
   13. Step-by-step derivation

       1. *-commutative 14.7%

          \[\leadsto \color{blue}{\left(y \cdot \left(y3 \cdot y4\right)\right) \cdot c} \]

       2. *-commutative 14.7%

          \[\leadsto \left(y \cdot \color{blue}{\left(y4 \cdot y3\right)}\right) \cdot c \]

       3. associate-*r* 10.4%

          \[\leadsto \color{blue}{\left(\left(y \cdot y4\right) \cdot y3\right)} \cdot c \]

       4. remove-double-neg 10.4%

          \[\leadsto \left(\left(\color{blue}{\left(-\left(-y\right)\right)} \cdot y4\right) \cdot y3\right) \cdot c \]

       5. distribute-lft-neg-in 10.4%

          \[\leadsto \left(\color{blue}{\left(-\left(-y\right) \cdot y4\right)} \cdot y3\right) \cdot c \]

       6. *-commutative 10.4%

          \[\leadsto \left(\left(-\color{blue}{y4 \cdot \left(-y\right)}\right) \cdot y3\right) \cdot c \]

       7. associate-*r* 14.3%

          \[\leadsto \color{blue}{\left(-y4 \cdot \left(-y\right)\right) \cdot \left(y3 \cdot c\right)} \]

       8. *-commutative 14.3%

          \[\leadsto \left(-y4 \cdot \left(-y\right)\right) \cdot \color{blue}{\left(c \cdot y3\right)} \]

       9. distribute-rgt-neg-out 14.3%

          \[\leadsto \left(-\color{blue}{\left(-y4 \cdot y\right)}\right) \cdot \left(c \cdot y3\right) \]

       10. remove-double-neg 14.3%

           \[\leadsto \color{blue}{\left(y4 \cdot y\right)} \cdot \left(c \cdot y3\right) \]

       11. associate-*l* 27.4%

           \[\leadsto \color{blue}{y4 \cdot \left(y \cdot \left(c \cdot y3\right)\right)} \]

       12. *-commutative 27.4%

           \[\leadsto y4 \cdot \left(y \cdot \color{blue}{\left(y3 \cdot c\right)}\right) \]

   14. Simplified 27.4%

       \[\leadsto \color{blue}{y4 \cdot \left(y \cdot \left(y3 \cdot c\right)\right)} \]

   if 8.59999999999999983e-222 < y5 < 2.80000000000000002e74

   1. Initial program 43.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 43.2%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 49.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   6. Taylor expanded in y3 around inf 28.7%

      \[\leadsto \color{blue}{c \cdot \left(y3 \cdot \left(-1 \cdot \left(y0 \cdot z\right) - -1 \cdot \left(y \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. distribute-lft-out-- 28.7%

         \[\leadsto c \cdot \left(y3 \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot z - y \cdot y4\right)\right)}\right) \]

   8. Simplified 28.7%

      \[\leadsto \color{blue}{c \cdot \left(y3 \cdot \left(-1 \cdot \left(y0 \cdot z - y \cdot y4\right)\right)\right)} \]

   9. Taylor expanded in y0 around 0 15.4%

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 22.8%

          \[\leadsto \color{blue}{\left(c \cdot y\right) \cdot \left(y3 \cdot y4\right)} \]

       2. *-commutative 22.8%

          \[\leadsto \left(c \cdot y\right) \cdot \color{blue}{\left(y4 \cdot y3\right)} \]

   11. Simplified 22.8%

       \[\leadsto \color{blue}{\left(c \cdot y\right) \cdot \left(y4 \cdot y3\right)} \]

   if 2.80000000000000002e74 < y5

   1. Initial program 24.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 38.3%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in k around inf 34.3%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 34.3%

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - \color{blue}{y5 \cdot y0}\right)\right) \]

   6. Simplified 34.3%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y5 \cdot y0\right)\right)} \]

   7. Taylor expanded in y1 around 0 41.1%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 41.1%

         \[\leadsto \color{blue}{-k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)} \]

      2. associate-*r* 35.2%

         \[\leadsto -\color{blue}{\left(k \cdot y0\right) \cdot \left(y2 \cdot y5\right)} \]

   9. Simplified 35.2%

      \[\leadsto \color{blue}{-\left(k \cdot y0\right) \cdot \left(y2 \cdot y5\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 32.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -5.7 \cdot 10^{+74}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq -1.22 \cdot 10^{-203}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;y5 \leq -5.9 \cdot 10^{-291}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq 8.6 \cdot 10^{-222}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;y5 \leq 2.8 \cdot 10^{+74}:\\ \;\;\;\;\left(y \cdot c\right) \cdot \left(y3 \cdot y4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(k \cdot y0\right) \cdot \left(y2 \cdot \left(-y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 21.4% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{if}\;y5 \leq -6 \cdot 10^{+74}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq -1.95 \cdot 10^{-203}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y5 \leq -1.45 \cdot 10^{-291}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq 1.3 \cdot 10^{-219}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y5 \leq 3.2 \cdot 10^{+73}:\\ \;\;\;\;\left(y \cdot c\right) \cdot \left(y3 \cdot y4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-k\right) \cdot \left(y2 \cdot \left(y0 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y (* x b)))))
   (if (<= y5 -6e+74)
     (* j (* y0 (* y3 y5)))
     (if (<= y5 -1.95e-203)
       t_1
       (if (<= y5 -1.45e-291)
         (* y4 (* y (* c y3)))
         (if (<= y5 1.3e-219)
           t_1
           (if (<= y5 3.2e+73)
             (* (* y c) (* y3 y4))
             (* (- k) (* y2 (* y0 y5))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y * (x * b));
	double tmp;
	if (y5 <= -6e+74) {
		tmp = j * (y0 * (y3 * y5));
	} else if (y5 <= -1.95e-203) {
		tmp = t_1;
	} else if (y5 <= -1.45e-291) {
		tmp = y4 * (y * (c * y3));
	} else if (y5 <= 1.3e-219) {
		tmp = t_1;
	} else if (y5 <= 3.2e+73) {
		tmp = (y * c) * (y3 * y4);
	} else {
		tmp = -k * (y2 * (y0 * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (y * (x * b))
    if (y5 <= (-6d+74)) then
        tmp = j * (y0 * (y3 * y5))
    else if (y5 <= (-1.95d-203)) then
        tmp = t_1
    else if (y5 <= (-1.45d-291)) then
        tmp = y4 * (y * (c * y3))
    else if (y5 <= 1.3d-219) then
        tmp = t_1
    else if (y5 <= 3.2d+73) then
        tmp = (y * c) * (y3 * y4)
    else
        tmp = -k * (y2 * (y0 * y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y * (x * b));
	double tmp;
	if (y5 <= -6e+74) {
		tmp = j * (y0 * (y3 * y5));
	} else if (y5 <= -1.95e-203) {
		tmp = t_1;
	} else if (y5 <= -1.45e-291) {
		tmp = y4 * (y * (c * y3));
	} else if (y5 <= 1.3e-219) {
		tmp = t_1;
	} else if (y5 <= 3.2e+73) {
		tmp = (y * c) * (y3 * y4);
	} else {
		tmp = -k * (y2 * (y0 * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y * (x * b))
	tmp = 0
	if y5 <= -6e+74:
		tmp = j * (y0 * (y3 * y5))
	elif y5 <= -1.95e-203:
		tmp = t_1
	elif y5 <= -1.45e-291:
		tmp = y4 * (y * (c * y3))
	elif y5 <= 1.3e-219:
		tmp = t_1
	elif y5 <= 3.2e+73:
		tmp = (y * c) * (y3 * y4)
	else:
		tmp = -k * (y2 * (y0 * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y * Float64(x * b)))
	tmp = 0.0
	if (y5 <= -6e+74)
		tmp = Float64(j * Float64(y0 * Float64(y3 * y5)));
	elseif (y5 <= -1.95e-203)
		tmp = t_1;
	elseif (y5 <= -1.45e-291)
		tmp = Float64(y4 * Float64(y * Float64(c * y3)));
	elseif (y5 <= 1.3e-219)
		tmp = t_1;
	elseif (y5 <= 3.2e+73)
		tmp = Float64(Float64(y * c) * Float64(y3 * y4));
	else
		tmp = Float64(Float64(-k) * Float64(y2 * Float64(y0 * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y * (x * b));
	tmp = 0.0;
	if (y5 <= -6e+74)
		tmp = j * (y0 * (y3 * y5));
	elseif (y5 <= -1.95e-203)
		tmp = t_1;
	elseif (y5 <= -1.45e-291)
		tmp = y4 * (y * (c * y3));
	elseif (y5 <= 1.3e-219)
		tmp = t_1;
	elseif (y5 <= 3.2e+73)
		tmp = (y * c) * (y3 * y4);
	else
		tmp = -k * (y2 * (y0 * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -6e+74], N[(j * N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.95e-203], t$95$1, If[LessEqual[y5, -1.45e-291], N[(y4 * N[(y * N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.3e-219], t$95$1, If[LessEqual[y5, 3.2e+73], N[(N[(y * c), $MachinePrecision] * N[(y3 * y4), $MachinePrecision]), $MachinePrecision], N[((-k) * N[(y2 * N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y5 < -6e74

   1. Initial program 29.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around -inf 51.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 51.0%

         \[\leadsto \color{blue}{\left(-1 \cdot y5\right) \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. neg-mul-1 51.0%

         \[\leadsto \color{blue}{\left(-y5\right)} \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. fma-def 52.7%

         \[\leadsto \left(-y5\right) \cdot \left(\color{blue}{\mathsf{fma}\left(i, j \cdot t - k \cdot y, y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 52.7%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, \color{blue}{t \cdot j} - k \cdot y, y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 52.7%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 52.7%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   5. Simplified 52.7%

      \[\leadsto \color{blue}{\left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in j around -inf 54.9%

      \[\leadsto \color{blue}{j \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 48.4%

         \[\leadsto \color{blue}{\left(j \cdot y5\right) \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)} \]

      2. +-commutative 48.4%

         \[\leadsto \left(j \cdot y5\right) \cdot \color{blue}{\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)} \]

      3. mul-1-neg 48.4%

         \[\leadsto \left(j \cdot y5\right) \cdot \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right) \]

      4. unsub-neg 48.4%

         \[\leadsto \left(j \cdot y5\right) \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)} \]

   8. Simplified 48.4%

      \[\leadsto \color{blue}{\left(j \cdot y5\right) \cdot \left(y0 \cdot y3 - i \cdot t\right)} \]

   9. Taylor expanded in y0 around inf 41.2%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]

   if -6e74 < y5 < -1.95e-203 or -1.45000000000000001e-291 < y5 < 1.30000000000000001e-219

   1. Initial program 28.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.7%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 33.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in y around inf 34.9%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 34.9%

         \[\leadsto a \cdot \left(y \cdot \left(\color{blue}{x \cdot b} - y3 \cdot y5\right)\right) \]

      2. *-commutative 34.9%

         \[\leadsto a \cdot \left(y \cdot \left(x \cdot b - \color{blue}{y5 \cdot y3}\right)\right) \]

   8. Simplified 34.9%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(x \cdot b - y5 \cdot y3\right)\right)} \]

   9. Taylor expanded in x around inf 32.4%

      \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x\right)}\right) \]

   if -1.95e-203 < y5 < -1.45000000000000001e-291

   1. Initial program 21.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 21.9%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 31.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   6. Taylor expanded in y3 around inf 19.1%

      \[\leadsto \color{blue}{c \cdot \left(y3 \cdot \left(-1 \cdot \left(y0 \cdot z\right) - -1 \cdot \left(y \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. distribute-lft-out-- 19.1%

         \[\leadsto c \cdot \left(y3 \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot z - y \cdot y4\right)\right)}\right) \]

   8. Simplified 19.1%

      \[\leadsto \color{blue}{c \cdot \left(y3 \cdot \left(-1 \cdot \left(y0 \cdot z - y \cdot y4\right)\right)\right)} \]

   9. Taylor expanded in y0 around 0 10.4%

      \[\leadsto c \cdot \left(y3 \cdot \left(-1 \cdot \color{blue}{\left(-1 \cdot \left(y \cdot y4\right)\right)}\right)\right) \]
   10. Step-by-step derivation

       1. mul-1-neg 10.4%

          \[\leadsto c \cdot \left(y3 \cdot \left(-1 \cdot \color{blue}{\left(-y \cdot y4\right)}\right)\right) \]

       2. distribute-lft-neg-out 10.4%

          \[\leadsto c \cdot \left(y3 \cdot \left(-1 \cdot \color{blue}{\left(\left(-y\right) \cdot y4\right)}\right)\right) \]

       3. *-commutative 10.4%

          \[\leadsto c \cdot \left(y3 \cdot \left(-1 \cdot \color{blue}{\left(y4 \cdot \left(-y\right)\right)}\right)\right) \]

   11. Simplified 10.4%

       \[\leadsto c \cdot \left(y3 \cdot \left(-1 \cdot \color{blue}{\left(y4 \cdot \left(-y\right)\right)}\right)\right) \]

   12. Taylor expanded in c around 0 14.7%

       \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)} \]
   13. Step-by-step derivation

       1. *-commutative 14.7%

          \[\leadsto \color{blue}{\left(y \cdot \left(y3 \cdot y4\right)\right) \cdot c} \]

       2. *-commutative 14.7%

          \[\leadsto \left(y \cdot \color{blue}{\left(y4 \cdot y3\right)}\right) \cdot c \]

       3. associate-*r* 10.4%

          \[\leadsto \color{blue}{\left(\left(y \cdot y4\right) \cdot y3\right)} \cdot c \]

       4. remove-double-neg 10.4%

          \[\leadsto \left(\left(\color{blue}{\left(-\left(-y\right)\right)} \cdot y4\right) \cdot y3\right) \cdot c \]

       5. distribute-lft-neg-in 10.4%

          \[\leadsto \left(\color{blue}{\left(-\left(-y\right) \cdot y4\right)} \cdot y3\right) \cdot c \]

       6. *-commutative 10.4%

          \[\leadsto \left(\left(-\color{blue}{y4 \cdot \left(-y\right)}\right) \cdot y3\right) \cdot c \]

       7. associate-*r* 14.3%

          \[\leadsto \color{blue}{\left(-y4 \cdot \left(-y\right)\right) \cdot \left(y3 \cdot c\right)} \]

       8. *-commutative 14.3%

          \[\leadsto \left(-y4 \cdot \left(-y\right)\right) \cdot \color{blue}{\left(c \cdot y3\right)} \]

       9. distribute-rgt-neg-out 14.3%

          \[\leadsto \left(-\color{blue}{\left(-y4 \cdot y\right)}\right) \cdot \left(c \cdot y3\right) \]

       10. remove-double-neg 14.3%

           \[\leadsto \color{blue}{\left(y4 \cdot y\right)} \cdot \left(c \cdot y3\right) \]

       11. associate-*l* 27.4%

           \[\leadsto \color{blue}{y4 \cdot \left(y \cdot \left(c \cdot y3\right)\right)} \]

       12. *-commutative 27.4%

           \[\leadsto y4 \cdot \left(y \cdot \color{blue}{\left(y3 \cdot c\right)}\right) \]

   14. Simplified 27.4%

       \[\leadsto \color{blue}{y4 \cdot \left(y \cdot \left(y3 \cdot c\right)\right)} \]

   if 1.30000000000000001e-219 < y5 < 3.19999999999999982e73

   1. Initial program 43.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 43.2%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 49.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   6. Taylor expanded in y3 around inf 28.7%

      \[\leadsto \color{blue}{c \cdot \left(y3 \cdot \left(-1 \cdot \left(y0 \cdot z\right) - -1 \cdot \left(y \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. distribute-lft-out-- 28.7%

         \[\leadsto c \cdot \left(y3 \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot z - y \cdot y4\right)\right)}\right) \]

   8. Simplified 28.7%

      \[\leadsto \color{blue}{c \cdot \left(y3 \cdot \left(-1 \cdot \left(y0 \cdot z - y \cdot y4\right)\right)\right)} \]

   9. Taylor expanded in y0 around 0 15.4%

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 22.8%

          \[\leadsto \color{blue}{\left(c \cdot y\right) \cdot \left(y3 \cdot y4\right)} \]

       2. *-commutative 22.8%

          \[\leadsto \left(c \cdot y\right) \cdot \color{blue}{\left(y4 \cdot y3\right)} \]

   11. Simplified 22.8%

       \[\leadsto \color{blue}{\left(c \cdot y\right) \cdot \left(y4 \cdot y3\right)} \]

   if 3.19999999999999982e73 < y5

   1. Initial program 24.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 38.3%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in k around inf 34.3%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 34.3%

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - \color{blue}{y5 \cdot y0}\right)\right) \]

   6. Simplified 34.3%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y5 \cdot y0\right)\right)} \]

   7. Taylor expanded in y1 around 0 39.0%

      \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot y5\right)\right)}\right) \]
   8. Step-by-step derivation

      1. mul-1-neg 39.0%

         \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(-y0 \cdot y5\right)}\right) \]

      2. *-commutative 39.0%

         \[\leadsto k \cdot \left(y2 \cdot \left(-\color{blue}{y5 \cdot y0}\right)\right) \]

      3. distribute-rgt-neg-in 39.0%

         \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y5 \cdot \left(-y0\right)\right)}\right) \]

   9. Simplified 39.0%

      \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y5 \cdot \left(-y0\right)\right)}\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 33.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -6 \cdot 10^{+74}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq -1.95 \cdot 10^{-203}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;y5 \leq -1.45 \cdot 10^{-291}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq 1.3 \cdot 10^{-219}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;y5 \leq 3.2 \cdot 10^{+73}:\\ \;\;\;\;\left(y \cdot c\right) \cdot \left(y3 \cdot y4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-k\right) \cdot \left(y2 \cdot \left(y0 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 19.2% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.3 \cdot 10^{-176}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 1.12 \cdot 10^{-150}:\\ \;\;\;\;a \cdot \left(y \cdot \left(y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;j \leq 4.4 \cdot 10^{-23}:\\ \;\;\;\;\left(y1 \cdot y2\right) \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;j \leq 9.5 \cdot 10^{+115}:\\ \;\;\;\;\left(y1 \cdot y2\right) \cdot \left(k \cdot y4\right)\\ \mathbf{elif}\;j \leq 5.8 \cdot 10^{+201}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(t \cdot \left(-y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot y5\right) \cdot \left(y0 \cdot y3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -1.3e-176)
   (* y4 (* y (* c y3)))
   (if (<= j 1.12e-150)
     (* a (* y (* y3 (- y5))))
     (if (<= j 4.4e-23)
       (* (* y1 y2) (* x (- a)))
       (if (<= j 9.5e+115)
         (* (* y1 y2) (* k y4))
         (if (<= j 5.8e+201)
           (* (* i j) (* t (- y5)))
           (* (* j y5) (* y0 y3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -1.3e-176) {
		tmp = y4 * (y * (c * y3));
	} else if (j <= 1.12e-150) {
		tmp = a * (y * (y3 * -y5));
	} else if (j <= 4.4e-23) {
		tmp = (y1 * y2) * (x * -a);
	} else if (j <= 9.5e+115) {
		tmp = (y1 * y2) * (k * y4);
	} else if (j <= 5.8e+201) {
		tmp = (i * j) * (t * -y5);
	} else {
		tmp = (j * y5) * (y0 * y3);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (j <= (-1.3d-176)) then
        tmp = y4 * (y * (c * y3))
    else if (j <= 1.12d-150) then
        tmp = a * (y * (y3 * -y5))
    else if (j <= 4.4d-23) then
        tmp = (y1 * y2) * (x * -a)
    else if (j <= 9.5d+115) then
        tmp = (y1 * y2) * (k * y4)
    else if (j <= 5.8d+201) then
        tmp = (i * j) * (t * -y5)
    else
        tmp = (j * y5) * (y0 * y3)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -1.3e-176) {
		tmp = y4 * (y * (c * y3));
	} else if (j <= 1.12e-150) {
		tmp = a * (y * (y3 * -y5));
	} else if (j <= 4.4e-23) {
		tmp = (y1 * y2) * (x * -a);
	} else if (j <= 9.5e+115) {
		tmp = (y1 * y2) * (k * y4);
	} else if (j <= 5.8e+201) {
		tmp = (i * j) * (t * -y5);
	} else {
		tmp = (j * y5) * (y0 * y3);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if j <= -1.3e-176:
		tmp = y4 * (y * (c * y3))
	elif j <= 1.12e-150:
		tmp = a * (y * (y3 * -y5))
	elif j <= 4.4e-23:
		tmp = (y1 * y2) * (x * -a)
	elif j <= 9.5e+115:
		tmp = (y1 * y2) * (k * y4)
	elif j <= 5.8e+201:
		tmp = (i * j) * (t * -y5)
	else:
		tmp = (j * y5) * (y0 * y3)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (j <= -1.3e-176)
		tmp = Float64(y4 * Float64(y * Float64(c * y3)));
	elseif (j <= 1.12e-150)
		tmp = Float64(a * Float64(y * Float64(y3 * Float64(-y5))));
	elseif (j <= 4.4e-23)
		tmp = Float64(Float64(y1 * y2) * Float64(x * Float64(-a)));
	elseif (j <= 9.5e+115)
		tmp = Float64(Float64(y1 * y2) * Float64(k * y4));
	elseif (j <= 5.8e+201)
		tmp = Float64(Float64(i * j) * Float64(t * Float64(-y5)));
	else
		tmp = Float64(Float64(j * y5) * Float64(y0 * y3));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (j <= -1.3e-176)
		tmp = y4 * (y * (c * y3));
	elseif (j <= 1.12e-150)
		tmp = a * (y * (y3 * -y5));
	elseif (j <= 4.4e-23)
		tmp = (y1 * y2) * (x * -a);
	elseif (j <= 9.5e+115)
		tmp = (y1 * y2) * (k * y4);
	elseif (j <= 5.8e+201)
		tmp = (i * j) * (t * -y5);
	else
		tmp = (j * y5) * (y0 * y3);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[j, -1.3e-176], N[(y4 * N[(y * N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.12e-150], N[(a * N[(y * N[(y3 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.4e-23], N[(N[(y1 * y2), $MachinePrecision] * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 9.5e+115], N[(N[(y1 * y2), $MachinePrecision] * N[(k * y4), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.8e+201], N[(N[(i * j), $MachinePrecision] * N[(t * (-y5)), $MachinePrecision]), $MachinePrecision], N[(N[(j * y5), $MachinePrecision] * N[(y0 * y3), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -1.29999999999999996e-176

   1. Initial program 21.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 21.9%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 47.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   6. Taylor expanded in y3 around inf 31.4%

      \[\leadsto \color{blue}{c \cdot \left(y3 \cdot \left(-1 \cdot \left(y0 \cdot z\right) - -1 \cdot \left(y \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. distribute-lft-out-- 31.4%

         \[\leadsto c \cdot \left(y3 \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot z - y \cdot y4\right)\right)}\right) \]

   8. Simplified 31.4%

      \[\leadsto \color{blue}{c \cdot \left(y3 \cdot \left(-1 \cdot \left(y0 \cdot z - y \cdot y4\right)\right)\right)} \]

   9. Taylor expanded in y0 around 0 24.9%

      \[\leadsto c \cdot \left(y3 \cdot \left(-1 \cdot \color{blue}{\left(-1 \cdot \left(y \cdot y4\right)\right)}\right)\right) \]
   10. Step-by-step derivation

       1. mul-1-neg 24.9%

          \[\leadsto c \cdot \left(y3 \cdot \left(-1 \cdot \color{blue}{\left(-y \cdot y4\right)}\right)\right) \]

       2. distribute-lft-neg-out 24.9%

          \[\leadsto c \cdot \left(y3 \cdot \left(-1 \cdot \color{blue}{\left(\left(-y\right) \cdot y4\right)}\right)\right) \]

       3. *-commutative 24.9%

          \[\leadsto c \cdot \left(y3 \cdot \left(-1 \cdot \color{blue}{\left(y4 \cdot \left(-y\right)\right)}\right)\right) \]

   11. Simplified 24.9%

       \[\leadsto c \cdot \left(y3 \cdot \left(-1 \cdot \color{blue}{\left(y4 \cdot \left(-y\right)\right)}\right)\right) \]

   12. Taylor expanded in c around 0 26.2%

       \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)} \]
   13. Step-by-step derivation

       1. *-commutative 26.2%

          \[\leadsto \color{blue}{\left(y \cdot \left(y3 \cdot y4\right)\right) \cdot c} \]

       2. *-commutative 26.2%

          \[\leadsto \left(y \cdot \color{blue}{\left(y4 \cdot y3\right)}\right) \cdot c \]

       3. associate-*r* 24.9%

          \[\leadsto \color{blue}{\left(\left(y \cdot y4\right) \cdot y3\right)} \cdot c \]

       4. remove-double-neg 24.9%

          \[\leadsto \left(\left(\color{blue}{\left(-\left(-y\right)\right)} \cdot y4\right) \cdot y3\right) \cdot c \]

       5. distribute-lft-neg-in 24.9%

          \[\leadsto \left(\color{blue}{\left(-\left(-y\right) \cdot y4\right)} \cdot y3\right) \cdot c \]

       6. *-commutative 24.9%

          \[\leadsto \left(\left(-\color{blue}{y4 \cdot \left(-y\right)}\right) \cdot y3\right) \cdot c \]

       7. associate-*r* 27.4%

          \[\leadsto \color{blue}{\left(-y4 \cdot \left(-y\right)\right) \cdot \left(y3 \cdot c\right)} \]

       8. *-commutative 27.4%

          \[\leadsto \left(-y4 \cdot \left(-y\right)\right) \cdot \color{blue}{\left(c \cdot y3\right)} \]

       9. distribute-rgt-neg-out 27.4%

          \[\leadsto \left(-\color{blue}{\left(-y4 \cdot y\right)}\right) \cdot \left(c \cdot y3\right) \]

       10. remove-double-neg 27.4%

           \[\leadsto \color{blue}{\left(y4 \cdot y\right)} \cdot \left(c \cdot y3\right) \]

       11. associate-*l* 31.5%

           \[\leadsto \color{blue}{y4 \cdot \left(y \cdot \left(c \cdot y3\right)\right)} \]

       12. *-commutative 31.5%

           \[\leadsto y4 \cdot \left(y \cdot \color{blue}{\left(y3 \cdot c\right)}\right) \]

   14. Simplified 31.5%

       \[\leadsto \color{blue}{y4 \cdot \left(y \cdot \left(y3 \cdot c\right)\right)} \]

   if -1.29999999999999996e-176 < j < 1.12e-150

   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 37.6%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 42.8%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in y around inf 41.0%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 41.0%

         \[\leadsto a \cdot \left(y \cdot \left(\color{blue}{x \cdot b} - y3 \cdot y5\right)\right) \]

      2. *-commutative 41.0%

         \[\leadsto a \cdot \left(y \cdot \left(x \cdot b - \color{blue}{y5 \cdot y3}\right)\right) \]

   8. Simplified 41.0%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(x \cdot b - y5 \cdot y3\right)\right)} \]

   9. Taylor expanded in x around 0 31.5%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 31.5%

          \[\leadsto \color{blue}{-a \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)} \]

       2. *-commutative 31.5%

          \[\leadsto -\color{blue}{\left(y \cdot \left(y3 \cdot y5\right)\right) \cdot a} \]

       3. distribute-lft-neg-in 31.5%

          \[\leadsto \color{blue}{\left(-y \cdot \left(y3 \cdot y5\right)\right) \cdot a} \]

       4. distribute-rgt-neg-in 31.5%

          \[\leadsto \color{blue}{\left(y \cdot \left(-y3 \cdot y5\right)\right)} \cdot a \]

       5. distribute-rgt-neg-in 31.5%

          \[\leadsto \left(y \cdot \color{blue}{\left(y3 \cdot \left(-y5\right)\right)}\right) \cdot a \]

   11. Simplified 31.5%

       \[\leadsto \color{blue}{\left(y \cdot \left(y3 \cdot \left(-y5\right)\right)\right) \cdot a} \]

   if 1.12e-150 < j < 4.3999999999999999e-23

   1. Initial program 35.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 35.4%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in y1 around inf 42.5%

      \[\leadsto \color{blue}{y1 \cdot \left(y2 \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 42.3%

         \[\leadsto \color{blue}{\left(y1 \cdot y2\right) \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)} \]

      2. *-commutative 42.3%

         \[\leadsto \color{blue}{\left(y2 \cdot y1\right)} \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right) \]

      3. +-commutative 42.3%

         \[\leadsto \left(y2 \cdot y1\right) \cdot \color{blue}{\left(k \cdot y4 + -1 \cdot \left(a \cdot x\right)\right)} \]

      4. mul-1-neg 42.3%

         \[\leadsto \left(y2 \cdot y1\right) \cdot \left(k \cdot y4 + \color{blue}{\left(-a \cdot x\right)}\right) \]

      5. unsub-neg 42.3%

         \[\leadsto \left(y2 \cdot y1\right) \cdot \color{blue}{\left(k \cdot y4 - a \cdot x\right)} \]

   6. Simplified 42.3%

      \[\leadsto \color{blue}{\left(y2 \cdot y1\right) \cdot \left(k \cdot y4 - a \cdot x\right)} \]

   7. Taylor expanded in k around 0 32.7%

      \[\leadsto \left(y2 \cdot y1\right) \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 32.7%

         \[\leadsto \left(y2 \cdot y1\right) \cdot \color{blue}{\left(-a \cdot x\right)} \]

      2. distribute-lft-neg-out 32.7%

         \[\leadsto \left(y2 \cdot y1\right) \cdot \color{blue}{\left(\left(-a\right) \cdot x\right)} \]

      3. *-commutative 32.7%

         \[\leadsto \left(y2 \cdot y1\right) \cdot \color{blue}{\left(x \cdot \left(-a\right)\right)} \]

   9. Simplified 32.7%

      \[\leadsto \left(y2 \cdot y1\right) \cdot \color{blue}{\left(x \cdot \left(-a\right)\right)} \]

   if 4.3999999999999999e-23 < j < 9.4999999999999997e115

   1. Initial program 33.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 43.6%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in y1 around inf 30.7%

      \[\leadsto \color{blue}{y1 \cdot \left(y2 \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 30.7%

         \[\leadsto \color{blue}{\left(y1 \cdot y2\right) \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)} \]

      2. *-commutative 30.7%

         \[\leadsto \color{blue}{\left(y2 \cdot y1\right)} \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right) \]

      3. +-commutative 30.7%

         \[\leadsto \left(y2 \cdot y1\right) \cdot \color{blue}{\left(k \cdot y4 + -1 \cdot \left(a \cdot x\right)\right)} \]

      4. mul-1-neg 30.7%

         \[\leadsto \left(y2 \cdot y1\right) \cdot \left(k \cdot y4 + \color{blue}{\left(-a \cdot x\right)}\right) \]

      5. unsub-neg 30.7%

         \[\leadsto \left(y2 \cdot y1\right) \cdot \color{blue}{\left(k \cdot y4 - a \cdot x\right)} \]

   6. Simplified 30.7%

      \[\leadsto \color{blue}{\left(y2 \cdot y1\right) \cdot \left(k \cdot y4 - a \cdot x\right)} \]

   7. Taylor expanded in k around inf 34.2%

      \[\leadsto \left(y2 \cdot y1\right) \cdot \color{blue}{\left(k \cdot y4\right)} \]
   8. Step-by-step derivation

      1. *-commutative 34.2%

         \[\leadsto \left(y2 \cdot y1\right) \cdot \color{blue}{\left(y4 \cdot k\right)} \]

   9. Simplified 34.2%

      \[\leadsto \left(y2 \cdot y1\right) \cdot \color{blue}{\left(y4 \cdot k\right)} \]

   if 9.4999999999999997e115 < j < 5.8000000000000003e201

   1. Initial program 31.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around -inf 37.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 37.5%

         \[\leadsto \color{blue}{\left(-1 \cdot y5\right) \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. neg-mul-1 37.5%

         \[\leadsto \color{blue}{\left(-y5\right)} \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. fma-def 37.5%

         \[\leadsto \left(-y5\right) \cdot \left(\color{blue}{\mathsf{fma}\left(i, j \cdot t - k \cdot y, y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 37.5%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, \color{blue}{t \cdot j} - k \cdot y, y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 37.5%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 37.5%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   5. Simplified 37.5%

      \[\leadsto \color{blue}{\left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in j around -inf 38.6%

      \[\leadsto \color{blue}{j \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 43.6%

         \[\leadsto \color{blue}{\left(j \cdot y5\right) \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)} \]

      2. +-commutative 43.6%

         \[\leadsto \left(j \cdot y5\right) \cdot \color{blue}{\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)} \]

      3. mul-1-neg 43.6%

         \[\leadsto \left(j \cdot y5\right) \cdot \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right) \]

      4. unsub-neg 43.6%

         \[\leadsto \left(j \cdot y5\right) \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)} \]

   8. Simplified 43.6%

      \[\leadsto \color{blue}{\left(j \cdot y5\right) \cdot \left(y0 \cdot y3 - i \cdot t\right)} \]

   9. Taylor expanded in y0 around 0 18.3%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot \left(t \cdot y5\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 18.3%

          \[\leadsto \color{blue}{-i \cdot \left(j \cdot \left(t \cdot y5\right)\right)} \]

       2. associate-*r* 37.8%

          \[\leadsto -\color{blue}{\left(i \cdot j\right) \cdot \left(t \cdot y5\right)} \]

       3. distribute-rgt-neg-in 37.8%

          \[\leadsto \color{blue}{\left(i \cdot j\right) \cdot \left(-t \cdot y5\right)} \]

       4. *-commutative 37.8%

          \[\leadsto \color{blue}{\left(j \cdot i\right)} \cdot \left(-t \cdot y5\right) \]

       5. *-commutative 37.8%

          \[\leadsto \left(j \cdot i\right) \cdot \left(-\color{blue}{y5 \cdot t}\right) \]

   11. Simplified 37.8%

       \[\leadsto \color{blue}{\left(j \cdot i\right) \cdot \left(-y5 \cdot t\right)} \]

   if 5.8000000000000003e201 < j

   1. Initial program 26.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around -inf 30.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 30.5%

         \[\leadsto \color{blue}{\left(-1 \cdot y5\right) \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. neg-mul-1 30.5%

         \[\leadsto \color{blue}{\left(-y5\right)} \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. fma-def 34.9%

         \[\leadsto \left(-y5\right) \cdot \left(\color{blue}{\mathsf{fma}\left(i, j \cdot t - k \cdot y, y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 34.9%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, \color{blue}{t \cdot j} - k \cdot y, y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 34.9%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 34.9%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   5. Simplified 34.9%

      \[\leadsto \color{blue}{\left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in j around -inf 61.5%

      \[\leadsto \color{blue}{j \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 61.5%

         \[\leadsto \color{blue}{\left(j \cdot y5\right) \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)} \]

      2. +-commutative 61.5%

         \[\leadsto \left(j \cdot y5\right) \cdot \color{blue}{\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)} \]

      3. mul-1-neg 61.5%

         \[\leadsto \left(j \cdot y5\right) \cdot \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right) \]

      4. unsub-neg 61.5%

         \[\leadsto \left(j \cdot y5\right) \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)} \]

   8. Simplified 61.5%

      \[\leadsto \color{blue}{\left(j \cdot y5\right) \cdot \left(y0 \cdot y3 - i \cdot t\right)} \]

   9. Taylor expanded in y0 around inf 57.3%

      \[\leadsto \left(j \cdot y5\right) \cdot \color{blue}{\left(y0 \cdot y3\right)} \]
   10. Step-by-step derivation

       1. *-commutative 57.3%

          \[\leadsto \left(j \cdot y5\right) \cdot \color{blue}{\left(y3 \cdot y0\right)} \]

   11. Simplified 57.3%

       \[\leadsto \left(j \cdot y5\right) \cdot \color{blue}{\left(y3 \cdot y0\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 34.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.3 \cdot 10^{-176}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 1.12 \cdot 10^{-150}:\\ \;\;\;\;a \cdot \left(y \cdot \left(y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;j \leq 4.4 \cdot 10^{-23}:\\ \;\;\;\;\left(y1 \cdot y2\right) \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;j \leq 9.5 \cdot 10^{+115}:\\ \;\;\;\;\left(y1 \cdot y2\right) \cdot \left(k \cdot y4\right)\\ \mathbf{elif}\;j \leq 5.8 \cdot 10^{+201}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(t \cdot \left(-y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot y5\right) \cdot \left(y0 \cdot y3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 20.9% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ t_2 := a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{if}\;y5 \leq -5.2 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y5 \leq -1 \cdot 10^{-204}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y5 \leq -2.25 \cdot 10^{-291}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq 9 \cdot 10^{-218}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y5 \leq 1.18 \cdot 10^{+157}:\\ \;\;\;\;\left(y \cdot c\right) \cdot \left(y3 \cdot y4\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* y0 (* y3 y5)))) (t_2 (* a (* y (* x b)))))
   (if (<= y5 -5.2e+74)
     t_1
     (if (<= y5 -1e-204)
       t_2
       (if (<= y5 -2.25e-291)
         (* y4 (* y (* c y3)))
         (if (<= y5 9e-218)
           t_2
           (if (<= y5 1.18e+157) (* (* y c) (* y3 y4)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (y0 * (y3 * y5));
	double t_2 = a * (y * (x * b));
	double tmp;
	if (y5 <= -5.2e+74) {
		tmp = t_1;
	} else if (y5 <= -1e-204) {
		tmp = t_2;
	} else if (y5 <= -2.25e-291) {
		tmp = y4 * (y * (c * y3));
	} else if (y5 <= 9e-218) {
		tmp = t_2;
	} else if (y5 <= 1.18e+157) {
		tmp = (y * c) * (y3 * y4);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (y0 * (y3 * y5))
    t_2 = a * (y * (x * b))
    if (y5 <= (-5.2d+74)) then
        tmp = t_1
    else if (y5 <= (-1d-204)) then
        tmp = t_2
    else if (y5 <= (-2.25d-291)) then
        tmp = y4 * (y * (c * y3))
    else if (y5 <= 9d-218) then
        tmp = t_2
    else if (y5 <= 1.18d+157) then
        tmp = (y * c) * (y3 * y4)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (y0 * (y3 * y5));
	double t_2 = a * (y * (x * b));
	double tmp;
	if (y5 <= -5.2e+74) {
		tmp = t_1;
	} else if (y5 <= -1e-204) {
		tmp = t_2;
	} else if (y5 <= -2.25e-291) {
		tmp = y4 * (y * (c * y3));
	} else if (y5 <= 9e-218) {
		tmp = t_2;
	} else if (y5 <= 1.18e+157) {
		tmp = (y * c) * (y3 * y4);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = j * (y0 * (y3 * y5))
	t_2 = a * (y * (x * b))
	tmp = 0
	if y5 <= -5.2e+74:
		tmp = t_1
	elif y5 <= -1e-204:
		tmp = t_2
	elif y5 <= -2.25e-291:
		tmp = y4 * (y * (c * y3))
	elif y5 <= 9e-218:
		tmp = t_2
	elif y5 <= 1.18e+157:
		tmp = (y * c) * (y3 * y4)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(j * Float64(y0 * Float64(y3 * y5)))
	t_2 = Float64(a * Float64(y * Float64(x * b)))
	tmp = 0.0
	if (y5 <= -5.2e+74)
		tmp = t_1;
	elseif (y5 <= -1e-204)
		tmp = t_2;
	elseif (y5 <= -2.25e-291)
		tmp = Float64(y4 * Float64(y * Float64(c * y3)));
	elseif (y5 <= 9e-218)
		tmp = t_2;
	elseif (y5 <= 1.18e+157)
		tmp = Float64(Float64(y * c) * Float64(y3 * y4));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = j * (y0 * (y3 * y5));
	t_2 = a * (y * (x * b));
	tmp = 0.0;
	if (y5 <= -5.2e+74)
		tmp = t_1;
	elseif (y5 <= -1e-204)
		tmp = t_2;
	elseif (y5 <= -2.25e-291)
		tmp = y4 * (y * (c * y3));
	elseif (y5 <= 9e-218)
		tmp = t_2;
	elseif (y5 <= 1.18e+157)
		tmp = (y * c) * (y3 * y4);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(j * N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -5.2e+74], t$95$1, If[LessEqual[y5, -1e-204], t$95$2, If[LessEqual[y5, -2.25e-291], N[(y4 * N[(y * N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 9e-218], t$95$2, If[LessEqual[y5, 1.18e+157], N[(N[(y * c), $MachinePrecision] * N[(y3 * y4), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y5 < -5.2000000000000001e74 or 1.1799999999999999e157 < y5

   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 y5 around -inf 52.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 52.4%

         \[\leadsto \color{blue}{\left(-1 \cdot y5\right) \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. neg-mul-1 52.4%

         \[\leadsto \color{blue}{\left(-y5\right)} \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. fma-def 54.7%

         \[\leadsto \left(-y5\right) \cdot \left(\color{blue}{\mathsf{fma}\left(i, j \cdot t - k \cdot y, y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 54.7%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, \color{blue}{t \cdot j} - k \cdot y, y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 54.7%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 54.7%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   5. Simplified 54.7%

      \[\leadsto \color{blue}{\left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in j around -inf 47.4%

      \[\leadsto \color{blue}{j \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 43.2%

         \[\leadsto \color{blue}{\left(j \cdot y5\right) \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)} \]

      2. +-commutative 43.2%

         \[\leadsto \left(j \cdot y5\right) \cdot \color{blue}{\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)} \]

      3. mul-1-neg 43.2%

         \[\leadsto \left(j \cdot y5\right) \cdot \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right) \]

      4. unsub-neg 43.2%

         \[\leadsto \left(j \cdot y5\right) \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)} \]

   8. Simplified 43.2%

      \[\leadsto \color{blue}{\left(j \cdot y5\right) \cdot \left(y0 \cdot y3 - i \cdot t\right)} \]

   9. Taylor expanded in y0 around inf 39.8%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]

   if -5.2000000000000001e74 < y5 < -1e-204 or -2.24999999999999987e-291 < y5 < 8.99999999999999953e-218

   1. Initial program 28.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.7%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 33.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in y around inf 34.9%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 34.9%

         \[\leadsto a \cdot \left(y \cdot \left(\color{blue}{x \cdot b} - y3 \cdot y5\right)\right) \]

      2. *-commutative 34.9%

         \[\leadsto a \cdot \left(y \cdot \left(x \cdot b - \color{blue}{y5 \cdot y3}\right)\right) \]

   8. Simplified 34.9%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(x \cdot b - y5 \cdot y3\right)\right)} \]

   9. Taylor expanded in x around inf 32.4%

      \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x\right)}\right) \]

   if -1e-204 < y5 < -2.24999999999999987e-291

   1. Initial program 21.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 21.9%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 31.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   6. Taylor expanded in y3 around inf 19.1%

      \[\leadsto \color{blue}{c \cdot \left(y3 \cdot \left(-1 \cdot \left(y0 \cdot z\right) - -1 \cdot \left(y \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. distribute-lft-out-- 19.1%

         \[\leadsto c \cdot \left(y3 \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot z - y \cdot y4\right)\right)}\right) \]

   8. Simplified 19.1%

      \[\leadsto \color{blue}{c \cdot \left(y3 \cdot \left(-1 \cdot \left(y0 \cdot z - y \cdot y4\right)\right)\right)} \]

   9. Taylor expanded in y0 around 0 10.4%

      \[\leadsto c \cdot \left(y3 \cdot \left(-1 \cdot \color{blue}{\left(-1 \cdot \left(y \cdot y4\right)\right)}\right)\right) \]
   10. Step-by-step derivation

       1. mul-1-neg 10.4%

          \[\leadsto c \cdot \left(y3 \cdot \left(-1 \cdot \color{blue}{\left(-y \cdot y4\right)}\right)\right) \]

       2. distribute-lft-neg-out 10.4%

          \[\leadsto c \cdot \left(y3 \cdot \left(-1 \cdot \color{blue}{\left(\left(-y\right) \cdot y4\right)}\right)\right) \]

       3. *-commutative 10.4%

          \[\leadsto c \cdot \left(y3 \cdot \left(-1 \cdot \color{blue}{\left(y4 \cdot \left(-y\right)\right)}\right)\right) \]

   11. Simplified 10.4%

       \[\leadsto c \cdot \left(y3 \cdot \left(-1 \cdot \color{blue}{\left(y4 \cdot \left(-y\right)\right)}\right)\right) \]

   12. Taylor expanded in c around 0 14.7%

       \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)} \]
   13. Step-by-step derivation

       1. *-commutative 14.7%

          \[\leadsto \color{blue}{\left(y \cdot \left(y3 \cdot y4\right)\right) \cdot c} \]

       2. *-commutative 14.7%

          \[\leadsto \left(y \cdot \color{blue}{\left(y4 \cdot y3\right)}\right) \cdot c \]

       3. associate-*r* 10.4%

          \[\leadsto \color{blue}{\left(\left(y \cdot y4\right) \cdot y3\right)} \cdot c \]

       4. remove-double-neg 10.4%

          \[\leadsto \left(\left(\color{blue}{\left(-\left(-y\right)\right)} \cdot y4\right) \cdot y3\right) \cdot c \]

       5. distribute-lft-neg-in 10.4%

          \[\leadsto \left(\color{blue}{\left(-\left(-y\right) \cdot y4\right)} \cdot y3\right) \cdot c \]

       6. *-commutative 10.4%

          \[\leadsto \left(\left(-\color{blue}{y4 \cdot \left(-y\right)}\right) \cdot y3\right) \cdot c \]

       7. associate-*r* 14.3%

          \[\leadsto \color{blue}{\left(-y4 \cdot \left(-y\right)\right) \cdot \left(y3 \cdot c\right)} \]

       8. *-commutative 14.3%

          \[\leadsto \left(-y4 \cdot \left(-y\right)\right) \cdot \color{blue}{\left(c \cdot y3\right)} \]

       9. distribute-rgt-neg-out 14.3%

          \[\leadsto \left(-\color{blue}{\left(-y4 \cdot y\right)}\right) \cdot \left(c \cdot y3\right) \]

       10. remove-double-neg 14.3%

           \[\leadsto \color{blue}{\left(y4 \cdot y\right)} \cdot \left(c \cdot y3\right) \]

       11. associate-*l* 27.4%

           \[\leadsto \color{blue}{y4 \cdot \left(y \cdot \left(c \cdot y3\right)\right)} \]

       12. *-commutative 27.4%

           \[\leadsto y4 \cdot \left(y \cdot \color{blue}{\left(y3 \cdot c\right)}\right) \]

   14. Simplified 27.4%

       \[\leadsto \color{blue}{y4 \cdot \left(y \cdot \left(y3 \cdot c\right)\right)} \]

   if 8.99999999999999953e-218 < y5 < 1.1799999999999999e157

   1. Initial program 39.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 39.8%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 45.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   6. Taylor expanded in y3 around inf 26.8%

      \[\leadsto \color{blue}{c \cdot \left(y3 \cdot \left(-1 \cdot \left(y0 \cdot z\right) - -1 \cdot \left(y \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. distribute-lft-out-- 26.8%

         \[\leadsto c \cdot \left(y3 \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot z - y \cdot y4\right)\right)}\right) \]

   8. Simplified 26.8%

      \[\leadsto \color{blue}{c \cdot \left(y3 \cdot \left(-1 \cdot \left(y0 \cdot z - y \cdot y4\right)\right)\right)} \]

   9. Taylor expanded in y0 around 0 16.1%

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 23.6%

          \[\leadsto \color{blue}{\left(c \cdot y\right) \cdot \left(y3 \cdot y4\right)} \]

       2. *-commutative 23.6%

          \[\leadsto \left(c \cdot y\right) \cdot \color{blue}{\left(y4 \cdot y3\right)} \]

   11. Simplified 23.6%

       \[\leadsto \color{blue}{\left(c \cdot y\right) \cdot \left(y4 \cdot y3\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 32.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -5.2 \cdot 10^{+74}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq -1 \cdot 10^{-204}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;y5 \leq -2.25 \cdot 10^{-291}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq 9 \cdot 10^{-218}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;y5 \leq 1.18 \cdot 10^{+157}:\\ \;\;\;\;\left(y \cdot c\right) \cdot \left(y3 \cdot y4\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 27.9% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y3 \cdot \left(y \cdot y4\right)\right)\\ \mathbf{if}\;y4 \leq -2.6 \cdot 10^{+225}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y4 \leq -2.3 \cdot 10^{+144}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -1.7 \cdot 10^{+121}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(t \cdot \left(-y5\right)\right)\\ \mathbf{elif}\;y4 \leq 9 \cdot 10^{+197}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y3 (* y y4)))))
   (if (<= y4 -2.6e+225)
     t_1
     (if (<= y4 -2.3e+144)
       (* k (* y1 (* y2 y4)))
       (if (<= y4 -1.7e+121)
         (* (* i j) (* t (- y5)))
         (if (<= y4 9e+197) (* a (* y (- (* x b) (* 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 = c * (y3 * (y * y4));
	double tmp;
	if (y4 <= -2.6e+225) {
		tmp = t_1;
	} else if (y4 <= -2.3e+144) {
		tmp = k * (y1 * (y2 * y4));
	} else if (y4 <= -1.7e+121) {
		tmp = (i * j) * (t * -y5);
	} else if (y4 <= 9e+197) {
		tmp = a * (y * ((x * b) - (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 = c * (y3 * (y * y4))
    if (y4 <= (-2.6d+225)) then
        tmp = t_1
    else if (y4 <= (-2.3d+144)) then
        tmp = k * (y1 * (y2 * y4))
    else if (y4 <= (-1.7d+121)) then
        tmp = (i * j) * (t * -y5)
    else if (y4 <= 9d+197) then
        tmp = a * (y * ((x * b) - (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 = c * (y3 * (y * y4));
	double tmp;
	if (y4 <= -2.6e+225) {
		tmp = t_1;
	} else if (y4 <= -2.3e+144) {
		tmp = k * (y1 * (y2 * y4));
	} else if (y4 <= -1.7e+121) {
		tmp = (i * j) * (t * -y5);
	} else if (y4 <= 9e+197) {
		tmp = a * (y * ((x * b) - (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 = c * (y3 * (y * y4))
	tmp = 0
	if y4 <= -2.6e+225:
		tmp = t_1
	elif y4 <= -2.3e+144:
		tmp = k * (y1 * (y2 * y4))
	elif y4 <= -1.7e+121:
		tmp = (i * j) * (t * -y5)
	elif y4 <= 9e+197:
		tmp = a * (y * ((x * b) - (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(c * Float64(y3 * Float64(y * y4)))
	tmp = 0.0
	if (y4 <= -2.6e+225)
		tmp = t_1;
	elseif (y4 <= -2.3e+144)
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	elseif (y4 <= -1.7e+121)
		tmp = Float64(Float64(i * j) * Float64(t * Float64(-y5)));
	elseif (y4 <= 9e+197)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * 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 = c * (y3 * (y * y4));
	tmp = 0.0;
	if (y4 <= -2.6e+225)
		tmp = t_1;
	elseif (y4 <= -2.3e+144)
		tmp = k * (y1 * (y2 * y4));
	elseif (y4 <= -1.7e+121)
		tmp = (i * j) * (t * -y5);
	elseif (y4 <= 9e+197)
		tmp = a * (y * ((x * b) - (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[(c * N[(y3 * N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -2.6e+225], t$95$1, If[LessEqual[y4, -2.3e+144], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -1.7e+121], N[(N[(i * j), $MachinePrecision] * N[(t * (-y5)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 9e+197], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y4 < -2.60000000000000004e225 or 9.0000000000000006e197 < y4

   1. Initial program 19.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 19.1%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 38.5%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   6. Taylor expanded in y3 around inf 60.2%

      \[\leadsto \color{blue}{c \cdot \left(y3 \cdot \left(-1 \cdot \left(y0 \cdot z\right) - -1 \cdot \left(y \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. distribute-lft-out-- 60.2%

         \[\leadsto c \cdot \left(y3 \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot z - y \cdot y4\right)\right)}\right) \]

   8. Simplified 60.2%

      \[\leadsto \color{blue}{c \cdot \left(y3 \cdot \left(-1 \cdot \left(y0 \cdot z - y \cdot y4\right)\right)\right)} \]

   9. Taylor expanded in y0 around 0 62.3%

      \[\leadsto c \cdot \left(y3 \cdot \left(-1 \cdot \color{blue}{\left(-1 \cdot \left(y \cdot y4\right)\right)}\right)\right) \]
   10. Step-by-step derivation

       1. mul-1-neg 62.3%

          \[\leadsto c \cdot \left(y3 \cdot \left(-1 \cdot \color{blue}{\left(-y \cdot y4\right)}\right)\right) \]

       2. distribute-lft-neg-out 62.3%

          \[\leadsto c \cdot \left(y3 \cdot \left(-1 \cdot \color{blue}{\left(\left(-y\right) \cdot y4\right)}\right)\right) \]

       3. *-commutative 62.3%

          \[\leadsto c \cdot \left(y3 \cdot \left(-1 \cdot \color{blue}{\left(y4 \cdot \left(-y\right)\right)}\right)\right) \]

   11. Simplified 62.3%

       \[\leadsto c \cdot \left(y3 \cdot \left(-1 \cdot \color{blue}{\left(y4 \cdot \left(-y\right)\right)}\right)\right) \]

   if -2.60000000000000004e225 < y4 < -2.3000000000000001e144

   1. Initial program 31.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 43.8%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in k around inf 50.3%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 50.3%

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - \color{blue}{y5 \cdot y0}\right)\right) \]

   6. Simplified 50.3%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y5 \cdot y0\right)\right)} \]

   7. Taylor expanded in y1 around inf 44.3%

      \[\leadsto k \cdot \color{blue}{\left(y1 \cdot \left(y2 \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 44.3%

         \[\leadsto k \cdot \left(y1 \cdot \color{blue}{\left(y4 \cdot y2\right)}\right) \]

   9. Simplified 44.3%

      \[\leadsto k \cdot \color{blue}{\left(y1 \cdot \left(y4 \cdot y2\right)\right)} \]

   if -2.3000000000000001e144 < y4 < -1.70000000000000005e121

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around -inf 25.1%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 25.1%

         \[\leadsto \color{blue}{\left(-1 \cdot y5\right) \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. neg-mul-1 25.1%

         \[\leadsto \color{blue}{\left(-y5\right)} \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. fma-def 25.1%

         \[\leadsto \left(-y5\right) \cdot \left(\color{blue}{\mathsf{fma}\left(i, j \cdot t - k \cdot y, y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 25.1%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, \color{blue}{t \cdot j} - k \cdot y, y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 25.1%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 25.1%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   5. Simplified 25.1%

      \[\leadsto \color{blue}{\left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in j around -inf 51.3%

      \[\leadsto \color{blue}{j \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 51.3%

         \[\leadsto \color{blue}{\left(j \cdot y5\right) \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)} \]

      2. +-commutative 51.3%

         \[\leadsto \left(j \cdot y5\right) \cdot \color{blue}{\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)} \]

      3. mul-1-neg 51.3%

         \[\leadsto \left(j \cdot y5\right) \cdot \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right) \]

      4. unsub-neg 51.3%

         \[\leadsto \left(j \cdot y5\right) \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)} \]

   8. Simplified 51.3%

      \[\leadsto \color{blue}{\left(j \cdot y5\right) \cdot \left(y0 \cdot y3 - i \cdot t\right)} \]

   9. Taylor expanded in y0 around 0 51.2%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot \left(t \cdot y5\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 51.2%

          \[\leadsto \color{blue}{-i \cdot \left(j \cdot \left(t \cdot y5\right)\right)} \]

       2. associate-*r* 75.1%

          \[\leadsto -\color{blue}{\left(i \cdot j\right) \cdot \left(t \cdot y5\right)} \]

       3. distribute-rgt-neg-in 75.1%

          \[\leadsto \color{blue}{\left(i \cdot j\right) \cdot \left(-t \cdot y5\right)} \]

       4. *-commutative 75.1%

          \[\leadsto \color{blue}{\left(j \cdot i\right)} \cdot \left(-t \cdot y5\right) \]

       5. *-commutative 75.1%

          \[\leadsto \left(j \cdot i\right) \cdot \left(-\color{blue}{y5 \cdot t}\right) \]

   11. Simplified 75.1%

       \[\leadsto \color{blue}{\left(j \cdot i\right) \cdot \left(-y5 \cdot t\right)} \]

   if -1.70000000000000005e121 < y4 < 9.0000000000000006e197

   1. Initial program 33.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 33.9%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 36.2%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in y around inf 30.2%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 30.2%

         \[\leadsto a \cdot \left(y \cdot \left(\color{blue}{x \cdot b} - y3 \cdot y5\right)\right) \]

      2. *-commutative 30.2%

         \[\leadsto a \cdot \left(y \cdot \left(x \cdot b - \color{blue}{y5 \cdot y3}\right)\right) \]

   8. Simplified 30.2%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(x \cdot b - y5 \cdot y3\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 37.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -2.6 \cdot 10^{+225}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -2.3 \cdot 10^{+144}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -1.7 \cdot 10^{+121}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(t \cdot \left(-y5\right)\right)\\ \mathbf{elif}\;y4 \leq 9 \cdot 10^{+197}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 25.5% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{if}\;a \leq -7 \cdot 10^{-52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-152}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+111}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* z (- (* y1 y3) (* t b))))))
   (if (<= a -7e-52)
     t_1
     (if (<= a 1.05e-152)
       (* j (* y0 (* y3 y5)))
       (if (<= a 9.2e+111) (* c (* y3 (* y y4))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (z * ((y1 * y3) - (t * b)));
	double tmp;
	if (a <= -7e-52) {
		tmp = t_1;
	} else if (a <= 1.05e-152) {
		tmp = j * (y0 * (y3 * y5));
	} else if (a <= 9.2e+111) {
		tmp = c * (y3 * (y * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (z * ((y1 * y3) - (t * b)))
    if (a <= (-7d-52)) then
        tmp = t_1
    else if (a <= 1.05d-152) then
        tmp = j * (y0 * (y3 * y5))
    else if (a <= 9.2d+111) then
        tmp = c * (y3 * (y * y4))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (z * ((y1 * y3) - (t * b)));
	double tmp;
	if (a <= -7e-52) {
		tmp = t_1;
	} else if (a <= 1.05e-152) {
		tmp = j * (y0 * (y3 * y5));
	} else if (a <= 9.2e+111) {
		tmp = c * (y3 * (y * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (z * ((y1 * y3) - (t * b)))
	tmp = 0
	if a <= -7e-52:
		tmp = t_1
	elif a <= 1.05e-152:
		tmp = j * (y0 * (y3 * y5))
	elif a <= 9.2e+111:
		tmp = c * (y3 * (y * y4))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(z * Float64(Float64(y1 * y3) - Float64(t * b))))
	tmp = 0.0
	if (a <= -7e-52)
		tmp = t_1;
	elseif (a <= 1.05e-152)
		tmp = Float64(j * Float64(y0 * Float64(y3 * y5)));
	elseif (a <= 9.2e+111)
		tmp = Float64(c * Float64(y3 * Float64(y * y4)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (z * ((y1 * y3) - (t * b)));
	tmp = 0.0;
	if (a <= -7e-52)
		tmp = t_1;
	elseif (a <= 1.05e-152)
		tmp = j * (y0 * (y3 * y5));
	elseif (a <= 9.2e+111)
		tmp = c * (y3 * (y * y4));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7e-52], t$95$1, If[LessEqual[a, 1.05e-152], N[(j * N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.2e+111], N[(c * N[(y3 * N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.0000000000000001e-52 or 9.20000000000000008e111 < a

   1. Initial program 20.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 20.5%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 50.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in z around inf 45.8%

      \[\leadsto a \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 45.8%

         \[\leadsto a \cdot \left(z \cdot \color{blue}{\left(y1 \cdot y3 + -1 \cdot \left(b \cdot t\right)\right)}\right) \]

      2. mul-1-neg 45.8%

         \[\leadsto a \cdot \left(z \cdot \left(y1 \cdot y3 + \color{blue}{\left(-b \cdot t\right)}\right)\right) \]

      3. unsub-neg 45.8%

         \[\leadsto a \cdot \left(z \cdot \color{blue}{\left(y1 \cdot y3 - b \cdot t\right)}\right) \]

      4. *-commutative 45.8%

         \[\leadsto a \cdot \left(z \cdot \left(\color{blue}{y3 \cdot y1} - b \cdot t\right)\right) \]

      5. *-commutative 45.8%

         \[\leadsto a \cdot \left(z \cdot \left(y3 \cdot y1 - \color{blue}{t \cdot b}\right)\right) \]

   8. Simplified 45.8%

      \[\leadsto a \cdot \color{blue}{\left(z \cdot \left(y3 \cdot y1 - t \cdot b\right)\right)} \]

   if -7.0000000000000001e-52 < a < 1.04999999999999999e-152

   1. Initial program 41.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around -inf 34.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 34.0%

         \[\leadsto \color{blue}{\left(-1 \cdot y5\right) \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. neg-mul-1 34.0%

         \[\leadsto \color{blue}{\left(-y5\right)} \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. fma-def 38.2%

         \[\leadsto \left(-y5\right) \cdot \left(\color{blue}{\mathsf{fma}\left(i, j \cdot t - k \cdot y, y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 38.2%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, \color{blue}{t \cdot j} - k \cdot y, y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 38.2%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 38.2%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   5. Simplified 38.2%

      \[\leadsto \color{blue}{\left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in j around -inf 39.9%

      \[\leadsto \color{blue}{j \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 34.7%

         \[\leadsto \color{blue}{\left(j \cdot y5\right) \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)} \]

      2. +-commutative 34.7%

         \[\leadsto \left(j \cdot y5\right) \cdot \color{blue}{\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)} \]

      3. mul-1-neg 34.7%

         \[\leadsto \left(j \cdot y5\right) \cdot \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right) \]

      4. unsub-neg 34.7%

         \[\leadsto \left(j \cdot y5\right) \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)} \]

   8. Simplified 34.7%

      \[\leadsto \color{blue}{\left(j \cdot y5\right) \cdot \left(y0 \cdot y3 - i \cdot t\right)} \]

   9. Taylor expanded in y0 around inf 35.7%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]

   if 1.04999999999999999e-152 < a < 9.20000000000000008e111

   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 40.4%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 39.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   6. Taylor expanded in y3 around inf 32.6%

      \[\leadsto \color{blue}{c \cdot \left(y3 \cdot \left(-1 \cdot \left(y0 \cdot z\right) - -1 \cdot \left(y \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. distribute-lft-out-- 32.6%

         \[\leadsto c \cdot \left(y3 \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot z - y \cdot y4\right)\right)}\right) \]

   8. Simplified 32.6%

      \[\leadsto \color{blue}{c \cdot \left(y3 \cdot \left(-1 \cdot \left(y0 \cdot z - y \cdot y4\right)\right)\right)} \]

   9. Taylor expanded in y0 around 0 31.2%

      \[\leadsto c \cdot \left(y3 \cdot \left(-1 \cdot \color{blue}{\left(-1 \cdot \left(y \cdot y4\right)\right)}\right)\right) \]
   10. Step-by-step derivation

       1. mul-1-neg 31.2%

          \[\leadsto c \cdot \left(y3 \cdot \left(-1 \cdot \color{blue}{\left(-y \cdot y4\right)}\right)\right) \]

       2. distribute-lft-neg-out 31.2%

          \[\leadsto c \cdot \left(y3 \cdot \left(-1 \cdot \color{blue}{\left(\left(-y\right) \cdot y4\right)}\right)\right) \]

       3. *-commutative 31.2%

          \[\leadsto c \cdot \left(y3 \cdot \left(-1 \cdot \color{blue}{\left(y4 \cdot \left(-y\right)\right)}\right)\right) \]

   11. Simplified 31.2%

       \[\leadsto c \cdot \left(y3 \cdot \left(-1 \cdot \color{blue}{\left(y4 \cdot \left(-y\right)\right)}\right)\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 39.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{-52}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-152}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+111}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 21.1% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{if}\;b \leq -9.2 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{-209}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-119}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y (* x b)))))
   (if (<= b -9.2e-56)
     t_1
     (if (<= b 1.02e-209)
       (* j (* y0 (* y3 y5)))
       (if (<= b 1.8e-119) (* k (* y1 (* y2 y4))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y * (x * b));
	double tmp;
	if (b <= -9.2e-56) {
		tmp = t_1;
	} else if (b <= 1.02e-209) {
		tmp = j * (y0 * (y3 * y5));
	} else if (b <= 1.8e-119) {
		tmp = k * (y1 * (y2 * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (y * (x * b))
    if (b <= (-9.2d-56)) then
        tmp = t_1
    else if (b <= 1.02d-209) then
        tmp = j * (y0 * (y3 * y5))
    else if (b <= 1.8d-119) then
        tmp = k * (y1 * (y2 * y4))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y * (x * b));
	double tmp;
	if (b <= -9.2e-56) {
		tmp = t_1;
	} else if (b <= 1.02e-209) {
		tmp = j * (y0 * (y3 * y5));
	} else if (b <= 1.8e-119) {
		tmp = k * (y1 * (y2 * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y * (x * b))
	tmp = 0
	if b <= -9.2e-56:
		tmp = t_1
	elif b <= 1.02e-209:
		tmp = j * (y0 * (y3 * y5))
	elif b <= 1.8e-119:
		tmp = k * (y1 * (y2 * y4))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y * Float64(x * b)))
	tmp = 0.0
	if (b <= -9.2e-56)
		tmp = t_1;
	elseif (b <= 1.02e-209)
		tmp = Float64(j * Float64(y0 * Float64(y3 * y5)));
	elseif (b <= 1.8e-119)
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y * (x * b));
	tmp = 0.0;
	if (b <= -9.2e-56)
		tmp = t_1;
	elseif (b <= 1.02e-209)
		tmp = j * (y0 * (y3 * y5));
	elseif (b <= 1.8e-119)
		tmp = k * (y1 * (y2 * y4));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9.2e-56], t$95$1, If[LessEqual[b, 1.02e-209], N[(j * N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.8e-119], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.20000000000000009e-56 or 1.8e-119 < b

   1. Initial program 26.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 26.0%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 41.0%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in y around inf 36.7%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 36.7%

         \[\leadsto a \cdot \left(y \cdot \left(\color{blue}{x \cdot b} - y3 \cdot y5\right)\right) \]

      2. *-commutative 36.7%

         \[\leadsto a \cdot \left(y \cdot \left(x \cdot b - \color{blue}{y5 \cdot y3}\right)\right) \]

   8. Simplified 36.7%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(x \cdot b - y5 \cdot y3\right)\right)} \]

   9. Taylor expanded in x around inf 27.1%

      \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x\right)}\right) \]

   if -9.20000000000000009e-56 < b < 1.01999999999999999e-209

   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 y5 around -inf 43.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 43.5%

         \[\leadsto \color{blue}{\left(-1 \cdot y5\right) \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. neg-mul-1 43.5%

         \[\leadsto \color{blue}{\left(-y5\right)} \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. fma-def 45.8%

         \[\leadsto \left(-y5\right) \cdot \left(\color{blue}{\mathsf{fma}\left(i, j \cdot t - k \cdot y, y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 45.8%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, \color{blue}{t \cdot j} - k \cdot y, y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 45.8%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 45.8%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   5. Simplified 45.8%

      \[\leadsto \color{blue}{\left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in j around -inf 38.0%

      \[\leadsto \color{blue}{j \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 33.5%

         \[\leadsto \color{blue}{\left(j \cdot y5\right) \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)} \]

      2. +-commutative 33.5%

         \[\leadsto \left(j \cdot y5\right) \cdot \color{blue}{\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)} \]

      3. mul-1-neg 33.5%

         \[\leadsto \left(j \cdot y5\right) \cdot \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right) \]

      4. unsub-neg 33.5%

         \[\leadsto \left(j \cdot y5\right) \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)} \]

   8. Simplified 33.5%

      \[\leadsto \color{blue}{\left(j \cdot y5\right) \cdot \left(y0 \cdot y3 - i \cdot t\right)} \]

   9. Taylor expanded in y0 around inf 29.7%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]

   if 1.01999999999999999e-209 < b < 1.8e-119

   1. Initial program 60.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 50.4%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in k around inf 60.7%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 60.7%

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - \color{blue}{y5 \cdot y0}\right)\right) \]

   6. Simplified 60.7%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y5 \cdot y0\right)\right)} \]

   7. Taylor expanded in y1 around inf 60.8%

      \[\leadsto k \cdot \color{blue}{\left(y1 \cdot \left(y2 \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 60.8%

         \[\leadsto k \cdot \left(y1 \cdot \color{blue}{\left(y4 \cdot y2\right)}\right) \]

   9. Simplified 60.8%

      \[\leadsto k \cdot \color{blue}{\left(y1 \cdot \left(y4 \cdot y2\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 29.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.2 \cdot 10^{-56}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{-209}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-119}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 20.6% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.6 \cdot 10^{-56}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;b \leq 7.6 \cdot 10^{-210}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-123}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= b -5.6e-56)
   (* a (* b (* x y)))
   (if (<= b 7.6e-210)
     (* j (* y0 (* y3 y5)))
     (if (<= b 3.2e-123) (* k (* y1 (* y2 y4))) (* a (* y (* x b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -5.6e-56) {
		tmp = a * (b * (x * y));
	} else if (b <= 7.6e-210) {
		tmp = j * (y0 * (y3 * y5));
	} else if (b <= 3.2e-123) {
		tmp = k * (y1 * (y2 * y4));
	} else {
		tmp = a * (y * (x * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (b <= (-5.6d-56)) then
        tmp = a * (b * (x * y))
    else if (b <= 7.6d-210) then
        tmp = j * (y0 * (y3 * y5))
    else if (b <= 3.2d-123) then
        tmp = k * (y1 * (y2 * y4))
    else
        tmp = a * (y * (x * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -5.6e-56) {
		tmp = a * (b * (x * y));
	} else if (b <= 7.6e-210) {
		tmp = j * (y0 * (y3 * y5));
	} else if (b <= 3.2e-123) {
		tmp = k * (y1 * (y2 * y4));
	} else {
		tmp = a * (y * (x * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if b <= -5.6e-56:
		tmp = a * (b * (x * y))
	elif b <= 7.6e-210:
		tmp = j * (y0 * (y3 * y5))
	elif b <= 3.2e-123:
		tmp = k * (y1 * (y2 * y4))
	else:
		tmp = a * (y * (x * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (b <= -5.6e-56)
		tmp = Float64(a * Float64(b * Float64(x * y)));
	elseif (b <= 7.6e-210)
		tmp = Float64(j * Float64(y0 * Float64(y3 * y5)));
	elseif (b <= 3.2e-123)
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	else
		tmp = Float64(a * Float64(y * Float64(x * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (b <= -5.6e-56)
		tmp = a * (b * (x * y));
	elseif (b <= 7.6e-210)
		tmp = j * (y0 * (y3 * y5));
	elseif (b <= 3.2e-123)
		tmp = k * (y1 * (y2 * y4));
	else
		tmp = a * (y * (x * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[b, -5.6e-56], N[(a * N[(b * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.6e-210], N[(j * N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.2e-123], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -5.59999999999999986e-56

   1. Initial program 31.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.1%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 43.7%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in y around inf 35.9%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 35.9%

         \[\leadsto a \cdot \left(y \cdot \left(\color{blue}{x \cdot b} - y3 \cdot y5\right)\right) \]

      2. *-commutative 35.9%

         \[\leadsto a \cdot \left(y \cdot \left(x \cdot b - \color{blue}{y5 \cdot y3}\right)\right) \]

   8. Simplified 35.9%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(x \cdot b - y5 \cdot y3\right)\right)} \]

   9. Taylor expanded in x around inf 29.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 29.5%

          \[\leadsto \color{blue}{\left(b \cdot \left(x \cdot y\right)\right) \cdot a} \]

       2. *-commutative 29.5%

          \[\leadsto \left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \cdot a \]

   11. Simplified 29.5%

       \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x\right)\right) \cdot a} \]

   if -5.59999999999999986e-56 < b < 7.60000000000000006e-210

   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 y5 around -inf 43.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 43.5%

         \[\leadsto \color{blue}{\left(-1 \cdot y5\right) \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. neg-mul-1 43.5%

         \[\leadsto \color{blue}{\left(-y5\right)} \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. fma-def 45.8%

         \[\leadsto \left(-y5\right) \cdot \left(\color{blue}{\mathsf{fma}\left(i, j \cdot t - k \cdot y, y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 45.8%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, \color{blue}{t \cdot j} - k \cdot y, y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 45.8%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 45.8%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   5. Simplified 45.8%

      \[\leadsto \color{blue}{\left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in j around -inf 38.0%

      \[\leadsto \color{blue}{j \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 33.5%

         \[\leadsto \color{blue}{\left(j \cdot y5\right) \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)} \]

      2. +-commutative 33.5%

         \[\leadsto \left(j \cdot y5\right) \cdot \color{blue}{\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)} \]

      3. mul-1-neg 33.5%

         \[\leadsto \left(j \cdot y5\right) \cdot \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right) \]

      4. unsub-neg 33.5%

         \[\leadsto \left(j \cdot y5\right) \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)} \]

   8. Simplified 33.5%

      \[\leadsto \color{blue}{\left(j \cdot y5\right) \cdot \left(y0 \cdot y3 - i \cdot t\right)} \]

   9. Taylor expanded in y0 around inf 29.7%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]

   if 7.60000000000000006e-210 < b < 3.19999999999999979e-123

   1. Initial program 60.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 50.4%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in k around inf 60.7%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 60.7%

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - \color{blue}{y5 \cdot y0}\right)\right) \]

   6. Simplified 60.7%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y5 \cdot y0\right)\right)} \]

   7. Taylor expanded in y1 around inf 60.8%

      \[\leadsto k \cdot \color{blue}{\left(y1 \cdot \left(y2 \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 60.8%

         \[\leadsto k \cdot \left(y1 \cdot \color{blue}{\left(y4 \cdot y2\right)}\right) \]

   9. Simplified 60.8%

      \[\leadsto k \cdot \color{blue}{\left(y1 \cdot \left(y4 \cdot y2\right)\right)} \]

   if 3.19999999999999979e-123 < b

   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 a around inf 38.8%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in y around inf 37.3%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 37.3%

         \[\leadsto a \cdot \left(y \cdot \left(\color{blue}{x \cdot b} - y3 \cdot y5\right)\right) \]

      2. *-commutative 37.3%

         \[\leadsto a \cdot \left(y \cdot \left(x \cdot b - \color{blue}{y5 \cdot y3}\right)\right) \]

   8. Simplified 37.3%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(x \cdot b - y5 \cdot y3\right)\right)} \]

   9. Taylor expanded in x around inf 25.1%

      \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x\right)}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 29.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.6 \cdot 10^{-56}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;b \leq 7.6 \cdot 10^{-210}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-123}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 18.7% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1 \cdot 10^{-176}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 3.9 \cdot 10^{-155}:\\ \;\;\;\;a \cdot \left(y \cdot \left(y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;j \leq 4.8 \cdot 10^{-32}:\\ \;\;\;\;\left(a \cdot b\right) \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot y5\right) \cdot \left(y0 \cdot y3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -1e-176)
   (* y4 (* y (* c y3)))
   (if (<= j 3.9e-155)
     (* a (* y (* y3 (- y5))))
     (if (<= j 4.8e-32) (* (* a b) (* x y)) (* (* j y5) (* y0 y3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -1e-176) {
		tmp = y4 * (y * (c * y3));
	} else if (j <= 3.9e-155) {
		tmp = a * (y * (y3 * -y5));
	} else if (j <= 4.8e-32) {
		tmp = (a * b) * (x * y);
	} else {
		tmp = (j * y5) * (y0 * y3);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (j <= (-1d-176)) then
        tmp = y4 * (y * (c * y3))
    else if (j <= 3.9d-155) then
        tmp = a * (y * (y3 * -y5))
    else if (j <= 4.8d-32) then
        tmp = (a * b) * (x * y)
    else
        tmp = (j * y5) * (y0 * y3)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -1e-176) {
		tmp = y4 * (y * (c * y3));
	} else if (j <= 3.9e-155) {
		tmp = a * (y * (y3 * -y5));
	} else if (j <= 4.8e-32) {
		tmp = (a * b) * (x * y);
	} else {
		tmp = (j * y5) * (y0 * y3);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if j <= -1e-176:
		tmp = y4 * (y * (c * y3))
	elif j <= 3.9e-155:
		tmp = a * (y * (y3 * -y5))
	elif j <= 4.8e-32:
		tmp = (a * b) * (x * y)
	else:
		tmp = (j * y5) * (y0 * y3)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (j <= -1e-176)
		tmp = Float64(y4 * Float64(y * Float64(c * y3)));
	elseif (j <= 3.9e-155)
		tmp = Float64(a * Float64(y * Float64(y3 * Float64(-y5))));
	elseif (j <= 4.8e-32)
		tmp = Float64(Float64(a * b) * Float64(x * y));
	else
		tmp = Float64(Float64(j * y5) * Float64(y0 * y3));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (j <= -1e-176)
		tmp = y4 * (y * (c * y3));
	elseif (j <= 3.9e-155)
		tmp = a * (y * (y3 * -y5));
	elseif (j <= 4.8e-32)
		tmp = (a * b) * (x * y);
	else
		tmp = (j * y5) * (y0 * y3);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[j, -1e-176], N[(y4 * N[(y * N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.9e-155], N[(a * N[(y * N[(y3 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.8e-32], N[(N[(a * b), $MachinePrecision] * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(N[(j * y5), $MachinePrecision] * N[(y0 * y3), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1e-176

   1. Initial program 21.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 21.9%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 47.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   6. Taylor expanded in y3 around inf 31.4%

      \[\leadsto \color{blue}{c \cdot \left(y3 \cdot \left(-1 \cdot \left(y0 \cdot z\right) - -1 \cdot \left(y \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. distribute-lft-out-- 31.4%

         \[\leadsto c \cdot \left(y3 \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot z - y \cdot y4\right)\right)}\right) \]

   8. Simplified 31.4%

      \[\leadsto \color{blue}{c \cdot \left(y3 \cdot \left(-1 \cdot \left(y0 \cdot z - y \cdot y4\right)\right)\right)} \]

   9. Taylor expanded in y0 around 0 24.9%

      \[\leadsto c \cdot \left(y3 \cdot \left(-1 \cdot \color{blue}{\left(-1 \cdot \left(y \cdot y4\right)\right)}\right)\right) \]
   10. Step-by-step derivation

       1. mul-1-neg 24.9%

          \[\leadsto c \cdot \left(y3 \cdot \left(-1 \cdot \color{blue}{\left(-y \cdot y4\right)}\right)\right) \]

       2. distribute-lft-neg-out 24.9%

          \[\leadsto c \cdot \left(y3 \cdot \left(-1 \cdot \color{blue}{\left(\left(-y\right) \cdot y4\right)}\right)\right) \]

       3. *-commutative 24.9%

          \[\leadsto c \cdot \left(y3 \cdot \left(-1 \cdot \color{blue}{\left(y4 \cdot \left(-y\right)\right)}\right)\right) \]

   11. Simplified 24.9%

       \[\leadsto c \cdot \left(y3 \cdot \left(-1 \cdot \color{blue}{\left(y4 \cdot \left(-y\right)\right)}\right)\right) \]

   12. Taylor expanded in c around 0 26.2%

       \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)} \]
   13. Step-by-step derivation

       1. *-commutative 26.2%

          \[\leadsto \color{blue}{\left(y \cdot \left(y3 \cdot y4\right)\right) \cdot c} \]

       2. *-commutative 26.2%

          \[\leadsto \left(y \cdot \color{blue}{\left(y4 \cdot y3\right)}\right) \cdot c \]

       3. associate-*r* 24.9%

          \[\leadsto \color{blue}{\left(\left(y \cdot y4\right) \cdot y3\right)} \cdot c \]

       4. remove-double-neg 24.9%

          \[\leadsto \left(\left(\color{blue}{\left(-\left(-y\right)\right)} \cdot y4\right) \cdot y3\right) \cdot c \]

       5. distribute-lft-neg-in 24.9%

          \[\leadsto \left(\color{blue}{\left(-\left(-y\right) \cdot y4\right)} \cdot y3\right) \cdot c \]

       6. *-commutative 24.9%

          \[\leadsto \left(\left(-\color{blue}{y4 \cdot \left(-y\right)}\right) \cdot y3\right) \cdot c \]

       7. associate-*r* 27.4%

          \[\leadsto \color{blue}{\left(-y4 \cdot \left(-y\right)\right) \cdot \left(y3 \cdot c\right)} \]

       8. *-commutative 27.4%

          \[\leadsto \left(-y4 \cdot \left(-y\right)\right) \cdot \color{blue}{\left(c \cdot y3\right)} \]

       9. distribute-rgt-neg-out 27.4%

          \[\leadsto \left(-\color{blue}{\left(-y4 \cdot y\right)}\right) \cdot \left(c \cdot y3\right) \]

       10. remove-double-neg 27.4%

           \[\leadsto \color{blue}{\left(y4 \cdot y\right)} \cdot \left(c \cdot y3\right) \]

       11. associate-*l* 31.5%

           \[\leadsto \color{blue}{y4 \cdot \left(y \cdot \left(c \cdot y3\right)\right)} \]

       12. *-commutative 31.5%

           \[\leadsto y4 \cdot \left(y \cdot \color{blue}{\left(y3 \cdot c\right)}\right) \]

   14. Simplified 31.5%

       \[\leadsto \color{blue}{y4 \cdot \left(y \cdot \left(y3 \cdot c\right)\right)} \]

   if -1e-176 < j < 3.9000000000000003e-155

   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 38.1%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 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 y around inf 40.2%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 40.2%

         \[\leadsto a \cdot \left(y \cdot \left(\color{blue}{x \cdot b} - y3 \cdot y5\right)\right) \]

      2. *-commutative 40.2%

         \[\leadsto a \cdot \left(y \cdot \left(x \cdot b - \color{blue}{y5 \cdot y3}\right)\right) \]

   8. Simplified 40.2%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(x \cdot b - y5 \cdot y3\right)\right)} \]

   9. Taylor expanded in x around 0 31.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 31.9%

          \[\leadsto \color{blue}{-a \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)} \]

       2. *-commutative 31.9%

          \[\leadsto -\color{blue}{\left(y \cdot \left(y3 \cdot y5\right)\right) \cdot a} \]

       3. distribute-lft-neg-in 31.9%

          \[\leadsto \color{blue}{\left(-y \cdot \left(y3 \cdot y5\right)\right) \cdot a} \]

       4. distribute-rgt-neg-in 31.9%

          \[\leadsto \color{blue}{\left(y \cdot \left(-y3 \cdot y5\right)\right)} \cdot a \]

       5. distribute-rgt-neg-in 31.9%

          \[\leadsto \left(y \cdot \color{blue}{\left(y3 \cdot \left(-y5\right)\right)}\right) \cdot a \]

   11. Simplified 31.9%

       \[\leadsto \color{blue}{\left(y \cdot \left(y3 \cdot \left(-y5\right)\right)\right) \cdot a} \]

   if 3.9000000000000003e-155 < j < 4.8000000000000003e-32

   1. Initial program 36.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 36.6%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 32.8%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in y around inf 31.1%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 31.1%

         \[\leadsto a \cdot \left(y \cdot \left(\color{blue}{x \cdot b} - y3 \cdot y5\right)\right) \]

      2. *-commutative 31.1%

         \[\leadsto a \cdot \left(y \cdot \left(x \cdot b - \color{blue}{y5 \cdot y3}\right)\right) \]

   8. Simplified 31.1%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(x \cdot b - y5 \cdot y3\right)\right)} \]

   9. Taylor expanded in x around inf 31.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 31.3%

          \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot \left(x \cdot y\right)} \]

       2. *-commutative 31.3%

          \[\leadsto \left(a \cdot b\right) \cdot \color{blue}{\left(y \cdot x\right)} \]

   11. Simplified 31.3%

       \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot \left(y \cdot x\right)} \]

   if 4.8000000000000003e-32 < j

   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 y5 around -inf 27.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 27.6%

         \[\leadsto \color{blue}{\left(-1 \cdot y5\right) \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. neg-mul-1 27.6%

         \[\leadsto \color{blue}{\left(-y5\right)} \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. fma-def 31.6%

         \[\leadsto \left(-y5\right) \cdot \left(\color{blue}{\mathsf{fma}\left(i, j \cdot t - k \cdot y, y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 31.6%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, \color{blue}{t \cdot j} - k \cdot y, y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 31.6%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 31.6%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   5. Simplified 31.6%

      \[\leadsto \color{blue}{\left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in j around -inf 41.9%

      \[\leadsto \color{blue}{j \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 44.4%

         \[\leadsto \color{blue}{\left(j \cdot y5\right) \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)} \]

      2. +-commutative 44.4%

         \[\leadsto \left(j \cdot y5\right) \cdot \color{blue}{\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)} \]

      3. mul-1-neg 44.4%

         \[\leadsto \left(j \cdot y5\right) \cdot \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right) \]

      4. unsub-neg 44.4%

         \[\leadsto \left(j \cdot y5\right) \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)} \]

   8. Simplified 44.4%

      \[\leadsto \color{blue}{\left(j \cdot y5\right) \cdot \left(y0 \cdot y3 - i \cdot t\right)} \]

   9. Taylor expanded in y0 around inf 33.7%

      \[\leadsto \left(j \cdot y5\right) \cdot \color{blue}{\left(y0 \cdot y3\right)} \]
   10. Step-by-step derivation

       1. *-commutative 33.7%

          \[\leadsto \left(j \cdot y5\right) \cdot \color{blue}{\left(y3 \cdot y0\right)} \]

   11. Simplified 33.7%

       \[\leadsto \left(j \cdot y5\right) \cdot \color{blue}{\left(y3 \cdot y0\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 32.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1 \cdot 10^{-176}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 3.9 \cdot 10^{-155}:\\ \;\;\;\;a \cdot \left(y \cdot \left(y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;j \leq 4.8 \cdot 10^{-32}:\\ \;\;\;\;\left(a \cdot b\right) \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot y5\right) \cdot \left(y0 \cdot y3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 31: 19.7% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.6 \cdot 10^{+108} \lor \neg \left(a \leq 4.9 \cdot 10^{+165}\right):\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= a -4.6e+108) (not (<= a 4.9e+165)))
   (* a (* y (* x b)))
   (* c (* y (* y3 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 ((a <= -4.6e+108) || !(a <= 4.9e+165)) {
		tmp = a * (y * (x * b));
	} else {
		tmp = c * (y * (y3 * 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 ((a <= (-4.6d+108)) .or. (.not. (a <= 4.9d+165))) then
        tmp = a * (y * (x * b))
    else
        tmp = c * (y * (y3 * 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 ((a <= -4.6e+108) || !(a <= 4.9e+165)) {
		tmp = a * (y * (x * b));
	} else {
		tmp = c * (y * (y3 * 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 (a <= -4.6e+108) or not (a <= 4.9e+165):
		tmp = a * (y * (x * b))
	else:
		tmp = c * (y * (y3 * 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 ((a <= -4.6e+108) || !(a <= 4.9e+165))
		tmp = Float64(a * Float64(y * Float64(x * b)));
	else
		tmp = Float64(c * Float64(y * Float64(y3 * 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 ((a <= -4.6e+108) || ~((a <= 4.9e+165)))
		tmp = a * (y * (x * b));
	else
		tmp = c * (y * (y3 * 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[Or[LessEqual[a, -4.6e+108], N[Not[LessEqual[a, 4.9e+165]], $MachinePrecision]], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.5999999999999998e108 or 4.89999999999999986e165 < a

   1. Initial program 19.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 19.4%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 57.5%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in y around inf 37.3%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 37.3%

         \[\leadsto a \cdot \left(y \cdot \left(\color{blue}{x \cdot b} - y3 \cdot y5\right)\right) \]

      2. *-commutative 37.3%

         \[\leadsto a \cdot \left(y \cdot \left(x \cdot b - \color{blue}{y5 \cdot y3}\right)\right) \]

   8. Simplified 37.3%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(x \cdot b - y5 \cdot y3\right)\right)} \]

   9. Taylor expanded in x around inf 26.9%

      \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x\right)}\right) \]

   if -4.5999999999999998e108 < a < 4.89999999999999986e165

   1. Initial program 35.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 36.4%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 37.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   6. Taylor expanded in y3 around inf 31.2%

      \[\leadsto \color{blue}{c \cdot \left(y3 \cdot \left(-1 \cdot \left(y0 \cdot z\right) - -1 \cdot \left(y \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. distribute-lft-out-- 31.2%

         \[\leadsto c \cdot \left(y3 \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot z - y \cdot y4\right)\right)}\right) \]

   8. Simplified 31.2%

      \[\leadsto \color{blue}{c \cdot \left(y3 \cdot \left(-1 \cdot \left(y0 \cdot z - y \cdot y4\right)\right)\right)} \]

   9. Taylor expanded in y0 around 0 24.1%

      \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y3 \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 24.1%

          \[\leadsto c \cdot \left(y \cdot \color{blue}{\left(y4 \cdot y3\right)}\right) \]

   11. Simplified 24.1%

       \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y4 \cdot y3\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 25.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.6 \cdot 10^{+108} \lor \neg \left(a \leq 4.9 \cdot 10^{+165}\right):\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 32: 21.1% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{-57} \lor \neg \left(b \leq 3.25 \cdot 10^{-102}\right):\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= b -1.7e-57) (not (<= b 3.25e-102)))
   (* a (* y (* x b)))
   (* j (* y0 (* y3 y5)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((b <= -1.7e-57) || !(b <= 3.25e-102)) {
		tmp = a * (y * (x * b));
	} else {
		tmp = j * (y0 * (y3 * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((b <= (-1.7d-57)) .or. (.not. (b <= 3.25d-102))) then
        tmp = a * (y * (x * b))
    else
        tmp = j * (y0 * (y3 * y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((b <= -1.7e-57) || !(b <= 3.25e-102)) {
		tmp = a * (y * (x * b));
	} else {
		tmp = j * (y0 * (y3 * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (b <= -1.7e-57) or not (b <= 3.25e-102):
		tmp = a * (y * (x * b))
	else:
		tmp = j * (y0 * (y3 * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((b <= -1.7e-57) || !(b <= 3.25e-102))
		tmp = Float64(a * Float64(y * Float64(x * b)));
	else
		tmp = Float64(j * Float64(y0 * Float64(y3 * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((b <= -1.7e-57) || ~((b <= 3.25e-102)))
		tmp = a * (y * (x * b));
	else
		tmp = j * (y0 * (y3 * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[b, -1.7e-57], N[Not[LessEqual[b, 3.25e-102]], $MachinePrecision]], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.70000000000000008e-57 or 3.2500000000000001e-102 < b

   1. Initial program 26.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 26.6%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 42.0%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in y around inf 37.6%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 37.6%

         \[\leadsto a \cdot \left(y \cdot \left(\color{blue}{x \cdot b} - y3 \cdot y5\right)\right) \]

      2. *-commutative 37.6%

         \[\leadsto a \cdot \left(y \cdot \left(x \cdot b - \color{blue}{y5 \cdot y3}\right)\right) \]

   8. Simplified 37.6%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(x \cdot b - y5 \cdot y3\right)\right)} \]

   9. Taylor expanded in x around inf 27.7%

      \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x\right)}\right) \]

   if -1.70000000000000008e-57 < b < 3.2500000000000001e-102

   1. Initial program 36.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around -inf 42.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 42.4%

         \[\leadsto \color{blue}{\left(-1 \cdot y5\right) \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. neg-mul-1 42.4%

         \[\leadsto \color{blue}{\left(-y5\right)} \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. fma-def 44.4%

         \[\leadsto \left(-y5\right) \cdot \left(\color{blue}{\mathsf{fma}\left(i, j \cdot t - k \cdot y, y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 44.4%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, \color{blue}{t \cdot j} - k \cdot y, y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 44.4%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 44.4%

         \[\leadsto \left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   5. Simplified 44.4%

      \[\leadsto \color{blue}{\left(-y5\right) \cdot \left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in j around -inf 35.9%

      \[\leadsto \color{blue}{j \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 32.0%

         \[\leadsto \color{blue}{\left(j \cdot y5\right) \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)} \]

      2. +-commutative 32.0%

         \[\leadsto \left(j \cdot y5\right) \cdot \color{blue}{\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)} \]

      3. mul-1-neg 32.0%

         \[\leadsto \left(j \cdot y5\right) \cdot \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right) \]

      4. unsub-neg 32.0%

         \[\leadsto \left(j \cdot y5\right) \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)} \]

   8. Simplified 32.0%

      \[\leadsto \color{blue}{\left(j \cdot y5\right) \cdot \left(y0 \cdot y3 - i \cdot t\right)} \]

   9. Taylor expanded in y0 around inf 27.7%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 27.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{-57} \lor \neg \left(b \leq 3.25 \cdot 10^{-102}\right):\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 33: 16.5% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(y \cdot \left(x \cdot b\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* y (* x b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (y * (x * b));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = a * (y * (x * b))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (y * (x * b));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * (y * (x * b))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(y * Float64(x * b)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * (y * (x * b));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 30.5%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

3. Simplified 30.9%

   \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
4. Add Preprocessing

5. Taylor expanded in a around inf 37.0%

   \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

6. Taylor expanded in y around inf 29.6%

   \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]
7. Step-by-step derivation

   1. *-commutative 29.6%

      \[\leadsto a \cdot \left(y \cdot \left(\color{blue}{x \cdot b} - y3 \cdot y5\right)\right) \]

   2. *-commutative 29.6%

      \[\leadsto a \cdot \left(y \cdot \left(x \cdot b - \color{blue}{y5 \cdot y3}\right)\right) \]

8. Simplified 29.6%

   \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(x \cdot b - y5 \cdot y3\right)\right)} \]

9. Taylor expanded in x around inf 19.7%

   \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x\right)}\right) \]

10. Final simplification 19.7%

    \[\leadsto a \cdot \left(y \cdot \left(x \cdot b\right)\right) \]
11. Add Preprocessing

Developer target: 28.5% 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 2024018 
(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :name "Linear.Matrix:det44 from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< y4 -7.206256231996481e+60) (- (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))))) (- (/ (- (* y2 t) (* y3 y)) (/ 1.0 (- (* y4 c) (* y5 a)))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (if (< y4 -3.364603505246317e-66) (+ (- (- (- (* (* t c) (* i z)) (* (* a t) (* b z))) (* (* y c) (* i x))) (* (- (* b y0) (* i y1)) (- (* j x) (* k z)))) (- (* (- (* y0 c) (* a y1)) (- (* x y2) (* z y3))) (- (* (- (* t y2) (* y y3)) (- (* y4 c) (* a y5))) (* (- (* y1 y4) (* y5 y0)) (- (* k y2) (* j y3)))))) (if (< y4 -1.2000065055686116e-105) (+ (+ (- (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))) (* (* y3 y) (- (* y5 a) (* y4 c)))) (+ (* (* y5 a) (* t y2)) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* x y2) (* z y3)) (- (* c y0) (* a y1))) (- (* (- (* b y0) (* i y1)) (- (* j x) (* k z))) (* (- (* y x) (* z t)) (- (* b a) (* i c)))))) (if (< y4 6.718963124057495e-279) (+ (- (- (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k))) (* (* y5 t) (* i j))) (- (* (- (* y2 t) (* y3 y)) (- (* y4 c) (* y5 a))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))) (if (< y4 4.77962681403792e-222) (+ (+ (- (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))) (* (* y3 y) (- (* y5 a) (* y4 c)))) (+ (* (* y5 a) (* t y2)) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* x y2) (* z y3)) (- (* c y0) (* a y1))) (- (* (- (* b y0) (* i y1)) (- (* j x) (* k z))) (* (- (* y x) (* z t)) (- (* b a) (* i c)))))) (if (< y4 2.2852241541266835e-175) (+ (- (- (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k))) (* (* y5 t) (* i j))) (- (* (- (* y2 t) (* y3 y)) (- (* y4 c) (* y5 a))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))) (+ (- (+ (+ (- (* (- (* x y) (* z t)) (- (* a b) (* c i))) (- (* k (* i (* z y1))) (+ (* j (* i (* x y1))) (* y0 (* k (* z b)))))) (- (* z (* y3 (* a y1))) (+ (* y2 (* x (* a y1))) (* y0 (* z (* c y3)))))) (* (- (* t j) (* y k)) (- (* y4 b) (* y5 i)))) (* (- (* t y2) (* y y3)) (- (* y4 c) (* y5 a)))) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))))))))

  (+ (- (+ (+ (- (* (- (* x y) (* z t)) (- (* a b) (* c i))) (* (- (* x j) (* z k)) (- (* y0 b) (* y1 i)))) (* (- (* x y2) (* z y3)) (- (* y0 c) (* y1 a)))) (* (- (* t j) (* y k)) (- (* y4 b) (* y5 i)))) (* (- (* t y2) (* y y3)) (- (* y4 c) (* y5 a)))) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0)))))