Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 29.5% → 39.7%

Time: 1.4min

Alternatives: 41

Speedup: 4.5×

• 88.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 29.5% 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: 39.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot j - z \cdot k\\ t_2 := t \cdot j - y \cdot k\\ t_3 := z \cdot k - x \cdot j\\ t_4 := x \cdot y - z \cdot t\\ t_5 := i \cdot \left(y1 \cdot t_1 - \left(c \cdot t_4 + y5 \cdot t_2\right)\right)\\ t_6 := z \cdot y3 - x \cdot y2\\ t_7 := x \cdot y2 - z \cdot y3\\ t_8 := c \cdot \left(y0 \cdot t_7 + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ t_9 := k \cdot y2 - j \cdot y3\\ t_10 := \left(\left(a \cdot \left(b \cdot t_4\right) + \left(b \cdot \left(y4 \cdot t_2\right) + t_7 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + b \cdot \left(y0 \cdot t_3\right)\right) + \left(t_9 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot y2 - y \cdot y3\right) \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{if}\;i \leq -1.9 \cdot 10^{+64}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq -1.7 \cdot 10^{-27}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;i \leq -1.15 \cdot 10^{-104}:\\ \;\;\;\;t_10\\ \mathbf{elif}\;i \leq -7.5 \cdot 10^{-123}:\\ \;\;\;\;x \cdot \left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq -3.4 \cdot 10^{-173}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;i \leq 1.65 \cdot 10^{-283}:\\ \;\;\;\;y0 \cdot \left(b \cdot t_3 - \left(y5 \cdot t_9 + t_6 \cdot c\right)\right)\\ \mathbf{elif}\;i \leq 1.18 \cdot 10^{-176}:\\ \;\;\;\;t_10\\ \mathbf{elif}\;i \leq 2.1 \cdot 10^{-106}:\\ \;\;\;\;t \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - c \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq 1.4 \cdot 10^{+51}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot \left(c \cdot i - a \cdot b\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{+220}:\\ \;\;\;\;y1 \cdot \left(i \cdot t_1 - \left(y4 \cdot \left(j \cdot y3 - k \cdot y2\right) - a \cdot t_6\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* x j) (* z k)))
        (t_2 (- (* t j) (* y k)))
        (t_3 (- (* z k) (* x j)))
        (t_4 (- (* x y) (* z t)))
        (t_5 (* i (- (* y1 t_1) (+ (* c t_4) (* y5 t_2)))))
        (t_6 (- (* z y3) (* x y2)))
        (t_7 (- (* x y2) (* z y3)))
        (t_8 (* c (+ (* y0 t_7) (* y4 (- (* y y3) (* t y2))))))
        (t_9 (- (* k y2) (* j y3)))
        (t_10
         (+
          (+
           (+
            (* a (* b t_4))
            (+ (* b (* y4 t_2)) (* t_7 (- (* c y0) (* a y1)))))
           (* b (* y0 t_3)))
          (+
           (* t_9 (- (* y1 y4) (* y0 y5)))
           (* (- (* t y2) (* y y3)) (- (* a y5) (* c y4)))))))
   (if (<= i -1.9e+64)
     t_5
     (if (<= i -1.7e-27)
       t_8
       (if (<= i -1.15e-104)
         t_10
         (if (<= i -7.5e-123)
           (* x (* y1 (- (* i j) (* a y2))))
           (if (<= i -3.4e-173)
             t_8
             (if (<= i 1.65e-283)
               (* y0 (- (* b t_3) (+ (* y5 t_9) (* t_6 c))))
               (if (<= i 1.18e-176)
                 t_10
                 (if (<= i 2.1e-106)
                   (* t (- (* j (- (* b y4) (* i y5))) (* c (* y2 y4))))
                   (if (<= i 1.4e+51)
                     (*
                      z
                      (+
                       (* k (- (* b y0) (* i y1)))
                       (+
                        (* t (- (* c i) (* a b)))
                        (* y3 (- (* a y1) (* c y0))))))
                     (if (<= i 1.3e+220)
                       (*
                        y1
                        (-
                         (* i t_1)
                         (- (* y4 (- (* j y3) (* k y2))) (* a t_6))))
                       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 = (x * j) - (z * k);
	double t_2 = (t * j) - (y * k);
	double t_3 = (z * k) - (x * j);
	double t_4 = (x * y) - (z * t);
	double t_5 = i * ((y1 * t_1) - ((c * t_4) + (y5 * t_2)));
	double t_6 = (z * y3) - (x * y2);
	double t_7 = (x * y2) - (z * y3);
	double t_8 = c * ((y0 * t_7) + (y4 * ((y * y3) - (t * y2))));
	double t_9 = (k * y2) - (j * y3);
	double t_10 = (((a * (b * t_4)) + ((b * (y4 * t_2)) + (t_7 * ((c * y0) - (a * y1))))) + (b * (y0 * t_3))) + ((t_9 * ((y1 * y4) - (y0 * y5))) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4))));
	double tmp;
	if (i <= -1.9e+64) {
		tmp = t_5;
	} else if (i <= -1.7e-27) {
		tmp = t_8;
	} else if (i <= -1.15e-104) {
		tmp = t_10;
	} else if (i <= -7.5e-123) {
		tmp = x * (y1 * ((i * j) - (a * y2)));
	} else if (i <= -3.4e-173) {
		tmp = t_8;
	} else if (i <= 1.65e-283) {
		tmp = y0 * ((b * t_3) - ((y5 * t_9) + (t_6 * c)));
	} else if (i <= 1.18e-176) {
		tmp = t_10;
	} else if (i <= 2.1e-106) {
		tmp = t * ((j * ((b * y4) - (i * y5))) - (c * (y2 * y4)));
	} else if (i <= 1.4e+51) {
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	} else if (i <= 1.3e+220) {
		tmp = y1 * ((i * t_1) - ((y4 * ((j * y3) - (k * y2))) - (a * t_6)));
	} 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_10
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = (x * j) - (z * k)
    t_2 = (t * j) - (y * k)
    t_3 = (z * k) - (x * j)
    t_4 = (x * y) - (z * t)
    t_5 = i * ((y1 * t_1) - ((c * t_4) + (y5 * t_2)))
    t_6 = (z * y3) - (x * y2)
    t_7 = (x * y2) - (z * y3)
    t_8 = c * ((y0 * t_7) + (y4 * ((y * y3) - (t * y2))))
    t_9 = (k * y2) - (j * y3)
    t_10 = (((a * (b * t_4)) + ((b * (y4 * t_2)) + (t_7 * ((c * y0) - (a * y1))))) + (b * (y0 * t_3))) + ((t_9 * ((y1 * y4) - (y0 * y5))) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4))))
    if (i <= (-1.9d+64)) then
        tmp = t_5
    else if (i <= (-1.7d-27)) then
        tmp = t_8
    else if (i <= (-1.15d-104)) then
        tmp = t_10
    else if (i <= (-7.5d-123)) then
        tmp = x * (y1 * ((i * j) - (a * y2)))
    else if (i <= (-3.4d-173)) then
        tmp = t_8
    else if (i <= 1.65d-283) then
        tmp = y0 * ((b * t_3) - ((y5 * t_9) + (t_6 * c)))
    else if (i <= 1.18d-176) then
        tmp = t_10
    else if (i <= 2.1d-106) then
        tmp = t * ((j * ((b * y4) - (i * y5))) - (c * (y2 * y4)))
    else if (i <= 1.4d+51) then
        tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))))
    else if (i <= 1.3d+220) then
        tmp = y1 * ((i * t_1) - ((y4 * ((j * y3) - (k * y2))) - (a * t_6)))
    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 = (x * j) - (z * k);
	double t_2 = (t * j) - (y * k);
	double t_3 = (z * k) - (x * j);
	double t_4 = (x * y) - (z * t);
	double t_5 = i * ((y1 * t_1) - ((c * t_4) + (y5 * t_2)));
	double t_6 = (z * y3) - (x * y2);
	double t_7 = (x * y2) - (z * y3);
	double t_8 = c * ((y0 * t_7) + (y4 * ((y * y3) - (t * y2))));
	double t_9 = (k * y2) - (j * y3);
	double t_10 = (((a * (b * t_4)) + ((b * (y4 * t_2)) + (t_7 * ((c * y0) - (a * y1))))) + (b * (y0 * t_3))) + ((t_9 * ((y1 * y4) - (y0 * y5))) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4))));
	double tmp;
	if (i <= -1.9e+64) {
		tmp = t_5;
	} else if (i <= -1.7e-27) {
		tmp = t_8;
	} else if (i <= -1.15e-104) {
		tmp = t_10;
	} else if (i <= -7.5e-123) {
		tmp = x * (y1 * ((i * j) - (a * y2)));
	} else if (i <= -3.4e-173) {
		tmp = t_8;
	} else if (i <= 1.65e-283) {
		tmp = y0 * ((b * t_3) - ((y5 * t_9) + (t_6 * c)));
	} else if (i <= 1.18e-176) {
		tmp = t_10;
	} else if (i <= 2.1e-106) {
		tmp = t * ((j * ((b * y4) - (i * y5))) - (c * (y2 * y4)));
	} else if (i <= 1.4e+51) {
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	} else if (i <= 1.3e+220) {
		tmp = y1 * ((i * t_1) - ((y4 * ((j * y3) - (k * y2))) - (a * t_6)));
	} 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 = (x * j) - (z * k)
	t_2 = (t * j) - (y * k)
	t_3 = (z * k) - (x * j)
	t_4 = (x * y) - (z * t)
	t_5 = i * ((y1 * t_1) - ((c * t_4) + (y5 * t_2)))
	t_6 = (z * y3) - (x * y2)
	t_7 = (x * y2) - (z * y3)
	t_8 = c * ((y0 * t_7) + (y4 * ((y * y3) - (t * y2))))
	t_9 = (k * y2) - (j * y3)
	t_10 = (((a * (b * t_4)) + ((b * (y4 * t_2)) + (t_7 * ((c * y0) - (a * y1))))) + (b * (y0 * t_3))) + ((t_9 * ((y1 * y4) - (y0 * y5))) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4))))
	tmp = 0
	if i <= -1.9e+64:
		tmp = t_5
	elif i <= -1.7e-27:
		tmp = t_8
	elif i <= -1.15e-104:
		tmp = t_10
	elif i <= -7.5e-123:
		tmp = x * (y1 * ((i * j) - (a * y2)))
	elif i <= -3.4e-173:
		tmp = t_8
	elif i <= 1.65e-283:
		tmp = y0 * ((b * t_3) - ((y5 * t_9) + (t_6 * c)))
	elif i <= 1.18e-176:
		tmp = t_10
	elif i <= 2.1e-106:
		tmp = t * ((j * ((b * y4) - (i * y5))) - (c * (y2 * y4)))
	elif i <= 1.4e+51:
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))))
	elif i <= 1.3e+220:
		tmp = y1 * ((i * t_1) - ((y4 * ((j * y3) - (k * y2))) - (a * t_6)))
	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(x * j) - Float64(z * k))
	t_2 = Float64(Float64(t * j) - Float64(y * k))
	t_3 = Float64(Float64(z * k) - Float64(x * j))
	t_4 = Float64(Float64(x * y) - Float64(z * t))
	t_5 = Float64(i * Float64(Float64(y1 * t_1) - Float64(Float64(c * t_4) + Float64(y5 * t_2))))
	t_6 = Float64(Float64(z * y3) - Float64(x * y2))
	t_7 = Float64(Float64(x * y2) - Float64(z * y3))
	t_8 = Float64(c * Float64(Float64(y0 * t_7) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))))
	t_9 = Float64(Float64(k * y2) - Float64(j * y3))
	t_10 = Float64(Float64(Float64(Float64(a * Float64(b * t_4)) + Float64(Float64(b * Float64(y4 * t_2)) + Float64(t_7 * Float64(Float64(c * y0) - Float64(a * y1))))) + Float64(b * Float64(y0 * t_3))) + Float64(Float64(t_9 * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(Float64(Float64(t * y2) - Float64(y * y3)) * Float64(Float64(a * y5) - Float64(c * y4)))))
	tmp = 0.0
	if (i <= -1.9e+64)
		tmp = t_5;
	elseif (i <= -1.7e-27)
		tmp = t_8;
	elseif (i <= -1.15e-104)
		tmp = t_10;
	elseif (i <= -7.5e-123)
		tmp = Float64(x * Float64(y1 * Float64(Float64(i * j) - Float64(a * y2))));
	elseif (i <= -3.4e-173)
		tmp = t_8;
	elseif (i <= 1.65e-283)
		tmp = Float64(y0 * Float64(Float64(b * t_3) - Float64(Float64(y5 * t_9) + Float64(t_6 * c))));
	elseif (i <= 1.18e-176)
		tmp = t_10;
	elseif (i <= 2.1e-106)
		tmp = Float64(t * Float64(Float64(j * Float64(Float64(b * y4) - Float64(i * y5))) - Float64(c * Float64(y2 * y4))));
	elseif (i <= 1.4e+51)
		tmp = Float64(z * Float64(Float64(k * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(Float64(t * Float64(Float64(c * i) - Float64(a * b))) + Float64(y3 * Float64(Float64(a * y1) - Float64(c * y0))))));
	elseif (i <= 1.3e+220)
		tmp = Float64(y1 * Float64(Float64(i * t_1) - Float64(Float64(y4 * Float64(Float64(j * y3) - Float64(k * y2))) - Float64(a * t_6))));
	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 = (x * j) - (z * k);
	t_2 = (t * j) - (y * k);
	t_3 = (z * k) - (x * j);
	t_4 = (x * y) - (z * t);
	t_5 = i * ((y1 * t_1) - ((c * t_4) + (y5 * t_2)));
	t_6 = (z * y3) - (x * y2);
	t_7 = (x * y2) - (z * y3);
	t_8 = c * ((y0 * t_7) + (y4 * ((y * y3) - (t * y2))));
	t_9 = (k * y2) - (j * y3);
	t_10 = (((a * (b * t_4)) + ((b * (y4 * t_2)) + (t_7 * ((c * y0) - (a * y1))))) + (b * (y0 * t_3))) + ((t_9 * ((y1 * y4) - (y0 * y5))) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4))));
	tmp = 0.0;
	if (i <= -1.9e+64)
		tmp = t_5;
	elseif (i <= -1.7e-27)
		tmp = t_8;
	elseif (i <= -1.15e-104)
		tmp = t_10;
	elseif (i <= -7.5e-123)
		tmp = x * (y1 * ((i * j) - (a * y2)));
	elseif (i <= -3.4e-173)
		tmp = t_8;
	elseif (i <= 1.65e-283)
		tmp = y0 * ((b * t_3) - ((y5 * t_9) + (t_6 * c)));
	elseif (i <= 1.18e-176)
		tmp = t_10;
	elseif (i <= 2.1e-106)
		tmp = t * ((j * ((b * y4) - (i * y5))) - (c * (y2 * y4)));
	elseif (i <= 1.4e+51)
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	elseif (i <= 1.3e+220)
		tmp = y1 * ((i * t_1) - ((y4 * ((j * y3) - (k * y2))) - (a * t_6)));
	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[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(i * N[(N[(y1 * t$95$1), $MachinePrecision] - N[(N[(c * t$95$4), $MachinePrecision] + N[(y5 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(c * N[(N[(y0 * t$95$7), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$10 = N[(N[(N[(N[(a * N[(b * t$95$4), $MachinePrecision]), $MachinePrecision] + N[(N[(b * N[(y4 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(t$95$7 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(y0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$9 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $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]), $MachinePrecision]}, If[LessEqual[i, -1.9e+64], t$95$5, If[LessEqual[i, -1.7e-27], t$95$8, If[LessEqual[i, -1.15e-104], t$95$10, If[LessEqual[i, -7.5e-123], N[(x * N[(y1 * N[(N[(i * j), $MachinePrecision] - N[(a * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -3.4e-173], t$95$8, If[LessEqual[i, 1.65e-283], N[(y0 * N[(N[(b * t$95$3), $MachinePrecision] - N[(N[(y5 * t$95$9), $MachinePrecision] + N[(t$95$6 * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.18e-176], t$95$10, If[LessEqual[i, 2.1e-106], N[(t * N[(N[(j * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.4e+51], N[(z * N[(N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.3e+220], N[(y1 * N[(N[(i * t$95$1), $MachinePrecision] - N[(N[(y4 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$5]]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if i < -1.9000000000000001e64 or 1.29999999999999997e220 < i

   1. Initial program 22.3%

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

   3. Simplified 22.3%

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

   4. Taylor expanded in i around -inf 59.2%

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

   if -1.9000000000000001e64 < i < -1.69999999999999985e-27 or -7.50000000000000011e-123 < i < -3.3999999999999999e-173

   1. Initial program 7.7%

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

   3. Simplified 7.7%

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

   4. Taylor expanded in c around inf 47.8%

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

   5. Taylor expanded in i around 0 59.3%

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

      1. *-commutative 59.3%

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

      2. *-commutative 59.3%

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

   7. Simplified 59.3%

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

   if -1.69999999999999985e-27 < i < -1.15e-104 or 1.6500000000000001e-283 < i < 1.18e-176

   1. Initial program 71.9%

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

   3. Simplified 71.9%

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

   4. Taylor expanded in i around 0 75.0%

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

   if -1.15e-104 < i < -7.50000000000000011e-123

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in y1 around inf 33.3%

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

   5. Taylor expanded in x around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

   7. Simplified 100.0%

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

   if -3.3999999999999999e-173 < i < 1.6500000000000001e-283

   1. Initial program 55.5%

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

   3. Simplified 55.5%

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

   4. Taylor expanded in y0 around inf 71.3%

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

   if 1.18e-176 < i < 2.10000000000000003e-106

   1. Initial program 20.0%

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

   3. Simplified 20.0%

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

   4. Taylor expanded in t around inf 60.0%

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

   5. Taylor expanded in z around 0 70.0%

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

   6. Taylor expanded in a around 0 80.0%

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

   if 2.10000000000000003e-106 < i < 1.40000000000000002e51

   1. Initial program 40.4%

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

   3. Simplified 40.4%

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

   4. Taylor expanded in z around -inf 64.4%

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

   if 1.40000000000000002e51 < i < 1.29999999999999997e220

   1. Initial program 28.4%

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

   3. Simplified 28.4%

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

   4. Taylor expanded in y1 around inf 54.3%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.9 \cdot 10^{+64}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) - \left(c \cdot \left(x \cdot y - z \cdot t\right) + y5 \cdot \left(t \cdot j - y \cdot k\right)\right)\right)\\ \mathbf{elif}\;i \leq -1.7 \cdot 10^{-27}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq -1.15 \cdot 10^{-104}:\\ \;\;\;\;\left(\left(a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right) + \left(b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\right) + \left(\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot y2 - y \cdot y3\right) \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq -7.5 \cdot 10^{-123}:\\ \;\;\;\;x \cdot \left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq -3.4 \cdot 10^{-173}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq 1.65 \cdot 10^{-283}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right) - \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(z \cdot y3 - x \cdot y2\right) \cdot c\right)\right)\\ \mathbf{elif}\;i \leq 1.18 \cdot 10^{-176}:\\ \;\;\;\;\left(\left(a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right) + \left(b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\right) + \left(\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot y2 - y \cdot y3\right) \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq 2.1 \cdot 10^{-106}:\\ \;\;\;\;t \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - c \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq 1.4 \cdot 10^{+51}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot \left(c \cdot i - a \cdot b\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{+220}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) - \left(y4 \cdot \left(j \cdot y3 - k \cdot y2\right) - a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) - \left(c \cdot \left(x \cdot y - z \cdot t\right) + y5 \cdot \left(t \cdot j - y \cdot k\right)\right)\right)\\ \end{array} \]

Alternative 2: 54.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot y4 - i \cdot y5\\ t_2 := \left(\left(\left(\left(\left(a \cdot b - c \cdot i\right) \cdot \left(x \cdot y - z \cdot t\right) + \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot t_1\right) + \left(t \cdot y2 - y \cdot y3\right) \cdot \left(a \cdot y5 - c \cdot y4\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ \mathbf{if}\;t_2 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \langle \left( \langle \left( \left(j \cdot t_1\right) \right)_{\text{binary64}} \rangle_{\text{binary32}} \right)_{\text{binary32}} \rangle_{\text{binary64}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* b y4) (* i y5)))
        (t_2
         (+
          (+
           (+
            (+
             (+
              (* (- (* a b) (* c i)) (- (* x y) (* z t)))
              (* (- (* x j) (* z k)) (- (* i y1) (* b y0))))
             (* (- (* x y2) (* z y3)) (- (* c y0) (* a y1))))
            (* (- (* t j) (* y k)) t_1))
           (* (- (* t y2) (* y y3)) (- (* a y5) (* c y4))))
          (* (- (* k y2) (* j y3)) (- (* y1 y4) (* y0 y5))))))
   (if (<= t_2 INFINITY)
     t_2
     (*
      t
      (cast
       (! :precision binary32 (cast (! :precision binary64 (* j t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (b * y4) - (i * y5);
	double t_2 = (((((((a * b) - (c * i)) * ((x * y) - (z * t))) + (((x * j) - (z * k)) * ((i * y1) - (b * y0)))) + (((x * y2) - (z * y3)) * ((c * y0) - (a * y1)))) + (((t * j) - (y * k)) * t_1)) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4)))) + (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5)));
	double tmp;
	if (t_2 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		double tmp_3 = j * t_1;
		double tmp_2 = (float) tmp_3;
		tmp = t * ((double) tmp_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(b * y4) - Float64(i * y5))
	t_2 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(a * b) - Float64(c * i)) * Float64(Float64(x * y) - Float64(z * t))) + Float64(Float64(Float64(x * j) - Float64(z * k)) * Float64(Float64(i * y1) - Float64(b * y0)))) + Float64(Float64(Float64(x * y2) - Float64(z * y3)) * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(Float64(Float64(t * j) - Float64(y * k)) * t_1)) + Float64(Float64(Float64(t * y2) - Float64(y * y3)) * Float64(Float64(a * y5) - Float64(c * y4)))) + Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y1 * y4) - Float64(y0 * y5))))
	tmp = 0.0
	if (t_2 <= Inf)
		tmp = t_2;
	else
		tmp_3 = Float64(j * t_1)
		tmp_2 = Float32(tmp_3)
		tmp = Float64(t * Float64(tmp_2));
	end
	return tmp
end

MATLAB

function tmp_5 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (b * y4) - (i * y5);
	t_2 = (((((((a * b) - (c * i)) * ((x * y) - (z * t))) + (((x * j) - (z * k)) * ((i * y1) - (b * y0)))) + (((x * y2) - (z * y3)) * ((c * y0) - (a * y1)))) + (((t * j) - (y * k)) * t_1)) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4)))) + (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5)));
	tmp = 0.0;
	if (t_2 <= Inf)
		tmp = t_2;
	else
		tmp_4 = j * t_1;
		tmp_3 = single(tmp_4);
		tmp = t * double(tmp_3);
	end
	tmp_5 = tmp;
end

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 90.8%

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

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

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in t around inf 29.3%

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

   5. Taylor expanded in j around inf 33.3%

      \[\leadsto t \cdot \color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. rewrite-binary64/binary32-simplify 41.0%

         \[\leadsto \color{blue}{t \cdot \langle \left( \langle \left( \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \right)_{\text{binary64}} \rangle_{\text{binary32}} \right)_{\text{binary32}} \rangle_{\text{binary64}}} \]

   7. Applied rewrite-once 41.0%

      \[\leadsto t \cdot \color{blue}{\langle \color{blue}{\left( \color{blue}{\langle \color{blue}{\left( \color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \right)_{\text{binary64}}} \rangle_{\text{binary32}}} \right)_{\text{binary32}}} \rangle_{\text{binary64}}} \]
   8. Step-by-step derivation

      1. *-commutative 41.0%

         \[\leadsto t \cdot \langle \left( \langle \left( \left(j \cdot \left(y4 \cdot b - i \cdot y5\right)\right) \right)_{\text{binary64}} \rangle_{\text{binary32}} \right)_{\text{binary32}} \rangle_{\text{binary64}} \]

   9. Simplified 41.0%

      \[\leadsto t \cdot \color{blue}{\langle \color{blue}{\left( \color{blue}{\langle \color{blue}{\left( \color{blue}{\left(j \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} \right)_{\text{binary64}}} \rangle_{\text{binary32}}} \right)_{\text{binary32}}} \rangle_{\text{binary64}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(a \cdot b - c \cdot i\right) \cdot \left(x \cdot y - z \cdot t\right) + \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + \left(t \cdot y2 - y \cdot y3\right) \cdot \left(a \cdot y5 - c \cdot y4\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \leq \infty:\\ \;\;\;\;\left(\left(\left(\left(\left(a \cdot b - c \cdot i\right) \cdot \left(x \cdot y - z \cdot t\right) + \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + \left(t \cdot y2 - y \cdot y3\right) \cdot \left(a \cdot y5 - c \cdot y4\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \langle \left( \langle \left( \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \right)_{\text{binary64}} \rangle_{\text{binary32}} \right)_{\text{binary32}} \rangle_{\text{binary64}}\\ \end{array} \]

Alternative 3: 52.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 90.8%

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

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

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in c around inf 37.3%

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

   5. Taylor expanded in i around 0 39.4%

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

      1. *-commutative 39.4%

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

      2. *-commutative 39.4%

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

   7. Simplified 39.4%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 58.7%

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

Alternative 4: 40.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - c \cdot \left(y2 \cdot y4\right)\right)\\ t_2 := x \cdot y - z \cdot t\\ t_3 := x \cdot y2 - z \cdot y3\\ t_4 := z \cdot k - x \cdot j\\ t_5 := t \cdot j - y \cdot k\\ t_6 := i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) - \left(c \cdot t_2 + y5 \cdot t_5\right)\right)\\ \mathbf{if}\;i \leq -3.3 \cdot 10^{+78}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;i \leq -1.3 \cdot 10^{-28}:\\ \;\;\;\;c \cdot \left(y0 \cdot t_3 + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq -1.35 \cdot 10^{-176}:\\ \;\;\;\;b \cdot \left(\left(y4 \cdot t_5 + a \cdot t_2\right) + y0 \cdot t_4\right)\\ \mathbf{elif}\;i \leq 1.05 \cdot 10^{-176}:\\ \;\;\;\;y0 \cdot \left(c \cdot t_3 + b \cdot t_4\right) + \left(\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot y2 - y \cdot y3\right) \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{-106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{+55}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot \left(c \cdot i - a \cdot b\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;i \leq 1.25 \cdot 10^{+152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 3.75 \cdot 10^{+171}:\\ \;\;\;\;i \cdot \left(c \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;i \leq 5.5 \cdot 10^{+221}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_6\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* t (- (* j (- (* b y4) (* i y5))) (* c (* y2 y4)))))
        (t_2 (- (* x y) (* z t)))
        (t_3 (- (* x y2) (* z y3)))
        (t_4 (- (* z k) (* x j)))
        (t_5 (- (* t j) (* y k)))
        (t_6 (* i (- (* y1 (- (* x j) (* z k))) (+ (* c t_2) (* y5 t_5))))))
   (if (<= i -3.3e+78)
     t_6
     (if (<= i -1.3e-28)
       (* c (+ (* y0 t_3) (* y4 (- (* y y3) (* t y2)))))
       (if (<= i -1.35e-176)
         (* b (+ (+ (* y4 t_5) (* a t_2)) (* y0 t_4)))
         (if (<= i 1.05e-176)
           (+
            (* y0 (+ (* c t_3) (* b t_4)))
            (+
             (* (- (* k y2) (* j y3)) (- (* y1 y4) (* y0 y5)))
             (* (- (* t y2) (* y y3)) (- (* a y5) (* c y4)))))
           (if (<= i 2.2e-106)
             t_1
             (if (<= i 2.5e+55)
               (*
                z
                (+
                 (* k (- (* b y0) (* i y1)))
                 (+ (* t (- (* c i) (* a b))) (* y3 (- (* a y1) (* c y0))))))
               (if (<= i 1.25e+152)
                 t_1
                 (if (<= i 3.75e+171)
                   (* i (* c (- (* z t) (* x y))))
                   (if (<= i 5.5e+221)
                     (* a (* y3 (- (* z y1) (* y y5))))
                     t_6)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * ((j * ((b * y4) - (i * y5))) - (c * (y2 * y4)));
	double t_2 = (x * y) - (z * t);
	double t_3 = (x * y2) - (z * y3);
	double t_4 = (z * k) - (x * j);
	double t_5 = (t * j) - (y * k);
	double t_6 = i * ((y1 * ((x * j) - (z * k))) - ((c * t_2) + (y5 * t_5)));
	double tmp;
	if (i <= -3.3e+78) {
		tmp = t_6;
	} else if (i <= -1.3e-28) {
		tmp = c * ((y0 * t_3) + (y4 * ((y * y3) - (t * y2))));
	} else if (i <= -1.35e-176) {
		tmp = b * (((y4 * t_5) + (a * t_2)) + (y0 * t_4));
	} else if (i <= 1.05e-176) {
		tmp = (y0 * ((c * t_3) + (b * t_4))) + ((((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4))));
	} else if (i <= 2.2e-106) {
		tmp = t_1;
	} else if (i <= 2.5e+55) {
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	} else if (i <= 1.25e+152) {
		tmp = t_1;
	} else if (i <= 3.75e+171) {
		tmp = i * (c * ((z * t) - (x * y)));
	} else if (i <= 5.5e+221) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else {
		tmp = t_6;
	}
	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 = t * ((j * ((b * y4) - (i * y5))) - (c * (y2 * y4)))
    t_2 = (x * y) - (z * t)
    t_3 = (x * y2) - (z * y3)
    t_4 = (z * k) - (x * j)
    t_5 = (t * j) - (y * k)
    t_6 = i * ((y1 * ((x * j) - (z * k))) - ((c * t_2) + (y5 * t_5)))
    if (i <= (-3.3d+78)) then
        tmp = t_6
    else if (i <= (-1.3d-28)) then
        tmp = c * ((y0 * t_3) + (y4 * ((y * y3) - (t * y2))))
    else if (i <= (-1.35d-176)) then
        tmp = b * (((y4 * t_5) + (a * t_2)) + (y0 * t_4))
    else if (i <= 1.05d-176) then
        tmp = (y0 * ((c * t_3) + (b * t_4))) + ((((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4))))
    else if (i <= 2.2d-106) then
        tmp = t_1
    else if (i <= 2.5d+55) then
        tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))))
    else if (i <= 1.25d+152) then
        tmp = t_1
    else if (i <= 3.75d+171) then
        tmp = i * (c * ((z * t) - (x * y)))
    else if (i <= 5.5d+221) then
        tmp = a * (y3 * ((z * y1) - (y * y5)))
    else
        tmp = t_6
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * ((j * ((b * y4) - (i * y5))) - (c * (y2 * y4)));
	double t_2 = (x * y) - (z * t);
	double t_3 = (x * y2) - (z * y3);
	double t_4 = (z * k) - (x * j);
	double t_5 = (t * j) - (y * k);
	double t_6 = i * ((y1 * ((x * j) - (z * k))) - ((c * t_2) + (y5 * t_5)));
	double tmp;
	if (i <= -3.3e+78) {
		tmp = t_6;
	} else if (i <= -1.3e-28) {
		tmp = c * ((y0 * t_3) + (y4 * ((y * y3) - (t * y2))));
	} else if (i <= -1.35e-176) {
		tmp = b * (((y4 * t_5) + (a * t_2)) + (y0 * t_4));
	} else if (i <= 1.05e-176) {
		tmp = (y0 * ((c * t_3) + (b * t_4))) + ((((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4))));
	} else if (i <= 2.2e-106) {
		tmp = t_1;
	} else if (i <= 2.5e+55) {
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	} else if (i <= 1.25e+152) {
		tmp = t_1;
	} else if (i <= 3.75e+171) {
		tmp = i * (c * ((z * t) - (x * y)));
	} else if (i <= 5.5e+221) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else {
		tmp = t_6;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = t * ((j * ((b * y4) - (i * y5))) - (c * (y2 * y4)))
	t_2 = (x * y) - (z * t)
	t_3 = (x * y2) - (z * y3)
	t_4 = (z * k) - (x * j)
	t_5 = (t * j) - (y * k)
	t_6 = i * ((y1 * ((x * j) - (z * k))) - ((c * t_2) + (y5 * t_5)))
	tmp = 0
	if i <= -3.3e+78:
		tmp = t_6
	elif i <= -1.3e-28:
		tmp = c * ((y0 * t_3) + (y4 * ((y * y3) - (t * y2))))
	elif i <= -1.35e-176:
		tmp = b * (((y4 * t_5) + (a * t_2)) + (y0 * t_4))
	elif i <= 1.05e-176:
		tmp = (y0 * ((c * t_3) + (b * t_4))) + ((((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4))))
	elif i <= 2.2e-106:
		tmp = t_1
	elif i <= 2.5e+55:
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))))
	elif i <= 1.25e+152:
		tmp = t_1
	elif i <= 3.75e+171:
		tmp = i * (c * ((z * t) - (x * y)))
	elif i <= 5.5e+221:
		tmp = a * (y3 * ((z * y1) - (y * y5)))
	else:
		tmp = t_6
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(t * Float64(Float64(j * Float64(Float64(b * y4) - Float64(i * y5))) - Float64(c * Float64(y2 * y4))))
	t_2 = Float64(Float64(x * y) - Float64(z * t))
	t_3 = Float64(Float64(x * y2) - Float64(z * y3))
	t_4 = Float64(Float64(z * k) - Float64(x * j))
	t_5 = Float64(Float64(t * j) - Float64(y * k))
	t_6 = Float64(i * Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) - Float64(Float64(c * t_2) + Float64(y5 * t_5))))
	tmp = 0.0
	if (i <= -3.3e+78)
		tmp = t_6;
	elseif (i <= -1.3e-28)
		tmp = Float64(c * Float64(Float64(y0 * t_3) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (i <= -1.35e-176)
		tmp = Float64(b * Float64(Float64(Float64(y4 * t_5) + Float64(a * t_2)) + Float64(y0 * t_4)));
	elseif (i <= 1.05e-176)
		tmp = Float64(Float64(y0 * Float64(Float64(c * t_3) + Float64(b * t_4))) + Float64(Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(Float64(Float64(t * y2) - Float64(y * y3)) * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (i <= 2.2e-106)
		tmp = t_1;
	elseif (i <= 2.5e+55)
		tmp = Float64(z * Float64(Float64(k * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(Float64(t * Float64(Float64(c * i) - Float64(a * b))) + Float64(y3 * Float64(Float64(a * y1) - Float64(c * y0))))));
	elseif (i <= 1.25e+152)
		tmp = t_1;
	elseif (i <= 3.75e+171)
		tmp = Float64(i * Float64(c * Float64(Float64(z * t) - Float64(x * y))));
	elseif (i <= 5.5e+221)
		tmp = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))));
	else
		tmp = t_6;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = t * ((j * ((b * y4) - (i * y5))) - (c * (y2 * y4)));
	t_2 = (x * y) - (z * t);
	t_3 = (x * y2) - (z * y3);
	t_4 = (z * k) - (x * j);
	t_5 = (t * j) - (y * k);
	t_6 = i * ((y1 * ((x * j) - (z * k))) - ((c * t_2) + (y5 * t_5)));
	tmp = 0.0;
	if (i <= -3.3e+78)
		tmp = t_6;
	elseif (i <= -1.3e-28)
		tmp = c * ((y0 * t_3) + (y4 * ((y * y3) - (t * y2))));
	elseif (i <= -1.35e-176)
		tmp = b * (((y4 * t_5) + (a * t_2)) + (y0 * t_4));
	elseif (i <= 1.05e-176)
		tmp = (y0 * ((c * t_3) + (b * t_4))) + ((((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4))));
	elseif (i <= 2.2e-106)
		tmp = t_1;
	elseif (i <= 2.5e+55)
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	elseif (i <= 1.25e+152)
		tmp = t_1;
	elseif (i <= 3.75e+171)
		tmp = i * (c * ((z * t) - (x * y)));
	elseif (i <= 5.5e+221)
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	else
		tmp = t_6;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(t * N[(N[(j * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(i * N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(c * t$95$2), $MachinePrecision] + N[(y5 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -3.3e+78], t$95$6, If[LessEqual[i, -1.3e-28], N[(c * N[(N[(y0 * t$95$3), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.35e-176], N[(b * N[(N[(N[(y4 * t$95$5), $MachinePrecision] + N[(a * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.05e-176], N[(N[(y0 * N[(N[(c * t$95$3), $MachinePrecision] + N[(b * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $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]), $MachinePrecision], If[LessEqual[i, 2.2e-106], t$95$1, If[LessEqual[i, 2.5e+55], N[(z * N[(N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.25e+152], t$95$1, If[LessEqual[i, 3.75e+171], N[(i * N[(c * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.5e+221], N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$6]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if i < -3.3e78 or 5.5000000000000003e221 < i

   1. Initial program 22.6%

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

   3. Simplified 22.6%

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

   4. Taylor expanded in i around -inf 59.9%

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

   if -3.3e78 < i < -1.3e-28

   1. Initial program 5.9%

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

   3. Simplified 5.9%

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

   4. Taylor expanded in c around inf 43.5%

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

   5. Taylor expanded in i around 0 55.2%

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

      1. *-commutative 55.2%

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

      2. *-commutative 55.2%

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

   7. Simplified 55.2%

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

   if -1.3e-28 < i < -1.3499999999999999e-176

   1. Initial program 47.9%

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

   3. Simplified 47.9%

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

   4. Taylor expanded in b around inf 59.6%

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

   if -1.3499999999999999e-176 < i < 1.04999999999999996e-176

   1. Initial program 58.6%

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

   3. Simplified 58.6%

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

   4. Taylor expanded in y0 around inf 63.8%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 63.8%

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

      2. *-commutative 63.8%

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

      3. *-commutative 63.8%

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

   6. Simplified 63.8%

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

   if 1.04999999999999996e-176 < i < 2.19999999999999994e-106 or 2.50000000000000023e55 < i < 1.25e152

   1. Initial program 28.9%

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

   3. Simplified 28.9%

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

   4. Taylor expanded in t around inf 54.4%

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

   5. Taylor expanded in z around 0 65.1%

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

   6. Taylor expanded in a around 0 71.9%

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

   if 2.19999999999999994e-106 < i < 2.50000000000000023e55

   1. Initial program 38.8%

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

   3. Simplified 38.8%

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

   4. Taylor expanded in z around -inf 62.0%

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

   if 1.25e152 < i < 3.7499999999999999e171

   1. Initial program 79.7%

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

   3. Simplified 79.7%

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

   4. Taylor expanded in i around -inf 42.1%

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

   5. Taylor expanded in c around inf 82.1%

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

   if 3.7499999999999999e171 < i < 5.5000000000000003e221

   1. Initial program 6.3%

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

   3. Simplified 6.3%

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

   4. Taylor expanded in y3 around -inf 44.3%

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

   5. Taylor expanded in a around -inf 56.7%

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

      1. associate-*r* 56.7%

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

      2. neg-mul-1 56.7%

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

   7. Simplified 56.7%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(-a\right) \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.3 \cdot 10^{+78}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) - \left(c \cdot \left(x \cdot y - z \cdot t\right) + y5 \cdot \left(t \cdot j - y \cdot k\right)\right)\right)\\ \mathbf{elif}\;i \leq -1.3 \cdot 10^{-28}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq -1.35 \cdot 10^{-176}:\\ \;\;\;\;b \cdot \left(\left(y4 \cdot \left(t \cdot j - y \cdot k\right) + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;i \leq 1.05 \cdot 10^{-176}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right) + \left(\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot y2 - y \cdot y3\right) \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{-106}:\\ \;\;\;\;t \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - c \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{+55}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot \left(c \cdot i - a \cdot b\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;i \leq 1.25 \cdot 10^{+152}:\\ \;\;\;\;t \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - c \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq 3.75 \cdot 10^{+171}:\\ \;\;\;\;i \cdot \left(c \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;i \leq 5.5 \cdot 10^{+221}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) - \left(c \cdot \left(x \cdot y - z \cdot t\right) + y5 \cdot \left(t \cdot j - y \cdot k\right)\right)\right)\\ \end{array} \]

Alternative 5: 40.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ t_2 := z \cdot k - x \cdot j\\ t_3 := y0 \cdot \left(b \cdot t_2 - \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(z \cdot y3 - x \cdot y2\right) \cdot c\right)\right)\\ t_4 := t \cdot j - y \cdot k\\ t_5 := i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) - \left(c \cdot t_1 + y5 \cdot t_4\right)\right)\\ t_6 := t \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - c \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{if}\;i \leq -1.25 \cdot 10^{+61}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq -9.5 \cdot 10^{-28}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq -2.6 \cdot 10^{-176}:\\ \;\;\;\;b \cdot \left(\left(y4 \cdot t_4 + a \cdot t_1\right) + y0 \cdot t_2\right)\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{-176}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 3.1 \cdot 10^{-133}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;i \leq 4.9 \cdot 10^{-72}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 195000000000:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot \left(c \cdot i - a \cdot b\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;i \leq 6.6 \cdot 10^{+53}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{+151}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;i \leq 9.5 \cdot 10^{+170}:\\ \;\;\;\;i \cdot \left(c \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;i \leq 5.5 \cdot 10^{+221}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t)))
        (t_2 (- (* z k) (* x j)))
        (t_3
         (*
          y0
          (-
           (* b t_2)
           (+ (* y5 (- (* k y2) (* j y3))) (* (- (* z y3) (* x y2)) c)))))
        (t_4 (- (* t j) (* y k)))
        (t_5 (* i (- (* y1 (- (* x j) (* z k))) (+ (* c t_1) (* y5 t_4)))))
        (t_6 (* t (- (* j (- (* b y4) (* i y5))) (* c (* y2 y4))))))
   (if (<= i -1.25e+61)
     t_5
     (if (<= i -9.5e-28)
       (* c (+ (* y0 (- (* x y2) (* z y3))) (* y4 (- (* y y3) (* t y2)))))
       (if (<= i -2.6e-176)
         (* b (+ (+ (* y4 t_4) (* a t_1)) (* y0 t_2)))
         (if (<= i 1.3e-176)
           t_3
           (if (<= i 3.1e-133)
             t_6
             (if (<= i 4.9e-72)
               t_3
               (if (<= i 195000000000.0)
                 (*
                  z
                  (+
                   (* k (- (* b y0) (* i y1)))
                   (+ (* t (- (* c i) (* a b))) (* y3 (- (* a y1) (* c y0))))))
                 (if (<= i 6.6e+53)
                   (* b (* k (- (* z y0) (* y y4))))
                   (if (<= i 2.5e+151)
                     t_6
                     (if (<= i 9.5e+170)
                       (* i (* c (- (* z t) (* x y))))
                       (if (<= i 5.5e+221)
                         (* a (* y3 (- (* z y1) (* y y5))))
                         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 = (x * y) - (z * t);
	double t_2 = (z * k) - (x * j);
	double t_3 = y0 * ((b * t_2) - ((y5 * ((k * y2) - (j * y3))) + (((z * y3) - (x * y2)) * c)));
	double t_4 = (t * j) - (y * k);
	double t_5 = i * ((y1 * ((x * j) - (z * k))) - ((c * t_1) + (y5 * t_4)));
	double t_6 = t * ((j * ((b * y4) - (i * y5))) - (c * (y2 * y4)));
	double tmp;
	if (i <= -1.25e+61) {
		tmp = t_5;
	} else if (i <= -9.5e-28) {
		tmp = c * ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2))));
	} else if (i <= -2.6e-176) {
		tmp = b * (((y4 * t_4) + (a * t_1)) + (y0 * t_2));
	} else if (i <= 1.3e-176) {
		tmp = t_3;
	} else if (i <= 3.1e-133) {
		tmp = t_6;
	} else if (i <= 4.9e-72) {
		tmp = t_3;
	} else if (i <= 195000000000.0) {
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	} else if (i <= 6.6e+53) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (i <= 2.5e+151) {
		tmp = t_6;
	} else if (i <= 9.5e+170) {
		tmp = i * (c * ((z * t) - (x * y)));
	} else if (i <= 5.5e+221) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} 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 = (x * y) - (z * t)
    t_2 = (z * k) - (x * j)
    t_3 = y0 * ((b * t_2) - ((y5 * ((k * y2) - (j * y3))) + (((z * y3) - (x * y2)) * c)))
    t_4 = (t * j) - (y * k)
    t_5 = i * ((y1 * ((x * j) - (z * k))) - ((c * t_1) + (y5 * t_4)))
    t_6 = t * ((j * ((b * y4) - (i * y5))) - (c * (y2 * y4)))
    if (i <= (-1.25d+61)) then
        tmp = t_5
    else if (i <= (-9.5d-28)) then
        tmp = c * ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2))))
    else if (i <= (-2.6d-176)) then
        tmp = b * (((y4 * t_4) + (a * t_1)) + (y0 * t_2))
    else if (i <= 1.3d-176) then
        tmp = t_3
    else if (i <= 3.1d-133) then
        tmp = t_6
    else if (i <= 4.9d-72) then
        tmp = t_3
    else if (i <= 195000000000.0d0) then
        tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))))
    else if (i <= 6.6d+53) then
        tmp = b * (k * ((z * y0) - (y * y4)))
    else if (i <= 2.5d+151) then
        tmp = t_6
    else if (i <= 9.5d+170) then
        tmp = i * (c * ((z * t) - (x * y)))
    else if (i <= 5.5d+221) then
        tmp = a * (y3 * ((z * y1) - (y * y5)))
    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 = (x * y) - (z * t);
	double t_2 = (z * k) - (x * j);
	double t_3 = y0 * ((b * t_2) - ((y5 * ((k * y2) - (j * y3))) + (((z * y3) - (x * y2)) * c)));
	double t_4 = (t * j) - (y * k);
	double t_5 = i * ((y1 * ((x * j) - (z * k))) - ((c * t_1) + (y5 * t_4)));
	double t_6 = t * ((j * ((b * y4) - (i * y5))) - (c * (y2 * y4)));
	double tmp;
	if (i <= -1.25e+61) {
		tmp = t_5;
	} else if (i <= -9.5e-28) {
		tmp = c * ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2))));
	} else if (i <= -2.6e-176) {
		tmp = b * (((y4 * t_4) + (a * t_1)) + (y0 * t_2));
	} else if (i <= 1.3e-176) {
		tmp = t_3;
	} else if (i <= 3.1e-133) {
		tmp = t_6;
	} else if (i <= 4.9e-72) {
		tmp = t_3;
	} else if (i <= 195000000000.0) {
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	} else if (i <= 6.6e+53) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (i <= 2.5e+151) {
		tmp = t_6;
	} else if (i <= 9.5e+170) {
		tmp = i * (c * ((z * t) - (x * y)));
	} else if (i <= 5.5e+221) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} 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 = (x * y) - (z * t)
	t_2 = (z * k) - (x * j)
	t_3 = y0 * ((b * t_2) - ((y5 * ((k * y2) - (j * y3))) + (((z * y3) - (x * y2)) * c)))
	t_4 = (t * j) - (y * k)
	t_5 = i * ((y1 * ((x * j) - (z * k))) - ((c * t_1) + (y5 * t_4)))
	t_6 = t * ((j * ((b * y4) - (i * y5))) - (c * (y2 * y4)))
	tmp = 0
	if i <= -1.25e+61:
		tmp = t_5
	elif i <= -9.5e-28:
		tmp = c * ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2))))
	elif i <= -2.6e-176:
		tmp = b * (((y4 * t_4) + (a * t_1)) + (y0 * t_2))
	elif i <= 1.3e-176:
		tmp = t_3
	elif i <= 3.1e-133:
		tmp = t_6
	elif i <= 4.9e-72:
		tmp = t_3
	elif i <= 195000000000.0:
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))))
	elif i <= 6.6e+53:
		tmp = b * (k * ((z * y0) - (y * y4)))
	elif i <= 2.5e+151:
		tmp = t_6
	elif i <= 9.5e+170:
		tmp = i * (c * ((z * t) - (x * y)))
	elif i <= 5.5e+221:
		tmp = a * (y3 * ((z * y1) - (y * y5)))
	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(x * y) - Float64(z * t))
	t_2 = Float64(Float64(z * k) - Float64(x * j))
	t_3 = Float64(y0 * Float64(Float64(b * t_2) - Float64(Float64(y5 * Float64(Float64(k * y2) - Float64(j * y3))) + Float64(Float64(Float64(z * y3) - Float64(x * y2)) * c))))
	t_4 = Float64(Float64(t * j) - Float64(y * k))
	t_5 = Float64(i * Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) - Float64(Float64(c * t_1) + Float64(y5 * t_4))))
	t_6 = Float64(t * Float64(Float64(j * Float64(Float64(b * y4) - Float64(i * y5))) - Float64(c * Float64(y2 * y4))))
	tmp = 0.0
	if (i <= -1.25e+61)
		tmp = t_5;
	elseif (i <= -9.5e-28)
		tmp = Float64(c * Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (i <= -2.6e-176)
		tmp = Float64(b * Float64(Float64(Float64(y4 * t_4) + Float64(a * t_1)) + Float64(y0 * t_2)));
	elseif (i <= 1.3e-176)
		tmp = t_3;
	elseif (i <= 3.1e-133)
		tmp = t_6;
	elseif (i <= 4.9e-72)
		tmp = t_3;
	elseif (i <= 195000000000.0)
		tmp = Float64(z * Float64(Float64(k * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(Float64(t * Float64(Float64(c * i) - Float64(a * b))) + Float64(y3 * Float64(Float64(a * y1) - Float64(c * y0))))));
	elseif (i <= 6.6e+53)
		tmp = Float64(b * Float64(k * Float64(Float64(z * y0) - Float64(y * y4))));
	elseif (i <= 2.5e+151)
		tmp = t_6;
	elseif (i <= 9.5e+170)
		tmp = Float64(i * Float64(c * Float64(Float64(z * t) - Float64(x * y))));
	elseif (i <= 5.5e+221)
		tmp = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))));
	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 = (x * y) - (z * t);
	t_2 = (z * k) - (x * j);
	t_3 = y0 * ((b * t_2) - ((y5 * ((k * y2) - (j * y3))) + (((z * y3) - (x * y2)) * c)));
	t_4 = (t * j) - (y * k);
	t_5 = i * ((y1 * ((x * j) - (z * k))) - ((c * t_1) + (y5 * t_4)));
	t_6 = t * ((j * ((b * y4) - (i * y5))) - (c * (y2 * y4)));
	tmp = 0.0;
	if (i <= -1.25e+61)
		tmp = t_5;
	elseif (i <= -9.5e-28)
		tmp = c * ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2))));
	elseif (i <= -2.6e-176)
		tmp = b * (((y4 * t_4) + (a * t_1)) + (y0 * t_2));
	elseif (i <= 1.3e-176)
		tmp = t_3;
	elseif (i <= 3.1e-133)
		tmp = t_6;
	elseif (i <= 4.9e-72)
		tmp = t_3;
	elseif (i <= 195000000000.0)
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	elseif (i <= 6.6e+53)
		tmp = b * (k * ((z * y0) - (y * y4)));
	elseif (i <= 2.5e+151)
		tmp = t_6;
	elseif (i <= 9.5e+170)
		tmp = i * (c * ((z * t) - (x * y)));
	elseif (i <= 5.5e+221)
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	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[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y0 * N[(N[(b * t$95$2), $MachinePrecision] - N[(N[(y5 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(i * N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(c * t$95$1), $MachinePrecision] + N[(y5 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(t * N[(N[(j * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.25e+61], t$95$5, If[LessEqual[i, -9.5e-28], N[(c * N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -2.6e-176], N[(b * N[(N[(N[(y4 * t$95$4), $MachinePrecision] + N[(a * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.3e-176], t$95$3, If[LessEqual[i, 3.1e-133], t$95$6, If[LessEqual[i, 4.9e-72], t$95$3, If[LessEqual[i, 195000000000.0], N[(z * N[(N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 6.6e+53], N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.5e+151], t$95$6, If[LessEqual[i, 9.5e+170], N[(i * N[(c * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.5e+221], N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$5]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if i < -1.25000000000000004e61 or 5.5000000000000003e221 < i

   1. Initial program 22.6%

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

   3. Simplified 22.6%

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

   4. Taylor expanded in i around -inf 59.9%

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

   if -1.25000000000000004e61 < i < -9.50000000000000001e-28

   1. Initial program 5.9%

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

   3. Simplified 5.9%

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

   4. Taylor expanded in c around inf 43.5%

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

   5. Taylor expanded in i around 0 55.2%

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

      1. *-commutative 55.2%

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

      2. *-commutative 55.2%

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

   7. Simplified 55.2%

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

   if -9.50000000000000001e-28 < i < -2.59999999999999992e-176

   1. Initial program 47.9%

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

   3. Simplified 47.9%

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

   4. Taylor expanded in b around inf 59.6%

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

   if -2.59999999999999992e-176 < i < 1.29999999999999996e-176 or 3.10000000000000016e-133 < i < 4.89999999999999991e-72

   1. Initial program 54.4%

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

   3. Simplified 54.4%

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

   4. Taylor expanded in y0 around inf 63.6%

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

   if 1.29999999999999996e-176 < i < 3.10000000000000016e-133 or 6.6000000000000004e53 < i < 2.5000000000000001e151

   1. Initial program 28.4%

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

   3. Simplified 28.4%

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

   4. Taylor expanded in t around inf 52.9%

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

   5. Taylor expanded in z around 0 64.9%

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

   6. Taylor expanded in a around 0 72.6%

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

   if 4.89999999999999991e-72 < i < 1.95e11

   1. Initial program 42.7%

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

   3. Simplified 42.7%

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

   4. Taylor expanded in z around -inf 78.7%

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

   if 1.95e11 < i < 6.6000000000000004e53

   1. Initial program 42.9%

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

   3. Simplified 42.9%

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

   4. Taylor expanded in b around inf 42.9%

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

   5. Taylor expanded in k around -inf 72.4%

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

      1. associate-*r* 72.4%

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

      2. neg-mul-1 72.4%

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

   7. Simplified 72.4%

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

   if 2.5000000000000001e151 < i < 9.5000000000000005e170

   1. Initial program 79.7%

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

   3. Simplified 79.7%

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

   4. Taylor expanded in i around -inf 42.1%

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

   5. Taylor expanded in c around inf 82.1%

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

   if 9.5000000000000005e170 < i < 5.5000000000000003e221

   1. Initial program 6.3%

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

   3. Simplified 6.3%

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

   4. Taylor expanded in y3 around -inf 44.3%

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

   5. Taylor expanded in a around -inf 56.7%

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

      1. associate-*r* 56.7%

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

      2. neg-mul-1 56.7%

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

   7. Simplified 56.7%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(-a\right) \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.25 \cdot 10^{+61}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) - \left(c \cdot \left(x \cdot y - z \cdot t\right) + y5 \cdot \left(t \cdot j - y \cdot k\right)\right)\right)\\ \mathbf{elif}\;i \leq -9.5 \cdot 10^{-28}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq -2.6 \cdot 10^{-176}:\\ \;\;\;\;b \cdot \left(\left(y4 \cdot \left(t \cdot j - y \cdot k\right) + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{-176}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right) - \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(z \cdot y3 - x \cdot y2\right) \cdot c\right)\right)\\ \mathbf{elif}\;i \leq 3.1 \cdot 10^{-133}:\\ \;\;\;\;t \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - c \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq 4.9 \cdot 10^{-72}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right) - \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(z \cdot y3 - x \cdot y2\right) \cdot c\right)\right)\\ \mathbf{elif}\;i \leq 195000000000:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot \left(c \cdot i - a \cdot b\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;i \leq 6.6 \cdot 10^{+53}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{+151}:\\ \;\;\;\;t \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - c \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq 9.5 \cdot 10^{+170}:\\ \;\;\;\;i \cdot \left(c \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;i \leq 5.5 \cdot 10^{+221}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) - \left(c \cdot \left(x \cdot y - z \cdot t\right) + y5 \cdot \left(t \cdot j - y \cdot k\right)\right)\right)\\ \end{array} \]

Alternative 6: 37.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot j - y \cdot k\\ t_2 := a \cdot y5 - c \cdot y4\\ t_3 := x \cdot y - z \cdot t\\ \mathbf{if}\;y2 \leq -1.02 \cdot 10^{+183}:\\ \;\;\;\;\left(c \cdot y2\right) \cdot \left(x \cdot y0 - t \cdot y4\right)\\ \mathbf{elif}\;y2 \leq -3.9 \cdot 10^{+114}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq -0.00048:\\ \;\;\;\;t \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + y2 \cdot t_2\right)\\ \mathbf{elif}\;y2 \leq -8 \cdot 10^{-194}:\\ \;\;\;\;b \cdot \left(\left(y4 \cdot t_1 + a \cdot t_3\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq -5.5 \cdot 10^{-219}:\\ \;\;\;\;c \cdot \left(\left(x \cdot \left(y0 \cdot y2\right) - y0 \cdot \left(z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 1.8 \cdot 10^{-129}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) - \left(c \cdot t_3 + y5 \cdot t_1\right)\right)\\ \mathbf{elif}\;y2 \leq 3.1 \cdot 10^{+91}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot t_1 + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 2.1 \cdot 10^{+127}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 8.2 \cdot 10^{+165}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot t_2\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* t j) (* y k)))
        (t_2 (- (* a y5) (* c y4)))
        (t_3 (- (* x y) (* z t))))
   (if (<= y2 -1.02e+183)
     (* (* c y2) (- (* x y0) (* t y4)))
     (if (<= y2 -3.9e+114)
       (* t (* z (- (* c i) (* a b))))
       (if (<= y2 -0.00048)
         (* t (+ (* j (- (* b y4) (* i y5))) (* y2 t_2)))
         (if (<= y2 -8e-194)
           (* b (+ (+ (* y4 t_1) (* a t_3)) (* y0 (- (* z k) (* x j)))))
           (if (<= y2 -5.5e-219)
             (*
              c
              (+
               (- (* x (* y0 y2)) (* y0 (* z y3)))
               (* y4 (- (* y y3) (* t y2)))))
             (if (<= y2 1.8e-129)
               (* i (- (* y1 (- (* x j) (* z k))) (+ (* c t_3) (* y5 t_1))))
               (if (<= y2 3.1e+91)
                 (*
                  y4
                  (-
                   (+ (* b t_1) (* y1 (- (* k y2) (* j y3))))
                   (* c (- (* t y2) (* y y3)))))
                 (if (<= y2 2.1e+127)
                   (* c (* y0 (- (* x y2) (* z y3))))
                   (if (<= y2 8.2e+165)
                     (*
                      y2
                      (+
                       (+
                        (* k (- (* y1 y4) (* y0 y5)))
                        (* x (- (* c y0) (* a y1))))
                       (* t t_2)))
                     (* c (* x (- (* y0 y2) (* y i)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (t * j) - (y * k);
	double t_2 = (a * y5) - (c * y4);
	double t_3 = (x * y) - (z * t);
	double tmp;
	if (y2 <= -1.02e+183) {
		tmp = (c * y2) * ((x * y0) - (t * y4));
	} else if (y2 <= -3.9e+114) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else if (y2 <= -0.00048) {
		tmp = t * ((j * ((b * y4) - (i * y5))) + (y2 * t_2));
	} else if (y2 <= -8e-194) {
		tmp = b * (((y4 * t_1) + (a * t_3)) + (y0 * ((z * k) - (x * j))));
	} else if (y2 <= -5.5e-219) {
		tmp = c * (((x * (y0 * y2)) - (y0 * (z * y3))) + (y4 * ((y * y3) - (t * y2))));
	} else if (y2 <= 1.8e-129) {
		tmp = i * ((y1 * ((x * j) - (z * k))) - ((c * t_3) + (y5 * t_1)));
	} else if (y2 <= 3.1e+91) {
		tmp = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) - (c * ((t * y2) - (y * y3))));
	} else if (y2 <= 2.1e+127) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (y2 <= 8.2e+165) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * t_2));
	} else {
		tmp = c * (x * ((y0 * y2) - (y * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (t * j) - (y * k)
    t_2 = (a * y5) - (c * y4)
    t_3 = (x * y) - (z * t)
    if (y2 <= (-1.02d+183)) then
        tmp = (c * y2) * ((x * y0) - (t * y4))
    else if (y2 <= (-3.9d+114)) then
        tmp = t * (z * ((c * i) - (a * b)))
    else if (y2 <= (-0.00048d0)) then
        tmp = t * ((j * ((b * y4) - (i * y5))) + (y2 * t_2))
    else if (y2 <= (-8d-194)) then
        tmp = b * (((y4 * t_1) + (a * t_3)) + (y0 * ((z * k) - (x * j))))
    else if (y2 <= (-5.5d-219)) then
        tmp = c * (((x * (y0 * y2)) - (y0 * (z * y3))) + (y4 * ((y * y3) - (t * y2))))
    else if (y2 <= 1.8d-129) then
        tmp = i * ((y1 * ((x * j) - (z * k))) - ((c * t_3) + (y5 * t_1)))
    else if (y2 <= 3.1d+91) then
        tmp = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) - (c * ((t * y2) - (y * y3))))
    else if (y2 <= 2.1d+127) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else if (y2 <= 8.2d+165) then
        tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * t_2))
    else
        tmp = c * (x * ((y0 * y2) - (y * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (t * j) - (y * k);
	double t_2 = (a * y5) - (c * y4);
	double t_3 = (x * y) - (z * t);
	double tmp;
	if (y2 <= -1.02e+183) {
		tmp = (c * y2) * ((x * y0) - (t * y4));
	} else if (y2 <= -3.9e+114) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else if (y2 <= -0.00048) {
		tmp = t * ((j * ((b * y4) - (i * y5))) + (y2 * t_2));
	} else if (y2 <= -8e-194) {
		tmp = b * (((y4 * t_1) + (a * t_3)) + (y0 * ((z * k) - (x * j))));
	} else if (y2 <= -5.5e-219) {
		tmp = c * (((x * (y0 * y2)) - (y0 * (z * y3))) + (y4 * ((y * y3) - (t * y2))));
	} else if (y2 <= 1.8e-129) {
		tmp = i * ((y1 * ((x * j) - (z * k))) - ((c * t_3) + (y5 * t_1)));
	} else if (y2 <= 3.1e+91) {
		tmp = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) - (c * ((t * y2) - (y * y3))));
	} else if (y2 <= 2.1e+127) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (y2 <= 8.2e+165) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * t_2));
	} else {
		tmp = c * (x * ((y0 * y2) - (y * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (t * j) - (y * k)
	t_2 = (a * y5) - (c * y4)
	t_3 = (x * y) - (z * t)
	tmp = 0
	if y2 <= -1.02e+183:
		tmp = (c * y2) * ((x * y0) - (t * y4))
	elif y2 <= -3.9e+114:
		tmp = t * (z * ((c * i) - (a * b)))
	elif y2 <= -0.00048:
		tmp = t * ((j * ((b * y4) - (i * y5))) + (y2 * t_2))
	elif y2 <= -8e-194:
		tmp = b * (((y4 * t_1) + (a * t_3)) + (y0 * ((z * k) - (x * j))))
	elif y2 <= -5.5e-219:
		tmp = c * (((x * (y0 * y2)) - (y0 * (z * y3))) + (y4 * ((y * y3) - (t * y2))))
	elif y2 <= 1.8e-129:
		tmp = i * ((y1 * ((x * j) - (z * k))) - ((c * t_3) + (y5 * t_1)))
	elif y2 <= 3.1e+91:
		tmp = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) - (c * ((t * y2) - (y * y3))))
	elif y2 <= 2.1e+127:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	elif y2 <= 8.2e+165:
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * t_2))
	else:
		tmp = c * (x * ((y0 * y2) - (y * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(t * j) - Float64(y * k))
	t_2 = Float64(Float64(a * y5) - Float64(c * y4))
	t_3 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if (y2 <= -1.02e+183)
		tmp = Float64(Float64(c * y2) * Float64(Float64(x * y0) - Float64(t * y4)));
	elseif (y2 <= -3.9e+114)
		tmp = Float64(t * Float64(z * Float64(Float64(c * i) - Float64(a * b))));
	elseif (y2 <= -0.00048)
		tmp = Float64(t * Float64(Float64(j * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(y2 * t_2)));
	elseif (y2 <= -8e-194)
		tmp = Float64(b * Float64(Float64(Float64(y4 * t_1) + Float64(a * t_3)) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (y2 <= -5.5e-219)
		tmp = Float64(c * Float64(Float64(Float64(x * Float64(y0 * y2)) - Float64(y0 * Float64(z * y3))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (y2 <= 1.8e-129)
		tmp = Float64(i * Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) - Float64(Float64(c * t_3) + Float64(y5 * t_1))));
	elseif (y2 <= 3.1e+91)
		tmp = Float64(y4 * Float64(Float64(Float64(b * t_1) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) - Float64(c * Float64(Float64(t * y2) - Float64(y * y3)))));
	elseif (y2 <= 2.1e+127)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (y2 <= 8.2e+165)
		tmp = Float64(y2 * Float64(Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(t * t_2)));
	else
		tmp = Float64(c * Float64(x * Float64(Float64(y0 * y2) - Float64(y * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (t * j) - (y * k);
	t_2 = (a * y5) - (c * y4);
	t_3 = (x * y) - (z * t);
	tmp = 0.0;
	if (y2 <= -1.02e+183)
		tmp = (c * y2) * ((x * y0) - (t * y4));
	elseif (y2 <= -3.9e+114)
		tmp = t * (z * ((c * i) - (a * b)));
	elseif (y2 <= -0.00048)
		tmp = t * ((j * ((b * y4) - (i * y5))) + (y2 * t_2));
	elseif (y2 <= -8e-194)
		tmp = b * (((y4 * t_1) + (a * t_3)) + (y0 * ((z * k) - (x * j))));
	elseif (y2 <= -5.5e-219)
		tmp = c * (((x * (y0 * y2)) - (y0 * (z * y3))) + (y4 * ((y * y3) - (t * y2))));
	elseif (y2 <= 1.8e-129)
		tmp = i * ((y1 * ((x * j) - (z * k))) - ((c * t_3) + (y5 * t_1)));
	elseif (y2 <= 3.1e+91)
		tmp = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) - (c * ((t * y2) - (y * y3))));
	elseif (y2 <= 2.1e+127)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	elseif (y2 <= 8.2e+165)
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * t_2));
	else
		tmp = c * (x * ((y0 * y2) - (y * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -1.02e+183], N[(N[(c * y2), $MachinePrecision] * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -3.9e+114], N[(t * N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -0.00048], N[(t * N[(N[(j * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -8e-194], N[(b * N[(N[(N[(y4 * t$95$1), $MachinePrecision] + N[(a * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -5.5e-219], N[(c * N[(N[(N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision] - N[(y0 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.8e-129], N[(i * N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(c * t$95$3), $MachinePrecision] + N[(y5 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 3.1e+91], N[(y4 * N[(N[(N[(b * t$95$1), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.1e+127], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 8.2e+165], N[(y2 * N[(N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(x * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if y2 < -1.02000000000000002e183

   1. Initial program 14.3%

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

   3. Simplified 14.3%

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

   4. Taylor expanded in c around inf 48.0%

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

   5. Taylor expanded in x around 0 57.5%

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

   6. Taylor expanded in y2 around inf 70.6%

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

      1. associate-*r* 70.6%

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

   8. Simplified 70.6%

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

   if -1.02000000000000002e183 < y2 < -3.9000000000000001e114

   1. Initial program 8.3%

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

   3. Simplified 8.3%

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

   4. Taylor expanded in t around inf 18.2%

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

   5. Taylor expanded in z around inf 85.4%

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

      1. associate-*r* 85.4%

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

      2. neg-mul-1 85.4%

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

   7. Simplified 85.4%

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

   if -3.9000000000000001e114 < y2 < -4.80000000000000012e-4

   1. Initial program 42.1%

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

   3. Simplified 42.1%

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

   4. Taylor expanded in t around inf 63.7%

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

   5. Taylor expanded in z around 0 63.6%

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

   if -4.80000000000000012e-4 < y2 < -8.00000000000000014e-194

   1. Initial program 39.0%

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

   3. Simplified 39.0%

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

   4. Taylor expanded in b around inf 53.3%

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

   if -8.00000000000000014e-194 < y2 < -5.50000000000000017e-219

   1. Initial program 59.7%

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

   3. Simplified 59.7%

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

   4. Taylor expanded in c around inf 40.6%

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

   5. Taylor expanded in x around 0 40.6%

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

   6. Taylor expanded in i around 0 61.1%

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

   if -5.50000000000000017e-219 < y2 < 1.8e-129

   1. Initial program 39.0%

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

   3. Simplified 39.0%

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

   4. Taylor expanded in i around -inf 52.3%

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

   if 1.8e-129 < y2 < 3.09999999999999998e91

   1. Initial program 35.9%

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

   3. Simplified 35.9%

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

   4. Taylor expanded in y4 around inf 54.2%

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

   if 3.09999999999999998e91 < y2 < 2.09999999999999992e127

   1. Initial program 55.6%

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

   3. Simplified 55.6%

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

   4. Taylor expanded in c around inf 63.2%

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

   5. Taylor expanded in y0 around inf 74.3%

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

   if 2.09999999999999992e127 < y2 < 8.2000000000000005e165

   1. Initial program 33.2%

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

   3. Simplified 33.2%

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

   4. Taylor expanded in y2 around inf 66.7%

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

   if 8.2000000000000005e165 < y2

   1. Initial program 23.8%

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

   3. Simplified 23.8%

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

   4. Taylor expanded in c around inf 55.9%

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

   5. Taylor expanded in x around inf 71.1%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right)\right)} \]
3. Recombined 10 regimes into one program.

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.02 \cdot 10^{+183}:\\ \;\;\;\;\left(c \cdot y2\right) \cdot \left(x \cdot y0 - t \cdot y4\right)\\ \mathbf{elif}\;y2 \leq -3.9 \cdot 10^{+114}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq -0.00048:\\ \;\;\;\;t \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -8 \cdot 10^{-194}:\\ \;\;\;\;b \cdot \left(\left(y4 \cdot \left(t \cdot j - y \cdot k\right) + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq -5.5 \cdot 10^{-219}:\\ \;\;\;\;c \cdot \left(\left(x \cdot \left(y0 \cdot y2\right) - y0 \cdot \left(z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 1.8 \cdot 10^{-129}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) - \left(c \cdot \left(x \cdot y - z \cdot t\right) + y5 \cdot \left(t \cdot j - y \cdot k\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 3.1 \cdot 10^{+91}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 2.1 \cdot 10^{+127}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 8.2 \cdot 10^{+165}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \end{array} \]

Alternative 7: 39.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ t_2 := a \cdot y1 - c \cdot y0\\ t_3 := t \cdot j - y \cdot k\\ t_4 := i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) - \left(c \cdot t_1 + y5 \cdot t_3\right)\right)\\ \mathbf{if}\;i \leq -1.7 \cdot 10^{+68}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq -2.3 \cdot 10^{-28}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq 7.8 \cdot 10^{-305}:\\ \;\;\;\;b \cdot \left(\left(y4 \cdot t_3 + a \cdot t_1\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;i \leq 2.1 \cdot 10^{-106}:\\ \;\;\;\;t \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{+32}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot \left(c \cdot i - a \cdot b\right) + y3 \cdot t_2\right)\right)\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{+60}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot t_2\right)\right)\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{+132}:\\ \;\;\;\;\left(c \cdot y2\right) \cdot \left(x \cdot y0 - t \cdot y4\right)\\ \mathbf{elif}\;i \leq 1.58 \cdot 10^{+209}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(y0 \cdot \left(j \cdot y3 - k \cdot y2\right) - i \cdot t_3\right)\right)\\ \mathbf{elif}\;i \leq 5.8 \cdot 10^{+252}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t)))
        (t_2 (- (* a y1) (* c y0)))
        (t_3 (- (* t j) (* y k)))
        (t_4 (* i (- (* y1 (- (* x j) (* z k))) (+ (* c t_1) (* y5 t_3))))))
   (if (<= i -1.7e+68)
     t_4
     (if (<= i -2.3e-28)
       (* c (+ (* y0 (- (* x y2) (* z y3))) (* y4 (- (* y y3) (* t y2)))))
       (if (<= i 7.8e-305)
         (* b (+ (+ (* y4 t_3) (* a t_1)) (* y0 (- (* z k) (* x j)))))
         (if (<= i 2.1e-106)
           (* t (+ (* j (- (* b y4) (* i y5))) (* y2 (- (* a y5) (* c y4)))))
           (if (<= i 2.2e+32)
             (*
              z
              (+
               (* k (- (* b y0) (* i y1)))
               (+ (* t (- (* c i) (* a b))) (* y3 t_2))))
             (if (<= i 1.1e+60)
               (*
                y3
                (+
                 (* y (- (* c y4) (* a y5)))
                 (+ (* j (- (* y0 y5) (* y1 y4))) (* z t_2))))
               (if (<= i 2.5e+132)
                 (* (* c y2) (- (* x y0) (* t y4)))
                 (if (<= i 1.58e+209)
                   (*
                    y5
                    (+
                     (* a (- (* t y2) (* y y3)))
                     (- (* y0 (- (* j y3) (* k y2))) (* i t_3))))
                   (if (<= i 5.8e+252)
                     (* c (* x (- (* y0 y2) (* y i))))
                     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 = (x * y) - (z * t);
	double t_2 = (a * y1) - (c * y0);
	double t_3 = (t * j) - (y * k);
	double t_4 = i * ((y1 * ((x * j) - (z * k))) - ((c * t_1) + (y5 * t_3)));
	double tmp;
	if (i <= -1.7e+68) {
		tmp = t_4;
	} else if (i <= -2.3e-28) {
		tmp = c * ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2))));
	} else if (i <= 7.8e-305) {
		tmp = b * (((y4 * t_3) + (a * t_1)) + (y0 * ((z * k) - (x * j))));
	} else if (i <= 2.1e-106) {
		tmp = t * ((j * ((b * y4) - (i * y5))) + (y2 * ((a * y5) - (c * y4))));
	} else if (i <= 2.2e+32) {
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * t_2)));
	} else if (i <= 1.1e+60) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * t_2)));
	} else if (i <= 2.5e+132) {
		tmp = (c * y2) * ((x * y0) - (t * y4));
	} else if (i <= 1.58e+209) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((y0 * ((j * y3) - (k * y2))) - (i * t_3)));
	} else if (i <= 5.8e+252) {
		tmp = c * (x * ((y0 * y2) - (y * i)));
	} 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) :: tmp
    t_1 = (x * y) - (z * t)
    t_2 = (a * y1) - (c * y0)
    t_3 = (t * j) - (y * k)
    t_4 = i * ((y1 * ((x * j) - (z * k))) - ((c * t_1) + (y5 * t_3)))
    if (i <= (-1.7d+68)) then
        tmp = t_4
    else if (i <= (-2.3d-28)) then
        tmp = c * ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2))))
    else if (i <= 7.8d-305) then
        tmp = b * (((y4 * t_3) + (a * t_1)) + (y0 * ((z * k) - (x * j))))
    else if (i <= 2.1d-106) then
        tmp = t * ((j * ((b * y4) - (i * y5))) + (y2 * ((a * y5) - (c * y4))))
    else if (i <= 2.2d+32) then
        tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * t_2)))
    else if (i <= 1.1d+60) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * t_2)))
    else if (i <= 2.5d+132) then
        tmp = (c * y2) * ((x * y0) - (t * y4))
    else if (i <= 1.58d+209) then
        tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((y0 * ((j * y3) - (k * y2))) - (i * t_3)))
    else if (i <= 5.8d+252) then
        tmp = c * (x * ((y0 * y2) - (y * i)))
    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 = (x * y) - (z * t);
	double t_2 = (a * y1) - (c * y0);
	double t_3 = (t * j) - (y * k);
	double t_4 = i * ((y1 * ((x * j) - (z * k))) - ((c * t_1) + (y5 * t_3)));
	double tmp;
	if (i <= -1.7e+68) {
		tmp = t_4;
	} else if (i <= -2.3e-28) {
		tmp = c * ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2))));
	} else if (i <= 7.8e-305) {
		tmp = b * (((y4 * t_3) + (a * t_1)) + (y0 * ((z * k) - (x * j))));
	} else if (i <= 2.1e-106) {
		tmp = t * ((j * ((b * y4) - (i * y5))) + (y2 * ((a * y5) - (c * y4))));
	} else if (i <= 2.2e+32) {
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * t_2)));
	} else if (i <= 1.1e+60) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * t_2)));
	} else if (i <= 2.5e+132) {
		tmp = (c * y2) * ((x * y0) - (t * y4));
	} else if (i <= 1.58e+209) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((y0 * ((j * y3) - (k * y2))) - (i * t_3)));
	} else if (i <= 5.8e+252) {
		tmp = c * (x * ((y0 * y2) - (y * i)));
	} 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 = (x * y) - (z * t)
	t_2 = (a * y1) - (c * y0)
	t_3 = (t * j) - (y * k)
	t_4 = i * ((y1 * ((x * j) - (z * k))) - ((c * t_1) + (y5 * t_3)))
	tmp = 0
	if i <= -1.7e+68:
		tmp = t_4
	elif i <= -2.3e-28:
		tmp = c * ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2))))
	elif i <= 7.8e-305:
		tmp = b * (((y4 * t_3) + (a * t_1)) + (y0 * ((z * k) - (x * j))))
	elif i <= 2.1e-106:
		tmp = t * ((j * ((b * y4) - (i * y5))) + (y2 * ((a * y5) - (c * y4))))
	elif i <= 2.2e+32:
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * t_2)))
	elif i <= 1.1e+60:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * t_2)))
	elif i <= 2.5e+132:
		tmp = (c * y2) * ((x * y0) - (t * y4))
	elif i <= 1.58e+209:
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((y0 * ((j * y3) - (k * y2))) - (i * t_3)))
	elif i <= 5.8e+252:
		tmp = c * (x * ((y0 * y2) - (y * i)))
	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(x * y) - Float64(z * t))
	t_2 = Float64(Float64(a * y1) - Float64(c * y0))
	t_3 = Float64(Float64(t * j) - Float64(y * k))
	t_4 = Float64(i * Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) - Float64(Float64(c * t_1) + Float64(y5 * t_3))))
	tmp = 0.0
	if (i <= -1.7e+68)
		tmp = t_4;
	elseif (i <= -2.3e-28)
		tmp = Float64(c * Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (i <= 7.8e-305)
		tmp = Float64(b * Float64(Float64(Float64(y4 * t_3) + Float64(a * t_1)) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (i <= 2.1e-106)
		tmp = Float64(t * Float64(Float64(j * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (i <= 2.2e+32)
		tmp = Float64(z * Float64(Float64(k * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(Float64(t * Float64(Float64(c * i) - Float64(a * b))) + Float64(y3 * t_2))));
	elseif (i <= 1.1e+60)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(z * t_2))));
	elseif (i <= 2.5e+132)
		tmp = Float64(Float64(c * y2) * Float64(Float64(x * y0) - Float64(t * y4)));
	elseif (i <= 1.58e+209)
		tmp = Float64(y5 * Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))) - Float64(i * t_3))));
	elseif (i <= 5.8e+252)
		tmp = Float64(c * Float64(x * Float64(Float64(y0 * y2) - Float64(y * i))));
	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 = (x * y) - (z * t);
	t_2 = (a * y1) - (c * y0);
	t_3 = (t * j) - (y * k);
	t_4 = i * ((y1 * ((x * j) - (z * k))) - ((c * t_1) + (y5 * t_3)));
	tmp = 0.0;
	if (i <= -1.7e+68)
		tmp = t_4;
	elseif (i <= -2.3e-28)
		tmp = c * ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2))));
	elseif (i <= 7.8e-305)
		tmp = b * (((y4 * t_3) + (a * t_1)) + (y0 * ((z * k) - (x * j))));
	elseif (i <= 2.1e-106)
		tmp = t * ((j * ((b * y4) - (i * y5))) + (y2 * ((a * y5) - (c * y4))));
	elseif (i <= 2.2e+32)
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * t_2)));
	elseif (i <= 1.1e+60)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * t_2)));
	elseif (i <= 2.5e+132)
		tmp = (c * y2) * ((x * y0) - (t * y4));
	elseif (i <= 1.58e+209)
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((y0 * ((j * y3) - (k * y2))) - (i * t_3)));
	elseif (i <= 5.8e+252)
		tmp = c * (x * ((y0 * y2) - (y * i)));
	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[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(i * N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(c * t$95$1), $MachinePrecision] + N[(y5 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.7e+68], t$95$4, If[LessEqual[i, -2.3e-28], N[(c * N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 7.8e-305], N[(b * N[(N[(N[(y4 * t$95$3), $MachinePrecision] + N[(a * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.1e-106], N[(t * N[(N[(j * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.2e+32], N[(z * N[(N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.1e+60], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.5e+132], N[(N[(c * y2), $MachinePrecision] * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.58e+209], N[(y5 * N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.8e+252], N[(c * N[(x * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if i < -1.70000000000000008e68 or 5.79999999999999992e252 < i

   1. Initial program 23.1%

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

   3. Simplified 23.1%

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

   4. Taylor expanded in i around -inf 58.1%

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

   if -1.70000000000000008e68 < i < -2.29999999999999986e-28

   1. Initial program 5.9%

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

   3. Simplified 5.9%

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

   4. Taylor expanded in c around inf 43.5%

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

   5. Taylor expanded in i around 0 55.2%

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

      1. *-commutative 55.2%

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

      2. *-commutative 55.2%

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

   7. Simplified 55.2%

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

   if -2.29999999999999986e-28 < i < 7.8000000000000005e-305

   1. Initial program 55.2%

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

   3. Simplified 55.2%

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

   4. Taylor expanded in b around inf 54.4%

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

   if 7.8000000000000005e-305 < i < 2.10000000000000003e-106

   1. Initial program 44.3%

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

   3. Simplified 44.3%

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

   4. Taylor expanded in t around inf 48.2%

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

   5. Taylor expanded in z around 0 51.1%

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

   if 2.10000000000000003e-106 < i < 2.20000000000000001e32

   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%

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

   4. Taylor expanded in z around -inf 65.6%

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

   if 2.20000000000000001e32 < i < 1.09999999999999998e60

   1. Initial program 50.0%

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

   3. Simplified 50.0%

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

   4. Taylor expanded in y3 around -inf 83.3%

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

   if 1.09999999999999998e60 < i < 2.5000000000000001e132

   1. Initial program 23.8%

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

   3. Simplified 23.8%

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

   4. Taylor expanded in c around inf 23.4%

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

   5. Taylor expanded in x around 0 31.8%

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

   6. Taylor expanded in y2 around inf 70.4%

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

      1. associate-*r* 70.6%

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

   8. Simplified 70.6%

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

   if 2.5000000000000001e132 < i < 1.58e209

   1. Initial program 28.5%

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

   3. Simplified 28.5%

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

   4. Taylor expanded in y5 around -inf 62.1%

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

   if 1.58e209 < i < 5.79999999999999992e252

   1. Initial program 12.5%

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

   3. Simplified 12.5%

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

   4. Taylor expanded in c around inf 75.0%

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

   5. Taylor expanded in x around inf 88.2%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.7 \cdot 10^{+68}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) - \left(c \cdot \left(x \cdot y - z \cdot t\right) + y5 \cdot \left(t \cdot j - y \cdot k\right)\right)\right)\\ \mathbf{elif}\;i \leq -2.3 \cdot 10^{-28}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq 7.8 \cdot 10^{-305}:\\ \;\;\;\;b \cdot \left(\left(y4 \cdot \left(t \cdot j - y \cdot k\right) + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;i \leq 2.1 \cdot 10^{-106}:\\ \;\;\;\;t \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{+32}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot \left(c \cdot i - a \cdot b\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{+60}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{+132}:\\ \;\;\;\;\left(c \cdot y2\right) \cdot \left(x \cdot y0 - t \cdot y4\right)\\ \mathbf{elif}\;i \leq 1.58 \cdot 10^{+209}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(y0 \cdot \left(j \cdot y3 - k \cdot y2\right) - i \cdot \left(t \cdot j - y \cdot k\right)\right)\right)\\ \mathbf{elif}\;i \leq 5.8 \cdot 10^{+252}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) - \left(c \cdot \left(x \cdot y - z \cdot t\right) + y5 \cdot \left(t \cdot j - y \cdot k\right)\right)\right)\\ \end{array} \]

Alternative 8: 41.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ t_2 := z \cdot y3 - x \cdot y2\\ t_3 := t \cdot j - y \cdot k\\ t_4 := x \cdot j - z \cdot k\\ t_5 := i \cdot \left(y1 \cdot t_4 - \left(c \cdot t_1 + y5 \cdot t_3\right)\right)\\ t_6 := z \cdot k - x \cdot j\\ t_7 := y0 \cdot \left(b \cdot t_6 - \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right) + t_2 \cdot c\right)\right)\\ \mathbf{if}\;i \leq -1.05 \cdot 10^{+75}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq -4.2 \cdot 10^{-26}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq -4.7 \cdot 10^{-176}:\\ \;\;\;\;b \cdot \left(\left(y4 \cdot t_3 + a \cdot t_1\right) + y0 \cdot t_6\right)\\ \mathbf{elif}\;i \leq 1.7 \cdot 10^{-176}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;i \leq 2.7 \cdot 10^{-132}:\\ \;\;\;\;t \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - c \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq 10^{-71}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;i \leq 900000000:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot \left(c \cdot i - a \cdot b\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;i \leq 7.8 \cdot 10^{+50}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq 1.2 \cdot 10^{+220}:\\ \;\;\;\;y1 \cdot \left(i \cdot t_4 - \left(y4 \cdot \left(j \cdot y3 - k \cdot y2\right) - a \cdot t_2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t)))
        (t_2 (- (* z y3) (* x y2)))
        (t_3 (- (* t j) (* y k)))
        (t_4 (- (* x j) (* z k)))
        (t_5 (* i (- (* y1 t_4) (+ (* c t_1) (* y5 t_3)))))
        (t_6 (- (* z k) (* x j)))
        (t_7 (* y0 (- (* b t_6) (+ (* y5 (- (* k y2) (* j y3))) (* t_2 c))))))
   (if (<= i -1.05e+75)
     t_5
     (if (<= i -4.2e-26)
       (* c (+ (* y0 (- (* x y2) (* z y3))) (* y4 (- (* y y3) (* t y2)))))
       (if (<= i -4.7e-176)
         (* b (+ (+ (* y4 t_3) (* a t_1)) (* y0 t_6)))
         (if (<= i 1.7e-176)
           t_7
           (if (<= i 2.7e-132)
             (* t (- (* j (- (* b y4) (* i y5))) (* c (* y2 y4))))
             (if (<= i 1e-71)
               t_7
               (if (<= i 900000000.0)
                 (*
                  z
                  (+
                   (* k (- (* b y0) (* i y1)))
                   (+ (* t (- (* c i) (* a b))) (* y3 (- (* a y1) (* c y0))))))
                 (if (<= i 7.8e+50)
                   (* b (* k (- (* z y0) (* y y4))))
                   (if (<= i 1.2e+220)
                     (*
                      y1
                      (- (* i t_4) (- (* y4 (- (* j y3) (* k y2))) (* a 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 = (x * y) - (z * t);
	double t_2 = (z * y3) - (x * y2);
	double t_3 = (t * j) - (y * k);
	double t_4 = (x * j) - (z * k);
	double t_5 = i * ((y1 * t_4) - ((c * t_1) + (y5 * t_3)));
	double t_6 = (z * k) - (x * j);
	double t_7 = y0 * ((b * t_6) - ((y5 * ((k * y2) - (j * y3))) + (t_2 * c)));
	double tmp;
	if (i <= -1.05e+75) {
		tmp = t_5;
	} else if (i <= -4.2e-26) {
		tmp = c * ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2))));
	} else if (i <= -4.7e-176) {
		tmp = b * (((y4 * t_3) + (a * t_1)) + (y0 * t_6));
	} else if (i <= 1.7e-176) {
		tmp = t_7;
	} else if (i <= 2.7e-132) {
		tmp = t * ((j * ((b * y4) - (i * y5))) - (c * (y2 * y4)));
	} else if (i <= 1e-71) {
		tmp = t_7;
	} else if (i <= 900000000.0) {
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	} else if (i <= 7.8e+50) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (i <= 1.2e+220) {
		tmp = y1 * ((i * t_4) - ((y4 * ((j * y3) - (k * y2))) - (a * 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) :: t_7
    real(8) :: tmp
    t_1 = (x * y) - (z * t)
    t_2 = (z * y3) - (x * y2)
    t_3 = (t * j) - (y * k)
    t_4 = (x * j) - (z * k)
    t_5 = i * ((y1 * t_4) - ((c * t_1) + (y5 * t_3)))
    t_6 = (z * k) - (x * j)
    t_7 = y0 * ((b * t_6) - ((y5 * ((k * y2) - (j * y3))) + (t_2 * c)))
    if (i <= (-1.05d+75)) then
        tmp = t_5
    else if (i <= (-4.2d-26)) then
        tmp = c * ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2))))
    else if (i <= (-4.7d-176)) then
        tmp = b * (((y4 * t_3) + (a * t_1)) + (y0 * t_6))
    else if (i <= 1.7d-176) then
        tmp = t_7
    else if (i <= 2.7d-132) then
        tmp = t * ((j * ((b * y4) - (i * y5))) - (c * (y2 * y4)))
    else if (i <= 1d-71) then
        tmp = t_7
    else if (i <= 900000000.0d0) then
        tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))))
    else if (i <= 7.8d+50) then
        tmp = b * (k * ((z * y0) - (y * y4)))
    else if (i <= 1.2d+220) then
        tmp = y1 * ((i * t_4) - ((y4 * ((j * y3) - (k * y2))) - (a * 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 = (x * y) - (z * t);
	double t_2 = (z * y3) - (x * y2);
	double t_3 = (t * j) - (y * k);
	double t_4 = (x * j) - (z * k);
	double t_5 = i * ((y1 * t_4) - ((c * t_1) + (y5 * t_3)));
	double t_6 = (z * k) - (x * j);
	double t_7 = y0 * ((b * t_6) - ((y5 * ((k * y2) - (j * y3))) + (t_2 * c)));
	double tmp;
	if (i <= -1.05e+75) {
		tmp = t_5;
	} else if (i <= -4.2e-26) {
		tmp = c * ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2))));
	} else if (i <= -4.7e-176) {
		tmp = b * (((y4 * t_3) + (a * t_1)) + (y0 * t_6));
	} else if (i <= 1.7e-176) {
		tmp = t_7;
	} else if (i <= 2.7e-132) {
		tmp = t * ((j * ((b * y4) - (i * y5))) - (c * (y2 * y4)));
	} else if (i <= 1e-71) {
		tmp = t_7;
	} else if (i <= 900000000.0) {
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	} else if (i <= 7.8e+50) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (i <= 1.2e+220) {
		tmp = y1 * ((i * t_4) - ((y4 * ((j * y3) - (k * y2))) - (a * 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 = (x * y) - (z * t)
	t_2 = (z * y3) - (x * y2)
	t_3 = (t * j) - (y * k)
	t_4 = (x * j) - (z * k)
	t_5 = i * ((y1 * t_4) - ((c * t_1) + (y5 * t_3)))
	t_6 = (z * k) - (x * j)
	t_7 = y0 * ((b * t_6) - ((y5 * ((k * y2) - (j * y3))) + (t_2 * c)))
	tmp = 0
	if i <= -1.05e+75:
		tmp = t_5
	elif i <= -4.2e-26:
		tmp = c * ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2))))
	elif i <= -4.7e-176:
		tmp = b * (((y4 * t_3) + (a * t_1)) + (y0 * t_6))
	elif i <= 1.7e-176:
		tmp = t_7
	elif i <= 2.7e-132:
		tmp = t * ((j * ((b * y4) - (i * y5))) - (c * (y2 * y4)))
	elif i <= 1e-71:
		tmp = t_7
	elif i <= 900000000.0:
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))))
	elif i <= 7.8e+50:
		tmp = b * (k * ((z * y0) - (y * y4)))
	elif i <= 1.2e+220:
		tmp = y1 * ((i * t_4) - ((y4 * ((j * y3) - (k * y2))) - (a * 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(x * y) - Float64(z * t))
	t_2 = Float64(Float64(z * y3) - Float64(x * y2))
	t_3 = Float64(Float64(t * j) - Float64(y * k))
	t_4 = Float64(Float64(x * j) - Float64(z * k))
	t_5 = Float64(i * Float64(Float64(y1 * t_4) - Float64(Float64(c * t_1) + Float64(y5 * t_3))))
	t_6 = Float64(Float64(z * k) - Float64(x * j))
	t_7 = Float64(y0 * Float64(Float64(b * t_6) - Float64(Float64(y5 * Float64(Float64(k * y2) - Float64(j * y3))) + Float64(t_2 * c))))
	tmp = 0.0
	if (i <= -1.05e+75)
		tmp = t_5;
	elseif (i <= -4.2e-26)
		tmp = Float64(c * Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (i <= -4.7e-176)
		tmp = Float64(b * Float64(Float64(Float64(y4 * t_3) + Float64(a * t_1)) + Float64(y0 * t_6)));
	elseif (i <= 1.7e-176)
		tmp = t_7;
	elseif (i <= 2.7e-132)
		tmp = Float64(t * Float64(Float64(j * Float64(Float64(b * y4) - Float64(i * y5))) - Float64(c * Float64(y2 * y4))));
	elseif (i <= 1e-71)
		tmp = t_7;
	elseif (i <= 900000000.0)
		tmp = Float64(z * Float64(Float64(k * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(Float64(t * Float64(Float64(c * i) - Float64(a * b))) + Float64(y3 * Float64(Float64(a * y1) - Float64(c * y0))))));
	elseif (i <= 7.8e+50)
		tmp = Float64(b * Float64(k * Float64(Float64(z * y0) - Float64(y * y4))));
	elseif (i <= 1.2e+220)
		tmp = Float64(y1 * Float64(Float64(i * t_4) - Float64(Float64(y4 * Float64(Float64(j * y3) - Float64(k * y2))) - Float64(a * 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 = (x * y) - (z * t);
	t_2 = (z * y3) - (x * y2);
	t_3 = (t * j) - (y * k);
	t_4 = (x * j) - (z * k);
	t_5 = i * ((y1 * t_4) - ((c * t_1) + (y5 * t_3)));
	t_6 = (z * k) - (x * j);
	t_7 = y0 * ((b * t_6) - ((y5 * ((k * y2) - (j * y3))) + (t_2 * c)));
	tmp = 0.0;
	if (i <= -1.05e+75)
		tmp = t_5;
	elseif (i <= -4.2e-26)
		tmp = c * ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2))));
	elseif (i <= -4.7e-176)
		tmp = b * (((y4 * t_3) + (a * t_1)) + (y0 * t_6));
	elseif (i <= 1.7e-176)
		tmp = t_7;
	elseif (i <= 2.7e-132)
		tmp = t * ((j * ((b * y4) - (i * y5))) - (c * (y2 * y4)));
	elseif (i <= 1e-71)
		tmp = t_7;
	elseif (i <= 900000000.0)
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	elseif (i <= 7.8e+50)
		tmp = b * (k * ((z * y0) - (y * y4)));
	elseif (i <= 1.2e+220)
		tmp = y1 * ((i * t_4) - ((y4 * ((j * y3) - (k * y2))) - (a * 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[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(i * N[(N[(y1 * t$95$4), $MachinePrecision] - N[(N[(c * t$95$1), $MachinePrecision] + N[(y5 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(y0 * N[(N[(b * t$95$6), $MachinePrecision] - N[(N[(y5 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.05e+75], t$95$5, If[LessEqual[i, -4.2e-26], N[(c * N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -4.7e-176], N[(b * N[(N[(N[(y4 * t$95$3), $MachinePrecision] + N[(a * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.7e-176], t$95$7, If[LessEqual[i, 2.7e-132], N[(t * N[(N[(j * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1e-71], t$95$7, If[LessEqual[i, 900000000.0], N[(z * N[(N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 7.8e+50], N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.2e+220], N[(y1 * N[(N[(i * t$95$4), $MachinePrecision] - N[(N[(y4 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$5]]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if i < -1.04999999999999999e75 or 1.1999999999999999e220 < i

   1. Initial program 22.3%

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

   3. Simplified 22.3%

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

   4. Taylor expanded in i around -inf 59.2%

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

   if -1.04999999999999999e75 < i < -4.20000000000000016e-26

   1. Initial program 5.9%

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

   3. Simplified 5.9%

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

   4. Taylor expanded in c around inf 43.5%

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

   5. Taylor expanded in i around 0 55.2%

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

      1. *-commutative 55.2%

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

      2. *-commutative 55.2%

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

   7. Simplified 55.2%

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

   if -4.20000000000000016e-26 < i < -4.69999999999999984e-176

   1. Initial program 47.9%

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

   3. Simplified 47.9%

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

   4. Taylor expanded in b around inf 59.6%

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

   if -4.69999999999999984e-176 < i < 1.6999999999999999e-176 or 2.6999999999999999e-132 < i < 9.9999999999999992e-72

   1. Initial program 54.4%

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

   3. Simplified 54.4%

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

   4. Taylor expanded in y0 around inf 63.6%

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

   if 1.6999999999999999e-176 < i < 2.6999999999999999e-132

   1. Initial program 14.3%

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

   3. Simplified 14.3%

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

   4. Taylor expanded in t around inf 57.2%

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

   5. Taylor expanded in z around 0 71.5%

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

   6. Taylor expanded in a around 0 85.7%

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

   if 9.9999999999999992e-72 < i < 9e8

   1. Initial program 42.7%

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

   3. Simplified 42.7%

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

   4. Taylor expanded in z around -inf 78.7%

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

   if 9e8 < i < 7.79999999999999935e50

   1. Initial program 50.0%

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

   3. Simplified 50.0%

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

   4. Taylor expanded in b around inf 50.0%

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

   5. Taylor expanded in k around -inf 84.1%

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

      1. associate-*r* 84.1%

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

      2. neg-mul-1 84.1%

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

   7. Simplified 84.1%

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

   if 7.79999999999999935e50 < i < 1.1999999999999999e220

   1. Initial program 28.4%

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

   3. Simplified 28.4%

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

   4. Taylor expanded in y1 around inf 54.3%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.05 \cdot 10^{+75}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) - \left(c \cdot \left(x \cdot y - z \cdot t\right) + y5 \cdot \left(t \cdot j - y \cdot k\right)\right)\right)\\ \mathbf{elif}\;i \leq -4.2 \cdot 10^{-26}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq -4.7 \cdot 10^{-176}:\\ \;\;\;\;b \cdot \left(\left(y4 \cdot \left(t \cdot j - y \cdot k\right) + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;i \leq 1.7 \cdot 10^{-176}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right) - \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(z \cdot y3 - x \cdot y2\right) \cdot c\right)\right)\\ \mathbf{elif}\;i \leq 2.7 \cdot 10^{-132}:\\ \;\;\;\;t \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - c \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq 10^{-71}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right) - \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(z \cdot y3 - x \cdot y2\right) \cdot c\right)\right)\\ \mathbf{elif}\;i \leq 900000000:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot \left(c \cdot i - a \cdot b\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;i \leq 7.8 \cdot 10^{+50}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq 1.2 \cdot 10^{+220}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) - \left(y4 \cdot \left(j \cdot y3 - k \cdot y2\right) - a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) - \left(c \cdot \left(x \cdot y - z \cdot t\right) + y5 \cdot \left(t \cdot j - y \cdot k\right)\right)\right)\\ \end{array} \]

Alternative 9: 35.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot y4 - i \cdot y5\\ \mathbf{if}\;c \leq -3.2 \cdot 10^{+100}:\\ \;\;\;\;c \cdot \left(\left(x \cdot \left(y0 \cdot y2\right) - y0 \cdot \left(z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -1.9 \cdot 10^{-51}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;c \leq -1.9 \cdot 10^{-241}:\\ \;\;\;\;t \cdot \left(j \cdot t_1 + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{-284}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq 1.75 \cdot 10^{-243}:\\ \;\;\;\;j \cdot \left(t \cdot t_1\right)\\ \mathbf{elif}\;c \leq 1.08 \cdot 10^{+126}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{+205}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq 1.05 \cdot 10^{+244}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* b y4) (* i y5))))
   (if (<= c -3.2e+100)
     (* c (+ (- (* x (* y0 y2)) (* y0 (* z y3))) (* y4 (- (* y y3) (* t y2)))))
     (if (<= c -1.9e-51)
       (* y1 (* z (- (* a y3) (* i k))))
       (if (<= c -1.9e-241)
         (* t (+ (* j t_1) (* y2 (- (* a y5) (* c y4)))))
         (if (<= c 2.1e-284)
           (*
            x
            (+
             (+ (* y (- (* a b) (* c i))) (* y2 (- (* c y0) (* a y1))))
             (* j (- (* i y1) (* b y0)))))
           (if (<= c 1.75e-243)
             (* j (* t t_1))
             (if (<= c 1.08e+126)
               (*
                y3
                (+ (* y (- (* c y4) (* a y5))) (* j (- (* y0 y5) (* y1 y4)))))
               (if (<= c 2.2e+205)
                 (* t (* y4 (- (* b j) (* c y2))))
                 (if (<= c 1.05e+244)
                   (* c (* y0 (- (* x y2) (* z y3))))
                   (*
                    y4
                    (-
                     (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
                     (* c (- (* t y2) (* y y3)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (b * y4) - (i * y5);
	double tmp;
	if (c <= -3.2e+100) {
		tmp = c * (((x * (y0 * y2)) - (y0 * (z * y3))) + (y4 * ((y * y3) - (t * y2))));
	} else if (c <= -1.9e-51) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (c <= -1.9e-241) {
		tmp = t * ((j * t_1) + (y2 * ((a * y5) - (c * y4))));
	} else if (c <= 2.1e-284) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	} else if (c <= 1.75e-243) {
		tmp = j * (t * t_1);
	} else if (c <= 1.08e+126) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))));
	} else if (c <= 2.2e+205) {
		tmp = t * (y4 * ((b * j) - (c * y2)));
	} else if (c <= 1.05e+244) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) - (c * ((t * y2) - (y * y3))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * y4) - (i * y5)
    if (c <= (-3.2d+100)) then
        tmp = c * (((x * (y0 * y2)) - (y0 * (z * y3))) + (y4 * ((y * y3) - (t * y2))))
    else if (c <= (-1.9d-51)) then
        tmp = y1 * (z * ((a * y3) - (i * k)))
    else if (c <= (-1.9d-241)) then
        tmp = t * ((j * t_1) + (y2 * ((a * y5) - (c * y4))))
    else if (c <= 2.1d-284) then
        tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
    else if (c <= 1.75d-243) then
        tmp = j * (t * t_1)
    else if (c <= 1.08d+126) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))))
    else if (c <= 2.2d+205) then
        tmp = t * (y4 * ((b * j) - (c * y2)))
    else if (c <= 1.05d+244) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else
        tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) - (c * ((t * y2) - (y * y3))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (b * y4) - (i * y5);
	double tmp;
	if (c <= -3.2e+100) {
		tmp = c * (((x * (y0 * y2)) - (y0 * (z * y3))) + (y4 * ((y * y3) - (t * y2))));
	} else if (c <= -1.9e-51) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (c <= -1.9e-241) {
		tmp = t * ((j * t_1) + (y2 * ((a * y5) - (c * y4))));
	} else if (c <= 2.1e-284) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	} else if (c <= 1.75e-243) {
		tmp = j * (t * t_1);
	} else if (c <= 1.08e+126) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))));
	} else if (c <= 2.2e+205) {
		tmp = t * (y4 * ((b * j) - (c * y2)));
	} else if (c <= 1.05e+244) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) - (c * ((t * y2) - (y * y3))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (b * y4) - (i * y5)
	tmp = 0
	if c <= -3.2e+100:
		tmp = c * (((x * (y0 * y2)) - (y0 * (z * y3))) + (y4 * ((y * y3) - (t * y2))))
	elif c <= -1.9e-51:
		tmp = y1 * (z * ((a * y3) - (i * k)))
	elif c <= -1.9e-241:
		tmp = t * ((j * t_1) + (y2 * ((a * y5) - (c * y4))))
	elif c <= 2.1e-284:
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
	elif c <= 1.75e-243:
		tmp = j * (t * t_1)
	elif c <= 1.08e+126:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))))
	elif c <= 2.2e+205:
		tmp = t * (y4 * ((b * j) - (c * y2)))
	elif c <= 1.05e+244:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	else:
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) - (c * ((t * y2) - (y * y3))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(b * y4) - Float64(i * y5))
	tmp = 0.0
	if (c <= -3.2e+100)
		tmp = Float64(c * Float64(Float64(Float64(x * Float64(y0 * y2)) - Float64(y0 * Float64(z * y3))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (c <= -1.9e-51)
		tmp = Float64(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * k))));
	elseif (c <= -1.9e-241)
		tmp = Float64(t * Float64(Float64(j * t_1) + Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (c <= 2.1e-284)
		tmp = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (c <= 1.75e-243)
		tmp = Float64(j * Float64(t * t_1));
	elseif (c <= 1.08e+126)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4)))));
	elseif (c <= 2.2e+205)
		tmp = Float64(t * Float64(y4 * Float64(Float64(b * j) - Float64(c * y2))));
	elseif (c <= 1.05e+244)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	else
		tmp = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) - Float64(c * Float64(Float64(t * y2) - Float64(y * y3)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (b * y4) - (i * y5);
	tmp = 0.0;
	if (c <= -3.2e+100)
		tmp = c * (((x * (y0 * y2)) - (y0 * (z * y3))) + (y4 * ((y * y3) - (t * y2))));
	elseif (c <= -1.9e-51)
		tmp = y1 * (z * ((a * y3) - (i * k)));
	elseif (c <= -1.9e-241)
		tmp = t * ((j * t_1) + (y2 * ((a * y5) - (c * y4))));
	elseif (c <= 2.1e-284)
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	elseif (c <= 1.75e-243)
		tmp = j * (t * t_1);
	elseif (c <= 1.08e+126)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))));
	elseif (c <= 2.2e+205)
		tmp = t * (y4 * ((b * j) - (c * y2)));
	elseif (c <= 1.05e+244)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	else
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) - (c * ((t * y2) - (y * y3))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.2e+100], N[(c * N[(N[(N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision] - N[(y0 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.9e-51], N[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.9e-241], N[(t * N[(N[(j * t$95$1), $MachinePrecision] + N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.1e-284], N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.75e-243], N[(j * N[(t * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.08e+126], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.2e+205], N[(t * N[(y4 * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.05e+244], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if c < -3.1999999999999999e100

   1. Initial program 25.6%

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

   3. Simplified 25.6%

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

   4. Taylor expanded in c around inf 58.1%

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

   5. Taylor expanded in x around 0 60.5%

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

   6. Taylor expanded in i around 0 65.1%

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

   if -3.1999999999999999e100 < c < -1.90000000000000001e-51

   1. Initial program 37.7%

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

   3. Simplified 37.7%

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

   4. Taylor expanded in y1 around inf 38.5%

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

   5. Taylor expanded in z around inf 47.6%

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

   if -1.90000000000000001e-51 < c < -1.8999999999999999e-241

   1. Initial program 30.7%

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

   3. Simplified 30.7%

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

   4. Taylor expanded in t around inf 53.5%

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

   5. Taylor expanded in z around 0 59.1%

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

   if -1.8999999999999999e-241 < c < 2.09999999999999991e-284

   1. Initial program 38.0%

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

   3. Simplified 38.0%

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

   4. Taylor expanded in x around inf 48.4%

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

   if 2.09999999999999991e-284 < c < 1.74999999999999989e-243

   1. Initial program 25.3%

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

   3. Simplified 25.3%

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

   4. Taylor expanded in t around inf 58.5%

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

   5. Taylor expanded in j around inf 75.7%

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

   if 1.74999999999999989e-243 < c < 1.0799999999999999e126

   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%

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

   4. Taylor expanded in y3 around -inf 53.2%

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

   5. Taylor expanded in z around 0 47.1%

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

   if 1.0799999999999999e126 < c < 2.1999999999999998e205

   1. Initial program 35.3%

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

   3. Simplified 35.3%

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

   4. Taylor expanded in t around inf 47.5%

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

   5. Taylor expanded in y4 around inf 65.5%

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

   if 2.1999999999999998e205 < c < 1.05e244

   1. Initial program 27.3%

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

   3. Simplified 27.3%

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

   4. Taylor expanded in c around inf 63.6%

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

   5. Taylor expanded in y0 around inf 81.9%

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

   if 1.05e244 < c

   1. Initial program 37.5%

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

   3. Simplified 37.5%

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

   4. Taylor expanded in y4 around inf 100.0%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.2 \cdot 10^{+100}:\\ \;\;\;\;c \cdot \left(\left(x \cdot \left(y0 \cdot y2\right) - y0 \cdot \left(z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -1.9 \cdot 10^{-51}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;c \leq -1.9 \cdot 10^{-241}:\\ \;\;\;\;t \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{-284}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq 1.75 \cdot 10^{-243}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;c \leq 1.08 \cdot 10^{+126}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{+205}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq 1.05 \cdot 10^{+244}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \end{array} \]

Alternative 10: 41.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ t_2 := t \cdot j - y \cdot k\\ t_3 := i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) - \left(c \cdot t_1 + y5 \cdot t_2\right)\right)\\ \mathbf{if}\;i \leq -8.5 \cdot 10^{+72}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -3.8 \cdot 10^{-29}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq 3.2 \cdot 10^{-305}:\\ \;\;\;\;b \cdot \left(\left(y4 \cdot t_2 + a \cdot t_1\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;i \leq 1.05 \cdot 10^{+60}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;i \leq 4.6 \cdot 10^{+127}:\\ \;\;\;\;\left(c \cdot y2\right) \cdot \left(x \cdot y0 - t \cdot y4\right)\\ \mathbf{elif}\;i \leq 6 \cdot 10^{+188} \lor \neg \left(i \leq 5.5 \cdot 10^{+221}\right):\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t)))
        (t_2 (- (* t j) (* y k)))
        (t_3 (* i (- (* y1 (- (* x j) (* z k))) (+ (* c t_1) (* y5 t_2))))))
   (if (<= i -8.5e+72)
     t_3
     (if (<= i -3.8e-29)
       (* c (+ (* y0 (- (* x y2) (* z y3))) (* y4 (- (* y y3) (* t y2)))))
       (if (<= i 3.2e-305)
         (* b (+ (+ (* y4 t_2) (* a t_1)) (* y0 (- (* z k) (* x j)))))
         (if (<= i 1.05e+60)
           (*
            y3
            (+
             (* y (- (* c y4) (* a y5)))
             (+ (* j (- (* y0 y5) (* y1 y4))) (* z (- (* a y1) (* c y0))))))
           (if (<= i 4.6e+127)
             (* (* c y2) (- (* x y0) (* t y4)))
             (if (or (<= i 6e+188) (not (<= i 5.5e+221)))
               t_3
               (* a (* y3 (- (* z y1) (* y y5))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (x * y) - (z * t);
	double t_2 = (t * j) - (y * k);
	double t_3 = i * ((y1 * ((x * j) - (z * k))) - ((c * t_1) + (y5 * t_2)));
	double tmp;
	if (i <= -8.5e+72) {
		tmp = t_3;
	} else if (i <= -3.8e-29) {
		tmp = c * ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2))));
	} else if (i <= 3.2e-305) {
		tmp = b * (((y4 * t_2) + (a * t_1)) + (y0 * ((z * k) - (x * j))));
	} else if (i <= 1.05e+60) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	} else if (i <= 4.6e+127) {
		tmp = (c * y2) * ((x * y0) - (t * y4));
	} else if ((i <= 6e+188) || !(i <= 5.5e+221)) {
		tmp = t_3;
	} else {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (x * y) - (z * t)
    t_2 = (t * j) - (y * k)
    t_3 = i * ((y1 * ((x * j) - (z * k))) - ((c * t_1) + (y5 * t_2)))
    if (i <= (-8.5d+72)) then
        tmp = t_3
    else if (i <= (-3.8d-29)) then
        tmp = c * ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2))))
    else if (i <= 3.2d-305) then
        tmp = b * (((y4 * t_2) + (a * t_1)) + (y0 * ((z * k) - (x * j))))
    else if (i <= 1.05d+60) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))))
    else if (i <= 4.6d+127) then
        tmp = (c * y2) * ((x * y0) - (t * y4))
    else if ((i <= 6d+188) .or. (.not. (i <= 5.5d+221))) then
        tmp = t_3
    else
        tmp = a * (y3 * ((z * y1) - (y * y5)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (x * y) - (z * t);
	double t_2 = (t * j) - (y * k);
	double t_3 = i * ((y1 * ((x * j) - (z * k))) - ((c * t_1) + (y5 * t_2)));
	double tmp;
	if (i <= -8.5e+72) {
		tmp = t_3;
	} else if (i <= -3.8e-29) {
		tmp = c * ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2))));
	} else if (i <= 3.2e-305) {
		tmp = b * (((y4 * t_2) + (a * t_1)) + (y0 * ((z * k) - (x * j))));
	} else if (i <= 1.05e+60) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	} else if (i <= 4.6e+127) {
		tmp = (c * y2) * ((x * y0) - (t * y4));
	} else if ((i <= 6e+188) || !(i <= 5.5e+221)) {
		tmp = t_3;
	} else {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (x * y) - (z * t)
	t_2 = (t * j) - (y * k)
	t_3 = i * ((y1 * ((x * j) - (z * k))) - ((c * t_1) + (y5 * t_2)))
	tmp = 0
	if i <= -8.5e+72:
		tmp = t_3
	elif i <= -3.8e-29:
		tmp = c * ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2))))
	elif i <= 3.2e-305:
		tmp = b * (((y4 * t_2) + (a * t_1)) + (y0 * ((z * k) - (x * j))))
	elif i <= 1.05e+60:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))))
	elif i <= 4.6e+127:
		tmp = (c * y2) * ((x * y0) - (t * y4))
	elif (i <= 6e+188) or not (i <= 5.5e+221):
		tmp = t_3
	else:
		tmp = a * (y3 * ((z * y1) - (y * y5)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	t_2 = Float64(Float64(t * j) - Float64(y * k))
	t_3 = Float64(i * Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) - Float64(Float64(c * t_1) + Float64(y5 * t_2))))
	tmp = 0.0
	if (i <= -8.5e+72)
		tmp = t_3;
	elseif (i <= -3.8e-29)
		tmp = Float64(c * Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (i <= 3.2e-305)
		tmp = Float64(b * Float64(Float64(Float64(y4 * t_2) + Float64(a * t_1)) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (i <= 1.05e+60)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(z * Float64(Float64(a * y1) - Float64(c * y0))))));
	elseif (i <= 4.6e+127)
		tmp = Float64(Float64(c * y2) * Float64(Float64(x * y0) - Float64(t * y4)));
	elseif ((i <= 6e+188) || !(i <= 5.5e+221))
		tmp = t_3;
	else
		tmp = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (x * y) - (z * t);
	t_2 = (t * j) - (y * k);
	t_3 = i * ((y1 * ((x * j) - (z * k))) - ((c * t_1) + (y5 * t_2)));
	tmp = 0.0;
	if (i <= -8.5e+72)
		tmp = t_3;
	elseif (i <= -3.8e-29)
		tmp = c * ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2))));
	elseif (i <= 3.2e-305)
		tmp = b * (((y4 * t_2) + (a * t_1)) + (y0 * ((z * k) - (x * j))));
	elseif (i <= 1.05e+60)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	elseif (i <= 4.6e+127)
		tmp = (c * y2) * ((x * y0) - (t * y4));
	elseif ((i <= 6e+188) || ~((i <= 5.5e+221)))
		tmp = t_3;
	else
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(i * N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(c * t$95$1), $MachinePrecision] + N[(y5 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -8.5e+72], t$95$3, If[LessEqual[i, -3.8e-29], N[(c * N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.2e-305], N[(b * N[(N[(N[(y4 * t$95$2), $MachinePrecision] + N[(a * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.05e+60], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.6e+127], N[(N[(c * y2), $MachinePrecision] * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[i, 6e+188], N[Not[LessEqual[i, 5.5e+221]], $MachinePrecision]], t$95$3, N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -8.5000000000000004e72 or 4.6000000000000003e127 < i < 6.0000000000000001e188 or 5.5000000000000003e221 < i

   1. Initial program 24.2%

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

   3. Simplified 24.2%

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

   4. Taylor expanded in i around -inf 59.0%

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

   if -8.5000000000000004e72 < i < -3.79999999999999976e-29

   1. Initial program 5.9%

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

   3. Simplified 5.9%

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

   4. Taylor expanded in c around inf 43.5%

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

   5. Taylor expanded in i around 0 55.2%

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

      1. *-commutative 55.2%

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

      2. *-commutative 55.2%

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

   7. Simplified 55.2%

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

   if -3.79999999999999976e-29 < i < 3.20000000000000009e-305

   1. Initial program 55.2%

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

   3. Simplified 55.2%

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

   4. Taylor expanded in b around inf 54.4%

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

   if 3.20000000000000009e-305 < i < 1.0500000000000001e60

   1. Initial program 43.1%

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

   3. Simplified 43.1%

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

   4. Taylor expanded in y3 around -inf 48.6%

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

   if 1.0500000000000001e60 < i < 4.6000000000000003e127

   1. Initial program 23.8%

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

   3. Simplified 23.8%

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

   4. Taylor expanded in c around inf 23.4%

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

   5. Taylor expanded in x around 0 31.8%

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

   6. Taylor expanded in y2 around inf 70.4%

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

      1. associate-*r* 70.6%

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

   8. Simplified 70.6%

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

   if 6.0000000000000001e188 < i < 5.5000000000000003e221

   1. Initial program 12.5%

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

   3. Simplified 12.5%

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

   4. Taylor expanded in y3 around -inf 62.5%

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

   5. Taylor expanded in a around -inf 87.5%

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

      1. associate-*r* 87.5%

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

      2. neg-mul-1 87.5%

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

   7. Simplified 87.5%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(-a\right) \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -8.5 \cdot 10^{+72}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) - \left(c \cdot \left(x \cdot y - z \cdot t\right) + y5 \cdot \left(t \cdot j - y \cdot k\right)\right)\right)\\ \mathbf{elif}\;i \leq -3.8 \cdot 10^{-29}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq 3.2 \cdot 10^{-305}:\\ \;\;\;\;b \cdot \left(\left(y4 \cdot \left(t \cdot j - y \cdot k\right) + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;i \leq 1.05 \cdot 10^{+60}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;i \leq 4.6 \cdot 10^{+127}:\\ \;\;\;\;\left(c \cdot y2\right) \cdot \left(x \cdot y0 - t \cdot y4\right)\\ \mathbf{elif}\;i \leq 6 \cdot 10^{+188} \lor \neg \left(i \leq 5.5 \cdot 10^{+221}\right):\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) - \left(c \cdot \left(x \cdot y - z \cdot t\right) + y5 \cdot \left(t \cdot j - y \cdot k\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \end{array} \]

Alternative 11: 40.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ t_2 := t \cdot j - y \cdot k\\ t_3 := i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) - \left(c \cdot t_1 + y5 \cdot t_2\right)\right)\\ \mathbf{if}\;i \leq -6 \cdot 10^{+77}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -1.5 \cdot 10^{-28}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq 8.8 \cdot 10^{-305}:\\ \;\;\;\;b \cdot \left(\left(y4 \cdot t_2 + a \cdot t_1\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;i \leq 3.05 \cdot 10^{+60}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;i \leq 5 \cdot 10^{+127}:\\ \;\;\;\;\left(c \cdot y2\right) \cdot \left(x \cdot y0 - t \cdot y4\right)\\ \mathbf{elif}\;i \leq 8 \cdot 10^{+218}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(y0 \cdot \left(j \cdot y3 - k \cdot y2\right) - i \cdot t_2\right)\right)\\ \mathbf{elif}\;i \leq 5.8 \cdot 10^{+252}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t)))
        (t_2 (- (* t j) (* y k)))
        (t_3 (* i (- (* y1 (- (* x j) (* z k))) (+ (* c t_1) (* y5 t_2))))))
   (if (<= i -6e+77)
     t_3
     (if (<= i -1.5e-28)
       (* c (+ (* y0 (- (* x y2) (* z y3))) (* y4 (- (* y y3) (* t y2)))))
       (if (<= i 8.8e-305)
         (* b (+ (+ (* y4 t_2) (* a t_1)) (* y0 (- (* z k) (* x j)))))
         (if (<= i 3.05e+60)
           (*
            y3
            (+
             (* y (- (* c y4) (* a y5)))
             (+ (* j (- (* y0 y5) (* y1 y4))) (* z (- (* a y1) (* c y0))))))
           (if (<= i 5e+127)
             (* (* c y2) (- (* x y0) (* t y4)))
             (if (<= i 8e+218)
               (*
                y5
                (+
                 (* a (- (* t y2) (* y y3)))
                 (- (* y0 (- (* j y3) (* k y2))) (* i t_2))))
               (if (<= i 5.8e+252)
                 (* c (* x (- (* y0 y2) (* y i))))
                 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (x * y) - (z * t);
	double t_2 = (t * j) - (y * k);
	double t_3 = i * ((y1 * ((x * j) - (z * k))) - ((c * t_1) + (y5 * t_2)));
	double tmp;
	if (i <= -6e+77) {
		tmp = t_3;
	} else if (i <= -1.5e-28) {
		tmp = c * ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2))));
	} else if (i <= 8.8e-305) {
		tmp = b * (((y4 * t_2) + (a * t_1)) + (y0 * ((z * k) - (x * j))));
	} else if (i <= 3.05e+60) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	} else if (i <= 5e+127) {
		tmp = (c * y2) * ((x * y0) - (t * y4));
	} else if (i <= 8e+218) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((y0 * ((j * y3) - (k * y2))) - (i * t_2)));
	} else if (i <= 5.8e+252) {
		tmp = c * (x * ((y0 * y2) - (y * i)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (x * y) - (z * t)
    t_2 = (t * j) - (y * k)
    t_3 = i * ((y1 * ((x * j) - (z * k))) - ((c * t_1) + (y5 * t_2)))
    if (i <= (-6d+77)) then
        tmp = t_3
    else if (i <= (-1.5d-28)) then
        tmp = c * ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2))))
    else if (i <= 8.8d-305) then
        tmp = b * (((y4 * t_2) + (a * t_1)) + (y0 * ((z * k) - (x * j))))
    else if (i <= 3.05d+60) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))))
    else if (i <= 5d+127) then
        tmp = (c * y2) * ((x * y0) - (t * y4))
    else if (i <= 8d+218) then
        tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((y0 * ((j * y3) - (k * y2))) - (i * t_2)))
    else if (i <= 5.8d+252) then
        tmp = c * (x * ((y0 * y2) - (y * i)))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (x * y) - (z * t);
	double t_2 = (t * j) - (y * k);
	double t_3 = i * ((y1 * ((x * j) - (z * k))) - ((c * t_1) + (y5 * t_2)));
	double tmp;
	if (i <= -6e+77) {
		tmp = t_3;
	} else if (i <= -1.5e-28) {
		tmp = c * ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2))));
	} else if (i <= 8.8e-305) {
		tmp = b * (((y4 * t_2) + (a * t_1)) + (y0 * ((z * k) - (x * j))));
	} else if (i <= 3.05e+60) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	} else if (i <= 5e+127) {
		tmp = (c * y2) * ((x * y0) - (t * y4));
	} else if (i <= 8e+218) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((y0 * ((j * y3) - (k * y2))) - (i * t_2)));
	} else if (i <= 5.8e+252) {
		tmp = c * (x * ((y0 * y2) - (y * i)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (x * y) - (z * t)
	t_2 = (t * j) - (y * k)
	t_3 = i * ((y1 * ((x * j) - (z * k))) - ((c * t_1) + (y5 * t_2)))
	tmp = 0
	if i <= -6e+77:
		tmp = t_3
	elif i <= -1.5e-28:
		tmp = c * ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2))))
	elif i <= 8.8e-305:
		tmp = b * (((y4 * t_2) + (a * t_1)) + (y0 * ((z * k) - (x * j))))
	elif i <= 3.05e+60:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))))
	elif i <= 5e+127:
		tmp = (c * y2) * ((x * y0) - (t * y4))
	elif i <= 8e+218:
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((y0 * ((j * y3) - (k * y2))) - (i * t_2)))
	elif i <= 5.8e+252:
		tmp = c * (x * ((y0 * y2) - (y * i)))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	t_2 = Float64(Float64(t * j) - Float64(y * k))
	t_3 = Float64(i * Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) - Float64(Float64(c * t_1) + Float64(y5 * t_2))))
	tmp = 0.0
	if (i <= -6e+77)
		tmp = t_3;
	elseif (i <= -1.5e-28)
		tmp = Float64(c * Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (i <= 8.8e-305)
		tmp = Float64(b * Float64(Float64(Float64(y4 * t_2) + Float64(a * t_1)) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (i <= 3.05e+60)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(z * Float64(Float64(a * y1) - Float64(c * y0))))));
	elseif (i <= 5e+127)
		tmp = Float64(Float64(c * y2) * Float64(Float64(x * y0) - Float64(t * y4)));
	elseif (i <= 8e+218)
		tmp = Float64(y5 * Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))) - Float64(i * t_2))));
	elseif (i <= 5.8e+252)
		tmp = Float64(c * Float64(x * Float64(Float64(y0 * y2) - Float64(y * i))));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (x * y) - (z * t);
	t_2 = (t * j) - (y * k);
	t_3 = i * ((y1 * ((x * j) - (z * k))) - ((c * t_1) + (y5 * t_2)));
	tmp = 0.0;
	if (i <= -6e+77)
		tmp = t_3;
	elseif (i <= -1.5e-28)
		tmp = c * ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2))));
	elseif (i <= 8.8e-305)
		tmp = b * (((y4 * t_2) + (a * t_1)) + (y0 * ((z * k) - (x * j))));
	elseif (i <= 3.05e+60)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	elseif (i <= 5e+127)
		tmp = (c * y2) * ((x * y0) - (t * y4));
	elseif (i <= 8e+218)
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((y0 * ((j * y3) - (k * y2))) - (i * t_2)));
	elseif (i <= 5.8e+252)
		tmp = c * (x * ((y0 * y2) - (y * i)));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(i * N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(c * t$95$1), $MachinePrecision] + N[(y5 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -6e+77], t$95$3, If[LessEqual[i, -1.5e-28], N[(c * N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 8.8e-305], N[(b * N[(N[(N[(y4 * t$95$2), $MachinePrecision] + N[(a * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.05e+60], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5e+127], N[(N[(c * y2), $MachinePrecision] * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 8e+218], N[(y5 * N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.8e+252], N[(c * N[(x * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if i < -5.9999999999999996e77 or 5.79999999999999992e252 < i

   1. Initial program 23.1%

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

   3. Simplified 23.1%

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

   4. Taylor expanded in i around -inf 58.1%

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

   if -5.9999999999999996e77 < i < -1.50000000000000001e-28

   1. Initial program 5.9%

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

   3. Simplified 5.9%

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

   4. Taylor expanded in c around inf 43.5%

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

   5. Taylor expanded in i around 0 55.2%

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

      1. *-commutative 55.2%

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

      2. *-commutative 55.2%

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

   7. Simplified 55.2%

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

   if -1.50000000000000001e-28 < i < 8.79999999999999987e-305

   1. Initial program 55.2%

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

   3. Simplified 55.2%

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

   4. Taylor expanded in b around inf 54.4%

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

   if 8.79999999999999987e-305 < i < 3.05e60

   1. Initial program 43.1%

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

   3. Simplified 43.1%

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

   4. Taylor expanded in y3 around -inf 48.6%

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

   if 3.05e60 < i < 5.0000000000000004e127

   1. Initial program 23.8%

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

   3. Simplified 23.8%

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

   4. Taylor expanded in c around inf 23.4%

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

   5. Taylor expanded in x around 0 31.8%

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

   6. Taylor expanded in y2 around inf 70.4%

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

      1. associate-*r* 70.6%

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

   8. Simplified 70.6%

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

   if 5.0000000000000004e127 < i < 8.00000000000000066e218

   1. Initial program 28.5%

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

   3. Simplified 28.5%

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

   4. Taylor expanded in y5 around -inf 62.1%

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

   if 8.00000000000000066e218 < i < 5.79999999999999992e252

   1. Initial program 12.5%

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

   3. Simplified 12.5%

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

   4. Taylor expanded in c around inf 75.0%

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

   5. Taylor expanded in x around inf 88.2%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -6 \cdot 10^{+77}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) - \left(c \cdot \left(x \cdot y - z \cdot t\right) + y5 \cdot \left(t \cdot j - y \cdot k\right)\right)\right)\\ \mathbf{elif}\;i \leq -1.5 \cdot 10^{-28}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq 8.8 \cdot 10^{-305}:\\ \;\;\;\;b \cdot \left(\left(y4 \cdot \left(t \cdot j - y \cdot k\right) + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;i \leq 3.05 \cdot 10^{+60}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;i \leq 5 \cdot 10^{+127}:\\ \;\;\;\;\left(c \cdot y2\right) \cdot \left(x \cdot y0 - t \cdot y4\right)\\ \mathbf{elif}\;i \leq 8 \cdot 10^{+218}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(y0 \cdot \left(j \cdot y3 - k \cdot y2\right) - i \cdot \left(t \cdot j - y \cdot k\right)\right)\right)\\ \mathbf{elif}\;i \leq 5.8 \cdot 10^{+252}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) - \left(c \cdot \left(x \cdot y - z \cdot t\right) + y5 \cdot \left(t \cdot j - y \cdot k\right)\right)\right)\\ \end{array} \]

Alternative 12: 38.8% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -6.2 \cdot 10^{+126}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq -3.4 \cdot 10^{-18}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(y0 \cdot \left(j \cdot y3 - k \cdot y2\right) - i \cdot \left(t \cdot j - y \cdot k\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -1.5 \cdot 10^{-229}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 5.2 \cdot 10^{-71}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 6.5 \cdot 10^{+161}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) - i \cdot \left(x \cdot y - z \cdot t\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y1 -6.2e+126)
   (* j (* y1 (- (* x i) (* y3 y4))))
   (if (<= y1 -3.4e-18)
     (*
      y5
      (+
       (* a (- (* t y2) (* y y3)))
       (- (* y0 (- (* j y3) (* k y2))) (* i (- (* t j) (* y k))))))
     (if (<= y1 -1.5e-229)
       (*
        y2
        (+
         (+ (* k (- (* y1 y4) (* y0 y5))) (* x (- (* c y0) (* a y1))))
         (* t (- (* a y5) (* c y4)))))
       (if (<= y1 5.2e-71)
         (*
          y3
          (+
           (* y (- (* c y4) (* a y5)))
           (+ (* j (- (* y0 y5) (* y1 y4))) (* z (- (* a y1) (* c y0))))))
         (if (<= y1 6.5e+161)
           (*
            c
            (+
             (- (* y0 (- (* x y2) (* z y3))) (* i (- (* x y) (* z t))))
             (* y4 (- (* y y3) (* t y2)))))
           (* i (* y1 (- (* x j) (* z k))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y1 <= -6.2e+126) {
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	} else if (y1 <= -3.4e-18) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((y0 * ((j * y3) - (k * y2))) - (i * ((t * j) - (y * k)))));
	} else if (y1 <= -1.5e-229) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else if (y1 <= 5.2e-71) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	} else if (y1 <= 6.5e+161) {
		tmp = c * (((y0 * ((x * y2) - (z * y3))) - (i * ((x * y) - (z * t)))) + (y4 * ((y * y3) - (t * y2))));
	} else {
		tmp = i * (y1 * ((x * j) - (z * k)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y1 <= (-6.2d+126)) then
        tmp = j * (y1 * ((x * i) - (y3 * y4)))
    else if (y1 <= (-3.4d-18)) then
        tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((y0 * ((j * y3) - (k * y2))) - (i * ((t * j) - (y * k)))))
    else if (y1 <= (-1.5d-229)) then
        tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
    else if (y1 <= 5.2d-71) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))))
    else if (y1 <= 6.5d+161) then
        tmp = c * (((y0 * ((x * y2) - (z * y3))) - (i * ((x * y) - (z * t)))) + (y4 * ((y * y3) - (t * y2))))
    else
        tmp = i * (y1 * ((x * j) - (z * k)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y1 <= -6.2e+126) {
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	} else if (y1 <= -3.4e-18) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((y0 * ((j * y3) - (k * y2))) - (i * ((t * j) - (y * k)))));
	} else if (y1 <= -1.5e-229) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else if (y1 <= 5.2e-71) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	} else if (y1 <= 6.5e+161) {
		tmp = c * (((y0 * ((x * y2) - (z * y3))) - (i * ((x * y) - (z * t)))) + (y4 * ((y * y3) - (t * y2))));
	} else {
		tmp = i * (y1 * ((x * j) - (z * k)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y1 <= -6.2e+126:
		tmp = j * (y1 * ((x * i) - (y3 * y4)))
	elif y1 <= -3.4e-18:
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((y0 * ((j * y3) - (k * y2))) - (i * ((t * j) - (y * k)))))
	elif y1 <= -1.5e-229:
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
	elif y1 <= 5.2e-71:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))))
	elif y1 <= 6.5e+161:
		tmp = c * (((y0 * ((x * y2) - (z * y3))) - (i * ((x * y) - (z * t)))) + (y4 * ((y * y3) - (t * y2))))
	else:
		tmp = i * (y1 * ((x * j) - (z * k)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y1 <= -6.2e+126)
		tmp = Float64(j * Float64(y1 * Float64(Float64(x * i) - Float64(y3 * y4))));
	elseif (y1 <= -3.4e-18)
		tmp = Float64(y5 * Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))) - Float64(i * Float64(Float64(t * j) - Float64(y * k))))));
	elseif (y1 <= -1.5e-229)
		tmp = Float64(y2 * Float64(Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y1 <= 5.2e-71)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(z * Float64(Float64(a * y1) - Float64(c * y0))))));
	elseif (y1 <= 6.5e+161)
		tmp = Float64(c * Float64(Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) - Float64(i * Float64(Float64(x * y) - Float64(z * t)))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	else
		tmp = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y1 <= -6.2e+126)
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	elseif (y1 <= -3.4e-18)
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((y0 * ((j * y3) - (k * y2))) - (i * ((t * j) - (y * k)))));
	elseif (y1 <= -1.5e-229)
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	elseif (y1 <= 5.2e-71)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	elseif (y1 <= 6.5e+161)
		tmp = c * (((y0 * ((x * y2) - (z * y3))) - (i * ((x * y) - (z * t)))) + (y4 * ((y * y3) - (t * y2))));
	else
		tmp = i * (y1 * ((x * j) - (z * k)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y1, -6.2e+126], N[(j * N[(y1 * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -3.4e-18], N[(y5 * N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -1.5e-229], N[(y2 * N[(N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 5.2e-71], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 6.5e+161], N[(c * N[(N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y1 < -6.2e126

   1. Initial program 3.4%

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

   3. Simplified 3.4%

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

   4. Taylor expanded in y1 around inf 48.5%

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

   5. Taylor expanded in j around -inf 62.4%

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

      1. associate-*r* 62.4%

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

      2. neg-mul-1 62.4%

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

   7. Simplified 62.4%

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

   if -6.2e126 < y1 < -3.40000000000000001e-18

   1. Initial program 30.4%

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

   3. Simplified 30.4%

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

   4. Taylor expanded in y5 around -inf 46.4%

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

   if -3.40000000000000001e-18 < y1 < -1.50000000000000001e-229

   1. Initial program 55.9%

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

   3. Simplified 55.9%

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

   4. Taylor expanded in y2 around inf 62.9%

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

   if -1.50000000000000001e-229 < y1 < 5.1999999999999997e-71

   1. Initial program 45.3%

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

   3. Simplified 45.3%

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

   4. Taylor expanded in y3 around -inf 58.0%

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

   if 5.1999999999999997e-71 < y1 < 6.5e161

   1. Initial program 32.3%

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

   3. Simplified 32.3%

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

   4. Taylor expanded in c around inf 53.9%

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

   if 6.5e161 < y1

   1. Initial program 13.8%

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

   3. Simplified 13.8%

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

   4. Taylor expanded in y1 around inf 48.8%

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

   5. Taylor expanded in i around inf 61.5%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -6.2 \cdot 10^{+126}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq -3.4 \cdot 10^{-18}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(y0 \cdot \left(j \cdot y3 - k \cdot y2\right) - i \cdot \left(t \cdot j - y \cdot k\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -1.5 \cdot 10^{-229}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 5.2 \cdot 10^{-71}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 6.5 \cdot 10^{+161}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) - i \cdot \left(x \cdot y - z \cdot t\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \end{array} \]

Alternative 13: 33.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\\ t_2 := j \cdot \left(b \cdot y4 - i \cdot y5\right)\\ t_3 := t \cdot \left(t_2 + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{if}\;c \leq -3.8 \cdot 10^{+108}:\\ \;\;\;\;c \cdot \left(t_1 + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -1.6 \cdot 10^{-50}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;c \leq -1.3 \cdot 10^{-221}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{-283}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq 5 \cdot 10^{-185}:\\ \;\;\;\;t \cdot t_2\\ \mathbf{elif}\;c \leq 3.7 \cdot 10^{+27}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;c \leq 2 \cdot 10^{+134}:\\ \;\;\;\;c \cdot t_1\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{+147}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq 1.42 \cdot 10^{+191}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot y2\right) \cdot \left(x \cdot y0 - t \cdot y4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y0 (- (* x y2) (* z y3))))
        (t_2 (* j (- (* b y4) (* i y5))))
        (t_3 (* t (+ t_2 (* y2 (- (* a y5) (* c y4)))))))
   (if (<= c -3.8e+108)
     (* c (+ t_1 (* y4 (- (* y y3) (* t y2)))))
     (if (<= c -1.6e-50)
       (* y1 (* z (- (* a y3) (* i k))))
       (if (<= c -1.3e-221)
         t_3
         (if (<= c 1.55e-283)
           (* b (* k (- (* z y0) (* y y4))))
           (if (<= c 5e-185)
             (* t t_2)
             (if (<= c 3.7e+27)
               (* b (+ (* a (- (* x y) (* z t))) (* y0 (- (* z k) (* x j)))))
               (if (<= c 2e+134)
                 (* c t_1)
                 (if (<= c 7.5e+147)
                   (* t (* y4 (- (* b j) (* c y2))))
                   (if (<= c 1.42e+191)
                     t_3
                     (* (* 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 = y0 * ((x * y2) - (z * y3));
	double t_2 = j * ((b * y4) - (i * y5));
	double t_3 = t * (t_2 + (y2 * ((a * y5) - (c * y4))));
	double tmp;
	if (c <= -3.8e+108) {
		tmp = c * (t_1 + (y4 * ((y * y3) - (t * y2))));
	} else if (c <= -1.6e-50) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (c <= -1.3e-221) {
		tmp = t_3;
	} else if (c <= 1.55e-283) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (c <= 5e-185) {
		tmp = t * t_2;
	} else if (c <= 3.7e+27) {
		tmp = b * ((a * ((x * y) - (z * t))) + (y0 * ((z * k) - (x * j))));
	} else if (c <= 2e+134) {
		tmp = c * t_1;
	} else if (c <= 7.5e+147) {
		tmp = t * (y4 * ((b * j) - (c * y2)));
	} else if (c <= 1.42e+191) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = y0 * ((x * y2) - (z * y3))
    t_2 = j * ((b * y4) - (i * y5))
    t_3 = t * (t_2 + (y2 * ((a * y5) - (c * y4))))
    if (c <= (-3.8d+108)) then
        tmp = c * (t_1 + (y4 * ((y * y3) - (t * y2))))
    else if (c <= (-1.6d-50)) then
        tmp = y1 * (z * ((a * y3) - (i * k)))
    else if (c <= (-1.3d-221)) then
        tmp = t_3
    else if (c <= 1.55d-283) then
        tmp = b * (k * ((z * y0) - (y * y4)))
    else if (c <= 5d-185) then
        tmp = t * t_2
    else if (c <= 3.7d+27) then
        tmp = b * ((a * ((x * y) - (z * t))) + (y0 * ((z * k) - (x * j))))
    else if (c <= 2d+134) then
        tmp = c * t_1
    else if (c <= 7.5d+147) then
        tmp = t * (y4 * ((b * j) - (c * y2)))
    else if (c <= 1.42d+191) then
        tmp = t_3
    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 = y0 * ((x * y2) - (z * y3));
	double t_2 = j * ((b * y4) - (i * y5));
	double t_3 = t * (t_2 + (y2 * ((a * y5) - (c * y4))));
	double tmp;
	if (c <= -3.8e+108) {
		tmp = c * (t_1 + (y4 * ((y * y3) - (t * y2))));
	} else if (c <= -1.6e-50) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (c <= -1.3e-221) {
		tmp = t_3;
	} else if (c <= 1.55e-283) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (c <= 5e-185) {
		tmp = t * t_2;
	} else if (c <= 3.7e+27) {
		tmp = b * ((a * ((x * y) - (z * t))) + (y0 * ((z * k) - (x * j))));
	} else if (c <= 2e+134) {
		tmp = c * t_1;
	} else if (c <= 7.5e+147) {
		tmp = t * (y4 * ((b * j) - (c * y2)));
	} else if (c <= 1.42e+191) {
		tmp = t_3;
	} 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 = y0 * ((x * y2) - (z * y3))
	t_2 = j * ((b * y4) - (i * y5))
	t_3 = t * (t_2 + (y2 * ((a * y5) - (c * y4))))
	tmp = 0
	if c <= -3.8e+108:
		tmp = c * (t_1 + (y4 * ((y * y3) - (t * y2))))
	elif c <= -1.6e-50:
		tmp = y1 * (z * ((a * y3) - (i * k)))
	elif c <= -1.3e-221:
		tmp = t_3
	elif c <= 1.55e-283:
		tmp = b * (k * ((z * y0) - (y * y4)))
	elif c <= 5e-185:
		tmp = t * t_2
	elif c <= 3.7e+27:
		tmp = b * ((a * ((x * y) - (z * t))) + (y0 * ((z * k) - (x * j))))
	elif c <= 2e+134:
		tmp = c * t_1
	elif c <= 7.5e+147:
		tmp = t * (y4 * ((b * j) - (c * y2)))
	elif c <= 1.42e+191:
		tmp = t_3
	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(y0 * Float64(Float64(x * y2) - Float64(z * y3)))
	t_2 = Float64(j * Float64(Float64(b * y4) - Float64(i * y5)))
	t_3 = Float64(t * Float64(t_2 + Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4)))))
	tmp = 0.0
	if (c <= -3.8e+108)
		tmp = Float64(c * Float64(t_1 + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (c <= -1.6e-50)
		tmp = Float64(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * k))));
	elseif (c <= -1.3e-221)
		tmp = t_3;
	elseif (c <= 1.55e-283)
		tmp = Float64(b * Float64(k * Float64(Float64(z * y0) - Float64(y * y4))));
	elseif (c <= 5e-185)
		tmp = Float64(t * t_2);
	elseif (c <= 3.7e+27)
		tmp = Float64(b * Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (c <= 2e+134)
		tmp = Float64(c * t_1);
	elseif (c <= 7.5e+147)
		tmp = Float64(t * Float64(y4 * Float64(Float64(b * j) - Float64(c * y2))));
	elseif (c <= 1.42e+191)
		tmp = t_3;
	else
		tmp = Float64(Float64(c * 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 = y0 * ((x * y2) - (z * y3));
	t_2 = j * ((b * y4) - (i * y5));
	t_3 = t * (t_2 + (y2 * ((a * y5) - (c * y4))));
	tmp = 0.0;
	if (c <= -3.8e+108)
		tmp = c * (t_1 + (y4 * ((y * y3) - (t * y2))));
	elseif (c <= -1.6e-50)
		tmp = y1 * (z * ((a * y3) - (i * k)));
	elseif (c <= -1.3e-221)
		tmp = t_3;
	elseif (c <= 1.55e-283)
		tmp = b * (k * ((z * y0) - (y * y4)));
	elseif (c <= 5e-185)
		tmp = t * t_2;
	elseif (c <= 3.7e+27)
		tmp = b * ((a * ((x * y) - (z * t))) + (y0 * ((z * k) - (x * j))));
	elseif (c <= 2e+134)
		tmp = c * t_1;
	elseif (c <= 7.5e+147)
		tmp = t * (y4 * ((b * j) - (c * y2)));
	elseif (c <= 1.42e+191)
		tmp = t_3;
	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[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(t$95$2 + N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.8e+108], N[(c * N[(t$95$1 + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.6e-50], N[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.3e-221], t$95$3, If[LessEqual[c, 1.55e-283], N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5e-185], N[(t * t$95$2), $MachinePrecision], If[LessEqual[c, 3.7e+27], N[(b * N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2e+134], N[(c * t$95$1), $MachinePrecision], If[LessEqual[c, 7.5e+147], N[(t * N[(y4 * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.42e+191], t$95$3, N[(N[(c * y2), $MachinePrecision] * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if c < -3.80000000000000008e108

   1. Initial program 25.6%

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

   3. Simplified 25.6%

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

   4. Taylor expanded in c around inf 58.1%

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

   5. Taylor expanded in i around 0 65.1%

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

      1. *-commutative 65.1%

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

      2. *-commutative 65.1%

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

   7. Simplified 65.1%

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

   if -3.80000000000000008e108 < c < -1.6e-50

   1. Initial program 37.7%

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

   3. Simplified 37.7%

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

   4. Taylor expanded in y1 around inf 38.5%

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

   5. Taylor expanded in z around inf 47.6%

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

   if -1.6e-50 < c < -1.3000000000000001e-221 or 7.50000000000000037e147 < c < 1.4199999999999999e191

   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 33.4%

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

   4. Taylor expanded in t around inf 55.5%

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

   5. Taylor expanded in z around 0 65.0%

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

   if -1.3000000000000001e-221 < c < 1.55000000000000002e-283

   1. Initial program 31.9%

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

   3. Simplified 31.9%

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

   4. Taylor expanded in b around inf 45.1%

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

   5. Taylor expanded in k around -inf 45.1%

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

      1. associate-*r* 45.1%

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

      2. neg-mul-1 45.1%

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

   7. Simplified 45.1%

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

   if 1.55000000000000002e-283 < c < 5.0000000000000003e-185

   1. Initial program 25.2%

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

   3. Simplified 25.2%

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

   4. Taylor expanded in t around inf 45.8%

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

   5. Taylor expanded in j around inf 55.7%

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

   if 5.0000000000000003e-185 < c < 3.70000000000000002e27

   1. Initial program 38.5%

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

   3. Simplified 38.5%

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

   4. Taylor expanded in b around inf 43.4%

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

   5. Taylor expanded in y4 around 0 52.7%

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

   if 3.70000000000000002e27 < c < 1.99999999999999984e134

   1. Initial program 42.7%

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

   3. Simplified 42.7%

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

   4. Taylor expanded in c around inf 42.7%

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

   5. Taylor expanded in y0 around inf 47.4%

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

   if 1.99999999999999984e134 < c < 7.50000000000000037e147

   1. Initial program 66.7%

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

   3. Simplified 66.7%

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

   4. Taylor expanded in t around inf 34.3%

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

   5. Taylor expanded in y4 around inf 100.0%

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

   if 1.4199999999999999e191 < c

   1. Initial program 33.3%

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

   3. Simplified 33.3%

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

   4. Taylor expanded in c around inf 57.1%

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

   5. Taylor expanded in x around 0 61.9%

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

   6. Taylor expanded in y2 around inf 62.5%

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

      1. associate-*r* 67.0%

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

   8. Simplified 67.0%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.8 \cdot 10^{+108}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -1.6 \cdot 10^{-50}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;c \leq -1.3 \cdot 10^{-221}:\\ \;\;\;\;t \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{-283}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq 5 \cdot 10^{-185}:\\ \;\;\;\;t \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;c \leq 3.7 \cdot 10^{+27}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;c \leq 2 \cdot 10^{+134}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{+147}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq 1.42 \cdot 10^{+191}:\\ \;\;\;\;t \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot y2\right) \cdot \left(x \cdot y0 - t \cdot y4\right)\\ \end{array} \]

Alternative 14: 35.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot y4 - i \cdot y5\\ \mathbf{if}\;c \leq -7 \cdot 10^{+94}:\\ \;\;\;\;c \cdot \left(\left(x \cdot \left(y0 \cdot y2\right) - y0 \cdot \left(z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -3.7 \cdot 10^{-51}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;c \leq -8.5 \cdot 10^{-242}:\\ \;\;\;\;t \cdot \left(j \cdot t_1 + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq 2.3 \cdot 10^{-283}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{-243}:\\ \;\;\;\;j \cdot \left(t \cdot t_1\right)\\ \mathbf{elif}\;c \leq 9 \cdot 10^{+124}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq 2.4 \cdot 10^{+205}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq 1.02 \cdot 10^{+240}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-c \cdot \left(y2 \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* b y4) (* i y5))))
   (if (<= c -7e+94)
     (* c (+ (- (* x (* y0 y2)) (* y0 (* z y3))) (* y4 (- (* y y3) (* t y2)))))
     (if (<= c -3.7e-51)
       (* y1 (* z (- (* a y3) (* i k))))
       (if (<= c -8.5e-242)
         (* t (+ (* j t_1) (* y2 (- (* a y5) (* c y4)))))
         (if (<= c 2.3e-283)
           (*
            x
            (+
             (+ (* y (- (* a b) (* c i))) (* y2 (- (* c y0) (* a y1))))
             (* j (- (* i y1) (* b y0)))))
           (if (<= c 1.15e-243)
             (* j (* t t_1))
             (if (<= c 9e+124)
               (*
                y3
                (+ (* y (- (* c y4) (* a y5))) (* j (- (* y0 y5) (* y1 y4)))))
               (if (<= c 2.4e+205)
                 (* t (* y4 (- (* b j) (* c y2))))
                 (if (<= c 1.02e+240)
                   (* c (* y0 (- (* x y2) (* z y3))))
                   (* t (- (* c (* y2 y4))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (b * y4) - (i * y5);
	double tmp;
	if (c <= -7e+94) {
		tmp = c * (((x * (y0 * y2)) - (y0 * (z * y3))) + (y4 * ((y * y3) - (t * y2))));
	} else if (c <= -3.7e-51) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (c <= -8.5e-242) {
		tmp = t * ((j * t_1) + (y2 * ((a * y5) - (c * y4))));
	} else if (c <= 2.3e-283) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	} else if (c <= 1.15e-243) {
		tmp = j * (t * t_1);
	} else if (c <= 9e+124) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))));
	} else if (c <= 2.4e+205) {
		tmp = t * (y4 * ((b * j) - (c * y2)));
	} else if (c <= 1.02e+240) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else {
		tmp = t * -(c * (y2 * y4));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * y4) - (i * y5)
    if (c <= (-7d+94)) then
        tmp = c * (((x * (y0 * y2)) - (y0 * (z * y3))) + (y4 * ((y * y3) - (t * y2))))
    else if (c <= (-3.7d-51)) then
        tmp = y1 * (z * ((a * y3) - (i * k)))
    else if (c <= (-8.5d-242)) then
        tmp = t * ((j * t_1) + (y2 * ((a * y5) - (c * y4))))
    else if (c <= 2.3d-283) then
        tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
    else if (c <= 1.15d-243) then
        tmp = j * (t * t_1)
    else if (c <= 9d+124) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))))
    else if (c <= 2.4d+205) then
        tmp = t * (y4 * ((b * j) - (c * y2)))
    else if (c <= 1.02d+240) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else
        tmp = t * -(c * (y2 * y4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (b * y4) - (i * y5);
	double tmp;
	if (c <= -7e+94) {
		tmp = c * (((x * (y0 * y2)) - (y0 * (z * y3))) + (y4 * ((y * y3) - (t * y2))));
	} else if (c <= -3.7e-51) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (c <= -8.5e-242) {
		tmp = t * ((j * t_1) + (y2 * ((a * y5) - (c * y4))));
	} else if (c <= 2.3e-283) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	} else if (c <= 1.15e-243) {
		tmp = j * (t * t_1);
	} else if (c <= 9e+124) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))));
	} else if (c <= 2.4e+205) {
		tmp = t * (y4 * ((b * j) - (c * y2)));
	} else if (c <= 1.02e+240) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else {
		tmp = t * -(c * (y2 * y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (b * y4) - (i * y5)
	tmp = 0
	if c <= -7e+94:
		tmp = c * (((x * (y0 * y2)) - (y0 * (z * y3))) + (y4 * ((y * y3) - (t * y2))))
	elif c <= -3.7e-51:
		tmp = y1 * (z * ((a * y3) - (i * k)))
	elif c <= -8.5e-242:
		tmp = t * ((j * t_1) + (y2 * ((a * y5) - (c * y4))))
	elif c <= 2.3e-283:
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
	elif c <= 1.15e-243:
		tmp = j * (t * t_1)
	elif c <= 9e+124:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))))
	elif c <= 2.4e+205:
		tmp = t * (y4 * ((b * j) - (c * y2)))
	elif c <= 1.02e+240:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	else:
		tmp = t * -(c * (y2 * y4))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(b * y4) - Float64(i * y5))
	tmp = 0.0
	if (c <= -7e+94)
		tmp = Float64(c * Float64(Float64(Float64(x * Float64(y0 * y2)) - Float64(y0 * Float64(z * y3))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (c <= -3.7e-51)
		tmp = Float64(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * k))));
	elseif (c <= -8.5e-242)
		tmp = Float64(t * Float64(Float64(j * t_1) + Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (c <= 2.3e-283)
		tmp = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (c <= 1.15e-243)
		tmp = Float64(j * Float64(t * t_1));
	elseif (c <= 9e+124)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4)))));
	elseif (c <= 2.4e+205)
		tmp = Float64(t * Float64(y4 * Float64(Float64(b * j) - Float64(c * y2))));
	elseif (c <= 1.02e+240)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	else
		tmp = Float64(t * Float64(-Float64(c * Float64(y2 * y4))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (b * y4) - (i * y5);
	tmp = 0.0;
	if (c <= -7e+94)
		tmp = c * (((x * (y0 * y2)) - (y0 * (z * y3))) + (y4 * ((y * y3) - (t * y2))));
	elseif (c <= -3.7e-51)
		tmp = y1 * (z * ((a * y3) - (i * k)));
	elseif (c <= -8.5e-242)
		tmp = t * ((j * t_1) + (y2 * ((a * y5) - (c * y4))));
	elseif (c <= 2.3e-283)
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	elseif (c <= 1.15e-243)
		tmp = j * (t * t_1);
	elseif (c <= 9e+124)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))));
	elseif (c <= 2.4e+205)
		tmp = t * (y4 * ((b * j) - (c * y2)));
	elseif (c <= 1.02e+240)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	else
		tmp = t * -(c * (y2 * y4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -7e+94], N[(c * N[(N[(N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision] - N[(y0 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3.7e-51], N[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -8.5e-242], N[(t * N[(N[(j * t$95$1), $MachinePrecision] + N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.3e-283], N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.15e-243], N[(j * N[(t * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 9e+124], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.4e+205], N[(t * N[(y4 * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.02e+240], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * (-N[(c * N[(y2 * y4), $MachinePrecision]), $MachinePrecision])), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if c < -6.9999999999999994e94

   1. Initial program 25.6%

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

   3. Simplified 25.6%

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

   4. Taylor expanded in c around inf 58.1%

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

   5. Taylor expanded in x around 0 60.5%

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

   6. Taylor expanded in i around 0 65.1%

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

   if -6.9999999999999994e94 < c < -3.69999999999999973e-51

   1. Initial program 37.7%

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

   3. Simplified 37.7%

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

   4. Taylor expanded in y1 around inf 38.5%

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

   5. Taylor expanded in z around inf 47.6%

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

   if -3.69999999999999973e-51 < c < -8.4999999999999997e-242

   1. Initial program 30.7%

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

   3. Simplified 30.7%

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

   4. Taylor expanded in t around inf 53.5%

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

   5. Taylor expanded in z around 0 59.1%

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

   if -8.4999999999999997e-242 < c < 2.2999999999999999e-283

   1. Initial program 38.0%

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

   3. Simplified 38.0%

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

   4. Taylor expanded in x around inf 48.4%

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

   if 2.2999999999999999e-283 < c < 1.15e-243

   1. Initial program 25.3%

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

   3. Simplified 25.3%

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

   4. Taylor expanded in t around inf 58.5%

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

   5. Taylor expanded in j around inf 75.7%

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

   if 1.15e-243 < c < 9.0000000000000008e124

   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%

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

   4. Taylor expanded in y3 around -inf 53.2%

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

   5. Taylor expanded in z around 0 47.1%

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

   if 9.0000000000000008e124 < c < 2.39999999999999986e205

   1. Initial program 35.3%

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

   3. Simplified 35.3%

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

   4. Taylor expanded in t around inf 47.5%

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

   5. Taylor expanded in y4 around inf 65.5%

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

   if 2.39999999999999986e205 < c < 1.02e240

   1. Initial program 22.2%

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

   3. Simplified 22.2%

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

   4. Taylor expanded in c around inf 66.7%

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

   5. Taylor expanded in y0 around inf 77.8%

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

   if 1.02e240 < c

   1. Initial program 40.0%

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

   3. Simplified 40.0%

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

   4. Taylor expanded in t around inf 60.0%

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

   5. Taylor expanded in z around 0 60.5%

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

   6. Taylor expanded in c around inf 90.0%

      \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(y2 \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 90.0%

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

   8. Simplified 90.0%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7 \cdot 10^{+94}:\\ \;\;\;\;c \cdot \left(\left(x \cdot \left(y0 \cdot y2\right) - y0 \cdot \left(z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -3.7 \cdot 10^{-51}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;c \leq -8.5 \cdot 10^{-242}:\\ \;\;\;\;t \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq 2.3 \cdot 10^{-283}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{-243}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;c \leq 9 \cdot 10^{+124}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq 2.4 \cdot 10^{+205}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq 1.02 \cdot 10^{+240}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-c \cdot \left(y2 \cdot y4\right)\right)\\ \end{array} \]

Alternative 15: 33.5% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\\ t_2 := j \cdot \left(b \cdot y4 - i \cdot y5\right)\\ \mathbf{if}\;c \leq -6.6 \cdot 10^{+94}:\\ \;\;\;\;c \cdot \left(t_1 + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -1.08 \cdot 10^{-51}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;c \leq -1.75 \cdot 10^{-220}:\\ \;\;\;\;t \cdot \left(t_2 - c \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq 1.4 \cdot 10^{-283}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq 1.42 \cdot 10^{-184}:\\ \;\;\;\;t \cdot t_2\\ \mathbf{elif}\;c \leq 5.6 \cdot 10^{+28}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;c \leq 1.38 \cdot 10^{+132}:\\ \;\;\;\;c \cdot t_1\\ \mathbf{elif}\;c \leq 4.9 \cdot 10^{+147}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq 5.1 \cdot 10^{+210}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y0 (- (* x y2) (* z y3)))) (t_2 (* j (- (* b y4) (* i y5)))))
   (if (<= c -6.6e+94)
     (* c (+ t_1 (* y4 (- (* y y3) (* t y2)))))
     (if (<= c -1.08e-51)
       (* y1 (* z (- (* a y3) (* i k))))
       (if (<= c -1.75e-220)
         (* t (- t_2 (* c (* y2 y4))))
         (if (<= c 1.4e-283)
           (* b (* k (- (* z y0) (* y y4))))
           (if (<= c 1.42e-184)
             (* t t_2)
             (if (<= c 5.6e+28)
               (* b (+ (* a (- (* x y) (* z t))) (* y0 (- (* z k) (* x j)))))
               (if (<= c 1.38e+132)
                 (* c t_1)
                 (if (<= c 4.9e+147)
                   (* t (* y4 (- (* b j) (* c y2))))
                   (if (<= c 5.1e+210)
                     (* t (* y2 (- (* a y5) (* c y4))))
                     (* 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 = y0 * ((x * y2) - (z * y3));
	double t_2 = j * ((b * y4) - (i * y5));
	double tmp;
	if (c <= -6.6e+94) {
		tmp = c * (t_1 + (y4 * ((y * y3) - (t * y2))));
	} else if (c <= -1.08e-51) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (c <= -1.75e-220) {
		tmp = t * (t_2 - (c * (y2 * y4)));
	} else if (c <= 1.4e-283) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (c <= 1.42e-184) {
		tmp = t * t_2;
	} else if (c <= 5.6e+28) {
		tmp = b * ((a * ((x * y) - (z * t))) + (y0 * ((z * k) - (x * j))));
	} else if (c <= 1.38e+132) {
		tmp = c * t_1;
	} else if (c <= 4.9e+147) {
		tmp = t * (y4 * ((b * j) - (c * y2)));
	} else if (c <= 5.1e+210) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} 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 = y0 * ((x * y2) - (z * y3))
    t_2 = j * ((b * y4) - (i * y5))
    if (c <= (-6.6d+94)) then
        tmp = c * (t_1 + (y4 * ((y * y3) - (t * y2))))
    else if (c <= (-1.08d-51)) then
        tmp = y1 * (z * ((a * y3) - (i * k)))
    else if (c <= (-1.75d-220)) then
        tmp = t * (t_2 - (c * (y2 * y4)))
    else if (c <= 1.4d-283) then
        tmp = b * (k * ((z * y0) - (y * y4)))
    else if (c <= 1.42d-184) then
        tmp = t * t_2
    else if (c <= 5.6d+28) then
        tmp = b * ((a * ((x * y) - (z * t))) + (y0 * ((z * k) - (x * j))))
    else if (c <= 1.38d+132) then
        tmp = c * t_1
    else if (c <= 4.9d+147) then
        tmp = t * (y4 * ((b * j) - (c * y2)))
    else if (c <= 5.1d+210) then
        tmp = t * (y2 * ((a * y5) - (c * y4)))
    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 = y0 * ((x * y2) - (z * y3));
	double t_2 = j * ((b * y4) - (i * y5));
	double tmp;
	if (c <= -6.6e+94) {
		tmp = c * (t_1 + (y4 * ((y * y3) - (t * y2))));
	} else if (c <= -1.08e-51) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (c <= -1.75e-220) {
		tmp = t * (t_2 - (c * (y2 * y4)));
	} else if (c <= 1.4e-283) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (c <= 1.42e-184) {
		tmp = t * t_2;
	} else if (c <= 5.6e+28) {
		tmp = b * ((a * ((x * y) - (z * t))) + (y0 * ((z * k) - (x * j))));
	} else if (c <= 1.38e+132) {
		tmp = c * t_1;
	} else if (c <= 4.9e+147) {
		tmp = t * (y4 * ((b * j) - (c * y2)));
	} else if (c <= 5.1e+210) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} 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 = y0 * ((x * y2) - (z * y3))
	t_2 = j * ((b * y4) - (i * y5))
	tmp = 0
	if c <= -6.6e+94:
		tmp = c * (t_1 + (y4 * ((y * y3) - (t * y2))))
	elif c <= -1.08e-51:
		tmp = y1 * (z * ((a * y3) - (i * k)))
	elif c <= -1.75e-220:
		tmp = t * (t_2 - (c * (y2 * y4)))
	elif c <= 1.4e-283:
		tmp = b * (k * ((z * y0) - (y * y4)))
	elif c <= 1.42e-184:
		tmp = t * t_2
	elif c <= 5.6e+28:
		tmp = b * ((a * ((x * y) - (z * t))) + (y0 * ((z * k) - (x * j))))
	elif c <= 1.38e+132:
		tmp = c * t_1
	elif c <= 4.9e+147:
		tmp = t * (y4 * ((b * j) - (c * y2)))
	elif c <= 5.1e+210:
		tmp = t * (y2 * ((a * y5) - (c * y4)))
	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(y0 * Float64(Float64(x * y2) - Float64(z * y3)))
	t_2 = Float64(j * Float64(Float64(b * y4) - Float64(i * y5)))
	tmp = 0.0
	if (c <= -6.6e+94)
		tmp = Float64(c * Float64(t_1 + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (c <= -1.08e-51)
		tmp = Float64(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * k))));
	elseif (c <= -1.75e-220)
		tmp = Float64(t * Float64(t_2 - Float64(c * Float64(y2 * y4))));
	elseif (c <= 1.4e-283)
		tmp = Float64(b * Float64(k * Float64(Float64(z * y0) - Float64(y * y4))));
	elseif (c <= 1.42e-184)
		tmp = Float64(t * t_2);
	elseif (c <= 5.6e+28)
		tmp = Float64(b * Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (c <= 1.38e+132)
		tmp = Float64(c * t_1);
	elseif (c <= 4.9e+147)
		tmp = Float64(t * Float64(y4 * Float64(Float64(b * j) - Float64(c * y2))));
	elseif (c <= 5.1e+210)
		tmp = Float64(t * Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))));
	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 = y0 * ((x * y2) - (z * y3));
	t_2 = j * ((b * y4) - (i * y5));
	tmp = 0.0;
	if (c <= -6.6e+94)
		tmp = c * (t_1 + (y4 * ((y * y3) - (t * y2))));
	elseif (c <= -1.08e-51)
		tmp = y1 * (z * ((a * y3) - (i * k)));
	elseif (c <= -1.75e-220)
		tmp = t * (t_2 - (c * (y2 * y4)));
	elseif (c <= 1.4e-283)
		tmp = b * (k * ((z * y0) - (y * y4)));
	elseif (c <= 1.42e-184)
		tmp = t * t_2;
	elseif (c <= 5.6e+28)
		tmp = b * ((a * ((x * y) - (z * t))) + (y0 * ((z * k) - (x * j))));
	elseif (c <= 1.38e+132)
		tmp = c * t_1;
	elseif (c <= 4.9e+147)
		tmp = t * (y4 * ((b * j) - (c * y2)));
	elseif (c <= 5.1e+210)
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	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[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -6.6e+94], N[(c * N[(t$95$1 + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.08e-51], N[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.75e-220], N[(t * N[(t$95$2 - N[(c * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.4e-283], N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.42e-184], N[(t * t$95$2), $MachinePrecision], If[LessEqual[c, 5.6e+28], N[(b * N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.38e+132], N[(c * t$95$1), $MachinePrecision], If[LessEqual[c, 4.9e+147], N[(t * N[(y4 * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.1e+210], N[(t * N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if c < -6.6e94

   1. Initial program 25.6%

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

   3. Simplified 25.6%

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

   4. Taylor expanded in c around inf 58.1%

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

   5. Taylor expanded in i around 0 65.1%

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

      1. *-commutative 65.1%

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

      2. *-commutative 65.1%

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

   7. Simplified 65.1%

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

   if -6.6e94 < c < -1.08000000000000004e-51

   1. Initial program 37.7%

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

   3. Simplified 37.7%

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

   4. Taylor expanded in y1 around inf 38.5%

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

   5. Taylor expanded in z around inf 47.6%

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

   if -1.08000000000000004e-51 < c < -1.74999999999999994e-220

   1. Initial program 34.5%

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

   3. Simplified 34.5%

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

   4. Taylor expanded in t around inf 53.9%

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

   5. Taylor expanded in z around 0 60.2%

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

   6. Taylor expanded in a around 0 51.2%

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

   if -1.74999999999999994e-220 < c < 1.3999999999999999e-283

   1. Initial program 31.9%

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

   3. Simplified 31.9%

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

   4. Taylor expanded in b around inf 45.1%

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

   5. Taylor expanded in k around -inf 45.1%

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

      1. associate-*r* 45.1%

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

      2. neg-mul-1 45.1%

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

   7. Simplified 45.1%

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

   if 1.3999999999999999e-283 < c < 1.41999999999999993e-184

   1. Initial program 25.2%

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

   3. Simplified 25.2%

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

   4. Taylor expanded in t around inf 45.8%

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

   5. Taylor expanded in j around inf 55.7%

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

   if 1.41999999999999993e-184 < c < 5.6000000000000003e28

   1. Initial program 38.5%

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

   3. Simplified 38.5%

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

   4. Taylor expanded in b around inf 43.4%

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

   5. Taylor expanded in y4 around 0 52.7%

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

   if 5.6000000000000003e28 < c < 1.38e132

   1. Initial program 42.7%

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

   3. Simplified 42.7%

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

   4. Taylor expanded in c around inf 42.7%

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

   5. Taylor expanded in y0 around inf 47.4%

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

   if 1.38e132 < c < 4.8999999999999998e147

   1. Initial program 66.7%

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

   3. Simplified 66.7%

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

   4. Taylor expanded in t around inf 34.3%

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

   5. Taylor expanded in y4 around inf 100.0%

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

   if 4.8999999999999998e147 < c < 5.1000000000000001e210

   1. Initial program 35.3%

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

   3. Simplified 35.3%

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

   4. Taylor expanded in t around inf 42.0%

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

   5. Taylor expanded in y2 around inf 65.3%

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

   if 5.1000000000000001e210 < c

   1. Initial program 28.6%

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

   3. Simplified 28.6%

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

   4. Taylor expanded in c around inf 50.0%

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

   5. Taylor expanded in y2 around inf 71.6%

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

      1. *-commutative 71.6%

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

      2. *-commutative 71.6%

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

   7. Simplified 71.6%

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(y0 \cdot x - y4 \cdot t\right)\right)} \]
3. Recombined 10 regimes into one program.

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.6 \cdot 10^{+94}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -1.08 \cdot 10^{-51}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;c \leq -1.75 \cdot 10^{-220}:\\ \;\;\;\;t \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - c \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq 1.4 \cdot 10^{-283}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq 1.42 \cdot 10^{-184}:\\ \;\;\;\;t \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;c \leq 5.6 \cdot 10^{+28}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;c \leq 1.38 \cdot 10^{+132}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;c \leq 4.9 \cdot 10^{+147}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq 5.1 \cdot 10^{+210}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \end{array} \]

Alternative 16: 34.1% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\\ t_2 := b \cdot y4 - i \cdot y5\\ \mathbf{if}\;c \leq -2.25 \cdot 10^{+119}:\\ \;\;\;\;c \cdot \left(t_1 + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -3.8 \cdot 10^{-50}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;c \leq -4.5 \cdot 10^{-221}:\\ \;\;\;\;t \cdot \left(j \cdot t_2 + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{-284}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq 8.8 \cdot 10^{-243}:\\ \;\;\;\;j \cdot \left(t \cdot t_2\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{+126}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{+205}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq 1.76 \cdot 10^{+239}:\\ \;\;\;\;c \cdot t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-c \cdot \left(y2 \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y0 (- (* x y2) (* z y3)))) (t_2 (- (* b y4) (* i y5))))
   (if (<= c -2.25e+119)
     (* c (+ t_1 (* y4 (- (* y y3) (* t y2)))))
     (if (<= c -3.8e-50)
       (* y1 (* z (- (* a y3) (* i k))))
       (if (<= c -4.5e-221)
         (* t (+ (* j t_2) (* y2 (- (* a y5) (* c y4)))))
         (if (<= c 8.5e-284)
           (* b (* k (- (* z y0) (* y y4))))
           (if (<= c 8.8e-243)
             (* j (* t t_2))
             (if (<= c 2.2e+126)
               (*
                y3
                (+ (* y (- (* c y4) (* a y5))) (* j (- (* y0 y5) (* y1 y4)))))
               (if (<= c 2.1e+205)
                 (* t (* y4 (- (* b j) (* c y2))))
                 (if (<= c 1.76e+239)
                   (* c t_1)
                   (* t (- (* c (* y2 y4))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * ((x * y2) - (z * y3));
	double t_2 = (b * y4) - (i * y5);
	double tmp;
	if (c <= -2.25e+119) {
		tmp = c * (t_1 + (y4 * ((y * y3) - (t * y2))));
	} else if (c <= -3.8e-50) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (c <= -4.5e-221) {
		tmp = t * ((j * t_2) + (y2 * ((a * y5) - (c * y4))));
	} else if (c <= 8.5e-284) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (c <= 8.8e-243) {
		tmp = j * (t * t_2);
	} else if (c <= 2.2e+126) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))));
	} else if (c <= 2.1e+205) {
		tmp = t * (y4 * ((b * j) - (c * y2)));
	} else if (c <= 1.76e+239) {
		tmp = c * t_1;
	} else {
		tmp = t * -(c * (y2 * 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 = y0 * ((x * y2) - (z * y3))
    t_2 = (b * y4) - (i * y5)
    if (c <= (-2.25d+119)) then
        tmp = c * (t_1 + (y4 * ((y * y3) - (t * y2))))
    else if (c <= (-3.8d-50)) then
        tmp = y1 * (z * ((a * y3) - (i * k)))
    else if (c <= (-4.5d-221)) then
        tmp = t * ((j * t_2) + (y2 * ((a * y5) - (c * y4))))
    else if (c <= 8.5d-284) then
        tmp = b * (k * ((z * y0) - (y * y4)))
    else if (c <= 8.8d-243) then
        tmp = j * (t * t_2)
    else if (c <= 2.2d+126) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))))
    else if (c <= 2.1d+205) then
        tmp = t * (y4 * ((b * j) - (c * y2)))
    else if (c <= 1.76d+239) then
        tmp = c * t_1
    else
        tmp = t * -(c * (y2 * y4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * ((x * y2) - (z * y3));
	double t_2 = (b * y4) - (i * y5);
	double tmp;
	if (c <= -2.25e+119) {
		tmp = c * (t_1 + (y4 * ((y * y3) - (t * y2))));
	} else if (c <= -3.8e-50) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (c <= -4.5e-221) {
		tmp = t * ((j * t_2) + (y2 * ((a * y5) - (c * y4))));
	} else if (c <= 8.5e-284) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (c <= 8.8e-243) {
		tmp = j * (t * t_2);
	} else if (c <= 2.2e+126) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))));
	} else if (c <= 2.1e+205) {
		tmp = t * (y4 * ((b * j) - (c * y2)));
	} else if (c <= 1.76e+239) {
		tmp = c * t_1;
	} else {
		tmp = t * -(c * (y2 * y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y0 * ((x * y2) - (z * y3))
	t_2 = (b * y4) - (i * y5)
	tmp = 0
	if c <= -2.25e+119:
		tmp = c * (t_1 + (y4 * ((y * y3) - (t * y2))))
	elif c <= -3.8e-50:
		tmp = y1 * (z * ((a * y3) - (i * k)))
	elif c <= -4.5e-221:
		tmp = t * ((j * t_2) + (y2 * ((a * y5) - (c * y4))))
	elif c <= 8.5e-284:
		tmp = b * (k * ((z * y0) - (y * y4)))
	elif c <= 8.8e-243:
		tmp = j * (t * t_2)
	elif c <= 2.2e+126:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))))
	elif c <= 2.1e+205:
		tmp = t * (y4 * ((b * j) - (c * y2)))
	elif c <= 1.76e+239:
		tmp = c * t_1
	else:
		tmp = t * -(c * (y2 * 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(y0 * Float64(Float64(x * y2) - Float64(z * y3)))
	t_2 = Float64(Float64(b * y4) - Float64(i * y5))
	tmp = 0.0
	if (c <= -2.25e+119)
		tmp = Float64(c * Float64(t_1 + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (c <= -3.8e-50)
		tmp = Float64(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * k))));
	elseif (c <= -4.5e-221)
		tmp = Float64(t * Float64(Float64(j * t_2) + Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (c <= 8.5e-284)
		tmp = Float64(b * Float64(k * Float64(Float64(z * y0) - Float64(y * y4))));
	elseif (c <= 8.8e-243)
		tmp = Float64(j * Float64(t * t_2));
	elseif (c <= 2.2e+126)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4)))));
	elseif (c <= 2.1e+205)
		tmp = Float64(t * Float64(y4 * Float64(Float64(b * j) - Float64(c * y2))));
	elseif (c <= 1.76e+239)
		tmp = Float64(c * t_1);
	else
		tmp = Float64(t * Float64(-Float64(c * Float64(y2 * y4))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y0 * ((x * y2) - (z * y3));
	t_2 = (b * y4) - (i * y5);
	tmp = 0.0;
	if (c <= -2.25e+119)
		tmp = c * (t_1 + (y4 * ((y * y3) - (t * y2))));
	elseif (c <= -3.8e-50)
		tmp = y1 * (z * ((a * y3) - (i * k)));
	elseif (c <= -4.5e-221)
		tmp = t * ((j * t_2) + (y2 * ((a * y5) - (c * y4))));
	elseif (c <= 8.5e-284)
		tmp = b * (k * ((z * y0) - (y * y4)));
	elseif (c <= 8.8e-243)
		tmp = j * (t * t_2);
	elseif (c <= 2.2e+126)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))));
	elseif (c <= 2.1e+205)
		tmp = t * (y4 * ((b * j) - (c * y2)));
	elseif (c <= 1.76e+239)
		tmp = c * t_1;
	else
		tmp = t * -(c * (y2 * 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[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.25e+119], N[(c * N[(t$95$1 + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3.8e-50], N[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -4.5e-221], N[(t * N[(N[(j * t$95$2), $MachinePrecision] + N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 8.5e-284], N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 8.8e-243], N[(j * N[(t * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.2e+126], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.1e+205], N[(t * N[(y4 * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.76e+239], N[(c * t$95$1), $MachinePrecision], N[(t * (-N[(c * N[(y2 * y4), $MachinePrecision]), $MachinePrecision])), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if c < -2.2500000000000001e119

   1. Initial program 25.6%

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

   3. Simplified 25.6%

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

   4. Taylor expanded in c around inf 58.1%

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

   5. Taylor expanded in i around 0 65.1%

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

      1. *-commutative 65.1%

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

      2. *-commutative 65.1%

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

   7. Simplified 65.1%

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

   if -2.2500000000000001e119 < c < -3.7999999999999999e-50

   1. Initial program 37.7%

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

   3. Simplified 37.7%

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

   4. Taylor expanded in y1 around inf 38.5%

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

   5. Taylor expanded in z around inf 47.6%

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

   if -3.7999999999999999e-50 < c < -4.50000000000000026e-221

   1. Initial program 34.5%

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

   3. Simplified 34.5%

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

   4. Taylor expanded in t around inf 53.9%

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

   5. Taylor expanded in z around 0 60.2%

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

   if -4.50000000000000026e-221 < c < 8.4999999999999995e-284

   1. Initial program 31.9%

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

   3. Simplified 31.9%

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

   4. Taylor expanded in b around inf 45.1%

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

   5. Taylor expanded in k around -inf 45.1%

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

      1. associate-*r* 45.1%

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

      2. neg-mul-1 45.1%

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

   7. Simplified 45.1%

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

   if 8.4999999999999995e-284 < c < 8.7999999999999996e-243

   1. Initial program 25.3%

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

   3. Simplified 25.3%

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

   4. Taylor expanded in t around inf 58.5%

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

   5. Taylor expanded in j around inf 75.7%

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

   if 8.7999999999999996e-243 < c < 2.19999999999999999e126

   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%

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

   4. Taylor expanded in y3 around -inf 53.2%

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

   5. Taylor expanded in z around 0 47.1%

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

   if 2.19999999999999999e126 < c < 2.1e205

   1. Initial program 35.3%

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

   3. Simplified 35.3%

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

   4. Taylor expanded in t around inf 47.5%

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

   5. Taylor expanded in y4 around inf 65.5%

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

   if 2.1e205 < c < 1.76e239

   1. Initial program 22.2%

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

   3. Simplified 22.2%

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

   4. Taylor expanded in c around inf 66.7%

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

   5. Taylor expanded in y0 around inf 77.8%

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

   if 1.76e239 < c

   1. Initial program 40.0%

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

   3. Simplified 40.0%

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

   4. Taylor expanded in t around inf 60.0%

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

   5. Taylor expanded in z around 0 60.5%

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

   6. Taylor expanded in c around inf 90.0%

      \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(y2 \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 90.0%

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

   8. Simplified 90.0%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.25 \cdot 10^{+119}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -3.8 \cdot 10^{-50}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;c \leq -4.5 \cdot 10^{-221}:\\ \;\;\;\;t \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{-284}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq 8.8 \cdot 10^{-243}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{+126}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{+205}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq 1.76 \cdot 10^{+239}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-c \cdot \left(y2 \cdot y4\right)\right)\\ \end{array} \]

Alternative 17: 34.1% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot y4 - i \cdot y5\\ \mathbf{if}\;c \leq -6.4 \cdot 10^{+94}:\\ \;\;\;\;c \cdot \left(\left(x \cdot \left(y0 \cdot y2\right) - y0 \cdot \left(z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -1.4 \cdot 10^{-50}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;c \leq -1.7 \cdot 10^{-233}:\\ \;\;\;\;t \cdot \left(j \cdot t_1 + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-284}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq 1.4 \cdot 10^{-241}:\\ \;\;\;\;j \cdot \left(t \cdot t_1\right)\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{+125}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{+205}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq 1.75 \cdot 10^{+238}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-c \cdot \left(y2 \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* b y4) (* i y5))))
   (if (<= c -6.4e+94)
     (* c (+ (- (* x (* y0 y2)) (* y0 (* z y3))) (* y4 (- (* y y3) (* t y2)))))
     (if (<= c -1.4e-50)
       (* y1 (* z (- (* a y3) (* i k))))
       (if (<= c -1.7e-233)
         (* t (+ (* j t_1) (* y2 (- (* a y5) (* c y4)))))
         (if (<= c 2.9e-284)
           (* b (* k (- (* z y0) (* y y4))))
           (if (<= c 1.4e-241)
             (* j (* t t_1))
             (if (<= c 1.8e+125)
               (*
                y3
                (+ (* y (- (* c y4) (* a y5))) (* j (- (* y0 y5) (* y1 y4)))))
               (if (<= c 2.5e+205)
                 (* t (* y4 (- (* b j) (* c y2))))
                 (if (<= c 1.75e+238)
                   (* c (* y0 (- (* x y2) (* z y3))))
                   (* t (- (* c (* y2 y4))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (b * y4) - (i * y5);
	double tmp;
	if (c <= -6.4e+94) {
		tmp = c * (((x * (y0 * y2)) - (y0 * (z * y3))) + (y4 * ((y * y3) - (t * y2))));
	} else if (c <= -1.4e-50) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (c <= -1.7e-233) {
		tmp = t * ((j * t_1) + (y2 * ((a * y5) - (c * y4))));
	} else if (c <= 2.9e-284) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (c <= 1.4e-241) {
		tmp = j * (t * t_1);
	} else if (c <= 1.8e+125) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))));
	} else if (c <= 2.5e+205) {
		tmp = t * (y4 * ((b * j) - (c * y2)));
	} else if (c <= 1.75e+238) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else {
		tmp = t * -(c * (y2 * y4));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * y4) - (i * y5)
    if (c <= (-6.4d+94)) then
        tmp = c * (((x * (y0 * y2)) - (y0 * (z * y3))) + (y4 * ((y * y3) - (t * y2))))
    else if (c <= (-1.4d-50)) then
        tmp = y1 * (z * ((a * y3) - (i * k)))
    else if (c <= (-1.7d-233)) then
        tmp = t * ((j * t_1) + (y2 * ((a * y5) - (c * y4))))
    else if (c <= 2.9d-284) then
        tmp = b * (k * ((z * y0) - (y * y4)))
    else if (c <= 1.4d-241) then
        tmp = j * (t * t_1)
    else if (c <= 1.8d+125) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))))
    else if (c <= 2.5d+205) then
        tmp = t * (y4 * ((b * j) - (c * y2)))
    else if (c <= 1.75d+238) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else
        tmp = t * -(c * (y2 * y4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (b * y4) - (i * y5);
	double tmp;
	if (c <= -6.4e+94) {
		tmp = c * (((x * (y0 * y2)) - (y0 * (z * y3))) + (y4 * ((y * y3) - (t * y2))));
	} else if (c <= -1.4e-50) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (c <= -1.7e-233) {
		tmp = t * ((j * t_1) + (y2 * ((a * y5) - (c * y4))));
	} else if (c <= 2.9e-284) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (c <= 1.4e-241) {
		tmp = j * (t * t_1);
	} else if (c <= 1.8e+125) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))));
	} else if (c <= 2.5e+205) {
		tmp = t * (y4 * ((b * j) - (c * y2)));
	} else if (c <= 1.75e+238) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else {
		tmp = t * -(c * (y2 * y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (b * y4) - (i * y5)
	tmp = 0
	if c <= -6.4e+94:
		tmp = c * (((x * (y0 * y2)) - (y0 * (z * y3))) + (y4 * ((y * y3) - (t * y2))))
	elif c <= -1.4e-50:
		tmp = y1 * (z * ((a * y3) - (i * k)))
	elif c <= -1.7e-233:
		tmp = t * ((j * t_1) + (y2 * ((a * y5) - (c * y4))))
	elif c <= 2.9e-284:
		tmp = b * (k * ((z * y0) - (y * y4)))
	elif c <= 1.4e-241:
		tmp = j * (t * t_1)
	elif c <= 1.8e+125:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))))
	elif c <= 2.5e+205:
		tmp = t * (y4 * ((b * j) - (c * y2)))
	elif c <= 1.75e+238:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	else:
		tmp = t * -(c * (y2 * y4))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(b * y4) - Float64(i * y5))
	tmp = 0.0
	if (c <= -6.4e+94)
		tmp = Float64(c * Float64(Float64(Float64(x * Float64(y0 * y2)) - Float64(y0 * Float64(z * y3))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (c <= -1.4e-50)
		tmp = Float64(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * k))));
	elseif (c <= -1.7e-233)
		tmp = Float64(t * Float64(Float64(j * t_1) + Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (c <= 2.9e-284)
		tmp = Float64(b * Float64(k * Float64(Float64(z * y0) - Float64(y * y4))));
	elseif (c <= 1.4e-241)
		tmp = Float64(j * Float64(t * t_1));
	elseif (c <= 1.8e+125)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4)))));
	elseif (c <= 2.5e+205)
		tmp = Float64(t * Float64(y4 * Float64(Float64(b * j) - Float64(c * y2))));
	elseif (c <= 1.75e+238)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	else
		tmp = Float64(t * Float64(-Float64(c * Float64(y2 * y4))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (b * y4) - (i * y5);
	tmp = 0.0;
	if (c <= -6.4e+94)
		tmp = c * (((x * (y0 * y2)) - (y0 * (z * y3))) + (y4 * ((y * y3) - (t * y2))));
	elseif (c <= -1.4e-50)
		tmp = y1 * (z * ((a * y3) - (i * k)));
	elseif (c <= -1.7e-233)
		tmp = t * ((j * t_1) + (y2 * ((a * y5) - (c * y4))));
	elseif (c <= 2.9e-284)
		tmp = b * (k * ((z * y0) - (y * y4)));
	elseif (c <= 1.4e-241)
		tmp = j * (t * t_1);
	elseif (c <= 1.8e+125)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))));
	elseif (c <= 2.5e+205)
		tmp = t * (y4 * ((b * j) - (c * y2)));
	elseif (c <= 1.75e+238)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	else
		tmp = t * -(c * (y2 * y4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -6.4e+94], N[(c * N[(N[(N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision] - N[(y0 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.4e-50], N[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.7e-233], N[(t * N[(N[(j * t$95$1), $MachinePrecision] + N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.9e-284], N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.4e-241], N[(j * N[(t * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.8e+125], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.5e+205], N[(t * N[(y4 * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.75e+238], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * (-N[(c * N[(y2 * y4), $MachinePrecision]), $MachinePrecision])), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if c < -6.40000000000000028e94

   1. Initial program 25.6%

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

   3. Simplified 25.6%

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

   4. Taylor expanded in c around inf 58.1%

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

   5. Taylor expanded in x around 0 60.5%

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

   6. Taylor expanded in i around 0 65.1%

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

   if -6.40000000000000028e94 < c < -1.3999999999999999e-50

   1. Initial program 37.7%

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

   3. Simplified 37.7%

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

   4. Taylor expanded in y1 around inf 38.5%

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

   5. Taylor expanded in z around inf 47.6%

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

   if -1.3999999999999999e-50 < c < -1.7000000000000001e-233

   1. Initial program 34.5%

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

   3. Simplified 34.5%

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

   4. Taylor expanded in t around inf 53.9%

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

   5. Taylor expanded in z around 0 60.2%

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

   if -1.7000000000000001e-233 < c < 2.9000000000000001e-284

   1. Initial program 31.9%

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

   3. Simplified 31.9%

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

   4. Taylor expanded in b around inf 45.1%

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

   5. Taylor expanded in k around -inf 45.1%

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

      1. associate-*r* 45.1%

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

      2. neg-mul-1 45.1%

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

   7. Simplified 45.1%

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

   if 2.9000000000000001e-284 < c < 1.4e-241

   1. Initial program 25.3%

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

   3. Simplified 25.3%

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

   4. Taylor expanded in t around inf 58.5%

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

   5. Taylor expanded in j around inf 75.7%

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

   if 1.4e-241 < c < 1.8000000000000002e125

   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%

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

   4. Taylor expanded in y3 around -inf 53.2%

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

   5. Taylor expanded in z around 0 47.1%

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

   if 1.8000000000000002e125 < c < 2.5000000000000001e205

   1. Initial program 35.3%

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

   3. Simplified 35.3%

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

   4. Taylor expanded in t around inf 47.5%

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

   5. Taylor expanded in y4 around inf 65.5%

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

   if 2.5000000000000001e205 < c < 1.75000000000000001e238

   1. Initial program 22.2%

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

   3. Simplified 22.2%

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

   4. Taylor expanded in c around inf 66.7%

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

   5. Taylor expanded in y0 around inf 77.8%

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

   if 1.75000000000000001e238 < c

   1. Initial program 40.0%

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

   3. Simplified 40.0%

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

   4. Taylor expanded in t around inf 60.0%

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

   5. Taylor expanded in z around 0 60.5%

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

   6. Taylor expanded in c around inf 90.0%

      \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(y2 \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 90.0%

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

   8. Simplified 90.0%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.4 \cdot 10^{+94}:\\ \;\;\;\;c \cdot \left(\left(x \cdot \left(y0 \cdot y2\right) - y0 \cdot \left(z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -1.4 \cdot 10^{-50}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;c \leq -1.7 \cdot 10^{-233}:\\ \;\;\;\;t \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-284}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq 1.4 \cdot 10^{-241}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{+125}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{+205}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq 1.75 \cdot 10^{+238}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-c \cdot \left(y2 \cdot y4\right)\right)\\ \end{array} \]

Alternative 18: 31.5% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ t_2 := z \cdot i - y2 \cdot y4\\ \mathbf{if}\;y4 \leq -6.2 \cdot 10^{+230}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y4 \leq -4.75 \cdot 10^{+92}:\\ \;\;\;\;c \cdot \left(t \cdot t_2\right)\\ \mathbf{elif}\;y4 \leq -2.75 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y4 \leq -132000000000:\\ \;\;\;\;t \cdot \left(c \cdot t_2\right)\\ \mathbf{elif}\;y4 \leq -2.25 \cdot 10^{-29}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;y4 \leq -9 \cdot 10^{-85}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i\right)\right)\\ \mathbf{elif}\;y4 \leq -5 \cdot 10^{-293}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y4 \leq 4.1 \cdot 10^{+120}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y4 \leq 5.4 \cdot 10^{+155}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* y4 (- (* t j) (* y k))))) (t_2 (- (* z i) (* y2 y4))))
   (if (<= y4 -6.2e+230)
     t_1
     (if (<= y4 -4.75e+92)
       (* c (* t t_2))
       (if (<= y4 -2.75e+48)
         t_1
         (if (<= y4 -132000000000.0)
           (* t (* c t_2))
           (if (<= y4 -2.25e-29)
             (* y1 (* z (- (* a y3) (* i k))))
             (if (<= y4 -9e-85)
               (* c (* z (* t i)))
               (if (<= y4 -5e-293)
                 (* b (* y0 (- (* z k) (* x j))))
                 (if (<= y4 4.1e+120)
                   (* c (* y0 (- (* x y2) (* z y3))))
                   (if (<= y4 5.4e+155)
                     (* t (* y4 (- (* b j) (* c y2))))
                     (* y1 (* y4 (- (* k y2) (* j 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 t_1 = b * (y4 * ((t * j) - (y * k)));
	double t_2 = (z * i) - (y2 * y4);
	double tmp;
	if (y4 <= -6.2e+230) {
		tmp = t_1;
	} else if (y4 <= -4.75e+92) {
		tmp = c * (t * t_2);
	} else if (y4 <= -2.75e+48) {
		tmp = t_1;
	} else if (y4 <= -132000000000.0) {
		tmp = t * (c * t_2);
	} else if (y4 <= -2.25e-29) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (y4 <= -9e-85) {
		tmp = c * (z * (t * i));
	} else if (y4 <= -5e-293) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y4 <= 4.1e+120) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (y4 <= 5.4e+155) {
		tmp = t * (y4 * ((b * j) - (c * y2)));
	} else {
		tmp = y1 * (y4 * ((k * y2) - (j * 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (y4 * ((t * j) - (y * k)))
    t_2 = (z * i) - (y2 * y4)
    if (y4 <= (-6.2d+230)) then
        tmp = t_1
    else if (y4 <= (-4.75d+92)) then
        tmp = c * (t * t_2)
    else if (y4 <= (-2.75d+48)) then
        tmp = t_1
    else if (y4 <= (-132000000000.0d0)) then
        tmp = t * (c * t_2)
    else if (y4 <= (-2.25d-29)) then
        tmp = y1 * (z * ((a * y3) - (i * k)))
    else if (y4 <= (-9d-85)) then
        tmp = c * (z * (t * i))
    else if (y4 <= (-5d-293)) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (y4 <= 4.1d+120) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else if (y4 <= 5.4d+155) then
        tmp = t * (y4 * ((b * j) - (c * y2)))
    else
        tmp = y1 * (y4 * ((k * y2) - (j * 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 t_1 = b * (y4 * ((t * j) - (y * k)));
	double t_2 = (z * i) - (y2 * y4);
	double tmp;
	if (y4 <= -6.2e+230) {
		tmp = t_1;
	} else if (y4 <= -4.75e+92) {
		tmp = c * (t * t_2);
	} else if (y4 <= -2.75e+48) {
		tmp = t_1;
	} else if (y4 <= -132000000000.0) {
		tmp = t * (c * t_2);
	} else if (y4 <= -2.25e-29) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (y4 <= -9e-85) {
		tmp = c * (z * (t * i));
	} else if (y4 <= -5e-293) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y4 <= 4.1e+120) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (y4 <= 5.4e+155) {
		tmp = t * (y4 * ((b * j) - (c * y2)));
	} else {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (y4 * ((t * j) - (y * k)))
	t_2 = (z * i) - (y2 * y4)
	tmp = 0
	if y4 <= -6.2e+230:
		tmp = t_1
	elif y4 <= -4.75e+92:
		tmp = c * (t * t_2)
	elif y4 <= -2.75e+48:
		tmp = t_1
	elif y4 <= -132000000000.0:
		tmp = t * (c * t_2)
	elif y4 <= -2.25e-29:
		tmp = y1 * (z * ((a * y3) - (i * k)))
	elif y4 <= -9e-85:
		tmp = c * (z * (t * i))
	elif y4 <= -5e-293:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif y4 <= 4.1e+120:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	elif y4 <= 5.4e+155:
		tmp = t * (y4 * ((b * j) - (c * y2)))
	else:
		tmp = y1 * (y4 * ((k * y2) - (j * y3)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))))
	t_2 = Float64(Float64(z * i) - Float64(y2 * y4))
	tmp = 0.0
	if (y4 <= -6.2e+230)
		tmp = t_1;
	elseif (y4 <= -4.75e+92)
		tmp = Float64(c * Float64(t * t_2));
	elseif (y4 <= -2.75e+48)
		tmp = t_1;
	elseif (y4 <= -132000000000.0)
		tmp = Float64(t * Float64(c * t_2));
	elseif (y4 <= -2.25e-29)
		tmp = Float64(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * k))));
	elseif (y4 <= -9e-85)
		tmp = Float64(c * Float64(z * Float64(t * i)));
	elseif (y4 <= -5e-293)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (y4 <= 4.1e+120)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (y4 <= 5.4e+155)
		tmp = Float64(t * Float64(y4 * Float64(Float64(b * j) - Float64(c * y2))));
	else
		tmp = Float64(y1 * Float64(y4 * Float64(Float64(k * y2) - Float64(j * 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)
	t_1 = b * (y4 * ((t * j) - (y * k)));
	t_2 = (z * i) - (y2 * y4);
	tmp = 0.0;
	if (y4 <= -6.2e+230)
		tmp = t_1;
	elseif (y4 <= -4.75e+92)
		tmp = c * (t * t_2);
	elseif (y4 <= -2.75e+48)
		tmp = t_1;
	elseif (y4 <= -132000000000.0)
		tmp = t * (c * t_2);
	elseif (y4 <= -2.25e-29)
		tmp = y1 * (z * ((a * y3) - (i * k)));
	elseif (y4 <= -9e-85)
		tmp = c * (z * (t * i));
	elseif (y4 <= -5e-293)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (y4 <= 4.1e+120)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	elseif (y4 <= 5.4e+155)
		tmp = t * (y4 * ((b * j) - (c * y2)));
	else
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -6.2e+230], t$95$1, If[LessEqual[y4, -4.75e+92], N[(c * N[(t * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -2.75e+48], t$95$1, If[LessEqual[y4, -132000000000.0], N[(t * N[(c * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -2.25e-29], N[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -9e-85], N[(c * N[(z * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -5e-293], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 4.1e+120], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 5.4e+155], N[(t * N[(y4 * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y4 < -6.19999999999999963e230 or -4.7499999999999998e92 < y4 < -2.7500000000000001e48

   1. Initial program 20.7%

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

   3. Simplified 20.7%

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

   4. Taylor expanded in b around inf 34.7%

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

   5. Taylor expanded in y4 around inf 72.8%

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

   if -6.19999999999999963e230 < y4 < -4.7499999999999998e92

   1. Initial program 34.6%

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

   3. Simplified 34.6%

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

   4. Taylor expanded in t around inf 31.1%

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

   5. Taylor expanded in c around inf 62.1%

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

   if -2.7500000000000001e48 < y4 < -1.32e11

   1. Initial program 41.4%

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

   3. Simplified 41.4%

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

   4. Taylor expanded in t around inf 58.9%

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

   5. Taylor expanded in c around inf 65.3%

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

   if -1.32e11 < y4 < -2.2499999999999999e-29

   1. Initial program 24.8%

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

   3. Simplified 24.8%

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

   4. Taylor expanded in y1 around inf 50.6%

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

   5. Taylor expanded in z around inf 58.9%

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

   if -2.2499999999999999e-29 < y4 < -9.00000000000000008e-85

   1. Initial program 73.2%

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

   3. Simplified 73.2%

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

   4. Taylor expanded in c around inf 82.0%

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

   5. Taylor expanded in z around inf 55.5%

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

   6. Taylor expanded in y0 around 0 56.0%

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

   if -9.00000000000000008e-85 < y4 < -5.0000000000000003e-293

   1. Initial program 37.5%

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

   3. Simplified 37.5%

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

   4. Taylor expanded in b around inf 45.6%

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

   5. Taylor expanded in y0 around inf 46.5%

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

   if -5.0000000000000003e-293 < y4 < 4.1e120

   1. Initial program 37.2%

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

   3. Simplified 37.2%

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

   4. Taylor expanded in c around inf 35.8%

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

   5. Taylor expanded in y0 around inf 36.0%

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

   if 4.1e120 < y4 < 5.39999999999999987e155

   1. Initial program 22.2%

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

   3. Simplified 22.2%

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

   4. Taylor expanded in t around inf 78.5%

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

   5. Taylor expanded in y4 around inf 68.5%

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

   if 5.39999999999999987e155 < y4

   1. Initial program 25.2%

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

   3. Simplified 25.2%

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

   4. Taylor expanded in y1 around inf 45.1%

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

   5. Taylor expanded in y4 around inf 59.0%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -6.2 \cdot 10^{+230}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y4 \leq -4.75 \cdot 10^{+92}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -2.75 \cdot 10^{+48}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y4 \leq -132000000000:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -2.25 \cdot 10^{-29}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;y4 \leq -9 \cdot 10^{-85}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i\right)\right)\\ \mathbf{elif}\;y4 \leq -5 \cdot 10^{-293}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y4 \leq 4.1 \cdot 10^{+120}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y4 \leq 5.4 \cdot 10^{+155}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \end{array} \]

Alternative 19: 28.8% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ t_2 := c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{if}\;y1 \leq -1.9 \cdot 10^{-272}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq 1.15 \cdot 10^{-221}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y1 \leq 5 \cdot 10^{-71}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y1 \leq 1.45 \cdot 10^{-49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y1 \leq 3.5 \cdot 10^{+54}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 3.2 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y1 \leq 3.8 \cdot 10^{+160}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y1 \leq 3.6 \cdot 10^{+161}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* x (- (* y a) (* j y0)))))
        (t_2 (* c (* y0 (- (* x y2) (* z y3))))))
   (if (<= y1 -1.9e-272)
     (* j (* t (- (* b y4) (* i y5))))
     (if (<= y1 1.15e-221)
       t_1
       (if (<= y1 5e-71)
         t_2
         (if (<= y1 1.45e-49)
           t_1
           (if (<= y1 3.5e+54)
             (* c (* y2 (- (* x y0) (* t y4))))
             (if (<= y1 3.2e+74)
               t_1
               (if (<= y1 3.8e+160)
                 t_2
                 (if (<= y1 3.6e+161)
                   (* c (* t (- (* z i) (* y2 y4))))
                   (* i (* y1 (- (* x j) (* z k))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (x * ((y * a) - (j * y0)));
	double t_2 = c * (y0 * ((x * y2) - (z * y3)));
	double tmp;
	if (y1 <= -1.9e-272) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (y1 <= 1.15e-221) {
		tmp = t_1;
	} else if (y1 <= 5e-71) {
		tmp = t_2;
	} else if (y1 <= 1.45e-49) {
		tmp = t_1;
	} else if (y1 <= 3.5e+54) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (y1 <= 3.2e+74) {
		tmp = t_1;
	} else if (y1 <= 3.8e+160) {
		tmp = t_2;
	} else if (y1 <= 3.6e+161) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else {
		tmp = i * (y1 * ((x * j) - (z * k)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (x * ((y * a) - (j * y0)))
    t_2 = c * (y0 * ((x * y2) - (z * y3)))
    if (y1 <= (-1.9d-272)) then
        tmp = j * (t * ((b * y4) - (i * y5)))
    else if (y1 <= 1.15d-221) then
        tmp = t_1
    else if (y1 <= 5d-71) then
        tmp = t_2
    else if (y1 <= 1.45d-49) then
        tmp = t_1
    else if (y1 <= 3.5d+54) then
        tmp = c * (y2 * ((x * y0) - (t * y4)))
    else if (y1 <= 3.2d+74) then
        tmp = t_1
    else if (y1 <= 3.8d+160) then
        tmp = t_2
    else if (y1 <= 3.6d+161) then
        tmp = c * (t * ((z * i) - (y2 * y4)))
    else
        tmp = i * (y1 * ((x * j) - (z * k)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (x * ((y * a) - (j * y0)));
	double t_2 = c * (y0 * ((x * y2) - (z * y3)));
	double tmp;
	if (y1 <= -1.9e-272) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (y1 <= 1.15e-221) {
		tmp = t_1;
	} else if (y1 <= 5e-71) {
		tmp = t_2;
	} else if (y1 <= 1.45e-49) {
		tmp = t_1;
	} else if (y1 <= 3.5e+54) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (y1 <= 3.2e+74) {
		tmp = t_1;
	} else if (y1 <= 3.8e+160) {
		tmp = t_2;
	} else if (y1 <= 3.6e+161) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else {
		tmp = i * (y1 * ((x * j) - (z * k)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (x * ((y * a) - (j * y0)))
	t_2 = c * (y0 * ((x * y2) - (z * y3)))
	tmp = 0
	if y1 <= -1.9e-272:
		tmp = j * (t * ((b * y4) - (i * y5)))
	elif y1 <= 1.15e-221:
		tmp = t_1
	elif y1 <= 5e-71:
		tmp = t_2
	elif y1 <= 1.45e-49:
		tmp = t_1
	elif y1 <= 3.5e+54:
		tmp = c * (y2 * ((x * y0) - (t * y4)))
	elif y1 <= 3.2e+74:
		tmp = t_1
	elif y1 <= 3.8e+160:
		tmp = t_2
	elif y1 <= 3.6e+161:
		tmp = c * (t * ((z * i) - (y2 * y4)))
	else:
		tmp = i * (y1 * ((x * j) - (z * k)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))))
	t_2 = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))))
	tmp = 0.0
	if (y1 <= -1.9e-272)
		tmp = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))));
	elseif (y1 <= 1.15e-221)
		tmp = t_1;
	elseif (y1 <= 5e-71)
		tmp = t_2;
	elseif (y1 <= 1.45e-49)
		tmp = t_1;
	elseif (y1 <= 3.5e+54)
		tmp = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))));
	elseif (y1 <= 3.2e+74)
		tmp = t_1;
	elseif (y1 <= 3.8e+160)
		tmp = t_2;
	elseif (y1 <= 3.6e+161)
		tmp = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))));
	else
		tmp = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (x * ((y * a) - (j * y0)));
	t_2 = c * (y0 * ((x * y2) - (z * y3)));
	tmp = 0.0;
	if (y1 <= -1.9e-272)
		tmp = j * (t * ((b * y4) - (i * y5)));
	elseif (y1 <= 1.15e-221)
		tmp = t_1;
	elseif (y1 <= 5e-71)
		tmp = t_2;
	elseif (y1 <= 1.45e-49)
		tmp = t_1;
	elseif (y1 <= 3.5e+54)
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	elseif (y1 <= 3.2e+74)
		tmp = t_1;
	elseif (y1 <= 3.8e+160)
		tmp = t_2;
	elseif (y1 <= 3.6e+161)
		tmp = c * (t * ((z * i) - (y2 * y4)));
	else
		tmp = i * (y1 * ((x * j) - (z * k)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $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[y1, -1.9e-272], N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.15e-221], t$95$1, If[LessEqual[y1, 5e-71], t$95$2, If[LessEqual[y1, 1.45e-49], t$95$1, If[LessEqual[y1, 3.5e+54], N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 3.2e+74], t$95$1, If[LessEqual[y1, 3.8e+160], t$95$2, If[LessEqual[y1, 3.6e+161], N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y1 < -1.89999999999999985e-272

   1. Initial program 32.7%

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

   3. Simplified 32.7%

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

   4. Taylor expanded in t around inf 36.5%

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

   5. Taylor expanded in j around inf 39.8%

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

   if -1.89999999999999985e-272 < y1 < 1.15e-221 or 4.99999999999999998e-71 < y1 < 1.45e-49 or 3.5000000000000001e54 < y1 < 3.19999999999999995e74

   1. Initial program 40.4%

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

   3. Simplified 40.4%

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

   4. Taylor expanded in b around inf 59.4%

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

   5. Taylor expanded in x around inf 67.1%

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

   if 1.15e-221 < y1 < 4.99999999999999998e-71 or 3.19999999999999995e74 < y1 < 3.80000000000000012e160

   1. Initial program 40.3%

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

   3. Simplified 40.3%

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

   4. Taylor expanded in c around inf 52.0%

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

   5. Taylor expanded in y0 around inf 49.4%

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

   if 1.45e-49 < y1 < 3.5000000000000001e54

   1. Initial program 30.6%

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

   3. Simplified 30.6%

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

   4. Taylor expanded in c around inf 57.3%

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

   5. Taylor expanded in y2 around inf 57.5%

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

      1. *-commutative 57.5%

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

      2. *-commutative 57.5%

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

   7. Simplified 57.5%

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

   if 3.80000000000000012e160 < y1 < 3.59999999999999984e161

   1. Initial program 50.0%

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

   3. Simplified 50.0%

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

   4. Taylor expanded in t around inf 50.0%

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

   5. Taylor expanded in c around inf 100.0%

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

   if 3.59999999999999984e161 < y1

   1. Initial program 13.8%

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

   3. Simplified 13.8%

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

   4. Taylor expanded in y1 around inf 48.8%

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

   5. Taylor expanded in i around inf 61.5%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -1.9 \cdot 10^{-272}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq 1.15 \cdot 10^{-221}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 5 \cdot 10^{-71}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq 1.45 \cdot 10^{-49}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 3.5 \cdot 10^{+54}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 3.2 \cdot 10^{+74}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 3.8 \cdot 10^{+160}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq 3.6 \cdot 10^{+161}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \end{array} \]

Alternative 20: 28.9% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ t_2 := c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{if}\;y1 \leq -5.5 \cdot 10^{-275}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq 5.5 \cdot 10^{-216}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y1 \leq 4.2 \cdot 10^{-71}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y1 \leq 2.9 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y1 \leq 3.8 \cdot 10^{+54}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 1.15 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y1 \leq 3 \cdot 10^{+151}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y1 \leq 3.4 \cdot 10^{+161}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* x (- (* y a) (* j y0)))))
        (t_2 (* c (* y0 (- (* x y2) (* z y3))))))
   (if (<= y1 -5.5e-275)
     (* j (* t (- (* b y4) (* i y5))))
     (if (<= y1 5.5e-216)
       t_1
       (if (<= y1 4.2e-71)
         t_2
         (if (<= y1 2.9e-47)
           t_1
           (if (<= y1 3.8e+54)
             (* c (* y2 (- (* x y0) (* t y4))))
             (if (<= y1 1.15e+79)
               t_1
               (if (<= y1 3e+151)
                 t_2
                 (if (<= y1 3.4e+161)
                   (* k (* y1 (- (* y2 y4) (* z i))))
                   (* i (* y1 (- (* x j) (* z k))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (x * ((y * a) - (j * y0)));
	double t_2 = c * (y0 * ((x * y2) - (z * y3)));
	double tmp;
	if (y1 <= -5.5e-275) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (y1 <= 5.5e-216) {
		tmp = t_1;
	} else if (y1 <= 4.2e-71) {
		tmp = t_2;
	} else if (y1 <= 2.9e-47) {
		tmp = t_1;
	} else if (y1 <= 3.8e+54) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (y1 <= 1.15e+79) {
		tmp = t_1;
	} else if (y1 <= 3e+151) {
		tmp = t_2;
	} else if (y1 <= 3.4e+161) {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	} else {
		tmp = i * (y1 * ((x * j) - (z * k)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (x * ((y * a) - (j * y0)))
    t_2 = c * (y0 * ((x * y2) - (z * y3)))
    if (y1 <= (-5.5d-275)) then
        tmp = j * (t * ((b * y4) - (i * y5)))
    else if (y1 <= 5.5d-216) then
        tmp = t_1
    else if (y1 <= 4.2d-71) then
        tmp = t_2
    else if (y1 <= 2.9d-47) then
        tmp = t_1
    else if (y1 <= 3.8d+54) then
        tmp = c * (y2 * ((x * y0) - (t * y4)))
    else if (y1 <= 1.15d+79) then
        tmp = t_1
    else if (y1 <= 3d+151) then
        tmp = t_2
    else if (y1 <= 3.4d+161) then
        tmp = k * (y1 * ((y2 * y4) - (z * i)))
    else
        tmp = i * (y1 * ((x * j) - (z * k)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (x * ((y * a) - (j * y0)));
	double t_2 = c * (y0 * ((x * y2) - (z * y3)));
	double tmp;
	if (y1 <= -5.5e-275) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (y1 <= 5.5e-216) {
		tmp = t_1;
	} else if (y1 <= 4.2e-71) {
		tmp = t_2;
	} else if (y1 <= 2.9e-47) {
		tmp = t_1;
	} else if (y1 <= 3.8e+54) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (y1 <= 1.15e+79) {
		tmp = t_1;
	} else if (y1 <= 3e+151) {
		tmp = t_2;
	} else if (y1 <= 3.4e+161) {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	} else {
		tmp = i * (y1 * ((x * j) - (z * k)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (x * ((y * a) - (j * y0)))
	t_2 = c * (y0 * ((x * y2) - (z * y3)))
	tmp = 0
	if y1 <= -5.5e-275:
		tmp = j * (t * ((b * y4) - (i * y5)))
	elif y1 <= 5.5e-216:
		tmp = t_1
	elif y1 <= 4.2e-71:
		tmp = t_2
	elif y1 <= 2.9e-47:
		tmp = t_1
	elif y1 <= 3.8e+54:
		tmp = c * (y2 * ((x * y0) - (t * y4)))
	elif y1 <= 1.15e+79:
		tmp = t_1
	elif y1 <= 3e+151:
		tmp = t_2
	elif y1 <= 3.4e+161:
		tmp = k * (y1 * ((y2 * y4) - (z * i)))
	else:
		tmp = i * (y1 * ((x * j) - (z * k)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))))
	t_2 = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))))
	tmp = 0.0
	if (y1 <= -5.5e-275)
		tmp = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))));
	elseif (y1 <= 5.5e-216)
		tmp = t_1;
	elseif (y1 <= 4.2e-71)
		tmp = t_2;
	elseif (y1 <= 2.9e-47)
		tmp = t_1;
	elseif (y1 <= 3.8e+54)
		tmp = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))));
	elseif (y1 <= 1.15e+79)
		tmp = t_1;
	elseif (y1 <= 3e+151)
		tmp = t_2;
	elseif (y1 <= 3.4e+161)
		tmp = Float64(k * Float64(y1 * Float64(Float64(y2 * y4) - Float64(z * i))));
	else
		tmp = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (x * ((y * a) - (j * y0)));
	t_2 = c * (y0 * ((x * y2) - (z * y3)));
	tmp = 0.0;
	if (y1 <= -5.5e-275)
		tmp = j * (t * ((b * y4) - (i * y5)));
	elseif (y1 <= 5.5e-216)
		tmp = t_1;
	elseif (y1 <= 4.2e-71)
		tmp = t_2;
	elseif (y1 <= 2.9e-47)
		tmp = t_1;
	elseif (y1 <= 3.8e+54)
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	elseif (y1 <= 1.15e+79)
		tmp = t_1;
	elseif (y1 <= 3e+151)
		tmp = t_2;
	elseif (y1 <= 3.4e+161)
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	else
		tmp = i * (y1 * ((x * j) - (z * k)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $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[y1, -5.5e-275], N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 5.5e-216], t$95$1, If[LessEqual[y1, 4.2e-71], t$95$2, If[LessEqual[y1, 2.9e-47], t$95$1, If[LessEqual[y1, 3.8e+54], N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.15e+79], t$95$1, If[LessEqual[y1, 3e+151], t$95$2, If[LessEqual[y1, 3.4e+161], N[(k * N[(y1 * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y1 < -5.49999999999999988e-275

   1. Initial program 32.7%

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

   3. Simplified 32.7%

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

   4. Taylor expanded in t around inf 36.5%

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

   5. Taylor expanded in j around inf 39.8%

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

   if -5.49999999999999988e-275 < y1 < 5.49999999999999991e-216 or 4.2000000000000002e-71 < y1 < 2.9e-47 or 3.8000000000000002e54 < y1 < 1.15e79

   1. Initial program 40.4%

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

   3. Simplified 40.4%

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

   4. Taylor expanded in b around inf 59.4%

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

   5. Taylor expanded in x around inf 67.1%

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

   if 5.49999999999999991e-216 < y1 < 4.2000000000000002e-71 or 1.15e79 < y1 < 2.9999999999999999e151

   1. Initial program 39.9%

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

   3. Simplified 39.9%

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

   4. Taylor expanded in c around inf 52.0%

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

   5. Taylor expanded in y0 around inf 49.3%

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

   if 2.9e-47 < y1 < 3.8000000000000002e54

   1. Initial program 30.6%

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

   3. Simplified 30.6%

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

   4. Taylor expanded in c around inf 57.3%

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

   5. Taylor expanded in y2 around inf 57.5%

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

      1. *-commutative 57.5%

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

      2. *-commutative 57.5%

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

   7. Simplified 57.5%

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

   if 2.9999999999999999e151 < y1 < 3.39999999999999993e161

   1. Initial program 50.0%

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

   3. Simplified 50.0%

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

   4. Taylor expanded in y1 around inf 51.1%

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

   5. Taylor expanded in k around inf 76.1%

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

   if 3.39999999999999993e161 < y1

   1. Initial program 13.8%

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

   3. Simplified 13.8%

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

   4. Taylor expanded in y1 around inf 48.8%

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

   5. Taylor expanded in i around inf 61.5%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -5.5 \cdot 10^{-275}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq 5.5 \cdot 10^{-216}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 4.2 \cdot 10^{-71}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq 2.9 \cdot 10^{-47}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 3.8 \cdot 10^{+54}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 1.15 \cdot 10^{+79}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 3 \cdot 10^{+151}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq 3.4 \cdot 10^{+161}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \end{array} \]

Alternative 21: 31.6% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ t_2 := z \cdot i - y2 \cdot y4\\ \mathbf{if}\;y4 \leq -1.38 \cdot 10^{+230}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y4 \leq -3.7 \cdot 10^{+91}:\\ \;\;\;\;c \cdot \left(t \cdot t_2\right)\\ \mathbf{elif}\;y4 \leq -5.2 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y4 \leq -4.5 \cdot 10^{-88}:\\ \;\;\;\;t \cdot \left(c \cdot t_2\right)\\ \mathbf{elif}\;y4 \leq -5.3 \cdot 10^{-294}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y4 \leq 5.4 \cdot 10^{+120}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y4 \leq 5.2 \cdot 10^{+155}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* y4 (- (* t j) (* y k))))) (t_2 (- (* z i) (* y2 y4))))
   (if (<= y4 -1.38e+230)
     t_1
     (if (<= y4 -3.7e+91)
       (* c (* t t_2))
       (if (<= y4 -5.2e+47)
         t_1
         (if (<= y4 -4.5e-88)
           (* t (* c t_2))
           (if (<= y4 -5.3e-294)
             (* b (* y0 (- (* z k) (* x j))))
             (if (<= y4 5.4e+120)
               (* c (* y0 (- (* x y2) (* z y3))))
               (if (<= y4 5.2e+155)
                 (* t (* y4 (- (* b j) (* c y2))))
                 (* y1 (* y4 (- (* k y2) (* j 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 t_1 = b * (y4 * ((t * j) - (y * k)));
	double t_2 = (z * i) - (y2 * y4);
	double tmp;
	if (y4 <= -1.38e+230) {
		tmp = t_1;
	} else if (y4 <= -3.7e+91) {
		tmp = c * (t * t_2);
	} else if (y4 <= -5.2e+47) {
		tmp = t_1;
	} else if (y4 <= -4.5e-88) {
		tmp = t * (c * t_2);
	} else if (y4 <= -5.3e-294) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y4 <= 5.4e+120) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (y4 <= 5.2e+155) {
		tmp = t * (y4 * ((b * j) - (c * y2)));
	} else {
		tmp = y1 * (y4 * ((k * y2) - (j * 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (y4 * ((t * j) - (y * k)))
    t_2 = (z * i) - (y2 * y4)
    if (y4 <= (-1.38d+230)) then
        tmp = t_1
    else if (y4 <= (-3.7d+91)) then
        tmp = c * (t * t_2)
    else if (y4 <= (-5.2d+47)) then
        tmp = t_1
    else if (y4 <= (-4.5d-88)) then
        tmp = t * (c * t_2)
    else if (y4 <= (-5.3d-294)) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (y4 <= 5.4d+120) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else if (y4 <= 5.2d+155) then
        tmp = t * (y4 * ((b * j) - (c * y2)))
    else
        tmp = y1 * (y4 * ((k * y2) - (j * 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 t_1 = b * (y4 * ((t * j) - (y * k)));
	double t_2 = (z * i) - (y2 * y4);
	double tmp;
	if (y4 <= -1.38e+230) {
		tmp = t_1;
	} else if (y4 <= -3.7e+91) {
		tmp = c * (t * t_2);
	} else if (y4 <= -5.2e+47) {
		tmp = t_1;
	} else if (y4 <= -4.5e-88) {
		tmp = t * (c * t_2);
	} else if (y4 <= -5.3e-294) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y4 <= 5.4e+120) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (y4 <= 5.2e+155) {
		tmp = t * (y4 * ((b * j) - (c * y2)));
	} else {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (y4 * ((t * j) - (y * k)))
	t_2 = (z * i) - (y2 * y4)
	tmp = 0
	if y4 <= -1.38e+230:
		tmp = t_1
	elif y4 <= -3.7e+91:
		tmp = c * (t * t_2)
	elif y4 <= -5.2e+47:
		tmp = t_1
	elif y4 <= -4.5e-88:
		tmp = t * (c * t_2)
	elif y4 <= -5.3e-294:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif y4 <= 5.4e+120:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	elif y4 <= 5.2e+155:
		tmp = t * (y4 * ((b * j) - (c * y2)))
	else:
		tmp = y1 * (y4 * ((k * y2) - (j * y3)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))))
	t_2 = Float64(Float64(z * i) - Float64(y2 * y4))
	tmp = 0.0
	if (y4 <= -1.38e+230)
		tmp = t_1;
	elseif (y4 <= -3.7e+91)
		tmp = Float64(c * Float64(t * t_2));
	elseif (y4 <= -5.2e+47)
		tmp = t_1;
	elseif (y4 <= -4.5e-88)
		tmp = Float64(t * Float64(c * t_2));
	elseif (y4 <= -5.3e-294)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (y4 <= 5.4e+120)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (y4 <= 5.2e+155)
		tmp = Float64(t * Float64(y4 * Float64(Float64(b * j) - Float64(c * y2))));
	else
		tmp = Float64(y1 * Float64(y4 * Float64(Float64(k * y2) - Float64(j * 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)
	t_1 = b * (y4 * ((t * j) - (y * k)));
	t_2 = (z * i) - (y2 * y4);
	tmp = 0.0;
	if (y4 <= -1.38e+230)
		tmp = t_1;
	elseif (y4 <= -3.7e+91)
		tmp = c * (t * t_2);
	elseif (y4 <= -5.2e+47)
		tmp = t_1;
	elseif (y4 <= -4.5e-88)
		tmp = t * (c * t_2);
	elseif (y4 <= -5.3e-294)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (y4 <= 5.4e+120)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	elseif (y4 <= 5.2e+155)
		tmp = t * (y4 * ((b * j) - (c * y2)));
	else
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -1.38e+230], t$95$1, If[LessEqual[y4, -3.7e+91], N[(c * N[(t * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -5.2e+47], t$95$1, If[LessEqual[y4, -4.5e-88], N[(t * N[(c * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -5.3e-294], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 5.4e+120], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 5.2e+155], N[(t * N[(y4 * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y4 < -1.3800000000000001e230 or -3.69999999999999984e91 < y4 < -5.20000000000000007e47

   1. Initial program 20.7%

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

   3. Simplified 20.7%

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

   4. Taylor expanded in b around inf 34.7%

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

   5. Taylor expanded in y4 around inf 72.8%

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

   if -1.3800000000000001e230 < y4 < -3.69999999999999984e91

   1. Initial program 34.6%

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

   3. Simplified 34.6%

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

   4. Taylor expanded in t around inf 31.1%

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

   5. Taylor expanded in c around inf 62.1%

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

   if -5.20000000000000007e47 < y4 < -4.49999999999999991e-88

   1. Initial program 45.9%

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

   3. Simplified 45.9%

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

   4. Taylor expanded in t around inf 46.7%

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

   5. Taylor expanded in c around inf 43.9%

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

   if -4.49999999999999991e-88 < y4 < -5.29999999999999969e-294

   1. Initial program 36.8%

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

   3. Simplified 36.8%

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

   4. Taylor expanded in b around inf 48.0%

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

   5. Taylor expanded in y0 around inf 48.8%

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

   if -5.29999999999999969e-294 < y4 < 5.3999999999999999e120

   1. Initial program 37.2%

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

   3. Simplified 37.2%

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

   4. Taylor expanded in c around inf 35.8%

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

   5. Taylor expanded in y0 around inf 36.0%

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

   if 5.3999999999999999e120 < y4 < 5.2000000000000004e155

   1. Initial program 22.2%

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

   3. Simplified 22.2%

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

   4. Taylor expanded in t around inf 78.5%

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

   5. Taylor expanded in y4 around inf 68.5%

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

   if 5.2000000000000004e155 < y4

   1. Initial program 25.2%

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

   3. Simplified 25.2%

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

   4. Taylor expanded in y1 around inf 45.1%

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

   5. Taylor expanded in y4 around inf 59.0%

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

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -1.38 \cdot 10^{+230}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y4 \leq -3.7 \cdot 10^{+91}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -5.2 \cdot 10^{+47}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y4 \leq -4.5 \cdot 10^{-88}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -5.3 \cdot 10^{-294}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y4 \leq 5.4 \cdot 10^{+120}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y4 \leq 5.2 \cdot 10^{+155}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \end{array} \]

Alternative 22: 30.6% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ t_2 := i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{if}\;j \leq -4 \cdot 10^{+232}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -6.4 \cdot 10^{+162}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq -4.4 \cdot 10^{+85}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -6.5 \cdot 10^{-201}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 1.2 \cdot 10^{-67}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 1.25 \cdot 10^{+241}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y0 (- (* x y2) (* z y3)))))
        (t_2 (* i (* y1 (- (* x j) (* z k))))))
   (if (<= j -4e+232)
     t_2
     (if (<= j -6.4e+162)
       (* b (* j (- (* t y4) (* x y0))))
       (if (<= j -4.4e+85)
         t_2
         (if (<= j -6.5e-201)
           t_1
           (if (<= j 1.2e-67)
             (* c (* t (- (* z i) (* y2 y4))))
             (if (<= j 1.25e+241) t_1 (* t (* y4 (* b j)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y0 * ((x * y2) - (z * y3)));
	double t_2 = i * (y1 * ((x * j) - (z * k)));
	double tmp;
	if (j <= -4e+232) {
		tmp = t_2;
	} else if (j <= -6.4e+162) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (j <= -4.4e+85) {
		tmp = t_2;
	} else if (j <= -6.5e-201) {
		tmp = t_1;
	} else if (j <= 1.2e-67) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (j <= 1.25e+241) {
		tmp = t_1;
	} else {
		tmp = t * (y4 * (b * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * (y0 * ((x * y2) - (z * y3)))
    t_2 = i * (y1 * ((x * j) - (z * k)))
    if (j <= (-4d+232)) then
        tmp = t_2
    else if (j <= (-6.4d+162)) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (j <= (-4.4d+85)) then
        tmp = t_2
    else if (j <= (-6.5d-201)) then
        tmp = t_1
    else if (j <= 1.2d-67) then
        tmp = c * (t * ((z * i) - (y2 * y4)))
    else if (j <= 1.25d+241) then
        tmp = t_1
    else
        tmp = t * (y4 * (b * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y0 * ((x * y2) - (z * y3)));
	double t_2 = i * (y1 * ((x * j) - (z * k)));
	double tmp;
	if (j <= -4e+232) {
		tmp = t_2;
	} else if (j <= -6.4e+162) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (j <= -4.4e+85) {
		tmp = t_2;
	} else if (j <= -6.5e-201) {
		tmp = t_1;
	} else if (j <= 1.2e-67) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (j <= 1.25e+241) {
		tmp = t_1;
	} else {
		tmp = t * (y4 * (b * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (y0 * ((x * y2) - (z * y3)))
	t_2 = i * (y1 * ((x * j) - (z * k)))
	tmp = 0
	if j <= -4e+232:
		tmp = t_2
	elif j <= -6.4e+162:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif j <= -4.4e+85:
		tmp = t_2
	elif j <= -6.5e-201:
		tmp = t_1
	elif j <= 1.2e-67:
		tmp = c * (t * ((z * i) - (y2 * y4)))
	elif j <= 1.25e+241:
		tmp = t_1
	else:
		tmp = t * (y4 * (b * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))))
	t_2 = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))))
	tmp = 0.0
	if (j <= -4e+232)
		tmp = t_2;
	elseif (j <= -6.4e+162)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (j <= -4.4e+85)
		tmp = t_2;
	elseif (j <= -6.5e-201)
		tmp = t_1;
	elseif (j <= 1.2e-67)
		tmp = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (j <= 1.25e+241)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(y4 * Float64(b * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (y0 * ((x * y2) - (z * y3)));
	t_2 = i * (y1 * ((x * j) - (z * k)));
	tmp = 0.0;
	if (j <= -4e+232)
		tmp = t_2;
	elseif (j <= -6.4e+162)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (j <= -4.4e+85)
		tmp = t_2;
	elseif (j <= -6.5e-201)
		tmp = t_1;
	elseif (j <= 1.2e-67)
		tmp = c * (t * ((z * i) - (y2 * y4)));
	elseif (j <= 1.25e+241)
		tmp = t_1;
	else
		tmp = t * (y4 * (b * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -4e+232], t$95$2, If[LessEqual[j, -6.4e+162], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -4.4e+85], t$95$2, If[LessEqual[j, -6.5e-201], t$95$1, If[LessEqual[j, 1.2e-67], N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.25e+241], t$95$1, N[(t * N[(y4 * N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -4.00000000000000023e232 or -6.4000000000000002e162 < j < -4.4000000000000003e85

   1. Initial program 9.5%

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

   3. Simplified 9.5%

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

   4. Taylor expanded in y1 around inf 38.3%

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

   5. Taylor expanded in i around inf 67.9%

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

   if -4.00000000000000023e232 < j < -6.4000000000000002e162

   1. Initial program 15.3%

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

   3. Simplified 15.3%

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

   4. Taylor expanded in b around inf 40.3%

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

   5. Taylor expanded in j around inf 55.4%

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

   if -4.4000000000000003e85 < j < -6.49999999999999974e-201 or 1.2e-67 < j < 1.25000000000000006e241

   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 33.4%

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

   4. Taylor expanded in c around inf 39.5%

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

   5. Taylor expanded in y0 around inf 41.5%

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

   if -6.49999999999999974e-201 < j < 1.2e-67

   1. Initial program 44.0%

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

   3. Simplified 44.0%

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

   4. Taylor expanded in t around inf 40.7%

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

   5. Taylor expanded in c around inf 39.3%

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

   if 1.25000000000000006e241 < j

   1. Initial program 47.1%

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

   3. Simplified 47.1%

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

   4. Taylor expanded in t around inf 59.4%

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

   5. Taylor expanded in j around inf 83.0%

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

   6. Taylor expanded in b around inf 71.5%

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

      1. *-commutative 71.5%

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

      2. associate-*r* 66.0%

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

      3. *-commutative 66.0%

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

      4. associate-*l* 71.6%

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

   8. Simplified 71.6%

      \[\leadsto t \cdot \color{blue}{\left(y4 \cdot \left(b \cdot j\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4 \cdot 10^{+232}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;j \leq -6.4 \cdot 10^{+162}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq -4.4 \cdot 10^{+85}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;j \leq -6.5 \cdot 10^{-201}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 1.2 \cdot 10^{-67}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 1.25 \cdot 10^{+241}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j\right)\right)\\ \end{array} \]

Alternative 23: 28.6% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ t_2 := c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{if}\;y1 \leq -1.15 \cdot 10^{-266}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq 2 \cdot 10^{-220}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y1 \leq 5.5 \cdot 10^{-71}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y1 \leq 1.85 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y1 \leq 1.8 \cdot 10^{+103}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 3.5 \cdot 10^{+161}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* x (- (* y a) (* j y0)))))
        (t_2 (* c (* y0 (- (* x y2) (* z y3))))))
   (if (<= y1 -1.15e-266)
     (* j (* t (- (* b y4) (* i y5))))
     (if (<= y1 2e-220)
       t_1
       (if (<= y1 5.5e-71)
         t_2
         (if (<= y1 1.85e-47)
           t_1
           (if (<= y1 1.8e+103)
             (* t (* c (- (* z i) (* y2 y4))))
             (if (<= y1 3.5e+161) t_2 (* i (* y1 (- (* x j) (* z k))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (x * ((y * a) - (j * y0)));
	double t_2 = c * (y0 * ((x * y2) - (z * y3)));
	double tmp;
	if (y1 <= -1.15e-266) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (y1 <= 2e-220) {
		tmp = t_1;
	} else if (y1 <= 5.5e-71) {
		tmp = t_2;
	} else if (y1 <= 1.85e-47) {
		tmp = t_1;
	} else if (y1 <= 1.8e+103) {
		tmp = t * (c * ((z * i) - (y2 * y4)));
	} else if (y1 <= 3.5e+161) {
		tmp = t_2;
	} else {
		tmp = i * (y1 * ((x * j) - (z * k)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (x * ((y * a) - (j * y0)))
    t_2 = c * (y0 * ((x * y2) - (z * y3)))
    if (y1 <= (-1.15d-266)) then
        tmp = j * (t * ((b * y4) - (i * y5)))
    else if (y1 <= 2d-220) then
        tmp = t_1
    else if (y1 <= 5.5d-71) then
        tmp = t_2
    else if (y1 <= 1.85d-47) then
        tmp = t_1
    else if (y1 <= 1.8d+103) then
        tmp = t * (c * ((z * i) - (y2 * y4)))
    else if (y1 <= 3.5d+161) then
        tmp = t_2
    else
        tmp = i * (y1 * ((x * j) - (z * k)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (x * ((y * a) - (j * y0)));
	double t_2 = c * (y0 * ((x * y2) - (z * y3)));
	double tmp;
	if (y1 <= -1.15e-266) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (y1 <= 2e-220) {
		tmp = t_1;
	} else if (y1 <= 5.5e-71) {
		tmp = t_2;
	} else if (y1 <= 1.85e-47) {
		tmp = t_1;
	} else if (y1 <= 1.8e+103) {
		tmp = t * (c * ((z * i) - (y2 * y4)));
	} else if (y1 <= 3.5e+161) {
		tmp = t_2;
	} else {
		tmp = i * (y1 * ((x * j) - (z * k)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (x * ((y * a) - (j * y0)))
	t_2 = c * (y0 * ((x * y2) - (z * y3)))
	tmp = 0
	if y1 <= -1.15e-266:
		tmp = j * (t * ((b * y4) - (i * y5)))
	elif y1 <= 2e-220:
		tmp = t_1
	elif y1 <= 5.5e-71:
		tmp = t_2
	elif y1 <= 1.85e-47:
		tmp = t_1
	elif y1 <= 1.8e+103:
		tmp = t * (c * ((z * i) - (y2 * y4)))
	elif y1 <= 3.5e+161:
		tmp = t_2
	else:
		tmp = i * (y1 * ((x * j) - (z * k)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))))
	t_2 = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))))
	tmp = 0.0
	if (y1 <= -1.15e-266)
		tmp = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))));
	elseif (y1 <= 2e-220)
		tmp = t_1;
	elseif (y1 <= 5.5e-71)
		tmp = t_2;
	elseif (y1 <= 1.85e-47)
		tmp = t_1;
	elseif (y1 <= 1.8e+103)
		tmp = Float64(t * Float64(c * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (y1 <= 3.5e+161)
		tmp = t_2;
	else
		tmp = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (x * ((y * a) - (j * y0)));
	t_2 = c * (y0 * ((x * y2) - (z * y3)));
	tmp = 0.0;
	if (y1 <= -1.15e-266)
		tmp = j * (t * ((b * y4) - (i * y5)));
	elseif (y1 <= 2e-220)
		tmp = t_1;
	elseif (y1 <= 5.5e-71)
		tmp = t_2;
	elseif (y1 <= 1.85e-47)
		tmp = t_1;
	elseif (y1 <= 1.8e+103)
		tmp = t * (c * ((z * i) - (y2 * y4)));
	elseif (y1 <= 3.5e+161)
		tmp = t_2;
	else
		tmp = i * (y1 * ((x * j) - (z * k)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $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[y1, -1.15e-266], N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 2e-220], t$95$1, If[LessEqual[y1, 5.5e-71], t$95$2, If[LessEqual[y1, 1.85e-47], t$95$1, If[LessEqual[y1, 1.8e+103], N[(t * N[(c * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 3.5e+161], t$95$2, N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y1 < -1.14999999999999998e-266

   1. Initial program 32.7%

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

   3. Simplified 32.7%

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

   4. Taylor expanded in t around inf 36.5%

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

   5. Taylor expanded in j around inf 39.8%

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

   if -1.14999999999999998e-266 < y1 < 1.99999999999999998e-220 or 5.4999999999999997e-71 < y1 < 1.85e-47

   1. Initial program 51.4%

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

   3. Simplified 51.4%

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

   4. Taylor expanded in b around inf 60.4%

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

   5. Taylor expanded in x around inf 66.8%

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

   if 1.99999999999999998e-220 < y1 < 5.4999999999999997e-71 or 1.80000000000000008e103 < y1 < 3.49999999999999988e161

   1. Initial program 36.8%

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

   3. Simplified 36.8%

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

   4. Taylor expanded in c around inf 51.3%

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

   5. Taylor expanded in y0 around inf 50.1%

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

   if 1.85e-47 < y1 < 1.80000000000000008e103

   1. Initial program 30.9%

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

   3. Simplified 30.9%

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

   4. Taylor expanded in t around inf 39.0%

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

   5. Taylor expanded in c around inf 52.1%

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

   if 3.49999999999999988e161 < y1

   1. Initial program 13.8%

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

   3. Simplified 13.8%

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

   4. Taylor expanded in y1 around inf 48.8%

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

   5. Taylor expanded in i around inf 61.5%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -1.15 \cdot 10^{-266}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq 2 \cdot 10^{-220}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 5.5 \cdot 10^{-71}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq 1.85 \cdot 10^{-47}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 1.8 \cdot 10^{+103}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 3.5 \cdot 10^{+161}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \end{array} \]

Alternative 24: 31.1% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{if}\;x \leq -1.6 \cdot 10^{-97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-258}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-149}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-33}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{+95}:\\ \;\;\;\;x \cdot \left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+157}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y0 (- (* x y2) (* z y3))))))
   (if (<= x -1.6e-97)
     t_1
     (if (<= x -7e-258)
       (* t (* y2 (- (* a y5) (* c y4))))
       (if (<= x 1.65e-149)
         (* b (* k (- (* z y0) (* y y4))))
         (if (<= x 2.4e-33)
           (* t (* c (- (* z i) (* y2 y4))))
           (if (<= x 2.05e+95)
             (* x (* y1 (- (* i j) (* a y2))))
             (if (<= x 6e+157) t_1 (* b (* x (- (* y a) (* j y0))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y0 * ((x * y2) - (z * y3)));
	double tmp;
	if (x <= -1.6e-97) {
		tmp = t_1;
	} else if (x <= -7e-258) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (x <= 1.65e-149) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (x <= 2.4e-33) {
		tmp = t * (c * ((z * i) - (y2 * y4)));
	} else if (x <= 2.05e+95) {
		tmp = x * (y1 * ((i * j) - (a * y2)));
	} else if (x <= 6e+157) {
		tmp = t_1;
	} else {
		tmp = b * (x * ((y * a) - (j * y0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (y0 * ((x * y2) - (z * y3)))
    if (x <= (-1.6d-97)) then
        tmp = t_1
    else if (x <= (-7d-258)) then
        tmp = t * (y2 * ((a * y5) - (c * y4)))
    else if (x <= 1.65d-149) then
        tmp = b * (k * ((z * y0) - (y * y4)))
    else if (x <= 2.4d-33) then
        tmp = t * (c * ((z * i) - (y2 * y4)))
    else if (x <= 2.05d+95) then
        tmp = x * (y1 * ((i * j) - (a * y2)))
    else if (x <= 6d+157) then
        tmp = t_1
    else
        tmp = b * (x * ((y * a) - (j * y0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y0 * ((x * y2) - (z * y3)));
	double tmp;
	if (x <= -1.6e-97) {
		tmp = t_1;
	} else if (x <= -7e-258) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (x <= 1.65e-149) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (x <= 2.4e-33) {
		tmp = t * (c * ((z * i) - (y2 * y4)));
	} else if (x <= 2.05e+95) {
		tmp = x * (y1 * ((i * j) - (a * y2)));
	} else if (x <= 6e+157) {
		tmp = t_1;
	} else {
		tmp = b * (x * ((y * a) - (j * y0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (y0 * ((x * y2) - (z * y3)))
	tmp = 0
	if x <= -1.6e-97:
		tmp = t_1
	elif x <= -7e-258:
		tmp = t * (y2 * ((a * y5) - (c * y4)))
	elif x <= 1.65e-149:
		tmp = b * (k * ((z * y0) - (y * y4)))
	elif x <= 2.4e-33:
		tmp = t * (c * ((z * i) - (y2 * y4)))
	elif x <= 2.05e+95:
		tmp = x * (y1 * ((i * j) - (a * y2)))
	elif x <= 6e+157:
		tmp = t_1
	else:
		tmp = b * (x * ((y * a) - (j * y0)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))))
	tmp = 0.0
	if (x <= -1.6e-97)
		tmp = t_1;
	elseif (x <= -7e-258)
		tmp = Float64(t * Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))));
	elseif (x <= 1.65e-149)
		tmp = Float64(b * Float64(k * Float64(Float64(z * y0) - Float64(y * y4))));
	elseif (x <= 2.4e-33)
		tmp = Float64(t * Float64(c * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (x <= 2.05e+95)
		tmp = Float64(x * Float64(y1 * Float64(Float64(i * j) - Float64(a * y2))));
	elseif (x <= 6e+157)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (y0 * ((x * y2) - (z * y3)));
	tmp = 0.0;
	if (x <= -1.6e-97)
		tmp = t_1;
	elseif (x <= -7e-258)
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	elseif (x <= 1.65e-149)
		tmp = b * (k * ((z * y0) - (y * y4)));
	elseif (x <= 2.4e-33)
		tmp = t * (c * ((z * i) - (y2 * y4)));
	elseif (x <= 2.05e+95)
		tmp = x * (y1 * ((i * j) - (a * y2)));
	elseif (x <= 6e+157)
		tmp = t_1;
	else
		tmp = b * (x * ((y * a) - (j * y0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.6e-97], t$95$1, If[LessEqual[x, -7e-258], N[(t * N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.65e-149], N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.4e-33], N[(t * N[(c * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.05e+95], N[(x * N[(y1 * N[(N[(i * j), $MachinePrecision] - N[(a * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6e+157], t$95$1, N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -1.5999999999999999e-97 or 2.04999999999999993e95 < x < 6.00000000000000021e157

   1. Initial program 32.2%

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

   3. Simplified 32.2%

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

   4. Taylor expanded in c around inf 49.0%

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

   5. Taylor expanded in y0 around inf 51.5%

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

   if -1.5999999999999999e-97 < x < -7.00000000000000003e-258

   1. Initial program 42.1%

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

   3. Simplified 42.1%

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

   4. Taylor expanded in t around inf 53.0%

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

   5. Taylor expanded in y2 around inf 45.6%

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

   if -7.00000000000000003e-258 < x < 1.65000000000000009e-149

   1. Initial program 31.4%

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

   3. Simplified 31.4%

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

   4. Taylor expanded in b around inf 41.1%

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

   5. Taylor expanded in k around -inf 39.3%

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

      1. associate-*r* 39.3%

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

      2. neg-mul-1 39.3%

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

   7. Simplified 39.3%

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

   if 1.65000000000000009e-149 < x < 2.4e-33

   1. Initial program 26.2%

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

   3. Simplified 26.2%

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

   4. Taylor expanded in t around inf 44.4%

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

   5. Taylor expanded in c around inf 53.1%

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

   if 2.4e-33 < x < 2.04999999999999993e95

   1. Initial program 37.0%

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

   3. Simplified 37.0%

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

   4. Taylor expanded in y1 around inf 41.7%

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

   5. Taylor expanded in x around -inf 45.7%

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

      1. mul-1-neg 45.7%

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

   7. Simplified 45.7%

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

   if 6.00000000000000021e157 < x

   1. Initial program 36.1%

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

   3. Simplified 36.1%

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

   4. Taylor expanded in b around inf 47.4%

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

   5. Taylor expanded in x around inf 56.3%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 48.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-97}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-258}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-149}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-33}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{+95}:\\ \;\;\;\;x \cdot \left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+157}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \end{array} \]

Alternative 25: 31.2% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{if}\;x \leq -2.95 \cdot 10^{-97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-260}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{-148}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-33}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+95}:\\ \;\;\;\;x \cdot \left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{+157}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y0 (- (* x y2) (* z y3))))))
   (if (<= x -2.95e-97)
     t_1
     (if (<= x 3.7e-260)
       (* t (* a (- (* y2 y5) (* z b))))
       (if (<= x 5.1e-148)
         (* b (* k (- (* z y0) (* y y4))))
         (if (<= x 9.5e-33)
           (* t (* c (- (* z i) (* y2 y4))))
           (if (<= x 1.4e+95)
             (* x (* y1 (- (* i j) (* a y2))))
             (if (<= x 1.02e+157) t_1 (* b (* x (- (* y a) (* j y0))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y0 * ((x * y2) - (z * y3)));
	double tmp;
	if (x <= -2.95e-97) {
		tmp = t_1;
	} else if (x <= 3.7e-260) {
		tmp = t * (a * ((y2 * y5) - (z * b)));
	} else if (x <= 5.1e-148) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (x <= 9.5e-33) {
		tmp = t * (c * ((z * i) - (y2 * y4)));
	} else if (x <= 1.4e+95) {
		tmp = x * (y1 * ((i * j) - (a * y2)));
	} else if (x <= 1.02e+157) {
		tmp = t_1;
	} else {
		tmp = b * (x * ((y * a) - (j * y0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (y0 * ((x * y2) - (z * y3)))
    if (x <= (-2.95d-97)) then
        tmp = t_1
    else if (x <= 3.7d-260) then
        tmp = t * (a * ((y2 * y5) - (z * b)))
    else if (x <= 5.1d-148) then
        tmp = b * (k * ((z * y0) - (y * y4)))
    else if (x <= 9.5d-33) then
        tmp = t * (c * ((z * i) - (y2 * y4)))
    else if (x <= 1.4d+95) then
        tmp = x * (y1 * ((i * j) - (a * y2)))
    else if (x <= 1.02d+157) then
        tmp = t_1
    else
        tmp = b * (x * ((y * a) - (j * y0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y0 * ((x * y2) - (z * y3)));
	double tmp;
	if (x <= -2.95e-97) {
		tmp = t_1;
	} else if (x <= 3.7e-260) {
		tmp = t * (a * ((y2 * y5) - (z * b)));
	} else if (x <= 5.1e-148) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (x <= 9.5e-33) {
		tmp = t * (c * ((z * i) - (y2 * y4)));
	} else if (x <= 1.4e+95) {
		tmp = x * (y1 * ((i * j) - (a * y2)));
	} else if (x <= 1.02e+157) {
		tmp = t_1;
	} else {
		tmp = b * (x * ((y * a) - (j * y0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (y0 * ((x * y2) - (z * y3)))
	tmp = 0
	if x <= -2.95e-97:
		tmp = t_1
	elif x <= 3.7e-260:
		tmp = t * (a * ((y2 * y5) - (z * b)))
	elif x <= 5.1e-148:
		tmp = b * (k * ((z * y0) - (y * y4)))
	elif x <= 9.5e-33:
		tmp = t * (c * ((z * i) - (y2 * y4)))
	elif x <= 1.4e+95:
		tmp = x * (y1 * ((i * j) - (a * y2)))
	elif x <= 1.02e+157:
		tmp = t_1
	else:
		tmp = b * (x * ((y * a) - (j * y0)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))))
	tmp = 0.0
	if (x <= -2.95e-97)
		tmp = t_1;
	elseif (x <= 3.7e-260)
		tmp = Float64(t * Float64(a * Float64(Float64(y2 * y5) - Float64(z * b))));
	elseif (x <= 5.1e-148)
		tmp = Float64(b * Float64(k * Float64(Float64(z * y0) - Float64(y * y4))));
	elseif (x <= 9.5e-33)
		tmp = Float64(t * Float64(c * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (x <= 1.4e+95)
		tmp = Float64(x * Float64(y1 * Float64(Float64(i * j) - Float64(a * y2))));
	elseif (x <= 1.02e+157)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (y0 * ((x * y2) - (z * y3)));
	tmp = 0.0;
	if (x <= -2.95e-97)
		tmp = t_1;
	elseif (x <= 3.7e-260)
		tmp = t * (a * ((y2 * y5) - (z * b)));
	elseif (x <= 5.1e-148)
		tmp = b * (k * ((z * y0) - (y * y4)));
	elseif (x <= 9.5e-33)
		tmp = t * (c * ((z * i) - (y2 * y4)));
	elseif (x <= 1.4e+95)
		tmp = x * (y1 * ((i * j) - (a * y2)));
	elseif (x <= 1.02e+157)
		tmp = t_1;
	else
		tmp = b * (x * ((y * a) - (j * y0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.95e-97], t$95$1, If[LessEqual[x, 3.7e-260], N[(t * N[(a * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.1e-148], N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.5e-33], N[(t * N[(c * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.4e+95], N[(x * N[(y1 * N[(N[(i * j), $MachinePrecision] - N[(a * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.02e+157], t$95$1, N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -2.9499999999999998e-97 or 1.3999999999999999e95 < x < 1.02000000000000003e157

   1. Initial program 32.6%

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

   3. Simplified 32.6%

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

   4. Taylor expanded in c around inf 49.5%

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

   5. Taylor expanded in y0 around inf 52.0%

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

   if -2.9499999999999998e-97 < x < 3.7000000000000002e-260

   1. Initial program 38.3%

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

   3. Simplified 38.3%

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

   4. Taylor expanded in t around inf 46.9%

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

   5. Taylor expanded in a around -inf 41.0%

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

      1. associate-*r* 41.0%

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

      2. neg-mul-1 41.0%

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

   7. Simplified 41.0%

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

   if 3.7000000000000002e-260 < x < 5.1e-148

   1. Initial program 27.8%

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

   3. Simplified 27.8%

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

   4. Taylor expanded in b around inf 28.5%

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

   5. Taylor expanded in k around -inf 51.2%

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

      1. associate-*r* 51.2%

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

      2. neg-mul-1 51.2%

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

   7. Simplified 51.2%

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

   if 5.1e-148 < x < 9.50000000000000019e-33

   1. Initial program 26.2%

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

   3. Simplified 26.2%

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

   4. Taylor expanded in t around inf 44.4%

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

   5. Taylor expanded in c around inf 53.1%

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

   if 9.50000000000000019e-33 < x < 1.3999999999999999e95

   1. Initial program 37.0%

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

   3. Simplified 37.0%

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

   4. Taylor expanded in y1 around inf 41.7%

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

   5. Taylor expanded in x around -inf 45.7%

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

      1. mul-1-neg 45.7%

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

   7. Simplified 45.7%

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

   if 1.02000000000000003e157 < x

   1. Initial program 36.1%

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

   3. Simplified 36.1%

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

   4. Taylor expanded in b around inf 47.4%

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

   5. Taylor expanded in x around inf 56.3%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.95 \cdot 10^{-97}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-260}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{-148}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-33}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+95}:\\ \;\;\;\;x \cdot \left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{+157}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \end{array} \]

Alternative 26: 28.1% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{if}\;y2 \leq -5.2 \cdot 10^{+168}:\\ \;\;\;\;t \cdot \left(-c \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -7.4 \cdot 10^{+90}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;y2 \leq 9.5 \cdot 10^{-138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq 1.7 \cdot 10^{-57}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y2 \leq 1.36 \cdot 10^{+130}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(y2 \cdot y4\right)\right) \cdot \left(-c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* j (- (* t y4) (* x y0))))))
   (if (<= y2 -5.2e+168)
     (* t (- (* c (* y2 y4))))
     (if (<= y2 -7.4e+90)
       (* (* c i) (* z t))
       (if (<= y2 9.5e-138)
         t_1
         (if (<= y2 1.7e-57)
           (* a (* b (- (* x y) (* z t))))
           (if (<= y2 1.36e+130) t_1 (* (* t (* y2 y4)) (- c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (j * ((t * y4) - (x * y0)));
	double tmp;
	if (y2 <= -5.2e+168) {
		tmp = t * -(c * (y2 * y4));
	} else if (y2 <= -7.4e+90) {
		tmp = (c * i) * (z * t);
	} else if (y2 <= 9.5e-138) {
		tmp = t_1;
	} else if (y2 <= 1.7e-57) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y2 <= 1.36e+130) {
		tmp = t_1;
	} else {
		tmp = (t * (y2 * y4)) * -c;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (j * ((t * y4) - (x * y0)))
    if (y2 <= (-5.2d+168)) then
        tmp = t * -(c * (y2 * y4))
    else if (y2 <= (-7.4d+90)) then
        tmp = (c * i) * (z * t)
    else if (y2 <= 9.5d-138) then
        tmp = t_1
    else if (y2 <= 1.7d-57) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (y2 <= 1.36d+130) then
        tmp = t_1
    else
        tmp = (t * (y2 * y4)) * -c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (j * ((t * y4) - (x * y0)));
	double tmp;
	if (y2 <= -5.2e+168) {
		tmp = t * -(c * (y2 * y4));
	} else if (y2 <= -7.4e+90) {
		tmp = (c * i) * (z * t);
	} else if (y2 <= 9.5e-138) {
		tmp = t_1;
	} else if (y2 <= 1.7e-57) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y2 <= 1.36e+130) {
		tmp = t_1;
	} else {
		tmp = (t * (y2 * y4)) * -c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (j * ((t * y4) - (x * y0)))
	tmp = 0
	if y2 <= -5.2e+168:
		tmp = t * -(c * (y2 * y4))
	elif y2 <= -7.4e+90:
		tmp = (c * i) * (z * t)
	elif y2 <= 9.5e-138:
		tmp = t_1
	elif y2 <= 1.7e-57:
		tmp = a * (b * ((x * y) - (z * t)))
	elif y2 <= 1.36e+130:
		tmp = t_1
	else:
		tmp = (t * (y2 * y4)) * -c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))))
	tmp = 0.0
	if (y2 <= -5.2e+168)
		tmp = Float64(t * Float64(-Float64(c * Float64(y2 * y4))));
	elseif (y2 <= -7.4e+90)
		tmp = Float64(Float64(c * i) * Float64(z * t));
	elseif (y2 <= 9.5e-138)
		tmp = t_1;
	elseif (y2 <= 1.7e-57)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y2 <= 1.36e+130)
		tmp = t_1;
	else
		tmp = Float64(Float64(t * Float64(y2 * y4)) * Float64(-c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (j * ((t * y4) - (x * y0)));
	tmp = 0.0;
	if (y2 <= -5.2e+168)
		tmp = t * -(c * (y2 * y4));
	elseif (y2 <= -7.4e+90)
		tmp = (c * i) * (z * t);
	elseif (y2 <= 9.5e-138)
		tmp = t_1;
	elseif (y2 <= 1.7e-57)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (y2 <= 1.36e+130)
		tmp = t_1;
	else
		tmp = (t * (y2 * y4)) * -c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -5.2e+168], N[(t * (-N[(c * N[(y2 * y4), $MachinePrecision]), $MachinePrecision])), $MachinePrecision], If[LessEqual[y2, -7.4e+90], N[(N[(c * i), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 9.5e-138], t$95$1, If[LessEqual[y2, 1.7e-57], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.36e+130], t$95$1, N[(N[(t * N[(y2 * y4), $MachinePrecision]), $MachinePrecision] * (-c)), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y2 < -5.2e168

   1. Initial program 12.5%

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

   3. Simplified 12.5%

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

   4. Taylor expanded in t around inf 33.7%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in z around 0 38.0%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   6. Taylor expanded in c around inf 54.7%

      \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(y2 \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 54.7%

         \[\leadsto t \cdot \color{blue}{\left(-c \cdot \left(y2 \cdot y4\right)\right)} \]

   8. Simplified 54.7%

      \[\leadsto t \cdot \color{blue}{\left(-c \cdot \left(y2 \cdot y4\right)\right)} \]

   if -5.2e168 < y2 < -7.4e90

   1. Initial program 15.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 15.4%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 32.2%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in c around inf 47.6%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(i \cdot z - y2 \cdot y4\right)\right)} \]

   6. Taylor expanded in i around inf 48.0%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 62.5%

         \[\leadsto \color{blue}{\left(c \cdot i\right) \cdot \left(t \cdot z\right)} \]

   8. Simplified 62.5%

      \[\leadsto \color{blue}{\left(c \cdot i\right) \cdot \left(t \cdot z\right)} \]

   if -7.4e90 < y2 < 9.49999999999999997e-138 or 1.70000000000000008e-57 < y2 < 1.36000000000000007e130

   1. Initial program 39.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 39.2%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 40.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in j around inf 37.1%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if 9.49999999999999997e-138 < y2 < 1.70000000000000008e-57

   1. Initial program 45.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 45.3%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 36.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in a around inf 36.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if 1.36000000000000007e130 < y2

   1. Initial program 27.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 27.0%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 32.2%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in z around 0 39.6%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   6. Taylor expanded in c around inf 45.1%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 45.1%

         \[\leadsto \color{blue}{-c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)} \]

   8. Simplified 45.1%

      \[\leadsto \color{blue}{-c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -5.2 \cdot 10^{+168}:\\ \;\;\;\;t \cdot \left(-c \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -7.4 \cdot 10^{+90}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;y2 \leq 9.5 \cdot 10^{-138}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 1.7 \cdot 10^{-57}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y2 \leq 1.36 \cdot 10^{+130}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(y2 \cdot y4\right)\right) \cdot \left(-c\right)\\ \end{array} \]

Alternative 27: 27.7% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -1.05 \cdot 10^{+169}:\\ \;\;\;\;t \cdot \left(-c \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -1.3 \cdot 10^{+92}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;y2 \leq 9.8 \cdot 10^{-138}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 2.45 \cdot 10^{-60}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y2 \leq 3.5 \cdot 10^{+127}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(y2 \cdot y4\right)\right) \cdot \left(-c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -1.05e+169)
   (* t (- (* c (* y2 y4))))
   (if (<= y2 -1.3e+92)
     (* (* c i) (* z t))
     (if (<= y2 9.8e-138)
       (* b (* j (- (* t y4) (* x y0))))
       (if (<= y2 2.45e-60)
         (* a (* b (- (* x y) (* z t))))
         (if (<= y2 3.5e+127)
           (* b (* y0 (- (* z k) (* x j))))
           (* (* t (* y2 y4)) (- c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -1.05e+169) {
		tmp = t * -(c * (y2 * y4));
	} else if (y2 <= -1.3e+92) {
		tmp = (c * i) * (z * t);
	} else if (y2 <= 9.8e-138) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y2 <= 2.45e-60) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y2 <= 3.5e+127) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else {
		tmp = (t * (y2 * y4)) * -c;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y2 <= (-1.05d+169)) then
        tmp = t * -(c * (y2 * y4))
    else if (y2 <= (-1.3d+92)) then
        tmp = (c * i) * (z * t)
    else if (y2 <= 9.8d-138) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (y2 <= 2.45d-60) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (y2 <= 3.5d+127) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else
        tmp = (t * (y2 * y4)) * -c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -1.05e+169) {
		tmp = t * -(c * (y2 * y4));
	} else if (y2 <= -1.3e+92) {
		tmp = (c * i) * (z * t);
	} else if (y2 <= 9.8e-138) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y2 <= 2.45e-60) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y2 <= 3.5e+127) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else {
		tmp = (t * (y2 * y4)) * -c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y2 <= -1.05e+169:
		tmp = t * -(c * (y2 * y4))
	elif y2 <= -1.3e+92:
		tmp = (c * i) * (z * t)
	elif y2 <= 9.8e-138:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif y2 <= 2.45e-60:
		tmp = a * (b * ((x * y) - (z * t)))
	elif y2 <= 3.5e+127:
		tmp = b * (y0 * ((z * k) - (x * j)))
	else:
		tmp = (t * (y2 * y4)) * -c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y2 <= -1.05e+169)
		tmp = Float64(t * Float64(-Float64(c * Float64(y2 * y4))));
	elseif (y2 <= -1.3e+92)
		tmp = Float64(Float64(c * i) * Float64(z * t));
	elseif (y2 <= 9.8e-138)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (y2 <= 2.45e-60)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y2 <= 3.5e+127)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	else
		tmp = Float64(Float64(t * Float64(y2 * y4)) * Float64(-c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y2 <= -1.05e+169)
		tmp = t * -(c * (y2 * y4));
	elseif (y2 <= -1.3e+92)
		tmp = (c * i) * (z * t);
	elseif (y2 <= 9.8e-138)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (y2 <= 2.45e-60)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (y2 <= 3.5e+127)
		tmp = b * (y0 * ((z * k) - (x * j)));
	else
		tmp = (t * (y2 * y4)) * -c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y2, -1.05e+169], N[(t * (-N[(c * N[(y2 * y4), $MachinePrecision]), $MachinePrecision])), $MachinePrecision], If[LessEqual[y2, -1.3e+92], N[(N[(c * i), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 9.8e-138], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.45e-60], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 3.5e+127], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(y2 * y4), $MachinePrecision]), $MachinePrecision] * (-c)), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y2 < -1.0500000000000001e169

   1. Initial program 12.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 12.5%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 33.7%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in z around 0 38.0%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   6. Taylor expanded in c around inf 54.7%

      \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(y2 \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 54.7%

         \[\leadsto t \cdot \color{blue}{\left(-c \cdot \left(y2 \cdot y4\right)\right)} \]

   8. Simplified 54.7%

      \[\leadsto t \cdot \color{blue}{\left(-c \cdot \left(y2 \cdot y4\right)\right)} \]

   if -1.0500000000000001e169 < y2 < -1.2999999999999999e92

   1. Initial program 15.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 15.4%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 32.2%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in c around inf 47.6%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(i \cdot z - y2 \cdot y4\right)\right)} \]

   6. Taylor expanded in i around inf 48.0%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 62.5%

         \[\leadsto \color{blue}{\left(c \cdot i\right) \cdot \left(t \cdot z\right)} \]

   8. Simplified 62.5%

      \[\leadsto \color{blue}{\left(c \cdot i\right) \cdot \left(t \cdot z\right)} \]

   if -1.2999999999999999e92 < y2 < 9.80000000000000033e-138

   1. Initial program 40.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 40.4%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 42.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in j around inf 39.1%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if 9.80000000000000033e-138 < y2 < 2.44999999999999994e-60

   1. Initial program 45.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 45.3%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 36.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in a around inf 36.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if 2.44999999999999994e-60 < y2 < 3.49999999999999978e127

   1. Initial program 36.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 36.7%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 30.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in y0 around inf 41.2%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   if 3.49999999999999978e127 < y2

   1. Initial program 25.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.8%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 33.1%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in z around 0 40.1%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   6. Taylor expanded in c around inf 45.4%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 45.4%

         \[\leadsto \color{blue}{-c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)} \]

   8. Simplified 45.4%

      \[\leadsto \color{blue}{-c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.05 \cdot 10^{+169}:\\ \;\;\;\;t \cdot \left(-c \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -1.3 \cdot 10^{+92}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;y2 \leq 9.8 \cdot 10^{-138}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 2.45 \cdot 10^{-60}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y2 \leq 3.5 \cdot 10^{+127}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(y2 \cdot y4\right)\right) \cdot \left(-c\right)\\ \end{array} \]

Alternative 28: 25.6% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{if}\;y5 \leq -1.45 \cdot 10^{-27}:\\ \;\;\;\;t \cdot \left(\left(i \cdot y5\right) \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y5 \leq 4.4 \cdot 10^{-214}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y5 \leq 2.8 \cdot 10^{-106}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq 1.52 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y5 \leq 9.5 \cdot 10^{+242}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* t (- (* z i) (* y2 y4))))))
   (if (<= y5 -1.45e-27)
     (* t (* (* i y5) (- j)))
     (if (<= y5 4.4e-214)
       t_1
       (if (<= y5 2.8e-106)
         (* b (* y0 (- (* z k) (* x j))))
         (if (<= y5 1.52e-33)
           t_1
           (if (<= y5 9.5e+242)
             (* b (* j (- (* t y4) (* x y0))))
             (* (* c i) (* z t)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (t * ((z * i) - (y2 * y4)));
	double tmp;
	if (y5 <= -1.45e-27) {
		tmp = t * ((i * y5) * -j);
	} else if (y5 <= 4.4e-214) {
		tmp = t_1;
	} else if (y5 <= 2.8e-106) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y5 <= 1.52e-33) {
		tmp = t_1;
	} else if (y5 <= 9.5e+242) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else {
		tmp = (c * i) * (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (t * ((z * i) - (y2 * y4)))
    if (y5 <= (-1.45d-27)) then
        tmp = t * ((i * y5) * -j)
    else if (y5 <= 4.4d-214) then
        tmp = t_1
    else if (y5 <= 2.8d-106) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (y5 <= 1.52d-33) then
        tmp = t_1
    else if (y5 <= 9.5d+242) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else
        tmp = (c * i) * (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (t * ((z * i) - (y2 * y4)));
	double tmp;
	if (y5 <= -1.45e-27) {
		tmp = t * ((i * y5) * -j);
	} else if (y5 <= 4.4e-214) {
		tmp = t_1;
	} else if (y5 <= 2.8e-106) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y5 <= 1.52e-33) {
		tmp = t_1;
	} else if (y5 <= 9.5e+242) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else {
		tmp = (c * i) * (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (t * ((z * i) - (y2 * y4)))
	tmp = 0
	if y5 <= -1.45e-27:
		tmp = t * ((i * y5) * -j)
	elif y5 <= 4.4e-214:
		tmp = t_1
	elif y5 <= 2.8e-106:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif y5 <= 1.52e-33:
		tmp = t_1
	elif y5 <= 9.5e+242:
		tmp = b * (j * ((t * y4) - (x * y0)))
	else:
		tmp = (c * i) * (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))))
	tmp = 0.0
	if (y5 <= -1.45e-27)
		tmp = Float64(t * Float64(Float64(i * y5) * Float64(-j)));
	elseif (y5 <= 4.4e-214)
		tmp = t_1;
	elseif (y5 <= 2.8e-106)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (y5 <= 1.52e-33)
		tmp = t_1;
	elseif (y5 <= 9.5e+242)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	else
		tmp = Float64(Float64(c * i) * Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (t * ((z * i) - (y2 * y4)));
	tmp = 0.0;
	if (y5 <= -1.45e-27)
		tmp = t * ((i * y5) * -j);
	elseif (y5 <= 4.4e-214)
		tmp = t_1;
	elseif (y5 <= 2.8e-106)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (y5 <= 1.52e-33)
		tmp = t_1;
	elseif (y5 <= 9.5e+242)
		tmp = b * (j * ((t * y4) - (x * y0)));
	else
		tmp = (c * i) * (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -1.45e-27], N[(t * N[(N[(i * y5), $MachinePrecision] * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 4.4e-214], t$95$1, If[LessEqual[y5, 2.8e-106], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.52e-33], t$95$1, If[LessEqual[y5, 9.5e+242], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y5 < -1.45000000000000002e-27

   1. Initial program 26.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 26.8%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 39.8%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in j around inf 43.1%

      \[\leadsto t \cdot \color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]

   6. Taylor expanded in b around 0 40.2%

      \[\leadsto t \cdot \left(j \cdot \color{blue}{\left(-1 \cdot \left(i \cdot y5\right)\right)}\right) \]
   7. Step-by-step derivation

      1. mul-1-neg 40.2%

         \[\leadsto t \cdot \left(j \cdot \color{blue}{\left(-i \cdot y5\right)}\right) \]

      2. *-commutative 40.2%

         \[\leadsto t \cdot \left(j \cdot \left(-\color{blue}{y5 \cdot i}\right)\right) \]

      3. distribute-rgt-neg-out 40.2%

         \[\leadsto t \cdot \left(j \cdot \color{blue}{\left(y5 \cdot \left(-i\right)\right)}\right) \]

   8. Simplified 40.2%

      \[\leadsto t \cdot \left(j \cdot \color{blue}{\left(y5 \cdot \left(-i\right)\right)}\right) \]

   if -1.45000000000000002e-27 < y5 < 4.40000000000000003e-214 or 2.79999999999999988e-106 < y5 < 1.52e-33

   1. Initial program 34.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 34.8%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 33.6%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in c around inf 41.3%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(i \cdot z - y2 \cdot y4\right)\right)} \]

   if 4.40000000000000003e-214 < y5 < 2.79999999999999988e-106

   1. Initial program 45.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 45.2%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 44.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in y0 around inf 55.9%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   if 1.52e-33 < y5 < 9.49999999999999995e242

   1. Initial program 42.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 42.5%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 38.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in j around inf 49.1%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if 9.49999999999999995e242 < y5

   1. Initial program 14.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 14.3%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 28.6%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in c around inf 30.0%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(i \cdot z - y2 \cdot y4\right)\right)} \]

   6. Taylor expanded in i around inf 30.3%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 44.0%

         \[\leadsto \color{blue}{\left(c \cdot i\right) \cdot \left(t \cdot z\right)} \]

   8. Simplified 44.0%

      \[\leadsto \color{blue}{\left(c \cdot i\right) \cdot \left(t \cdot z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -1.45 \cdot 10^{-27}:\\ \;\;\;\;t \cdot \left(\left(i \cdot y5\right) \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y5 \leq 4.4 \cdot 10^{-214}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 2.8 \cdot 10^{-106}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq 1.52 \cdot 10^{-33}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 9.5 \cdot 10^{+242}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(z \cdot t\right)\\ \end{array} \]

Alternative 29: 31.3% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{-96}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 2.45 \cdot 10^{-260}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-200}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-170}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 10^{-32}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -1.3e-96)
   (* c (* y0 (- (* x y2) (* z y3))))
   (if (<= x 2.45e-260)
     (* t (* a (- (* y2 y5) (* z b))))
     (if (<= x 1.6e-200)
       (* j (* y3 (- (* y0 y5) (* y1 y4))))
       (if (<= x 1.25e-170)
         (* b (* k (- (* z y0) (* y y4))))
         (if (<= x 1e-32)
           (* t (* c (- (* z i) (* y2 y4))))
           (* c (* x (- (* y0 y2) (* y i))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -1.3e-96) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (x <= 2.45e-260) {
		tmp = t * (a * ((y2 * y5) - (z * b)));
	} else if (x <= 1.6e-200) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (x <= 1.25e-170) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (x <= 1e-32) {
		tmp = t * (c * ((z * i) - (y2 * y4)));
	} else {
		tmp = c * (x * ((y0 * y2) - (y * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (x <= (-1.3d-96)) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else if (x <= 2.45d-260) then
        tmp = t * (a * ((y2 * y5) - (z * b)))
    else if (x <= 1.6d-200) then
        tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
    else if (x <= 1.25d-170) then
        tmp = b * (k * ((z * y0) - (y * y4)))
    else if (x <= 1d-32) then
        tmp = t * (c * ((z * i) - (y2 * y4)))
    else
        tmp = c * (x * ((y0 * y2) - (y * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -1.3e-96) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (x <= 2.45e-260) {
		tmp = t * (a * ((y2 * y5) - (z * b)));
	} else if (x <= 1.6e-200) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (x <= 1.25e-170) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (x <= 1e-32) {
		tmp = t * (c * ((z * i) - (y2 * y4)));
	} else {
		tmp = c * (x * ((y0 * y2) - (y * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if x <= -1.3e-96:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	elif x <= 2.45e-260:
		tmp = t * (a * ((y2 * y5) - (z * b)))
	elif x <= 1.6e-200:
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
	elif x <= 1.25e-170:
		tmp = b * (k * ((z * y0) - (y * y4)))
	elif x <= 1e-32:
		tmp = t * (c * ((z * i) - (y2 * y4)))
	else:
		tmp = c * (x * ((y0 * y2) - (y * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (x <= -1.3e-96)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (x <= 2.45e-260)
		tmp = Float64(t * Float64(a * Float64(Float64(y2 * y5) - Float64(z * b))));
	elseif (x <= 1.6e-200)
		tmp = Float64(j * Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))));
	elseif (x <= 1.25e-170)
		tmp = Float64(b * Float64(k * Float64(Float64(z * y0) - Float64(y * y4))));
	elseif (x <= 1e-32)
		tmp = Float64(t * Float64(c * Float64(Float64(z * i) - Float64(y2 * y4))));
	else
		tmp = Float64(c * Float64(x * Float64(Float64(y0 * y2) - Float64(y * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (x <= -1.3e-96)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	elseif (x <= 2.45e-260)
		tmp = t * (a * ((y2 * y5) - (z * b)));
	elseif (x <= 1.6e-200)
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	elseif (x <= 1.25e-170)
		tmp = b * (k * ((z * y0) - (y * y4)));
	elseif (x <= 1e-32)
		tmp = t * (c * ((z * i) - (y2 * y4)));
	else
		tmp = c * (x * ((y0 * y2) - (y * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[x, -1.3e-96], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.45e-260], N[(t * N[(a * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.6e-200], N[(j * N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.25e-170], N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1e-32], N[(t * N[(c * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(x * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -1.3000000000000001e-96

   1. Initial program 33.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 33.3%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 48.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y0 around inf 50.9%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   if -1.3000000000000001e-96 < x < 2.4500000000000001e-260

   1. Initial program 38.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 38.3%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 46.9%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in a around -inf 41.0%

      \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot \left(b \cdot z - y2 \cdot y5\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 41.0%

         \[\leadsto t \cdot \color{blue}{\left(\left(-1 \cdot a\right) \cdot \left(b \cdot z - y2 \cdot y5\right)\right)} \]

      2. neg-mul-1 41.0%

         \[\leadsto t \cdot \left(\color{blue}{\left(-a\right)} \cdot \left(b \cdot z - y2 \cdot y5\right)\right) \]

   7. Simplified 41.0%

      \[\leadsto t \cdot \color{blue}{\left(\left(-a\right) \cdot \left(b \cdot z - y2 \cdot y5\right)\right)} \]

   if 2.4500000000000001e-260 < x < 1.59999999999999991e-200

   1. Initial program 22.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 22.2%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y3 around -inf 33.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   5. Taylor expanded in j around inf 56.1%

      \[\leadsto -1 \cdot \color{blue}{\left(j \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} \]

   if 1.59999999999999991e-200 < x < 1.25000000000000003e-170

   1. Initial program 16.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 16.7%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 17.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in k around -inf 68.2%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 68.2%

         \[\leadsto b \cdot \color{blue}{\left(\left(-1 \cdot k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

      2. neg-mul-1 68.2%

         \[\leadsto b \cdot \left(\color{blue}{\left(-k\right)} \cdot \left(y \cdot y4 - y0 \cdot z\right)\right) \]

   7. Simplified 68.2%

      \[\leadsto b \cdot \color{blue}{\left(\left(-k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

   if 1.25000000000000003e-170 < x < 1.00000000000000006e-32

   1. Initial program 30.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.9%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 43.3%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in c around inf 50.9%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(i \cdot z - y2 \cdot y4\right)\right)} \]

   if 1.00000000000000006e-32 < x

   1. Initial program 35.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 35.1%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 35.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in x around inf 46.3%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{-96}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 2.45 \cdot 10^{-260}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-200}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-170}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 10^{-32}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \end{array} \]

Alternative 30: 29.3% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{if}\;j \leq -9.2 \cdot 10^{+218}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;j \leq -1.95 \cdot 10^{-202}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 7.2 \cdot 10^{-68}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{+240}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y0 (- (* x y2) (* z y3))))))
   (if (<= j -9.2e+218)
     (* b (* y4 (- (* t j) (* y k))))
     (if (<= j -1.95e-202)
       t_1
       (if (<= j 7.2e-68)
         (* c (* t (- (* z i) (* y2 y4))))
         (if (<= j 3.8e+240) t_1 (* t (* y4 (* b j)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y0 * ((x * y2) - (z * y3)));
	double tmp;
	if (j <= -9.2e+218) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (j <= -1.95e-202) {
		tmp = t_1;
	} else if (j <= 7.2e-68) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (j <= 3.8e+240) {
		tmp = t_1;
	} else {
		tmp = t * (y4 * (b * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (y0 * ((x * y2) - (z * y3)))
    if (j <= (-9.2d+218)) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (j <= (-1.95d-202)) then
        tmp = t_1
    else if (j <= 7.2d-68) then
        tmp = c * (t * ((z * i) - (y2 * y4)))
    else if (j <= 3.8d+240) then
        tmp = t_1
    else
        tmp = t * (y4 * (b * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y0 * ((x * y2) - (z * y3)));
	double tmp;
	if (j <= -9.2e+218) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (j <= -1.95e-202) {
		tmp = t_1;
	} else if (j <= 7.2e-68) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (j <= 3.8e+240) {
		tmp = t_1;
	} else {
		tmp = t * (y4 * (b * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (y0 * ((x * y2) - (z * y3)))
	tmp = 0
	if j <= -9.2e+218:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif j <= -1.95e-202:
		tmp = t_1
	elif j <= 7.2e-68:
		tmp = c * (t * ((z * i) - (y2 * y4)))
	elif j <= 3.8e+240:
		tmp = t_1
	else:
		tmp = t * (y4 * (b * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))))
	tmp = 0.0
	if (j <= -9.2e+218)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (j <= -1.95e-202)
		tmp = t_1;
	elseif (j <= 7.2e-68)
		tmp = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (j <= 3.8e+240)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(y4 * Float64(b * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (y0 * ((x * y2) - (z * y3)));
	tmp = 0.0;
	if (j <= -9.2e+218)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (j <= -1.95e-202)
		tmp = t_1;
	elseif (j <= 7.2e-68)
		tmp = c * (t * ((z * i) - (y2 * y4)));
	elseif (j <= 3.8e+240)
		tmp = t_1;
	else
		tmp = t * (y4 * (b * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -9.2e+218], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.95e-202], t$95$1, If[LessEqual[j, 7.2e-68], N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.8e+240], t$95$1, N[(t * N[(y4 * N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -9.2000000000000004e218

   1. Initial program 15.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 15.9%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 46.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in y4 around inf 62.4%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   if -9.2000000000000004e218 < j < -1.95e-202 or 7.20000000000000015e-68 < j < 3.8000000000000003e240

   1. Initial program 29.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 29.2%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 39.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y0 around inf 40.0%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   if -1.95e-202 < j < 7.20000000000000015e-68

   1. Initial program 44.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 44.0%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 40.7%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in c around inf 39.3%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(i \cdot z - y2 \cdot y4\right)\right)} \]

   if 3.8000000000000003e240 < j

   1. Initial program 47.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 47.1%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 59.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in j around inf 83.0%

      \[\leadsto t \cdot \color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]

   6. Taylor expanded in b around inf 71.5%

      \[\leadsto t \cdot \color{blue}{\left(b \cdot \left(j \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 71.5%

         \[\leadsto t \cdot \color{blue}{\left(\left(j \cdot y4\right) \cdot b\right)} \]

      2. associate-*r* 66.0%

         \[\leadsto t \cdot \color{blue}{\left(j \cdot \left(y4 \cdot b\right)\right)} \]

      3. *-commutative 66.0%

         \[\leadsto t \cdot \color{blue}{\left(\left(y4 \cdot b\right) \cdot j\right)} \]

      4. associate-*l* 71.6%

         \[\leadsto t \cdot \color{blue}{\left(y4 \cdot \left(b \cdot j\right)\right)} \]

   8. Simplified 71.6%

      \[\leadsto t \cdot \color{blue}{\left(y4 \cdot \left(b \cdot j\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -9.2 \cdot 10^{+218}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;j \leq -1.95 \cdot 10^{-202}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 7.2 \cdot 10^{-68}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{+240}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j\right)\right)\\ \end{array} \]

Alternative 31: 24.0% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y5 \leq -1.9 \cdot 10^{-25}:\\ \;\;\;\;t \cdot \left(\left(i \cdot y5\right) \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y5 \leq -5.1 \cdot 10^{-243}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i\right)\right)\\ \mathbf{elif}\;y5 \leq 4.7 \cdot 10^{-9}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y5 \leq 6.5 \cdot 10^{+188}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y5 -1.9e-25)
   (* t (* (* i y5) (- j)))
   (if (<= y5 -5.1e-243)
     (* t (* c (* z i)))
     (if (<= y5 4.7e-9)
       (* a (* b (- (* x y) (* z t))))
       (if (<= y5 6.5e+188) (* t (* y4 (* b j))) (* t (* a (* 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 tmp;
	if (y5 <= -1.9e-25) {
		tmp = t * ((i * y5) * -j);
	} else if (y5 <= -5.1e-243) {
		tmp = t * (c * (z * i));
	} else if (y5 <= 4.7e-9) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y5 <= 6.5e+188) {
		tmp = t * (y4 * (b * j));
	} else {
		tmp = t * (a * (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) :: tmp
    if (y5 <= (-1.9d-25)) then
        tmp = t * ((i * y5) * -j)
    else if (y5 <= (-5.1d-243)) then
        tmp = t * (c * (z * i))
    else if (y5 <= 4.7d-9) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (y5 <= 6.5d+188) then
        tmp = t * (y4 * (b * j))
    else
        tmp = t * (a * (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 tmp;
	if (y5 <= -1.9e-25) {
		tmp = t * ((i * y5) * -j);
	} else if (y5 <= -5.1e-243) {
		tmp = t * (c * (z * i));
	} else if (y5 <= 4.7e-9) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y5 <= 6.5e+188) {
		tmp = t * (y4 * (b * j));
	} else {
		tmp = t * (a * (y2 * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y5 <= -1.9e-25:
		tmp = t * ((i * y5) * -j)
	elif y5 <= -5.1e-243:
		tmp = t * (c * (z * i))
	elif y5 <= 4.7e-9:
		tmp = a * (b * ((x * y) - (z * t)))
	elif y5 <= 6.5e+188:
		tmp = t * (y4 * (b * j))
	else:
		tmp = t * (a * (y2 * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y5 <= -1.9e-25)
		tmp = Float64(t * Float64(Float64(i * y5) * Float64(-j)));
	elseif (y5 <= -5.1e-243)
		tmp = Float64(t * Float64(c * Float64(z * i)));
	elseif (y5 <= 4.7e-9)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y5 <= 6.5e+188)
		tmp = Float64(t * Float64(y4 * Float64(b * j)));
	else
		tmp = Float64(t * Float64(a * Float64(y2 * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y5 <= -1.9e-25)
		tmp = t * ((i * y5) * -j);
	elseif (y5 <= -5.1e-243)
		tmp = t * (c * (z * i));
	elseif (y5 <= 4.7e-9)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (y5 <= 6.5e+188)
		tmp = t * (y4 * (b * j));
	else
		tmp = t * (a * (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_] := If[LessEqual[y5, -1.9e-25], N[(t * N[(N[(i * y5), $MachinePrecision] * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -5.1e-243], N[(t * N[(c * N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 4.7e-9], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 6.5e+188], N[(t * N[(y4 * N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(a * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y5 < -1.8999999999999999e-25

   1. Initial program 26.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 26.8%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 39.8%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in j around inf 43.1%

      \[\leadsto t \cdot \color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]

   6. Taylor expanded in b around 0 40.2%

      \[\leadsto t \cdot \left(j \cdot \color{blue}{\left(-1 \cdot \left(i \cdot y5\right)\right)}\right) \]
   7. Step-by-step derivation

      1. mul-1-neg 40.2%

         \[\leadsto t \cdot \left(j \cdot \color{blue}{\left(-i \cdot y5\right)}\right) \]

      2. *-commutative 40.2%

         \[\leadsto t \cdot \left(j \cdot \left(-\color{blue}{y5 \cdot i}\right)\right) \]

      3. distribute-rgt-neg-out 40.2%

         \[\leadsto t \cdot \left(j \cdot \color{blue}{\left(y5 \cdot \left(-i\right)\right)}\right) \]

   8. Simplified 40.2%

      \[\leadsto t \cdot \left(j \cdot \color{blue}{\left(y5 \cdot \left(-i\right)\right)}\right) \]

   if -1.8999999999999999e-25 < y5 < -5.0999999999999997e-243

   1. Initial program 29.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 29.5%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 30.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in c around inf 39.8%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(i \cdot z - y2 \cdot y4\right)\right)} \]

   6. Taylor expanded in i around inf 30.8%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(i \cdot z\right)\right)} \]

   if -5.0999999999999997e-243 < y5 < 4.6999999999999999e-9

   1. Initial program 40.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 40.9%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 41.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in a around inf 33.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if 4.6999999999999999e-9 < y5 < 6.49999999999999953e188

   1. Initial program 42.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 42.0%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 36.8%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in j around inf 41.1%

      \[\leadsto t \cdot \color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]

   6. Taylor expanded in b around inf 39.2%

      \[\leadsto t \cdot \color{blue}{\left(b \cdot \left(j \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 39.2%

         \[\leadsto t \cdot \color{blue}{\left(\left(j \cdot y4\right) \cdot b\right)} \]

      2. associate-*r* 37.3%

         \[\leadsto t \cdot \color{blue}{\left(j \cdot \left(y4 \cdot b\right)\right)} \]

      3. *-commutative 37.3%

         \[\leadsto t \cdot \color{blue}{\left(\left(y4 \cdot b\right) \cdot j\right)} \]

      4. associate-*l* 41.4%

         \[\leadsto t \cdot \color{blue}{\left(y4 \cdot \left(b \cdot j\right)\right)} \]

   8. Simplified 41.4%

      \[\leadsto t \cdot \color{blue}{\left(y4 \cdot \left(b \cdot j\right)\right)} \]

   if 6.49999999999999953e188 < y5

   1. Initial program 29.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 29.6%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 33.6%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in a around -inf 48.9%

      \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot \left(b \cdot z - y2 \cdot y5\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 48.9%

         \[\leadsto t \cdot \color{blue}{\left(\left(-1 \cdot a\right) \cdot \left(b \cdot z - y2 \cdot y5\right)\right)} \]

      2. neg-mul-1 48.9%

         \[\leadsto t \cdot \left(\color{blue}{\left(-a\right)} \cdot \left(b \cdot z - y2 \cdot y5\right)\right) \]

   7. Simplified 48.9%

      \[\leadsto t \cdot \color{blue}{\left(\left(-a\right) \cdot \left(b \cdot z - y2 \cdot y5\right)\right)} \]

   8. Taylor expanded in b around 0 38.1%

      \[\leadsto t \cdot \color{blue}{\left(a \cdot \left(y2 \cdot y5\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 36.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -1.9 \cdot 10^{-25}:\\ \;\;\;\;t \cdot \left(\left(i \cdot y5\right) \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y5 \leq -5.1 \cdot 10^{-243}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i\right)\right)\\ \mathbf{elif}\;y5 \leq 4.7 \cdot 10^{-9}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y5 \leq 6.5 \cdot 10^{+188}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \]

Alternative 32: 21.8% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t \cdot \left(y2 \cdot y4\right)\right) \cdot \left(-c\right)\\ \mathbf{if}\;y2 \leq -5 \cdot 10^{+171}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq -3.35 \cdot 10^{+90}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;y2 \leq 1.02 \cdot 10^{-143}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq 4.4 \cdot 10^{+101}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* t (* y2 y4)) (- c))))
   (if (<= y2 -5e+171)
     t_1
     (if (<= y2 -3.35e+90)
       (* (* c i) (* z t))
       (if (<= y2 1.02e-143)
         (* y4 (* b (* t j)))
         (if (<= y2 4.4e+101) (* c (* z (* t i))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (t * (y2 * y4)) * -c;
	double tmp;
	if (y2 <= -5e+171) {
		tmp = t_1;
	} else if (y2 <= -3.35e+90) {
		tmp = (c * i) * (z * t);
	} else if (y2 <= 1.02e-143) {
		tmp = y4 * (b * (t * j));
	} else if (y2 <= 4.4e+101) {
		tmp = c * (z * (t * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t * (y2 * y4)) * -c
    if (y2 <= (-5d+171)) then
        tmp = t_1
    else if (y2 <= (-3.35d+90)) then
        tmp = (c * i) * (z * t)
    else if (y2 <= 1.02d-143) then
        tmp = y4 * (b * (t * j))
    else if (y2 <= 4.4d+101) then
        tmp = c * (z * (t * i))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (t * (y2 * y4)) * -c;
	double tmp;
	if (y2 <= -5e+171) {
		tmp = t_1;
	} else if (y2 <= -3.35e+90) {
		tmp = (c * i) * (z * t);
	} else if (y2 <= 1.02e-143) {
		tmp = y4 * (b * (t * j));
	} else if (y2 <= 4.4e+101) {
		tmp = c * (z * (t * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (t * (y2 * y4)) * -c
	tmp = 0
	if y2 <= -5e+171:
		tmp = t_1
	elif y2 <= -3.35e+90:
		tmp = (c * i) * (z * t)
	elif y2 <= 1.02e-143:
		tmp = y4 * (b * (t * j))
	elif y2 <= 4.4e+101:
		tmp = c * (z * (t * i))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(t * Float64(y2 * y4)) * Float64(-c))
	tmp = 0.0
	if (y2 <= -5e+171)
		tmp = t_1;
	elseif (y2 <= -3.35e+90)
		tmp = Float64(Float64(c * i) * Float64(z * t));
	elseif (y2 <= 1.02e-143)
		tmp = Float64(y4 * Float64(b * Float64(t * j)));
	elseif (y2 <= 4.4e+101)
		tmp = Float64(c * Float64(z * Float64(t * i)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (t * (y2 * y4)) * -c;
	tmp = 0.0;
	if (y2 <= -5e+171)
		tmp = t_1;
	elseif (y2 <= -3.35e+90)
		tmp = (c * i) * (z * t);
	elseif (y2 <= 1.02e-143)
		tmp = y4 * (b * (t * j));
	elseif (y2 <= 4.4e+101)
		tmp = c * (z * (t * i));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(t * N[(y2 * y4), $MachinePrecision]), $MachinePrecision] * (-c)), $MachinePrecision]}, If[LessEqual[y2, -5e+171], t$95$1, If[LessEqual[y2, -3.35e+90], N[(N[(c * i), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.02e-143], N[(y4 * N[(b * N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 4.4e+101], N[(c * N[(z * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y2 < -5.0000000000000004e171 or 4.4000000000000001e101 < y2

   1. Initial program 25.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.1%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 31.2%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in z around 0 36.8%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   6. Taylor expanded in c around inf 44.3%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 44.3%

         \[\leadsto \color{blue}{-c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)} \]

   8. Simplified 44.3%

      \[\leadsto \color{blue}{-c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)} \]

   if -5.0000000000000004e171 < y2 < -3.3500000000000001e90

   1. Initial program 15.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 15.4%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 32.2%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in c around inf 47.6%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(i \cdot z - y2 \cdot y4\right)\right)} \]

   6. Taylor expanded in i around inf 48.0%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 62.5%

         \[\leadsto \color{blue}{\left(c \cdot i\right) \cdot \left(t \cdot z\right)} \]

   8. Simplified 62.5%

      \[\leadsto \color{blue}{\left(c \cdot i\right) \cdot \left(t \cdot z\right)} \]

   if -3.3500000000000001e90 < y2 < 1.02e-143

   1. Initial program 40.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 40.3%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 40.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in j around inf 36.6%

      \[\leadsto t \cdot \color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]

   6. Taylor expanded in b around inf 26.9%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 26.9%

         \[\leadsto \color{blue}{\left(j \cdot \left(t \cdot y4\right)\right) \cdot b} \]

      2. associate-*r* 27.7%

         \[\leadsto \color{blue}{\left(\left(j \cdot t\right) \cdot y4\right)} \cdot b \]

      3. *-commutative 27.7%

         \[\leadsto \left(\color{blue}{\left(t \cdot j\right)} \cdot y4\right) \cdot b \]

      4. associate-*r* 26.9%

         \[\leadsto \color{blue}{\left(t \cdot j\right) \cdot \left(y4 \cdot b\right)} \]

      5. *-commutative 26.9%

         \[\leadsto \color{blue}{\left(y4 \cdot b\right) \cdot \left(t \cdot j\right)} \]

      6. associate-*l* 28.5%

         \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(t \cdot j\right)\right)} \]

   8. Simplified 28.5%

      \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(t \cdot j\right)\right)} \]

   if 1.02e-143 < y2 < 4.4000000000000001e101

   1. Initial program 36.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 36.7%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 35.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in z around inf 39.7%

      \[\leadsto \color{blue}{c \cdot \left(z \cdot \left(-1 \cdot \left(y0 \cdot y3\right) + i \cdot t\right)\right)} \]

   6. Taylor expanded in y0 around 0 27.5%

      \[\leadsto c \cdot \left(z \cdot \color{blue}{\left(i \cdot t\right)}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 34.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -5 \cdot 10^{+171}:\\ \;\;\;\;\left(t \cdot \left(y2 \cdot y4\right)\right) \cdot \left(-c\right)\\ \mathbf{elif}\;y2 \leq -3.35 \cdot 10^{+90}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;y2 \leq 1.02 \cdot 10^{-143}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq 4.4 \cdot 10^{+101}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(y2 \cdot y4\right)\right) \cdot \left(-c\right)\\ \end{array} \]

Alternative 33: 20.4% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y5 \leq -9.5 \cdot 10^{-25}:\\ \;\;\;\;\left(t \cdot j\right) \cdot \left(i \cdot \left(-y5\right)\right)\\ \mathbf{elif}\;y5 \leq -6 \cdot 10^{-155}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i\right)\right)\\ \mathbf{elif}\;y5 \leq 1.18 \cdot 10^{-32}:\\ \;\;\;\;\left(t \cdot \left(y2 \cdot y4\right)\right) \cdot \left(-c\right)\\ \mathbf{elif}\;y5 \leq 1.56 \cdot 10^{+189}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y5 -9.5e-25)
   (* (* t j) (* i (- y5)))
   (if (<= y5 -6e-155)
     (* t (* c (* z i)))
     (if (<= y5 1.18e-32)
       (* (* t (* y2 y4)) (- c))
       (if (<= y5 1.56e+189) (* b (* j (* t y4))) (* t (* a (* 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 tmp;
	if (y5 <= -9.5e-25) {
		tmp = (t * j) * (i * -y5);
	} else if (y5 <= -6e-155) {
		tmp = t * (c * (z * i));
	} else if (y5 <= 1.18e-32) {
		tmp = (t * (y2 * y4)) * -c;
	} else if (y5 <= 1.56e+189) {
		tmp = b * (j * (t * y4));
	} else {
		tmp = t * (a * (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) :: tmp
    if (y5 <= (-9.5d-25)) then
        tmp = (t * j) * (i * -y5)
    else if (y5 <= (-6d-155)) then
        tmp = t * (c * (z * i))
    else if (y5 <= 1.18d-32) then
        tmp = (t * (y2 * y4)) * -c
    else if (y5 <= 1.56d+189) then
        tmp = b * (j * (t * y4))
    else
        tmp = t * (a * (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 tmp;
	if (y5 <= -9.5e-25) {
		tmp = (t * j) * (i * -y5);
	} else if (y5 <= -6e-155) {
		tmp = t * (c * (z * i));
	} else if (y5 <= 1.18e-32) {
		tmp = (t * (y2 * y4)) * -c;
	} else if (y5 <= 1.56e+189) {
		tmp = b * (j * (t * y4));
	} else {
		tmp = t * (a * (y2 * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y5 <= -9.5e-25:
		tmp = (t * j) * (i * -y5)
	elif y5 <= -6e-155:
		tmp = t * (c * (z * i))
	elif y5 <= 1.18e-32:
		tmp = (t * (y2 * y4)) * -c
	elif y5 <= 1.56e+189:
		tmp = b * (j * (t * y4))
	else:
		tmp = t * (a * (y2 * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y5 <= -9.5e-25)
		tmp = Float64(Float64(t * j) * Float64(i * Float64(-y5)));
	elseif (y5 <= -6e-155)
		tmp = Float64(t * Float64(c * Float64(z * i)));
	elseif (y5 <= 1.18e-32)
		tmp = Float64(Float64(t * Float64(y2 * y4)) * Float64(-c));
	elseif (y5 <= 1.56e+189)
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	else
		tmp = Float64(t * Float64(a * Float64(y2 * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y5 <= -9.5e-25)
		tmp = (t * j) * (i * -y5);
	elseif (y5 <= -6e-155)
		tmp = t * (c * (z * i));
	elseif (y5 <= 1.18e-32)
		tmp = (t * (y2 * y4)) * -c;
	elseif (y5 <= 1.56e+189)
		tmp = b * (j * (t * y4));
	else
		tmp = t * (a * (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_] := If[LessEqual[y5, -9.5e-25], N[(N[(t * j), $MachinePrecision] * N[(i * (-y5)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -6e-155], N[(t * N[(c * N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.18e-32], N[(N[(t * N[(y2 * y4), $MachinePrecision]), $MachinePrecision] * (-c)), $MachinePrecision], If[LessEqual[y5, 1.56e+189], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(a * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y5 < -9.50000000000000065e-25

   1. Initial program 26.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 26.8%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 39.8%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in j around inf 43.1%

      \[\leadsto t \cdot \color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]

   6. Taylor expanded in b around 0 40.2%

      \[\leadsto t \cdot \left(j \cdot \color{blue}{\left(-1 \cdot \left(i \cdot y5\right)\right)}\right) \]
   7. Step-by-step derivation

      1. mul-1-neg 40.2%

         \[\leadsto t \cdot \left(j \cdot \color{blue}{\left(-i \cdot y5\right)}\right) \]

      2. *-commutative 40.2%

         \[\leadsto t \cdot \left(j \cdot \left(-\color{blue}{y5 \cdot i}\right)\right) \]

      3. distribute-rgt-neg-out 40.2%

         \[\leadsto t \cdot \left(j \cdot \color{blue}{\left(y5 \cdot \left(-i\right)\right)}\right) \]

   8. Simplified 40.2%

      \[\leadsto t \cdot \left(j \cdot \color{blue}{\left(y5 \cdot \left(-i\right)\right)}\right) \]
   9. Step-by-step derivation

      1. associate-*r* 37.5%

         \[\leadsto \color{blue}{\left(t \cdot j\right) \cdot \left(y5 \cdot \left(-i\right)\right)} \]

      2. distribute-rgt-neg-out 37.5%

         \[\leadsto \left(t \cdot j\right) \cdot \color{blue}{\left(-y5 \cdot i\right)} \]

      3. distribute-rgt-neg-out 37.5%

         \[\leadsto \color{blue}{-\left(t \cdot j\right) \cdot \left(y5 \cdot i\right)} \]

      4. *-commutative 37.5%

         \[\leadsto -\left(t \cdot j\right) \cdot \color{blue}{\left(i \cdot y5\right)} \]

   10. Applied egg-rr 37.5%

       \[\leadsto \color{blue}{-\left(t \cdot j\right) \cdot \left(i \cdot y5\right)} \]

   if -9.50000000000000065e-25 < y5 < -5.99999999999999967e-155

   1. Initial program 23.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 23.9%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 24.3%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in c around inf 48.7%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(i \cdot z - y2 \cdot y4\right)\right)} \]

   6. Taylor expanded in i around inf 40.9%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(i \cdot z\right)\right)} \]

   if -5.99999999999999967e-155 < y5 < 1.17999999999999997e-32

   1. Initial program 40.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 40.0%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 33.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in z around 0 27.0%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   6. Taylor expanded in c around inf 25.2%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 25.2%

         \[\leadsto \color{blue}{-c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)} \]

   8. Simplified 25.2%

      \[\leadsto \color{blue}{-c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)} \]

   if 1.17999999999999997e-32 < y5 < 1.56e189

   1. Initial program 41.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 41.7%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 36.0%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in j around inf 36.1%

      \[\leadsto t \cdot \color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]

   6. Taylor expanded in b around inf 38.0%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]

   if 1.56e189 < y5

   1. Initial program 29.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 29.6%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 33.6%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in a around -inf 48.9%

      \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot \left(b \cdot z - y2 \cdot y5\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 48.9%

         \[\leadsto t \cdot \color{blue}{\left(\left(-1 \cdot a\right) \cdot \left(b \cdot z - y2 \cdot y5\right)\right)} \]

      2. neg-mul-1 48.9%

         \[\leadsto t \cdot \left(\color{blue}{\left(-a\right)} \cdot \left(b \cdot z - y2 \cdot y5\right)\right) \]

   7. Simplified 48.9%

      \[\leadsto t \cdot \color{blue}{\left(\left(-a\right) \cdot \left(b \cdot z - y2 \cdot y5\right)\right)} \]

   8. Taylor expanded in b around 0 38.1%

      \[\leadsto t \cdot \color{blue}{\left(a \cdot \left(y2 \cdot y5\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 34.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -9.5 \cdot 10^{-25}:\\ \;\;\;\;\left(t \cdot j\right) \cdot \left(i \cdot \left(-y5\right)\right)\\ \mathbf{elif}\;y5 \leq -6 \cdot 10^{-155}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i\right)\right)\\ \mathbf{elif}\;y5 \leq 1.18 \cdot 10^{-32}:\\ \;\;\;\;\left(t \cdot \left(y2 \cdot y4\right)\right) \cdot \left(-c\right)\\ \mathbf{elif}\;y5 \leq 1.56 \cdot 10^{+189}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \]

Alternative 34: 21.0% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y5 \leq -3.9 \cdot 10^{-27}:\\ \;\;\;\;t \cdot \left(\left(i \cdot y5\right) \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y5 \leq -6 \cdot 10^{-155}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i\right)\right)\\ \mathbf{elif}\;y5 \leq 1.85 \cdot 10^{-32}:\\ \;\;\;\;\left(t \cdot \left(y2 \cdot y4\right)\right) \cdot \left(-c\right)\\ \mathbf{elif}\;y5 \leq 7.8 \cdot 10^{+189}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y5 -3.9e-27)
   (* t (* (* i y5) (- j)))
   (if (<= y5 -6e-155)
     (* t (* c (* z i)))
     (if (<= y5 1.85e-32)
       (* (* t (* y2 y4)) (- c))
       (if (<= y5 7.8e+189) (* b (* j (* t y4))) (* t (* a (* 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 tmp;
	if (y5 <= -3.9e-27) {
		tmp = t * ((i * y5) * -j);
	} else if (y5 <= -6e-155) {
		tmp = t * (c * (z * i));
	} else if (y5 <= 1.85e-32) {
		tmp = (t * (y2 * y4)) * -c;
	} else if (y5 <= 7.8e+189) {
		tmp = b * (j * (t * y4));
	} else {
		tmp = t * (a * (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) :: tmp
    if (y5 <= (-3.9d-27)) then
        tmp = t * ((i * y5) * -j)
    else if (y5 <= (-6d-155)) then
        tmp = t * (c * (z * i))
    else if (y5 <= 1.85d-32) then
        tmp = (t * (y2 * y4)) * -c
    else if (y5 <= 7.8d+189) then
        tmp = b * (j * (t * y4))
    else
        tmp = t * (a * (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 tmp;
	if (y5 <= -3.9e-27) {
		tmp = t * ((i * y5) * -j);
	} else if (y5 <= -6e-155) {
		tmp = t * (c * (z * i));
	} else if (y5 <= 1.85e-32) {
		tmp = (t * (y2 * y4)) * -c;
	} else if (y5 <= 7.8e+189) {
		tmp = b * (j * (t * y4));
	} else {
		tmp = t * (a * (y2 * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y5 <= -3.9e-27:
		tmp = t * ((i * y5) * -j)
	elif y5 <= -6e-155:
		tmp = t * (c * (z * i))
	elif y5 <= 1.85e-32:
		tmp = (t * (y2 * y4)) * -c
	elif y5 <= 7.8e+189:
		tmp = b * (j * (t * y4))
	else:
		tmp = t * (a * (y2 * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y5 <= -3.9e-27)
		tmp = Float64(t * Float64(Float64(i * y5) * Float64(-j)));
	elseif (y5 <= -6e-155)
		tmp = Float64(t * Float64(c * Float64(z * i)));
	elseif (y5 <= 1.85e-32)
		tmp = Float64(Float64(t * Float64(y2 * y4)) * Float64(-c));
	elseif (y5 <= 7.8e+189)
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	else
		tmp = Float64(t * Float64(a * Float64(y2 * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y5 <= -3.9e-27)
		tmp = t * ((i * y5) * -j);
	elseif (y5 <= -6e-155)
		tmp = t * (c * (z * i));
	elseif (y5 <= 1.85e-32)
		tmp = (t * (y2 * y4)) * -c;
	elseif (y5 <= 7.8e+189)
		tmp = b * (j * (t * y4));
	else
		tmp = t * (a * (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_] := If[LessEqual[y5, -3.9e-27], N[(t * N[(N[(i * y5), $MachinePrecision] * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -6e-155], N[(t * N[(c * N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.85e-32], N[(N[(t * N[(y2 * y4), $MachinePrecision]), $MachinePrecision] * (-c)), $MachinePrecision], If[LessEqual[y5, 7.8e+189], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(a * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y5 < -3.89999999999999972e-27

   1. Initial program 26.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 26.8%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 39.8%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in j around inf 43.1%

      \[\leadsto t \cdot \color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]

   6. Taylor expanded in b around 0 40.2%

      \[\leadsto t \cdot \left(j \cdot \color{blue}{\left(-1 \cdot \left(i \cdot y5\right)\right)}\right) \]
   7. Step-by-step derivation

      1. mul-1-neg 40.2%

         \[\leadsto t \cdot \left(j \cdot \color{blue}{\left(-i \cdot y5\right)}\right) \]

      2. *-commutative 40.2%

         \[\leadsto t \cdot \left(j \cdot \left(-\color{blue}{y5 \cdot i}\right)\right) \]

      3. distribute-rgt-neg-out 40.2%

         \[\leadsto t \cdot \left(j \cdot \color{blue}{\left(y5 \cdot \left(-i\right)\right)}\right) \]

   8. Simplified 40.2%

      \[\leadsto t \cdot \left(j \cdot \color{blue}{\left(y5 \cdot \left(-i\right)\right)}\right) \]

   if -3.89999999999999972e-27 < y5 < -5.99999999999999967e-155

   1. Initial program 23.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 23.9%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 24.3%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in c around inf 48.7%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(i \cdot z - y2 \cdot y4\right)\right)} \]

   6. Taylor expanded in i around inf 40.9%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(i \cdot z\right)\right)} \]

   if -5.99999999999999967e-155 < y5 < 1.85e-32

   1. Initial program 40.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 40.0%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 33.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in z around 0 27.0%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   6. Taylor expanded in c around inf 25.2%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 25.2%

         \[\leadsto \color{blue}{-c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)} \]

   8. Simplified 25.2%

      \[\leadsto \color{blue}{-c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)} \]

   if 1.85e-32 < y5 < 7.7999999999999999e189

   1. Initial program 41.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 41.7%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 36.0%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in j around inf 36.1%

      \[\leadsto t \cdot \color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]

   6. Taylor expanded in b around inf 38.0%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]

   if 7.7999999999999999e189 < y5

   1. Initial program 29.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 29.6%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 33.6%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in a around -inf 48.9%

      \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot \left(b \cdot z - y2 \cdot y5\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 48.9%

         \[\leadsto t \cdot \color{blue}{\left(\left(-1 \cdot a\right) \cdot \left(b \cdot z - y2 \cdot y5\right)\right)} \]

      2. neg-mul-1 48.9%

         \[\leadsto t \cdot \left(\color{blue}{\left(-a\right)} \cdot \left(b \cdot z - y2 \cdot y5\right)\right) \]

   7. Simplified 48.9%

      \[\leadsto t \cdot \color{blue}{\left(\left(-a\right) \cdot \left(b \cdot z - y2 \cdot y5\right)\right)} \]

   8. Taylor expanded in b around 0 38.1%

      \[\leadsto t \cdot \color{blue}{\left(a \cdot \left(y2 \cdot y5\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 35.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -3.9 \cdot 10^{-27}:\\ \;\;\;\;t \cdot \left(\left(i \cdot y5\right) \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y5 \leq -6 \cdot 10^{-155}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i\right)\right)\\ \mathbf{elif}\;y5 \leq 1.85 \cdot 10^{-32}:\\ \;\;\;\;\left(t \cdot \left(y2 \cdot y4\right)\right) \cdot \left(-c\right)\\ \mathbf{elif}\;y5 \leq 7.8 \cdot 10^{+189}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \]

Alternative 35: 19.0% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(z \cdot \left(t \cdot i\right)\right)\\ \mathbf{if}\;y2 \leq -2.15 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq 1.7 \cdot 10^{-144}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 2.8 \cdot 10^{+185}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* z (* t i)))))
   (if (<= y2 -2.15e+66)
     t_1
     (if (<= y2 1.7e-144)
       (* b (* j (* t y4)))
       (if (<= y2 2.8e+185) t_1 (* a (* t (* 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 = c * (z * (t * i));
	double tmp;
	if (y2 <= -2.15e+66) {
		tmp = t_1;
	} else if (y2 <= 1.7e-144) {
		tmp = b * (j * (t * y4));
	} else if (y2 <= 2.8e+185) {
		tmp = t_1;
	} else {
		tmp = a * (t * (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 = c * (z * (t * i))
    if (y2 <= (-2.15d+66)) then
        tmp = t_1
    else if (y2 <= 1.7d-144) then
        tmp = b * (j * (t * y4))
    else if (y2 <= 2.8d+185) then
        tmp = t_1
    else
        tmp = a * (t * (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 = c * (z * (t * i));
	double tmp;
	if (y2 <= -2.15e+66) {
		tmp = t_1;
	} else if (y2 <= 1.7e-144) {
		tmp = b * (j * (t * y4));
	} else if (y2 <= 2.8e+185) {
		tmp = t_1;
	} else {
		tmp = a * (t * (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 = c * (z * (t * i))
	tmp = 0
	if y2 <= -2.15e+66:
		tmp = t_1
	elif y2 <= 1.7e-144:
		tmp = b * (j * (t * y4))
	elif y2 <= 2.8e+185:
		tmp = t_1
	else:
		tmp = a * (t * (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(c * Float64(z * Float64(t * i)))
	tmp = 0.0
	if (y2 <= -2.15e+66)
		tmp = t_1;
	elseif (y2 <= 1.7e-144)
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	elseif (y2 <= 2.8e+185)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (z * (t * i));
	tmp = 0.0;
	if (y2 <= -2.15e+66)
		tmp = t_1;
	elseif (y2 <= 1.7e-144)
		tmp = b * (j * (t * y4));
	elseif (y2 <= 2.8e+185)
		tmp = t_1;
	else
		tmp = a * (t * (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[(c * N[(z * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -2.15e+66], t$95$1, If[LessEqual[y2, 1.7e-144], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.8e+185], t$95$1, N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y2 < -2.15000000000000013e66 or 1.70000000000000009e-144 < y2 < 2.79999999999999982e185

   1. Initial program 28.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.7%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 41.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in z around inf 34.7%

      \[\leadsto \color{blue}{c \cdot \left(z \cdot \left(-1 \cdot \left(y0 \cdot y3\right) + i \cdot t\right)\right)} \]

   6. Taylor expanded in y0 around 0 30.9%

      \[\leadsto c \cdot \left(z \cdot \color{blue}{\left(i \cdot t\right)}\right) \]

   if -2.15000000000000013e66 < y2 < 1.70000000000000009e-144

   1. Initial program 40.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 40.8%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 39.3%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in j around inf 36.1%

      \[\leadsto t \cdot \color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]

   6. Taylor expanded in b around inf 26.1%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]

   if 2.79999999999999982e185 < y2

   1. Initial program 27.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 27.0%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 33.9%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in a around -inf 37.8%

      \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot \left(b \cdot z - y2 \cdot y5\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 37.8%

         \[\leadsto t \cdot \color{blue}{\left(\left(-1 \cdot a\right) \cdot \left(b \cdot z - y2 \cdot y5\right)\right)} \]

      2. neg-mul-1 37.8%

         \[\leadsto t \cdot \left(\color{blue}{\left(-a\right)} \cdot \left(b \cdot z - y2 \cdot y5\right)\right) \]

   7. Simplified 37.8%

      \[\leadsto t \cdot \color{blue}{\left(\left(-a\right) \cdot \left(b \cdot z - y2 \cdot y5\right)\right)} \]

   8. Taylor expanded in b around 0 44.5%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 30.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -2.15 \cdot 10^{+66}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i\right)\right)\\ \mathbf{elif}\;y2 \leq 1.7 \cdot 10^{-144}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 2.8 \cdot 10^{+185}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \]

Alternative 36: 19.0% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -8.5 \cdot 10^{+90}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i\right)\right)\\ \mathbf{elif}\;y2 \leq 7.2 \cdot 10^{-143}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 4.1 \cdot 10^{+185}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -8.5e+90)
   (* t (* c (* z i)))
   (if (<= y2 7.2e-143)
     (* b (* j (* t y4)))
     (if (<= y2 4.1e+185) (* c (* z (* t i))) (* a (* t (* 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 tmp;
	if (y2 <= -8.5e+90) {
		tmp = t * (c * (z * i));
	} else if (y2 <= 7.2e-143) {
		tmp = b * (j * (t * y4));
	} else if (y2 <= 4.1e+185) {
		tmp = c * (z * (t * i));
	} else {
		tmp = a * (t * (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) :: tmp
    if (y2 <= (-8.5d+90)) then
        tmp = t * (c * (z * i))
    else if (y2 <= 7.2d-143) then
        tmp = b * (j * (t * y4))
    else if (y2 <= 4.1d+185) then
        tmp = c * (z * (t * i))
    else
        tmp = a * (t * (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 tmp;
	if (y2 <= -8.5e+90) {
		tmp = t * (c * (z * i));
	} else if (y2 <= 7.2e-143) {
		tmp = b * (j * (t * y4));
	} else if (y2 <= 4.1e+185) {
		tmp = c * (z * (t * i));
	} else {
		tmp = a * (t * (y2 * 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 y2 <= -8.5e+90:
		tmp = t * (c * (z * i))
	elif y2 <= 7.2e-143:
		tmp = b * (j * (t * y4))
	elif y2 <= 4.1e+185:
		tmp = c * (z * (t * i))
	else:
		tmp = a * (t * (y2 * 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 (y2 <= -8.5e+90)
		tmp = Float64(t * Float64(c * Float64(z * i)));
	elseif (y2 <= 7.2e-143)
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	elseif (y2 <= 4.1e+185)
		tmp = Float64(c * Float64(z * Float64(t * i)));
	else
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y2 <= -8.5e+90)
		tmp = t * (c * (z * i));
	elseif (y2 <= 7.2e-143)
		tmp = b * (j * (t * y4));
	elseif (y2 <= 4.1e+185)
		tmp = c * (z * (t * i));
	else
		tmp = a * (t * (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_] := If[LessEqual[y2, -8.5e+90], N[(t * N[(c * N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 7.2e-143], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 4.1e+185], N[(c * N[(z * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y2 < -8.5000000000000002e90

   1. Initial program 13.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 13.5%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 33.2%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in c around inf 57.5%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(i \cdot z - y2 \cdot y4\right)\right)} \]

   6. Taylor expanded in i around inf 41.8%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(i \cdot z\right)\right)} \]

   if -8.5000000000000002e90 < y2 < 7.1999999999999996e-143

   1. Initial program 40.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 40.3%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 40.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in j around inf 36.6%

      \[\leadsto t \cdot \color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]

   6. Taylor expanded in b around inf 26.9%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]

   if 7.1999999999999996e-143 < y2 < 4.1e185

   1. Initial program 37.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 37.2%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 40.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in z around inf 36.9%

      \[\leadsto \color{blue}{c \cdot \left(z \cdot \left(-1 \cdot \left(y0 \cdot y3\right) + i \cdot t\right)\right)} \]

   6. Taylor expanded in y0 around 0 25.0%

      \[\leadsto c \cdot \left(z \cdot \color{blue}{\left(i \cdot t\right)}\right) \]

   if 4.1e185 < y2

   1. Initial program 27.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 27.0%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 33.9%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in a around -inf 37.8%

      \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot \left(b \cdot z - y2 \cdot y5\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 37.8%

         \[\leadsto t \cdot \color{blue}{\left(\left(-1 \cdot a\right) \cdot \left(b \cdot z - y2 \cdot y5\right)\right)} \]

      2. neg-mul-1 37.8%

         \[\leadsto t \cdot \left(\color{blue}{\left(-a\right)} \cdot \left(b \cdot z - y2 \cdot y5\right)\right) \]

   7. Simplified 37.8%

      \[\leadsto t \cdot \color{blue}{\left(\left(-a\right) \cdot \left(b \cdot z - y2 \cdot y5\right)\right)} \]

   8. Taylor expanded in b around 0 44.5%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 30.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -8.5 \cdot 10^{+90}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i\right)\right)\\ \mathbf{elif}\;y2 \leq 7.2 \cdot 10^{-143}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 4.1 \cdot 10^{+185}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \]

Alternative 37: 19.1% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -1.4 \cdot 10^{+88}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i\right)\right)\\ \mathbf{elif}\;y2 \leq 1.2 \cdot 10^{-145}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq 1.15 \cdot 10^{+185}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -1.4e+88)
   (* t (* c (* z i)))
   (if (<= y2 1.2e-145)
     (* y4 (* b (* t j)))
     (if (<= y2 1.15e+185) (* c (* z (* t i))) (* a (* t (* 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 tmp;
	if (y2 <= -1.4e+88) {
		tmp = t * (c * (z * i));
	} else if (y2 <= 1.2e-145) {
		tmp = y4 * (b * (t * j));
	} else if (y2 <= 1.15e+185) {
		tmp = c * (z * (t * i));
	} else {
		tmp = a * (t * (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) :: tmp
    if (y2 <= (-1.4d+88)) then
        tmp = t * (c * (z * i))
    else if (y2 <= 1.2d-145) then
        tmp = y4 * (b * (t * j))
    else if (y2 <= 1.15d+185) then
        tmp = c * (z * (t * i))
    else
        tmp = a * (t * (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 tmp;
	if (y2 <= -1.4e+88) {
		tmp = t * (c * (z * i));
	} else if (y2 <= 1.2e-145) {
		tmp = y4 * (b * (t * j));
	} else if (y2 <= 1.15e+185) {
		tmp = c * (z * (t * i));
	} else {
		tmp = a * (t * (y2 * 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 y2 <= -1.4e+88:
		tmp = t * (c * (z * i))
	elif y2 <= 1.2e-145:
		tmp = y4 * (b * (t * j))
	elif y2 <= 1.15e+185:
		tmp = c * (z * (t * i))
	else:
		tmp = a * (t * (y2 * 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 (y2 <= -1.4e+88)
		tmp = Float64(t * Float64(c * Float64(z * i)));
	elseif (y2 <= 1.2e-145)
		tmp = Float64(y4 * Float64(b * Float64(t * j)));
	elseif (y2 <= 1.15e+185)
		tmp = Float64(c * Float64(z * Float64(t * i)));
	else
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y2 <= -1.4e+88)
		tmp = t * (c * (z * i));
	elseif (y2 <= 1.2e-145)
		tmp = y4 * (b * (t * j));
	elseif (y2 <= 1.15e+185)
		tmp = c * (z * (t * i));
	else
		tmp = a * (t * (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_] := If[LessEqual[y2, -1.4e+88], N[(t * N[(c * N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.2e-145], N[(y4 * N[(b * N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.15e+185], N[(c * N[(z * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y2 < -1.39999999999999994e88

   1. Initial program 13.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 13.5%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 33.2%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in c around inf 57.5%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(i \cdot z - y2 \cdot y4\right)\right)} \]

   6. Taylor expanded in i around inf 41.8%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(i \cdot z\right)\right)} \]

   if -1.39999999999999994e88 < y2 < 1.20000000000000008e-145

   1. Initial program 40.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 40.3%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 40.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in j around inf 36.6%

      \[\leadsto t \cdot \color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]

   6. Taylor expanded in b around inf 26.9%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 26.9%

         \[\leadsto \color{blue}{\left(j \cdot \left(t \cdot y4\right)\right) \cdot b} \]

      2. associate-*r* 27.7%

         \[\leadsto \color{blue}{\left(\left(j \cdot t\right) \cdot y4\right)} \cdot b \]

      3. *-commutative 27.7%

         \[\leadsto \left(\color{blue}{\left(t \cdot j\right)} \cdot y4\right) \cdot b \]

      4. associate-*r* 26.9%

         \[\leadsto \color{blue}{\left(t \cdot j\right) \cdot \left(y4 \cdot b\right)} \]

      5. *-commutative 26.9%

         \[\leadsto \color{blue}{\left(y4 \cdot b\right) \cdot \left(t \cdot j\right)} \]

      6. associate-*l* 28.5%

         \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(t \cdot j\right)\right)} \]

   8. Simplified 28.5%

      \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(t \cdot j\right)\right)} \]

   if 1.20000000000000008e-145 < y2 < 1.1500000000000001e185

   1. Initial program 37.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 37.2%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 40.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in z around inf 36.9%

      \[\leadsto \color{blue}{c \cdot \left(z \cdot \left(-1 \cdot \left(y0 \cdot y3\right) + i \cdot t\right)\right)} \]

   6. Taylor expanded in y0 around 0 25.0%

      \[\leadsto c \cdot \left(z \cdot \color{blue}{\left(i \cdot t\right)}\right) \]

   if 1.1500000000000001e185 < y2

   1. Initial program 27.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 27.0%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 33.9%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in a around -inf 37.8%

      \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot \left(b \cdot z - y2 \cdot y5\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 37.8%

         \[\leadsto t \cdot \color{blue}{\left(\left(-1 \cdot a\right) \cdot \left(b \cdot z - y2 \cdot y5\right)\right)} \]

      2. neg-mul-1 37.8%

         \[\leadsto t \cdot \left(\color{blue}{\left(-a\right)} \cdot \left(b \cdot z - y2 \cdot y5\right)\right) \]

   7. Simplified 37.8%

      \[\leadsto t \cdot \color{blue}{\left(\left(-a\right) \cdot \left(b \cdot z - y2 \cdot y5\right)\right)} \]

   8. Taylor expanded in b around 0 44.5%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 31.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.4 \cdot 10^{+88}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i\right)\right)\\ \mathbf{elif}\;y2 \leq 1.2 \cdot 10^{-145}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq 1.15 \cdot 10^{+185}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \]

Alternative 38: 22.9% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -4.1 \cdot 10^{-51} \lor \neg \left(y2 \leq 10^{-52}\right):\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= y2 -4.1e-51) (not (<= y2 1e-52)))
   (* a (* t (* y2 y5)))
   (* a (* (* x y) b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y2 <= -4.1e-51) || !(y2 <= 1e-52)) {
		tmp = a * (t * (y2 * y5));
	} else {
		tmp = a * ((x * y) * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((y2 <= (-4.1d-51)) .or. (.not. (y2 <= 1d-52))) then
        tmp = a * (t * (y2 * y5))
    else
        tmp = a * ((x * y) * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y2 <= -4.1e-51) || !(y2 <= 1e-52)) {
		tmp = a * (t * (y2 * y5));
	} else {
		tmp = a * ((x * y) * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (y2 <= -4.1e-51) or not (y2 <= 1e-52):
		tmp = a * (t * (y2 * y5))
	else:
		tmp = a * ((x * y) * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((y2 <= -4.1e-51) || !(y2 <= 1e-52))
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	else
		tmp = Float64(a * Float64(Float64(x * y) * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((y2 <= -4.1e-51) || ~((y2 <= 1e-52)))
		tmp = a * (t * (y2 * y5));
	else
		tmp = a * ((x * y) * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[y2, -4.1e-51], N[Not[LessEqual[y2, 1e-52]], $MachinePrecision]], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y2 < -4.09999999999999973e-51 or 1e-52 < y2

   1. Initial program 28.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.5%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 35.8%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in a around -inf 32.9%

      \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot \left(b \cdot z - y2 \cdot y5\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 32.9%

         \[\leadsto t \cdot \color{blue}{\left(\left(-1 \cdot a\right) \cdot \left(b \cdot z - y2 \cdot y5\right)\right)} \]

      2. neg-mul-1 32.9%

         \[\leadsto t \cdot \left(\color{blue}{\left(-a\right)} \cdot \left(b \cdot z - y2 \cdot y5\right)\right) \]

   7. Simplified 32.9%

      \[\leadsto t \cdot \color{blue}{\left(\left(-a\right) \cdot \left(b \cdot z - y2 \cdot y5\right)\right)} \]

   8. Taylor expanded in b around 0 28.9%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} \]

   if -4.09999999999999973e-51 < y2 < 1e-52

   1. Initial program 40.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 40.4%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 39.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in a around inf 29.7%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 17.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 23.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -4.1 \cdot 10^{-51} \lor \neg \left(y2 \leq 10^{-52}\right):\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \end{array} \]

Alternative 39: 22.8% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -6.2 \cdot 10^{-49} \lor \neg \left(y2 \leq 1.55 \cdot 10^{-51}\right):\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= y2 -6.2e-49) (not (<= y2 1.55e-51)))
   (* a (* t (* y2 y5)))
   (* a (* x (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y2 <= -6.2e-49) || !(y2 <= 1.55e-51)) {
		tmp = a * (t * (y2 * y5));
	} else {
		tmp = a * (x * (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((y2 <= (-6.2d-49)) .or. (.not. (y2 <= 1.55d-51))) then
        tmp = a * (t * (y2 * y5))
    else
        tmp = a * (x * (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y2 <= -6.2e-49) || !(y2 <= 1.55e-51)) {
		tmp = a * (t * (y2 * y5));
	} else {
		tmp = a * (x * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (y2 <= -6.2e-49) or not (y2 <= 1.55e-51):
		tmp = a * (t * (y2 * y5))
	else:
		tmp = a * (x * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((y2 <= -6.2e-49) || !(y2 <= 1.55e-51))
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	else
		tmp = Float64(a * Float64(x * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((y2 <= -6.2e-49) || ~((y2 <= 1.55e-51)))
		tmp = a * (t * (y2 * y5));
	else
		tmp = a * (x * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[y2, -6.2e-49], N[Not[LessEqual[y2, 1.55e-51]], $MachinePrecision]], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y2 < -6.2e-49 or 1.5499999999999999e-51 < y2

   1. Initial program 28.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.5%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 35.8%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in a around -inf 32.9%

      \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot \left(b \cdot z - y2 \cdot y5\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 32.9%

         \[\leadsto t \cdot \color{blue}{\left(\left(-1 \cdot a\right) \cdot \left(b \cdot z - y2 \cdot y5\right)\right)} \]

      2. neg-mul-1 32.9%

         \[\leadsto t \cdot \left(\color{blue}{\left(-a\right)} \cdot \left(b \cdot z - y2 \cdot y5\right)\right) \]

   7. Simplified 32.9%

      \[\leadsto t \cdot \color{blue}{\left(\left(-a\right) \cdot \left(b \cdot z - y2 \cdot y5\right)\right)} \]

   8. Taylor expanded in b around 0 28.9%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} \]

   if -6.2e-49 < y2 < 1.5499999999999999e-51

   1. Initial program 40.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 40.4%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 39.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in a around inf 29.7%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 17.3%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 17.3%

         \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot b\right)} \]

      2. associate-*l* 17.4%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(y \cdot b\right)\right)} \]

   8. Simplified 17.4%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(y \cdot b\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 23.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -6.2 \cdot 10^{-49} \lor \neg \left(y2 \leq 1.55 \cdot 10^{-51}\right):\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \end{array} \]

Alternative 40: 19.6% accurate, 10.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq 7 \cdot 10^{+31}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j 7e+31) (* a (* t (* y2 y5))) (* b (* j (* 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 tmp;
	if (j <= 7e+31) {
		tmp = a * (t * (y2 * y5));
	} else {
		tmp = b * (j * (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) :: tmp
    if (j <= 7d+31) then
        tmp = a * (t * (y2 * y5))
    else
        tmp = b * (j * (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 tmp;
	if (j <= 7e+31) {
		tmp = a * (t * (y2 * y5));
	} else {
		tmp = b * (j * (t * 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 j <= 7e+31:
		tmp = a * (t * (y2 * y5))
	else:
		tmp = b * (j * (t * 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 (j <= 7e+31)
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	else
		tmp = Float64(b * Float64(j * 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)
	tmp = 0.0;
	if (j <= 7e+31)
		tmp = a * (t * (y2 * y5));
	else
		tmp = b * (j * (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_] := If[LessEqual[j, 7e+31], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < 7e31

   1. Initial program 31.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.9%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 33.3%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in a around -inf 27.4%

      \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot \left(b \cdot z - y2 \cdot y5\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 27.4%

         \[\leadsto t \cdot \color{blue}{\left(\left(-1 \cdot a\right) \cdot \left(b \cdot z - y2 \cdot y5\right)\right)} \]

      2. neg-mul-1 27.4%

         \[\leadsto t \cdot \left(\color{blue}{\left(-a\right)} \cdot \left(b \cdot z - y2 \cdot y5\right)\right) \]

   7. Simplified 27.4%

      \[\leadsto t \cdot \color{blue}{\left(\left(-a\right) \cdot \left(b \cdot z - y2 \cdot y5\right)\right)} \]

   8. Taylor expanded in b around 0 19.6%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} \]

   if 7e31 < j

   1. Initial program 41.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 41.4%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 40.3%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in j around inf 44.1%

      \[\leadsto t \cdot \color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]

   6. Taylor expanded in b around inf 39.3%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 24.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq 7 \cdot 10^{+31}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \end{array} \]

Alternative 41: 17.3% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(\left(x \cdot y\right) \cdot b\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* (* x y) b)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * ((x * y) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = a * ((x * y) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * ((x * y) * b);
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * ((x * y) * b)

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(Float64(x * y) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * ((x * y) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 34.0%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

3. Simplified 34.0%

   \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

4. Taylor expanded in b around inf 36.2%

   \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

5. Taylor expanded in a around inf 25.9%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

6. Taylor expanded in x around inf 13.2%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]

7. Final simplification 13.2%

   \[\leadsto a \cdot \left(\left(x \cdot y\right) \cdot b\right) \]

Developer target: 27.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot c - y5 \cdot a\\ t_2 := x \cdot y2 - z \cdot y3\\ t_3 := y2 \cdot t - y3 \cdot y\\ t_4 := k \cdot y2 - j \cdot y3\\ t_5 := y4 \cdot b - y5 \cdot i\\ t_6 := \left(j \cdot t - k \cdot y\right) \cdot t_5\\ t_7 := b \cdot a - i \cdot c\\ t_8 := t_7 \cdot \left(y \cdot x - t \cdot z\right)\\ t_9 := j \cdot x - k \cdot z\\ t_10 := \left(b \cdot y0 - i \cdot y1\right) \cdot t_9\\ t_11 := t_9 \cdot \left(y0 \cdot b - i \cdot y1\right)\\ t_12 := y4 \cdot y1 - y5 \cdot y0\\ t_13 := t_4 \cdot t_12\\ t_14 := \left(y2 \cdot k - y3 \cdot j\right) \cdot t_12\\ t_15 := \left(\left(\left(\left(k \cdot y\right) \cdot \left(y5 \cdot i\right) - \left(y \cdot b\right) \cdot \left(y4 \cdot k\right)\right) - \left(y5 \cdot t\right) \cdot \left(i \cdot j\right)\right) - \left(t_3 \cdot t_1 - t_14\right)\right) + \left(t_8 - \left(t_11 - \left(y2 \cdot x - y3 \cdot z\right) \cdot \left(c \cdot y0 - y1 \cdot a\right)\right)\right)\\ t_16 := \left(\left(t_6 - \left(y3 \cdot y\right) \cdot \left(y5 \cdot a - y4 \cdot c\right)\right) + \left(\left(y5 \cdot a\right) \cdot \left(t \cdot y2\right) + t_13\right)\right) + \left(t_2 \cdot \left(c \cdot y0 - a \cdot y1\right) - \left(t_10 - \left(y \cdot x - z \cdot t\right) \cdot t_7\right)\right)\\ t_17 := t \cdot y2 - y \cdot y3\\ \mathbf{if}\;y4 < -7.206256231996481 \cdot 10^{+60}:\\ \;\;\;\;\left(t_8 - \left(t_11 - t_6\right)\right) - \left(\frac{t_3}{\frac{1}{t_1}} - t_14\right)\\ \mathbf{elif}\;y4 < -3.364603505246317 \cdot 10^{-66}:\\ \;\;\;\;\left(\left(\left(\left(t \cdot c\right) \cdot \left(i \cdot z\right) - \left(a \cdot t\right) \cdot \left(b \cdot z\right)\right) - \left(y \cdot c\right) \cdot \left(i \cdot x\right)\right) - t_10\right) + \left(\left(y0 \cdot c - a \cdot y1\right) \cdot t_2 - \left(t_17 \cdot \left(y4 \cdot c - a \cdot y5\right) - \left(y1 \cdot y4 - y5 \cdot y0\right) \cdot t_4\right)\right)\\ \mathbf{elif}\;y4 < -1.2000065055686116 \cdot 10^{-105}:\\ \;\;\;\;t_16\\ \mathbf{elif}\;y4 < 6.718963124057495 \cdot 10^{-279}:\\ \;\;\;\;t_15\\ \mathbf{elif}\;y4 < 4.77962681403792 \cdot 10^{-222}:\\ \;\;\;\;t_16\\ \mathbf{elif}\;y4 < 2.2852241541266835 \cdot 10^{-175}:\\ \;\;\;\;t_15\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(k \cdot \left(i \cdot \left(z \cdot y1\right)\right) - \left(j \cdot \left(i \cdot \left(x \cdot y1\right)\right) + y0 \cdot \left(k \cdot \left(z \cdot b\right)\right)\right)\right)\right) + \left(z \cdot \left(y3 \cdot \left(a \cdot y1\right)\right) - \left(y2 \cdot \left(x \cdot \left(a \cdot y1\right)\right) + y0 \cdot \left(z \cdot \left(c \cdot y3\right)\right)\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot t_5\right) - t_17 \cdot t_1\right) + t_13\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y4 c) (* y5 a)))
        (t_2 (- (* x y2) (* z y3)))
        (t_3 (- (* y2 t) (* y3 y)))
        (t_4 (- (* k y2) (* j y3)))
        (t_5 (- (* y4 b) (* y5 i)))
        (t_6 (* (- (* j t) (* k y)) t_5))
        (t_7 (- (* b a) (* i c)))
        (t_8 (* t_7 (- (* y x) (* t z))))
        (t_9 (- (* j x) (* k z)))
        (t_10 (* (- (* b y0) (* i y1)) t_9))
        (t_11 (* t_9 (- (* y0 b) (* i y1))))
        (t_12 (- (* y4 y1) (* y5 y0)))
        (t_13 (* t_4 t_12))
        (t_14 (* (- (* y2 k) (* y3 j)) t_12))
        (t_15
         (+
          (-
           (-
            (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k)))
            (* (* y5 t) (* i j)))
           (- (* t_3 t_1) t_14))
          (- t_8 (- t_11 (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))))
        (t_16
         (+
          (+
           (- t_6 (* (* y3 y) (- (* y5 a) (* y4 c))))
           (+ (* (* y5 a) (* t y2)) t_13))
          (-
           (* t_2 (- (* c y0) (* a y1)))
           (- t_10 (* (- (* y x) (* z t)) t_7)))))
        (t_17 (- (* t y2) (* y y3))))
   (if (< y4 -7.206256231996481e+60)
     (- (- t_8 (- t_11 t_6)) (- (/ t_3 (/ 1.0 t_1)) t_14))
     (if (< y4 -3.364603505246317e-66)
       (+
        (-
         (- (- (* (* t c) (* i z)) (* (* a t) (* b z))) (* (* y c) (* i x)))
         t_10)
        (-
         (* (- (* y0 c) (* a y1)) t_2)
         (- (* t_17 (- (* y4 c) (* a y5))) (* (- (* y1 y4) (* y5 y0)) t_4))))
       (if (< y4 -1.2000065055686116e-105)
         t_16
         (if (< y4 6.718963124057495e-279)
           t_15
           (if (< y4 4.77962681403792e-222)
             t_16
             (if (< y4 2.2852241541266835e-175)
               t_15
               (+
                (-
                 (+
                  (+
                   (-
                    (* (- (* x y) (* z t)) (- (* a b) (* c i)))
                    (-
                     (* k (* i (* z y1)))
                     (+ (* j (* i (* x y1))) (* y0 (* k (* z b))))))
                   (-
                    (* z (* y3 (* a y1)))
                    (+ (* y2 (* x (* a y1))) (* y0 (* z (* c y3))))))
                  (* (- (* t j) (* y k)) t_5))
                 (* t_17 t_1))
                t_13)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y4 * c) - (y5 * a);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (y2 * t) - (y3 * y);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = (y4 * b) - (y5 * i);
	double t_6 = ((j * t) - (k * y)) * t_5;
	double t_7 = (b * a) - (i * c);
	double t_8 = t_7 * ((y * x) - (t * z));
	double t_9 = (j * x) - (k * z);
	double t_10 = ((b * y0) - (i * y1)) * t_9;
	double t_11 = t_9 * ((y0 * b) - (i * y1));
	double t_12 = (y4 * y1) - (y5 * y0);
	double t_13 = t_4 * t_12;
	double t_14 = ((y2 * k) - (y3 * j)) * t_12;
	double t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	double t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	double t_17 = (t * y2) - (y * y3);
	double tmp;
	if (y4 < -7.206256231996481e+60) {
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	} else if (y4 < -3.364603505246317e-66) {
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	} else if (y4 < -1.2000065055686116e-105) {
		tmp = t_16;
	} else if (y4 < 6.718963124057495e-279) {
		tmp = t_15;
	} else if (y4 < 4.77962681403792e-222) {
		tmp = t_16;
	} else if (y4 < 2.2852241541266835e-175) {
		tmp = t_15;
	} else {
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_10
    real(8) :: t_11
    real(8) :: t_12
    real(8) :: t_13
    real(8) :: t_14
    real(8) :: t_15
    real(8) :: t_16
    real(8) :: t_17
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = (y4 * c) - (y5 * a)
    t_2 = (x * y2) - (z * y3)
    t_3 = (y2 * t) - (y3 * y)
    t_4 = (k * y2) - (j * y3)
    t_5 = (y4 * b) - (y5 * i)
    t_6 = ((j * t) - (k * y)) * t_5
    t_7 = (b * a) - (i * c)
    t_8 = t_7 * ((y * x) - (t * z))
    t_9 = (j * x) - (k * z)
    t_10 = ((b * y0) - (i * y1)) * t_9
    t_11 = t_9 * ((y0 * b) - (i * y1))
    t_12 = (y4 * y1) - (y5 * y0)
    t_13 = t_4 * t_12
    t_14 = ((y2 * k) - (y3 * j)) * t_12
    t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))))
    t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)))
    t_17 = (t * y2) - (y * y3)
    if (y4 < (-7.206256231996481d+60)) then
        tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0d0 / t_1)) - t_14)
    else if (y4 < (-3.364603505246317d-66)) then
        tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)))
    else if (y4 < (-1.2000065055686116d-105)) then
        tmp = t_16
    else if (y4 < 6.718963124057495d-279) then
        tmp = t_15
    else if (y4 < 4.77962681403792d-222) then
        tmp = t_16
    else if (y4 < 2.2852241541266835d-175) then
        tmp = t_15
    else
        tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y4 * c) - (y5 * a);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (y2 * t) - (y3 * y);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = (y4 * b) - (y5 * i);
	double t_6 = ((j * t) - (k * y)) * t_5;
	double t_7 = (b * a) - (i * c);
	double t_8 = t_7 * ((y * x) - (t * z));
	double t_9 = (j * x) - (k * z);
	double t_10 = ((b * y0) - (i * y1)) * t_9;
	double t_11 = t_9 * ((y0 * b) - (i * y1));
	double t_12 = (y4 * y1) - (y5 * y0);
	double t_13 = t_4 * t_12;
	double t_14 = ((y2 * k) - (y3 * j)) * t_12;
	double t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	double t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	double t_17 = (t * y2) - (y * y3);
	double tmp;
	if (y4 < -7.206256231996481e+60) {
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	} else if (y4 < -3.364603505246317e-66) {
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	} else if (y4 < -1.2000065055686116e-105) {
		tmp = t_16;
	} else if (y4 < 6.718963124057495e-279) {
		tmp = t_15;
	} else if (y4 < 4.77962681403792e-222) {
		tmp = t_16;
	} else if (y4 < 2.2852241541266835e-175) {
		tmp = t_15;
	} else {
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y4 * c) - (y5 * a)
	t_2 = (x * y2) - (z * y3)
	t_3 = (y2 * t) - (y3 * y)
	t_4 = (k * y2) - (j * y3)
	t_5 = (y4 * b) - (y5 * i)
	t_6 = ((j * t) - (k * y)) * t_5
	t_7 = (b * a) - (i * c)
	t_8 = t_7 * ((y * x) - (t * z))
	t_9 = (j * x) - (k * z)
	t_10 = ((b * y0) - (i * y1)) * t_9
	t_11 = t_9 * ((y0 * b) - (i * y1))
	t_12 = (y4 * y1) - (y5 * y0)
	t_13 = t_4 * t_12
	t_14 = ((y2 * k) - (y3 * j)) * t_12
	t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))))
	t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)))
	t_17 = (t * y2) - (y * y3)
	tmp = 0
	if y4 < -7.206256231996481e+60:
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14)
	elif y4 < -3.364603505246317e-66:
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)))
	elif y4 < -1.2000065055686116e-105:
		tmp = t_16
	elif y4 < 6.718963124057495e-279:
		tmp = t_15
	elif y4 < 4.77962681403792e-222:
		tmp = t_16
	elif y4 < 2.2852241541266835e-175:
		tmp = t_15
	else:
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y4 * c) - Float64(y5 * a))
	t_2 = Float64(Float64(x * y2) - Float64(z * y3))
	t_3 = Float64(Float64(y2 * t) - Float64(y3 * y))
	t_4 = Float64(Float64(k * y2) - Float64(j * y3))
	t_5 = Float64(Float64(y4 * b) - Float64(y5 * i))
	t_6 = Float64(Float64(Float64(j * t) - Float64(k * y)) * t_5)
	t_7 = Float64(Float64(b * a) - Float64(i * c))
	t_8 = Float64(t_7 * Float64(Float64(y * x) - Float64(t * z)))
	t_9 = Float64(Float64(j * x) - Float64(k * z))
	t_10 = Float64(Float64(Float64(b * y0) - Float64(i * y1)) * t_9)
	t_11 = Float64(t_9 * Float64(Float64(y0 * b) - Float64(i * y1)))
	t_12 = Float64(Float64(y4 * y1) - Float64(y5 * y0))
	t_13 = Float64(t_4 * t_12)
	t_14 = Float64(Float64(Float64(y2 * k) - Float64(y3 * j)) * t_12)
	t_15 = Float64(Float64(Float64(Float64(Float64(Float64(k * y) * Float64(y5 * i)) - Float64(Float64(y * b) * Float64(y4 * k))) - Float64(Float64(y5 * t) * Float64(i * j))) - Float64(Float64(t_3 * t_1) - t_14)) + Float64(t_8 - Float64(t_11 - Float64(Float64(Float64(y2 * x) - Float64(y3 * z)) * Float64(Float64(c * y0) - Float64(y1 * a))))))
	t_16 = Float64(Float64(Float64(t_6 - Float64(Float64(y3 * y) * Float64(Float64(y5 * a) - Float64(y4 * c)))) + Float64(Float64(Float64(y5 * a) * Float64(t * y2)) + t_13)) + Float64(Float64(t_2 * Float64(Float64(c * y0) - Float64(a * y1))) - Float64(t_10 - Float64(Float64(Float64(y * x) - Float64(z * t)) * t_7))))
	t_17 = Float64(Float64(t * y2) - Float64(y * y3))
	tmp = 0.0
	if (y4 < -7.206256231996481e+60)
		tmp = Float64(Float64(t_8 - Float64(t_11 - t_6)) - Float64(Float64(t_3 / Float64(1.0 / t_1)) - t_14));
	elseif (y4 < -3.364603505246317e-66)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(t * c) * Float64(i * z)) - Float64(Float64(a * t) * Float64(b * z))) - Float64(Float64(y * c) * Float64(i * x))) - t_10) + Float64(Float64(Float64(Float64(y0 * c) - Float64(a * y1)) * t_2) - Float64(Float64(t_17 * Float64(Float64(y4 * c) - Float64(a * y5))) - Float64(Float64(Float64(y1 * y4) - Float64(y5 * y0)) * t_4))));
	elseif (y4 < -1.2000065055686116e-105)
		tmp = t_16;
	elseif (y4 < 6.718963124057495e-279)
		tmp = t_15;
	elseif (y4 < 4.77962681403792e-222)
		tmp = t_16;
	elseif (y4 < 2.2852241541266835e-175)
		tmp = t_15;
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) - Float64(z * t)) * Float64(Float64(a * b) - Float64(c * i))) - Float64(Float64(k * Float64(i * Float64(z * y1))) - Float64(Float64(j * Float64(i * Float64(x * y1))) + Float64(y0 * Float64(k * Float64(z * b)))))) + Float64(Float64(z * Float64(y3 * Float64(a * y1))) - Float64(Float64(y2 * Float64(x * Float64(a * y1))) + Float64(y0 * Float64(z * Float64(c * y3)))))) + Float64(Float64(Float64(t * j) - Float64(y * k)) * t_5)) - Float64(t_17 * t_1)) + t_13);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y4 * c) - (y5 * a);
	t_2 = (x * y2) - (z * y3);
	t_3 = (y2 * t) - (y3 * y);
	t_4 = (k * y2) - (j * y3);
	t_5 = (y4 * b) - (y5 * i);
	t_6 = ((j * t) - (k * y)) * t_5;
	t_7 = (b * a) - (i * c);
	t_8 = t_7 * ((y * x) - (t * z));
	t_9 = (j * x) - (k * z);
	t_10 = ((b * y0) - (i * y1)) * t_9;
	t_11 = t_9 * ((y0 * b) - (i * y1));
	t_12 = (y4 * y1) - (y5 * y0);
	t_13 = t_4 * t_12;
	t_14 = ((y2 * k) - (y3 * j)) * t_12;
	t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	t_17 = (t * y2) - (y * y3);
	tmp = 0.0;
	if (y4 < -7.206256231996481e+60)
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	elseif (y4 < -3.364603505246317e-66)
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	elseif (y4 < -1.2000065055686116e-105)
		tmp = t_16;
	elseif (y4 < 6.718963124057495e-279)
		tmp = t_15;
	elseif (y4 < 4.77962681403792e-222)
		tmp = t_16;
	elseif (y4 < 2.2852241541266835e-175)
		tmp = t_15;
	else
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y4 * c), $MachinePrecision] - N[(y5 * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y2 * t), $MachinePrecision] - N[(y3 * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(y4 * b), $MachinePrecision] - N[(y5 * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision] * t$95$5), $MachinePrecision]}, Block[{t$95$7 = N[(N[(b * a), $MachinePrecision] - N[(i * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(t$95$7 * N[(N[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$10 = N[(N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision] * t$95$9), $MachinePrecision]}, Block[{t$95$11 = N[(t$95$9 * N[(N[(y0 * b), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$12 = N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$13 = N[(t$95$4 * t$95$12), $MachinePrecision]}, Block[{t$95$14 = N[(N[(N[(y2 * k), $MachinePrecision] - N[(y3 * j), $MachinePrecision]), $MachinePrecision] * t$95$12), $MachinePrecision]}, Block[{t$95$15 = N[(N[(N[(N[(N[(N[(k * y), $MachinePrecision] * N[(y5 * i), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] * N[(y4 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y5 * t), $MachinePrecision] * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$3 * t$95$1), $MachinePrecision] - t$95$14), $MachinePrecision]), $MachinePrecision] + N[(t$95$8 - N[(t$95$11 - N[(N[(N[(y2 * x), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision] * N[(N[(c * y0), $MachinePrecision] - N[(y1 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$16 = N[(N[(N[(t$95$6 - N[(N[(y3 * y), $MachinePrecision] * N[(N[(y5 * a), $MachinePrecision] - N[(y4 * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y5 * a), $MachinePrecision] * N[(t * y2), $MachinePrecision]), $MachinePrecision] + t$95$13), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$10 - N[(N[(N[(y * x), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$17 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, If[Less[y4, -7.206256231996481e+60], N[(N[(t$95$8 - N[(t$95$11 - t$95$6), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$3 / N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision] - t$95$14), $MachinePrecision]), $MachinePrecision], If[Less[y4, -3.364603505246317e-66], N[(N[(N[(N[(N[(N[(t * c), $MachinePrecision] * N[(i * z), $MachinePrecision]), $MachinePrecision] - N[(N[(a * t), $MachinePrecision] * N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * c), $MachinePrecision] * N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$10), $MachinePrecision] + N[(N[(N[(N[(y0 * c), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision] - N[(N[(t$95$17 * N[(N[(y4 * c), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(y1 * y4), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision] * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[y4, -1.2000065055686116e-105], t$95$16, If[Less[y4, 6.718963124057495e-279], t$95$15, If[Less[y4, 4.77962681403792e-222], t$95$16, If[Less[y4, 2.2852241541266835e-175], t$95$15, N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(k * N[(i * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * N[(i * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(k * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(y3 * N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y2 * N[(x * N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(z * N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * t$95$5), $MachinePrecision]), $MachinePrecision] - N[(t$95$17 * t$95$1), $MachinePrecision]), $MachinePrecision] + t$95$13), $MachinePrecision]]]]]]]]]]]]]]]]]]]]]]]]

Reproduce

herbie shell --seed 2023297 
(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)))))