Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 29.8% → 39.2%

Time: 2.4min

Alternatives: 44

Speedup: 1.7×

• 89.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 29.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 39.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot \left(x \cdot j - z \cdot k\right)\\ t_2 := t \cdot j - y \cdot k\\ t_3 := y \cdot k - t \cdot j\\ t_4 := i \cdot \left(t_1 + \left(y5 \cdot t_3 + c \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ t_5 := b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot t_2\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{if}\;i \leq -6.2 \cdot 10^{+243}:\\ \;\;\;\;i \cdot t_1\\ \mathbf{elif}\;i \leq -3 \cdot 10^{+207}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;i \leq -7.1 \cdot 10^{+168}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;i \leq -7 \cdot 10^{+125}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;i \leq -7.2 \cdot 10^{+77}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot t_3 + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;i \leq -7 \cdot 10^{+52}:\\ \;\;\;\;\left(t \cdot i\right) \cdot \left(z \cdot c - j \cdot y5\right)\\ \mathbf{elif}\;i \leq -3.4 \cdot 10^{-45}:\\ \;\;\;\;y3 \cdot \left(y5 \cdot \left(j \cdot y0 - y \cdot a\right)\right)\\ \mathbf{elif}\;i \leq -4.6 \cdot 10^{-85}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq -1.7 \cdot 10^{-144}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{-63}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot t_2 + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq 1.5 \cdot 10^{-12}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq 3.2 \cdot 10^{+47}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right) + y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;i \leq 7.2 \cdot 10^{+122}:\\ \;\;\;\;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}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y1 (- (* x j) (* z k))))
        (t_2 (- (* t j) (* y k)))
        (t_3 (- (* y k) (* t j)))
        (t_4 (* i (+ t_1 (+ (* y5 t_3) (* c (- (* z t) (* x y)))))))
        (t_5
         (*
          b
          (+
           (+ (* a (- (* x y) (* z t))) (* y4 t_2))
           (* y0 (- (* z k) (* x j)))))))
   (if (<= i -6.2e+243)
     (* i t_1)
     (if (<= i -3e+207)
       (* i (* y (- (* k y5) (* x c))))
       (if (<= i -7.1e+168)
         (* y1 (* z (- (* a y3) (* i k))))
         (if (<= i -7e+125)
           (* t (* z (- (* c i) (* a b))))
           (if (<= i -7.2e+77)
             (*
              y5
              (+
               (* a (- (* t y2) (* y y3)))
               (+ (* i t_3) (* y0 (- (* j y3) (* k y2))))))
             (if (<= i -7e+52)
               (* (* t i) (- (* z c) (* j y5)))
               (if (<= i -3.4e-45)
                 (* y3 (* y5 (- (* j y0) (* y a))))
                 (if (<= i -4.6e-85)
                   t_4
                   (if (<= i -1.7e-144)
                     t_5
                     (if (<= i 4.2e-63)
                       (*
                        y4
                        (+
                         (+ (* b t_2) (* y1 (- (* k y2) (* j y3))))
                         (* c (- (* y y3) (* t y2)))))
                       (if (<= i 1.5e-12)
                         t_5
                         (if (<= i 3.2e+47)
                           (*
                            k
                            (+
                             (* z (- (* b y0) (* i y1)))
                             (* y4 (- (* y1 y2) (* y b)))))
                           (if (<= i 7.2e+122)
                             (*
                              y2
                              (+
                               (+
                                (* k (- (* y1 y4) (* y0 y5)))
                                (* x (- (* c y0) (* a y1))))
                               (* t (- (* a y5) (* c y4)))))
                             t_4)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * ((x * j) - (z * k));
	double t_2 = (t * j) - (y * k);
	double t_3 = (y * k) - (t * j);
	double t_4 = i * (t_1 + ((y5 * t_3) + (c * ((z * t) - (x * y)))));
	double t_5 = b * (((a * ((x * y) - (z * t))) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))));
	double tmp;
	if (i <= -6.2e+243) {
		tmp = i * t_1;
	} else if (i <= -3e+207) {
		tmp = i * (y * ((k * y5) - (x * c)));
	} else if (i <= -7.1e+168) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (i <= -7e+125) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else if (i <= -7.2e+77) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * t_3) + (y0 * ((j * y3) - (k * y2)))));
	} else if (i <= -7e+52) {
		tmp = (t * i) * ((z * c) - (j * y5));
	} else if (i <= -3.4e-45) {
		tmp = y3 * (y5 * ((j * y0) - (y * a)));
	} else if (i <= -4.6e-85) {
		tmp = t_4;
	} else if (i <= -1.7e-144) {
		tmp = t_5;
	} else if (i <= 4.2e-63) {
		tmp = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (i <= 1.5e-12) {
		tmp = t_5;
	} else if (i <= 3.2e+47) {
		tmp = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))));
	} else if (i <= 7.2e+122) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = y1 * ((x * j) - (z * k))
    t_2 = (t * j) - (y * k)
    t_3 = (y * k) - (t * j)
    t_4 = i * (t_1 + ((y5 * t_3) + (c * ((z * t) - (x * y)))))
    t_5 = b * (((a * ((x * y) - (z * t))) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))))
    if (i <= (-6.2d+243)) then
        tmp = i * t_1
    else if (i <= (-3d+207)) then
        tmp = i * (y * ((k * y5) - (x * c)))
    else if (i <= (-7.1d+168)) then
        tmp = y1 * (z * ((a * y3) - (i * k)))
    else if (i <= (-7d+125)) then
        tmp = t * (z * ((c * i) - (a * b)))
    else if (i <= (-7.2d+77)) then
        tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * t_3) + (y0 * ((j * y3) - (k * y2)))))
    else if (i <= (-7d+52)) then
        tmp = (t * i) * ((z * c) - (j * y5))
    else if (i <= (-3.4d-45)) then
        tmp = y3 * (y5 * ((j * y0) - (y * a)))
    else if (i <= (-4.6d-85)) then
        tmp = t_4
    else if (i <= (-1.7d-144)) then
        tmp = t_5
    else if (i <= 4.2d-63) then
        tmp = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    else if (i <= 1.5d-12) then
        tmp = t_5
    else if (i <= 3.2d+47) then
        tmp = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))))
    else if (i <= 7.2d+122) then
        tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * ((x * j) - (z * k));
	double t_2 = (t * j) - (y * k);
	double t_3 = (y * k) - (t * j);
	double t_4 = i * (t_1 + ((y5 * t_3) + (c * ((z * t) - (x * y)))));
	double t_5 = b * (((a * ((x * y) - (z * t))) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))));
	double tmp;
	if (i <= -6.2e+243) {
		tmp = i * t_1;
	} else if (i <= -3e+207) {
		tmp = i * (y * ((k * y5) - (x * c)));
	} else if (i <= -7.1e+168) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (i <= -7e+125) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else if (i <= -7.2e+77) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * t_3) + (y0 * ((j * y3) - (k * y2)))));
	} else if (i <= -7e+52) {
		tmp = (t * i) * ((z * c) - (j * y5));
	} else if (i <= -3.4e-45) {
		tmp = y3 * (y5 * ((j * y0) - (y * a)));
	} else if (i <= -4.6e-85) {
		tmp = t_4;
	} else if (i <= -1.7e-144) {
		tmp = t_5;
	} else if (i <= 4.2e-63) {
		tmp = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (i <= 1.5e-12) {
		tmp = t_5;
	} else if (i <= 3.2e+47) {
		tmp = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))));
	} else if (i <= 7.2e+122) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y1 * ((x * j) - (z * k))
	t_2 = (t * j) - (y * k)
	t_3 = (y * k) - (t * j)
	t_4 = i * (t_1 + ((y5 * t_3) + (c * ((z * t) - (x * y)))))
	t_5 = b * (((a * ((x * y) - (z * t))) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))))
	tmp = 0
	if i <= -6.2e+243:
		tmp = i * t_1
	elif i <= -3e+207:
		tmp = i * (y * ((k * y5) - (x * c)))
	elif i <= -7.1e+168:
		tmp = y1 * (z * ((a * y3) - (i * k)))
	elif i <= -7e+125:
		tmp = t * (z * ((c * i) - (a * b)))
	elif i <= -7.2e+77:
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * t_3) + (y0 * ((j * y3) - (k * y2)))))
	elif i <= -7e+52:
		tmp = (t * i) * ((z * c) - (j * y5))
	elif i <= -3.4e-45:
		tmp = y3 * (y5 * ((j * y0) - (y * a)))
	elif i <= -4.6e-85:
		tmp = t_4
	elif i <= -1.7e-144:
		tmp = t_5
	elif i <= 4.2e-63:
		tmp = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	elif i <= 1.5e-12:
		tmp = t_5
	elif i <= 3.2e+47:
		tmp = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))))
	elif i <= 7.2e+122:
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
	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(y1 * Float64(Float64(x * j) - Float64(z * k)))
	t_2 = Float64(Float64(t * j) - Float64(y * k))
	t_3 = Float64(Float64(y * k) - Float64(t * j))
	t_4 = Float64(i * Float64(t_1 + Float64(Float64(y5 * t_3) + Float64(c * Float64(Float64(z * t) - Float64(x * y))))))
	t_5 = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * t_2)) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))))
	tmp = 0.0
	if (i <= -6.2e+243)
		tmp = Float64(i * t_1);
	elseif (i <= -3e+207)
		tmp = Float64(i * Float64(y * Float64(Float64(k * y5) - Float64(x * c))));
	elseif (i <= -7.1e+168)
		tmp = Float64(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * k))));
	elseif (i <= -7e+125)
		tmp = Float64(t * Float64(z * Float64(Float64(c * i) - Float64(a * b))));
	elseif (i <= -7.2e+77)
		tmp = Float64(y5 * Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(Float64(i * t_3) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))))));
	elseif (i <= -7e+52)
		tmp = Float64(Float64(t * i) * Float64(Float64(z * c) - Float64(j * y5)));
	elseif (i <= -3.4e-45)
		tmp = Float64(y3 * Float64(y5 * Float64(Float64(j * y0) - Float64(y * a))));
	elseif (i <= -4.6e-85)
		tmp = t_4;
	elseif (i <= -1.7e-144)
		tmp = t_5;
	elseif (i <= 4.2e-63)
		tmp = Float64(y4 * Float64(Float64(Float64(b * t_2) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (i <= 1.5e-12)
		tmp = t_5;
	elseif (i <= 3.2e+47)
		tmp = Float64(k * Float64(Float64(z * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(y4 * Float64(Float64(y1 * y2) - Float64(y * b)))));
	elseif (i <= 7.2e+122)
		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)))));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y1 * ((x * j) - (z * k));
	t_2 = (t * j) - (y * k);
	t_3 = (y * k) - (t * j);
	t_4 = i * (t_1 + ((y5 * t_3) + (c * ((z * t) - (x * y)))));
	t_5 = b * (((a * ((x * y) - (z * t))) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))));
	tmp = 0.0;
	if (i <= -6.2e+243)
		tmp = i * t_1;
	elseif (i <= -3e+207)
		tmp = i * (y * ((k * y5) - (x * c)));
	elseif (i <= -7.1e+168)
		tmp = y1 * (z * ((a * y3) - (i * k)));
	elseif (i <= -7e+125)
		tmp = t * (z * ((c * i) - (a * b)));
	elseif (i <= -7.2e+77)
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * t_3) + (y0 * ((j * y3) - (k * y2)))));
	elseif (i <= -7e+52)
		tmp = (t * i) * ((z * c) - (j * y5));
	elseif (i <= -3.4e-45)
		tmp = y3 * (y5 * ((j * y0) - (y * a)));
	elseif (i <= -4.6e-85)
		tmp = t_4;
	elseif (i <= -1.7e-144)
		tmp = t_5;
	elseif (i <= 4.2e-63)
		tmp = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	elseif (i <= 1.5e-12)
		tmp = t_5;
	elseif (i <= 3.2e+47)
		tmp = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))));
	elseif (i <= 7.2e+122)
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	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[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(i * N[(t$95$1 + N[(N[(y5 * t$95$3), $MachinePrecision] + N[(c * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -6.2e+243], N[(i * t$95$1), $MachinePrecision], If[LessEqual[i, -3e+207], N[(i * N[(y * N[(N[(k * y5), $MachinePrecision] - N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -7.1e+168], N[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -7e+125], N[(t * N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -7.2e+77], N[(y5 * N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(i * t$95$3), $MachinePrecision] + N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -7e+52], N[(N[(t * i), $MachinePrecision] * N[(N[(z * c), $MachinePrecision] - N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -3.4e-45], N[(y3 * N[(y5 * N[(N[(j * y0), $MachinePrecision] - N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -4.6e-85], t$95$4, If[LessEqual[i, -1.7e-144], t$95$5, If[LessEqual[i, 4.2e-63], N[(y4 * N[(N[(N[(b * t$95$2), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.5e-12], t$95$5, If[LessEqual[i, 3.2e+47], N[(k * N[(N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 7.2e+122], 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], t$95$4]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 12 regimes

2. if i < -6.2e243

   1. Initial program 28.6%

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

   3. Taylor expanded in y1 around inf 43.6%

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

   4. Taylor expanded in i around inf 78.9%

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

   if -6.2e243 < i < -2.99999999999999983e207

   1. Initial program 18.2%

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

   3. Taylor expanded in i around -inf 63.6%

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

   4. Taylor expanded in y around -inf 90.9%

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

      1. mul-1-neg 90.9%

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

      2. *-commutative 90.9%

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

      3. distribute-rgt-neg-in 90.9%

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

      4. +-commutative 90.9%

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

      5. mul-1-neg 90.9%

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

      6. unsub-neg 90.9%

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

      7. *-commutative 90.9%

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

      8. *-commutative 90.9%

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

   6. Simplified 90.9%

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

   if -2.99999999999999983e207 < i < -7.10000000000000012e168

   1. Initial program 25.0%

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

   3. Taylor expanded in y1 around inf 75.7%

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

   4. Taylor expanded in z around inf 87.8%

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

   if -7.10000000000000012e168 < i < -7.00000000000000023e125

   1. Initial program 14.3%

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

   3. Taylor expanded in t around inf 57.1%

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

   4. Taylor expanded in z around inf 74.0%

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

      1. associate-*r* 74.0%

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

      2. neg-mul-1 74.0%

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

      3. *-commutative 74.0%

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

   6. Simplified 74.0%

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

   if -7.00000000000000023e125 < i < -7.1999999999999996e77

   1. Initial program 59.8%

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

   3. Taylor expanded in y5 around -inf 60.6%

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

   if -7.1999999999999996e77 < i < -7e52

   1. Initial program 25.0%

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

   3. Taylor expanded in t around inf 50.0%

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

   4. Taylor expanded in i around inf 100.0%

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

      1. associate-*r* 100.0%

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

      2. +-commutative 100.0%

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

      3. mul-1-neg 100.0%

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

      4. unsub-neg 100.0%

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

      5. *-commutative 100.0%

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

      6. *-commutative 100.0%

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

   6. Simplified 100.0%

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

   if -7e52 < i < -3.40000000000000004e-45

   1. Initial program 53.3%

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

   3. Taylor expanded in y5 around -inf 66.7%

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

   4. Taylor expanded in y3 around inf 73.8%

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

      1. distribute-lft-out-- 73.8%

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

      2. *-commutative 73.8%

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

   6. Simplified 73.8%

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

   if -3.40000000000000004e-45 < i < -4.6000000000000001e-85 or 7.2000000000000005e122 < i

   1. Initial program 25.6%

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

   3. Taylor expanded in i around -inf 72.8%

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

   if -4.6000000000000001e-85 < i < -1.70000000000000009e-144 or 4.2e-63 < i < 1.5000000000000001e-12

   1. Initial program 29.5%

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

   3. Taylor expanded in b around inf 81.9%

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

   if -1.70000000000000009e-144 < i < 4.2e-63

   1. Initial program 42.2%

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

   3. Taylor expanded in y4 around inf 52.6%

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

   if 1.5000000000000001e-12 < i < 3.2e47

   1. Initial program 37.4%

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

   3. Taylor expanded in k around inf 56.8%

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

   4. Taylor expanded in y5 around 0 63.2%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(b \cdot \left(y \cdot y4\right)\right) + y1 \cdot \left(y2 \cdot y4\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   5. Step-by-step derivation

      1. cancel-sign-sub-inv 63.2%

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

      2. mul-1-neg 63.2%

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

      3. associate-*r* 63.2%

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

      4. distribute-lft-neg-in 63.2%

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

      5. mul-1-neg 63.2%

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

      6. associate-*r* 63.2%

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

      7. distribute-rgt-in 69.4%

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

      8. +-commutative 69.4%

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

      9. mul-1-neg 69.4%

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

      10. unsub-neg 69.4%

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

      11. *-commutative 69.4%

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

      12. metadata-eval 69.4%

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

      13. *-lft-identity 69.4%

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

      14. *-commutative 69.4%

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

      15. *-commutative 69.4%

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

   6. Simplified 69.4%

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

   if 3.2e47 < i < 7.2000000000000005e122

   1. Initial program 16.4%

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

   3. Taylor expanded in y2 around inf 58.2%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
3. Recombined 12 regimes into one program.

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -6.2 \cdot 10^{+243}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;i \leq -3 \cdot 10^{+207}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;i \leq -7.1 \cdot 10^{+168}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;i \leq -7 \cdot 10^{+125}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;i \leq -7.2 \cdot 10^{+77}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;i \leq -7 \cdot 10^{+52}:\\ \;\;\;\;\left(t \cdot i\right) \cdot \left(z \cdot c - j \cdot y5\right)\\ \mathbf{elif}\;i \leq -3.4 \cdot 10^{-45}:\\ \;\;\;\;y3 \cdot \left(y5 \cdot \left(j \cdot y0 - y \cdot a\right)\right)\\ \mathbf{elif}\;i \leq -4.6 \cdot 10^{-85}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) + c \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \mathbf{elif}\;i \leq -1.7 \cdot 10^{-144}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{-63}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq 1.5 \cdot 10^{-12}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;i \leq 3.2 \cdot 10^{+47}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right) + y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;i \leq 7.2 \cdot 10^{+122}:\\ \;\;\;\;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}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) + c \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 52.3% accurate, 0.5× speedup

Math

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

FPCore

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

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 90.8%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in i around -inf 46.8%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 63.0%

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

Alternative 3: 36.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot j - y \cdot k\\ t_2 := b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot t_1\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{if}\;i \leq -6.6 \cdot 10^{+243}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;i \leq -1.05 \cdot 10^{+205}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;i \leq -1.7 \cdot 10^{+170}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;i \leq -8.6 \cdot 10^{+125}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;i \leq -4.3 \cdot 10^{+120}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;i \leq -6.2 \cdot 10^{+43}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;i \leq -1.62 \cdot 10^{-75}:\\ \;\;\;\;y3 \cdot \left(y5 \cdot \left(j \cdot y0 - y \cdot a\right)\right)\\ \mathbf{elif}\;i \leq -2.05 \cdot 10^{-140}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 1.25 \cdot 10^{-62}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot t_1 + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq 1.26 \cdot 10^{-11}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 1.8 \cdot 10^{+44}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right) + y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{+113}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* t j) (* y k)))
        (t_2
         (*
          b
          (+
           (+ (* a (- (* x y) (* z t))) (* y4 t_1))
           (* y0 (- (* z k) (* x j)))))))
   (if (<= i -6.6e+243)
     (* i (* y1 (- (* x j) (* z k))))
     (if (<= i -1.05e+205)
       (* i (* y (- (* k y5) (* x c))))
       (if (<= i -1.7e+170)
         (* y1 (* z (- (* a y3) (* i k))))
         (if (<= i -8.6e+125)
           (* t (* z (- (* c i) (* a b))))
           (if (<= i -4.3e+120)
             (* i (* j (* x y1)))
             (if (<= i -6.2e+43)
               (* c (* i (- (* z t) (* x y))))
               (if (<= i -1.62e-75)
                 (* y3 (* y5 (- (* j y0) (* y a))))
                 (if (<= i -2.05e-140)
                   t_2
                   (if (<= i 1.25e-62)
                     (*
                      y4
                      (+
                       (+ (* b t_1) (* y1 (- (* k y2) (* j y3))))
                       (* c (- (* y y3) (* t y2)))))
                     (if (<= i 1.26e-11)
                       t_2
                       (if (<= i 1.8e+44)
                         (*
                          k
                          (+
                           (* z (- (* b y0) (* i y1)))
                           (* y4 (- (* y1 y2) (* y b)))))
                         (if (<= i 2.5e+113)
                           (*
                            y2
                            (+
                             (+
                              (* k (- (* y1 y4) (* y0 y5)))
                              (* x (- (* c y0) (* a y1))))
                             (* t (- (* a y5) (* c y4)))))
                           (* i (* y5 (- (* y k) (* t j))))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (t * j) - (y * k);
	double t_2 = b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + (y0 * ((z * k) - (x * j))));
	double tmp;
	if (i <= -6.6e+243) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (i <= -1.05e+205) {
		tmp = i * (y * ((k * y5) - (x * c)));
	} else if (i <= -1.7e+170) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (i <= -8.6e+125) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else if (i <= -4.3e+120) {
		tmp = i * (j * (x * y1));
	} else if (i <= -6.2e+43) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (i <= -1.62e-75) {
		tmp = y3 * (y5 * ((j * y0) - (y * a)));
	} else if (i <= -2.05e-140) {
		tmp = t_2;
	} else if (i <= 1.25e-62) {
		tmp = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (i <= 1.26e-11) {
		tmp = t_2;
	} else if (i <= 1.8e+44) {
		tmp = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))));
	} else if (i <= 2.5e+113) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else {
		tmp = i * (y5 * ((y * k) - (t * 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 = (t * j) - (y * k)
    t_2 = b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + (y0 * ((z * k) - (x * j))))
    if (i <= (-6.6d+243)) then
        tmp = i * (y1 * ((x * j) - (z * k)))
    else if (i <= (-1.05d+205)) then
        tmp = i * (y * ((k * y5) - (x * c)))
    else if (i <= (-1.7d+170)) then
        tmp = y1 * (z * ((a * y3) - (i * k)))
    else if (i <= (-8.6d+125)) then
        tmp = t * (z * ((c * i) - (a * b)))
    else if (i <= (-4.3d+120)) then
        tmp = i * (j * (x * y1))
    else if (i <= (-6.2d+43)) then
        tmp = c * (i * ((z * t) - (x * y)))
    else if (i <= (-1.62d-75)) then
        tmp = y3 * (y5 * ((j * y0) - (y * a)))
    else if (i <= (-2.05d-140)) then
        tmp = t_2
    else if (i <= 1.25d-62) then
        tmp = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    else if (i <= 1.26d-11) then
        tmp = t_2
    else if (i <= 1.8d+44) then
        tmp = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))))
    else if (i <= 2.5d+113) then
        tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
    else
        tmp = i * (y5 * ((y * k) - (t * j)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (t * j) - (y * k);
	double t_2 = b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + (y0 * ((z * k) - (x * j))));
	double tmp;
	if (i <= -6.6e+243) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (i <= -1.05e+205) {
		tmp = i * (y * ((k * y5) - (x * c)));
	} else if (i <= -1.7e+170) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (i <= -8.6e+125) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else if (i <= -4.3e+120) {
		tmp = i * (j * (x * y1));
	} else if (i <= -6.2e+43) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (i <= -1.62e-75) {
		tmp = y3 * (y5 * ((j * y0) - (y * a)));
	} else if (i <= -2.05e-140) {
		tmp = t_2;
	} else if (i <= 1.25e-62) {
		tmp = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (i <= 1.26e-11) {
		tmp = t_2;
	} else if (i <= 1.8e+44) {
		tmp = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))));
	} else if (i <= 2.5e+113) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else {
		tmp = i * (y5 * ((y * k) - (t * j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (t * j) - (y * k)
	t_2 = b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + (y0 * ((z * k) - (x * j))))
	tmp = 0
	if i <= -6.6e+243:
		tmp = i * (y1 * ((x * j) - (z * k)))
	elif i <= -1.05e+205:
		tmp = i * (y * ((k * y5) - (x * c)))
	elif i <= -1.7e+170:
		tmp = y1 * (z * ((a * y3) - (i * k)))
	elif i <= -8.6e+125:
		tmp = t * (z * ((c * i) - (a * b)))
	elif i <= -4.3e+120:
		tmp = i * (j * (x * y1))
	elif i <= -6.2e+43:
		tmp = c * (i * ((z * t) - (x * y)))
	elif i <= -1.62e-75:
		tmp = y3 * (y5 * ((j * y0) - (y * a)))
	elif i <= -2.05e-140:
		tmp = t_2
	elif i <= 1.25e-62:
		tmp = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	elif i <= 1.26e-11:
		tmp = t_2
	elif i <= 1.8e+44:
		tmp = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))))
	elif i <= 2.5e+113:
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
	else:
		tmp = i * (y5 * ((y * k) - (t * j)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(t * j) - Float64(y * k))
	t_2 = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * t_1)) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))))
	tmp = 0.0
	if (i <= -6.6e+243)
		tmp = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))));
	elseif (i <= -1.05e+205)
		tmp = Float64(i * Float64(y * Float64(Float64(k * y5) - Float64(x * c))));
	elseif (i <= -1.7e+170)
		tmp = Float64(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * k))));
	elseif (i <= -8.6e+125)
		tmp = Float64(t * Float64(z * Float64(Float64(c * i) - Float64(a * b))));
	elseif (i <= -4.3e+120)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (i <= -6.2e+43)
		tmp = Float64(c * Float64(i * Float64(Float64(z * t) - Float64(x * y))));
	elseif (i <= -1.62e-75)
		tmp = Float64(y3 * Float64(y5 * Float64(Float64(j * y0) - Float64(y * a))));
	elseif (i <= -2.05e-140)
		tmp = t_2;
	elseif (i <= 1.25e-62)
		tmp = Float64(y4 * Float64(Float64(Float64(b * t_1) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (i <= 1.26e-11)
		tmp = t_2;
	elseif (i <= 1.8e+44)
		tmp = Float64(k * Float64(Float64(z * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(y4 * Float64(Float64(y1 * y2) - Float64(y * b)))));
	elseif (i <= 2.5e+113)
		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)))));
	else
		tmp = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (t * j) - (y * k);
	t_2 = b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + (y0 * ((z * k) - (x * j))));
	tmp = 0.0;
	if (i <= -6.6e+243)
		tmp = i * (y1 * ((x * j) - (z * k)));
	elseif (i <= -1.05e+205)
		tmp = i * (y * ((k * y5) - (x * c)));
	elseif (i <= -1.7e+170)
		tmp = y1 * (z * ((a * y3) - (i * k)));
	elseif (i <= -8.6e+125)
		tmp = t * (z * ((c * i) - (a * b)));
	elseif (i <= -4.3e+120)
		tmp = i * (j * (x * y1));
	elseif (i <= -6.2e+43)
		tmp = c * (i * ((z * t) - (x * y)));
	elseif (i <= -1.62e-75)
		tmp = y3 * (y5 * ((j * y0) - (y * a)));
	elseif (i <= -2.05e-140)
		tmp = t_2;
	elseif (i <= 1.25e-62)
		tmp = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	elseif (i <= 1.26e-11)
		tmp = t_2;
	elseif (i <= 1.8e+44)
		tmp = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))));
	elseif (i <= 2.5e+113)
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	else
		tmp = i * (y5 * ((y * k) - (t * j)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -6.6e+243], N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.05e+205], N[(i * N[(y * N[(N[(k * y5), $MachinePrecision] - N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.7e+170], N[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -8.6e+125], N[(t * N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -4.3e+120], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -6.2e+43], N[(c * N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.62e-75], N[(y3 * N[(y5 * N[(N[(j * y0), $MachinePrecision] - N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -2.05e-140], t$95$2, If[LessEqual[i, 1.25e-62], 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[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.26e-11], t$95$2, If[LessEqual[i, 1.8e+44], N[(k * N[(N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.5e+113], 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], N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]

Derivation

1. Split input into 12 regimes

2. if i < -6.59999999999999989e243

   1. Initial program 28.6%

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

   3. Taylor expanded in y1 around inf 43.6%

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

   4. Taylor expanded in i around inf 78.9%

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

   if -6.59999999999999989e243 < i < -1.05e205

   1. Initial program 18.2%

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

   3. Taylor expanded in i around -inf 63.6%

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

   4. Taylor expanded in y around -inf 90.9%

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

      1. mul-1-neg 90.9%

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

      2. *-commutative 90.9%

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

      3. distribute-rgt-neg-in 90.9%

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

      4. +-commutative 90.9%

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

      5. mul-1-neg 90.9%

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

      6. unsub-neg 90.9%

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

      7. *-commutative 90.9%

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

      8. *-commutative 90.9%

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

   6. Simplified 90.9%

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

   if -1.05e205 < i < -1.7000000000000001e170

   1. Initial program 25.0%

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

   3. Taylor expanded in y1 around inf 75.7%

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

   4. Taylor expanded in z around inf 87.8%

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

   if -1.7000000000000001e170 < i < -8.60000000000000071e125

   1. Initial program 14.3%

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

   3. Taylor expanded in t around inf 57.1%

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

   4. Taylor expanded in z around inf 74.0%

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

      1. associate-*r* 74.0%

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

      2. neg-mul-1 74.0%

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

      3. *-commutative 74.0%

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

   6. Simplified 74.0%

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

   if -8.60000000000000071e125 < i < -4.3000000000000002e120

   1. Initial program 50.0%

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

   3. Taylor expanded in y1 around inf 50.0%

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

   4. Taylor expanded in i around inf 100.0%

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

   5. Taylor expanded in j around inf 100.0%

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

      1. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   if -4.3000000000000002e120 < i < -6.2000000000000003e43

   1. Initial program 46.6%

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

   3. Taylor expanded in i around -inf 46.9%

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

   4. Taylor expanded in c around inf 61.3%

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

      1. *-commutative 61.3%

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

   6. Simplified 61.3%

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

   if -6.2000000000000003e43 < i < -1.62000000000000002e-75

   1. Initial program 47.1%

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

   3. Taylor expanded in y5 around -inf 70.7%

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

   4. Taylor expanded in y3 around inf 65.7%

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

      1. distribute-lft-out-- 65.7%

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

      2. *-commutative 65.7%

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

   6. Simplified 65.7%

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

   if -1.62000000000000002e-75 < i < -2.0500000000000001e-140 or 1.25e-62 < i < 1.26e-11

   1. Initial program 32.1%

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

   3. Taylor expanded in b around inf 74.7%

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

   if -2.0500000000000001e-140 < i < 1.25e-62

   1. Initial program 42.2%

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

   3. Taylor expanded in y4 around inf 52.6%

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

   if 1.26e-11 < i < 1.8e44

   1. Initial program 37.4%

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

   3. Taylor expanded in k around inf 56.8%

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

   4. Taylor expanded in y5 around 0 63.2%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(b \cdot \left(y \cdot y4\right)\right) + y1 \cdot \left(y2 \cdot y4\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   5. Step-by-step derivation

      1. cancel-sign-sub-inv 63.2%

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

      2. mul-1-neg 63.2%

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

      3. associate-*r* 63.2%

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

      4. distribute-lft-neg-in 63.2%

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

      5. mul-1-neg 63.2%

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

      6. associate-*r* 63.2%

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

      7. distribute-rgt-in 69.4%

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

      8. +-commutative 69.4%

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

      9. mul-1-neg 69.4%

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

      10. unsub-neg 69.4%

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

      11. *-commutative 69.4%

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

      12. metadata-eval 69.4%

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

      13. *-lft-identity 69.4%

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

      14. *-commutative 69.4%

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

      15. *-commutative 69.4%

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

   6. Simplified 69.4%

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

   if 1.8e44 < i < 2.5e113

   1. Initial program 14.1%

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

   3. Taylor expanded in y2 around inf 60.4%

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

   if 2.5e113 < i

   1. Initial program 24.1%

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

   3. Taylor expanded in i around -inf 63.3%

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

   4. Taylor expanded in y5 around inf 52.7%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} \]
3. Recombined 12 regimes into one program.

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -6.6 \cdot 10^{+243}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;i \leq -1.05 \cdot 10^{+205}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;i \leq -1.7 \cdot 10^{+170}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;i \leq -8.6 \cdot 10^{+125}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;i \leq -4.3 \cdot 10^{+120}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;i \leq -6.2 \cdot 10^{+43}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;i \leq -1.62 \cdot 10^{-75}:\\ \;\;\;\;y3 \cdot \left(y5 \cdot \left(j \cdot y0 - y \cdot a\right)\right)\\ \mathbf{elif}\;i \leq -2.05 \cdot 10^{-140}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;i \leq 1.25 \cdot 10^{-62}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq 1.26 \cdot 10^{-11}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;i \leq 1.8 \cdot 10^{+44}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right) + y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{+113}:\\ \;\;\;\;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}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 39.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot j - y \cdot k\\ t_2 := y1 \cdot \left(x \cdot j - z \cdot k\right)\\ t_3 := i \cdot \left(t_2 + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) + c \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ t_4 := b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot t_1\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{if}\;i \leq -1.6 \cdot 10^{+244}:\\ \;\;\;\;i \cdot t_2\\ \mathbf{elif}\;i \leq -6.4 \cdot 10^{+202}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;i \leq -2.15 \cdot 10^{+166}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;i \leq -1.4 \cdot 10^{+126}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;i \leq -5.6 \cdot 10^{+65}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -8.5 \cdot 10^{-45}:\\ \;\;\;\;y3 \cdot \left(y5 \cdot \left(j \cdot y0 - y \cdot a\right)\right)\\ \mathbf{elif}\;i \leq -7 \cdot 10^{-83}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -1.28 \cdot 10^{-141}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq 2.7 \cdot 10^{-62}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot t_1 + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq 1.25 \cdot 10^{-10}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq 5.4 \cdot 10^{+44}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right) + y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;i \leq 1.85 \cdot 10^{+120}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* t j) (* y k)))
        (t_2 (* y1 (- (* x j) (* z k))))
        (t_3
         (*
          i
          (+ t_2 (+ (* y5 (- (* y k) (* t j))) (* c (- (* z t) (* x y)))))))
        (t_4
         (*
          b
          (+
           (+ (* a (- (* x y) (* z t))) (* y4 t_1))
           (* y0 (- (* z k) (* x j)))))))
   (if (<= i -1.6e+244)
     (* i t_2)
     (if (<= i -6.4e+202)
       (* i (* y (- (* k y5) (* x c))))
       (if (<= i -2.15e+166)
         (* y1 (* z (- (* a y3) (* i k))))
         (if (<= i -1.4e+126)
           (* t (* z (- (* c i) (* a b))))
           (if (<= i -5.6e+65)
             t_3
             (if (<= i -8.5e-45)
               (* y3 (* y5 (- (* j y0) (* y a))))
               (if (<= i -7e-83)
                 t_3
                 (if (<= i -1.28e-141)
                   t_4
                   (if (<= i 2.7e-62)
                     (*
                      y4
                      (+
                       (+ (* b t_1) (* y1 (- (* k y2) (* j y3))))
                       (* c (- (* y y3) (* t y2)))))
                     (if (<= i 1.25e-10)
                       t_4
                       (if (<= i 5.4e+44)
                         (*
                          k
                          (+
                           (* z (- (* b y0) (* i y1)))
                           (* y4 (- (* y1 y2) (* y b)))))
                         (if (<= i 1.85e+120)
                           (*
                            y2
                            (+
                             (+
                              (* k (- (* y1 y4) (* y0 y5)))
                              (* x (- (* c y0) (* a y1))))
                             (* t (- (* a y5) (* c y4)))))
                           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 = (t * j) - (y * k);
	double t_2 = y1 * ((x * j) - (z * k));
	double t_3 = i * (t_2 + ((y5 * ((y * k) - (t * j))) + (c * ((z * t) - (x * y)))));
	double t_4 = b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + (y0 * ((z * k) - (x * j))));
	double tmp;
	if (i <= -1.6e+244) {
		tmp = i * t_2;
	} else if (i <= -6.4e+202) {
		tmp = i * (y * ((k * y5) - (x * c)));
	} else if (i <= -2.15e+166) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (i <= -1.4e+126) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else if (i <= -5.6e+65) {
		tmp = t_3;
	} else if (i <= -8.5e-45) {
		tmp = y3 * (y5 * ((j * y0) - (y * a)));
	} else if (i <= -7e-83) {
		tmp = t_3;
	} else if (i <= -1.28e-141) {
		tmp = t_4;
	} else if (i <= 2.7e-62) {
		tmp = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (i <= 1.25e-10) {
		tmp = t_4;
	} else if (i <= 5.4e+44) {
		tmp = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))));
	} else if (i <= 1.85e+120) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (t * j) - (y * k)
    t_2 = y1 * ((x * j) - (z * k))
    t_3 = i * (t_2 + ((y5 * ((y * k) - (t * j))) + (c * ((z * t) - (x * y)))))
    t_4 = b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + (y0 * ((z * k) - (x * j))))
    if (i <= (-1.6d+244)) then
        tmp = i * t_2
    else if (i <= (-6.4d+202)) then
        tmp = i * (y * ((k * y5) - (x * c)))
    else if (i <= (-2.15d+166)) then
        tmp = y1 * (z * ((a * y3) - (i * k)))
    else if (i <= (-1.4d+126)) then
        tmp = t * (z * ((c * i) - (a * b)))
    else if (i <= (-5.6d+65)) then
        tmp = t_3
    else if (i <= (-8.5d-45)) then
        tmp = y3 * (y5 * ((j * y0) - (y * a)))
    else if (i <= (-7d-83)) then
        tmp = t_3
    else if (i <= (-1.28d-141)) then
        tmp = t_4
    else if (i <= 2.7d-62) then
        tmp = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    else if (i <= 1.25d-10) then
        tmp = t_4
    else if (i <= 5.4d+44) then
        tmp = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))))
    else if (i <= 1.85d+120) then
        tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
    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 = (t * j) - (y * k);
	double t_2 = y1 * ((x * j) - (z * k));
	double t_3 = i * (t_2 + ((y5 * ((y * k) - (t * j))) + (c * ((z * t) - (x * y)))));
	double t_4 = b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + (y0 * ((z * k) - (x * j))));
	double tmp;
	if (i <= -1.6e+244) {
		tmp = i * t_2;
	} else if (i <= -6.4e+202) {
		tmp = i * (y * ((k * y5) - (x * c)));
	} else if (i <= -2.15e+166) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (i <= -1.4e+126) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else if (i <= -5.6e+65) {
		tmp = t_3;
	} else if (i <= -8.5e-45) {
		tmp = y3 * (y5 * ((j * y0) - (y * a)));
	} else if (i <= -7e-83) {
		tmp = t_3;
	} else if (i <= -1.28e-141) {
		tmp = t_4;
	} else if (i <= 2.7e-62) {
		tmp = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (i <= 1.25e-10) {
		tmp = t_4;
	} else if (i <= 5.4e+44) {
		tmp = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))));
	} else if (i <= 1.85e+120) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} 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 = (t * j) - (y * k)
	t_2 = y1 * ((x * j) - (z * k))
	t_3 = i * (t_2 + ((y5 * ((y * k) - (t * j))) + (c * ((z * t) - (x * y)))))
	t_4 = b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + (y0 * ((z * k) - (x * j))))
	tmp = 0
	if i <= -1.6e+244:
		tmp = i * t_2
	elif i <= -6.4e+202:
		tmp = i * (y * ((k * y5) - (x * c)))
	elif i <= -2.15e+166:
		tmp = y1 * (z * ((a * y3) - (i * k)))
	elif i <= -1.4e+126:
		tmp = t * (z * ((c * i) - (a * b)))
	elif i <= -5.6e+65:
		tmp = t_3
	elif i <= -8.5e-45:
		tmp = y3 * (y5 * ((j * y0) - (y * a)))
	elif i <= -7e-83:
		tmp = t_3
	elif i <= -1.28e-141:
		tmp = t_4
	elif i <= 2.7e-62:
		tmp = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	elif i <= 1.25e-10:
		tmp = t_4
	elif i <= 5.4e+44:
		tmp = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))))
	elif i <= 1.85e+120:
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
	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(t * j) - Float64(y * k))
	t_2 = Float64(y1 * Float64(Float64(x * j) - Float64(z * k)))
	t_3 = Float64(i * Float64(t_2 + Float64(Float64(y5 * Float64(Float64(y * k) - Float64(t * j))) + Float64(c * Float64(Float64(z * t) - Float64(x * y))))))
	t_4 = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * t_1)) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))))
	tmp = 0.0
	if (i <= -1.6e+244)
		tmp = Float64(i * t_2);
	elseif (i <= -6.4e+202)
		tmp = Float64(i * Float64(y * Float64(Float64(k * y5) - Float64(x * c))));
	elseif (i <= -2.15e+166)
		tmp = Float64(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * k))));
	elseif (i <= -1.4e+126)
		tmp = Float64(t * Float64(z * Float64(Float64(c * i) - Float64(a * b))));
	elseif (i <= -5.6e+65)
		tmp = t_3;
	elseif (i <= -8.5e-45)
		tmp = Float64(y3 * Float64(y5 * Float64(Float64(j * y0) - Float64(y * a))));
	elseif (i <= -7e-83)
		tmp = t_3;
	elseif (i <= -1.28e-141)
		tmp = t_4;
	elseif (i <= 2.7e-62)
		tmp = Float64(y4 * Float64(Float64(Float64(b * t_1) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (i <= 1.25e-10)
		tmp = t_4;
	elseif (i <= 5.4e+44)
		tmp = Float64(k * Float64(Float64(z * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(y4 * Float64(Float64(y1 * y2) - Float64(y * b)))));
	elseif (i <= 1.85e+120)
		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)))));
	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 = (t * j) - (y * k);
	t_2 = y1 * ((x * j) - (z * k));
	t_3 = i * (t_2 + ((y5 * ((y * k) - (t * j))) + (c * ((z * t) - (x * y)))));
	t_4 = b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + (y0 * ((z * k) - (x * j))));
	tmp = 0.0;
	if (i <= -1.6e+244)
		tmp = i * t_2;
	elseif (i <= -6.4e+202)
		tmp = i * (y * ((k * y5) - (x * c)));
	elseif (i <= -2.15e+166)
		tmp = y1 * (z * ((a * y3) - (i * k)));
	elseif (i <= -1.4e+126)
		tmp = t * (z * ((c * i) - (a * b)));
	elseif (i <= -5.6e+65)
		tmp = t_3;
	elseif (i <= -8.5e-45)
		tmp = y3 * (y5 * ((j * y0) - (y * a)));
	elseif (i <= -7e-83)
		tmp = t_3;
	elseif (i <= -1.28e-141)
		tmp = t_4;
	elseif (i <= 2.7e-62)
		tmp = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	elseif (i <= 1.25e-10)
		tmp = t_4;
	elseif (i <= 5.4e+44)
		tmp = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))));
	elseif (i <= 1.85e+120)
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	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[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(i * N[(t$95$2 + N[(N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.6e+244], N[(i * t$95$2), $MachinePrecision], If[LessEqual[i, -6.4e+202], N[(i * N[(y * N[(N[(k * y5), $MachinePrecision] - N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -2.15e+166], N[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.4e+126], N[(t * N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -5.6e+65], t$95$3, If[LessEqual[i, -8.5e-45], N[(y3 * N[(y5 * N[(N[(j * y0), $MachinePrecision] - N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -7e-83], t$95$3, If[LessEqual[i, -1.28e-141], t$95$4, If[LessEqual[i, 2.7e-62], 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[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.25e-10], t$95$4, If[LessEqual[i, 5.4e+44], N[(k * N[(N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.85e+120], 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], t$95$3]]]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if i < -1.6000000000000001e244

   1. Initial program 28.6%

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

   3. Taylor expanded in y1 around inf 43.6%

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

   4. Taylor expanded in i around inf 78.9%

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

   if -1.6000000000000001e244 < i < -6.40000000000000024e202

   1. Initial program 18.2%

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

   3. Taylor expanded in i around -inf 63.6%

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

   4. Taylor expanded in y around -inf 90.9%

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

      1. mul-1-neg 90.9%

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

      2. *-commutative 90.9%

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

      3. distribute-rgt-neg-in 90.9%

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

      4. +-commutative 90.9%

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

      5. mul-1-neg 90.9%

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

      6. unsub-neg 90.9%

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

      7. *-commutative 90.9%

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

      8. *-commutative 90.9%

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

   6. Simplified 90.9%

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

   if -6.40000000000000024e202 < i < -2.15e166

   1. Initial program 25.0%

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

   3. Taylor expanded in y1 around inf 75.7%

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

   4. Taylor expanded in z around inf 87.8%

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

   if -2.15e166 < i < -1.40000000000000005e126

   1. Initial program 14.3%

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

   3. Taylor expanded in t around inf 57.1%

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

   4. Taylor expanded in z around inf 74.0%

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

      1. associate-*r* 74.0%

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

      2. neg-mul-1 74.0%

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

      3. *-commutative 74.0%

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

   6. Simplified 74.0%

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

   if -1.40000000000000005e126 < i < -5.5999999999999998e65 or -8.50000000000000041e-45 < i < -7.00000000000000061e-83 or 1.85000000000000012e120 < i

   1. Initial program 31.8%

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

   3. Taylor expanded in i around -inf 70.1%

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

   if -5.5999999999999998e65 < i < -8.50000000000000041e-45

   1. Initial program 47.1%

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

   3. Taylor expanded in y5 around -inf 58.9%

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

   4. Taylor expanded in y3 around inf 71.0%

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

      1. distribute-lft-out-- 71.0%

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

      2. *-commutative 71.0%

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

   6. Simplified 71.0%

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

   if -7.00000000000000061e-83 < i < -1.2799999999999999e-141 or 2.70000000000000019e-62 < i < 1.25000000000000008e-10

   1. Initial program 29.5%

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

   3. Taylor expanded in b around inf 81.9%

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

   if -1.2799999999999999e-141 < i < 2.70000000000000019e-62

   1. Initial program 42.2%

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

   3. Taylor expanded in y4 around inf 52.6%

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

   if 1.25000000000000008e-10 < i < 5.4e44

   1. Initial program 37.4%

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

   3. Taylor expanded in k around inf 56.8%

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

   4. Taylor expanded in y5 around 0 63.2%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(b \cdot \left(y \cdot y4\right)\right) + y1 \cdot \left(y2 \cdot y4\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   5. Step-by-step derivation

      1. cancel-sign-sub-inv 63.2%

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

      2. mul-1-neg 63.2%

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

      3. associate-*r* 63.2%

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

      4. distribute-lft-neg-in 63.2%

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

      5. mul-1-neg 63.2%

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

      6. associate-*r* 63.2%

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

      7. distribute-rgt-in 69.4%

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

      8. +-commutative 69.4%

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

      9. mul-1-neg 69.4%

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

      10. unsub-neg 69.4%

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

      11. *-commutative 69.4%

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

      12. metadata-eval 69.4%

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

      13. *-lft-identity 69.4%

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

      14. *-commutative 69.4%

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

      15. *-commutative 69.4%

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

   6. Simplified 69.4%

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

   if 5.4e44 < i < 1.85000000000000012e120

   1. Initial program 16.4%

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

   3. Taylor expanded in y2 around inf 58.2%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
3. Recombined 10 regimes into one program.

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.6 \cdot 10^{+244}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;i \leq -6.4 \cdot 10^{+202}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;i \leq -2.15 \cdot 10^{+166}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;i \leq -1.4 \cdot 10^{+126}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;i \leq -5.6 \cdot 10^{+65}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) + c \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \mathbf{elif}\;i \leq -8.5 \cdot 10^{-45}:\\ \;\;\;\;y3 \cdot \left(y5 \cdot \left(j \cdot y0 - y \cdot a\right)\right)\\ \mathbf{elif}\;i \leq -7 \cdot 10^{-83}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) + c \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \mathbf{elif}\;i \leq -1.28 \cdot 10^{-141}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;i \leq 2.7 \cdot 10^{-62}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq 1.25 \cdot 10^{-10}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;i \leq 5.4 \cdot 10^{+44}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right) + y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;i \leq 1.85 \cdot 10^{+120}:\\ \;\;\;\;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}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) + c \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 40.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot \left(x \cdot j - z \cdot k\right)\\ t_2 := t \cdot j - y \cdot k\\ t_3 := b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot t_2\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ t_4 := c \cdot y0 - a \cdot y1\\ t_5 := y4 \cdot \left(\left(b \cdot t_2 + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ t_6 := b \cdot y0 - i \cdot y1\\ t_7 := z \cdot \left(k \cdot t_6 + \left(t \cdot \left(c \cdot i - a \cdot b\right) - y3 \cdot t_4\right)\right)\\ t_8 := y \cdot k - t \cdot j\\ t_9 := i \cdot \left(t_1 + \left(y5 \cdot t_8 + c \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \mathbf{if}\;i \leq -3.3 \cdot 10^{+243}:\\ \;\;\;\;i \cdot t_1\\ \mathbf{elif}\;i \leq -5.6 \cdot 10^{+200}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;i \leq -1.36 \cdot 10^{+149}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;i \leq -1.4 \cdot 10^{-45}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot t_8 + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;i \leq -1.4 \cdot 10^{-82}:\\ \;\;\;\;t_9\\ \mathbf{elif}\;i \leq -7.8 \cdot 10^{-143}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -1.5 \cdot 10^{-252}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq 9.5 \cdot 10^{-296}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;i \leq 3.6 \cdot 10^{-63}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq 7.5 \cdot 10^{-12}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 2.15 \cdot 10^{+43}:\\ \;\;\;\;k \cdot \left(z \cdot t_6 + y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;i \leq 1.8 \cdot 10^{+120}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot t_4\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_9\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y1 (- (* x j) (* z k))))
        (t_2 (- (* t j) (* y k)))
        (t_3
         (*
          b
          (+
           (+ (* a (- (* x y) (* z t))) (* y4 t_2))
           (* y0 (- (* z k) (* x j))))))
        (t_4 (- (* c y0) (* a y1)))
        (t_5
         (*
          y4
          (+
           (+ (* b t_2) (* y1 (- (* k y2) (* j y3))))
           (* c (- (* y y3) (* t y2))))))
        (t_6 (- (* b y0) (* i y1)))
        (t_7 (* z (+ (* k t_6) (- (* t (- (* c i) (* a b))) (* y3 t_4)))))
        (t_8 (- (* y k) (* t j)))
        (t_9 (* i (+ t_1 (+ (* y5 t_8) (* c (- (* z t) (* x y))))))))
   (if (<= i -3.3e+243)
     (* i t_1)
     (if (<= i -5.6e+200)
       (* i (* y (- (* k y5) (* x c))))
       (if (<= i -1.36e+149)
         t_7
         (if (<= i -1.4e-45)
           (*
            y5
            (+
             (* a (- (* t y2) (* y y3)))
             (+ (* i t_8) (* y0 (- (* j y3) (* k y2))))))
           (if (<= i -1.4e-82)
             t_9
             (if (<= i -7.8e-143)
               t_3
               (if (<= i -1.5e-252)
                 t_5
                 (if (<= i 9.5e-296)
                   t_7
                   (if (<= i 3.6e-63)
                     t_5
                     (if (<= i 7.5e-12)
                       t_3
                       (if (<= i 2.15e+43)
                         (* k (+ (* z t_6) (* y4 (- (* y1 y2) (* y b)))))
                         (if (<= i 1.8e+120)
                           (*
                            y2
                            (+
                             (+ (* k (- (* y1 y4) (* y0 y5))) (* x t_4))
                             (* t (- (* a y5) (* c y4)))))
                           t_9))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * ((x * j) - (z * k));
	double t_2 = (t * j) - (y * k);
	double t_3 = b * (((a * ((x * y) - (z * t))) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))));
	double t_4 = (c * y0) - (a * y1);
	double t_5 = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double t_6 = (b * y0) - (i * y1);
	double t_7 = z * ((k * t_6) + ((t * ((c * i) - (a * b))) - (y3 * t_4)));
	double t_8 = (y * k) - (t * j);
	double t_9 = i * (t_1 + ((y5 * t_8) + (c * ((z * t) - (x * y)))));
	double tmp;
	if (i <= -3.3e+243) {
		tmp = i * t_1;
	} else if (i <= -5.6e+200) {
		tmp = i * (y * ((k * y5) - (x * c)));
	} else if (i <= -1.36e+149) {
		tmp = t_7;
	} else if (i <= -1.4e-45) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * t_8) + (y0 * ((j * y3) - (k * y2)))));
	} else if (i <= -1.4e-82) {
		tmp = t_9;
	} else if (i <= -7.8e-143) {
		tmp = t_3;
	} else if (i <= -1.5e-252) {
		tmp = t_5;
	} else if (i <= 9.5e-296) {
		tmp = t_7;
	} else if (i <= 3.6e-63) {
		tmp = t_5;
	} else if (i <= 7.5e-12) {
		tmp = t_3;
	} else if (i <= 2.15e+43) {
		tmp = k * ((z * t_6) + (y4 * ((y1 * y2) - (y * b))));
	} else if (i <= 1.8e+120) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_4)) + (t * ((a * y5) - (c * y4))));
	} else {
		tmp = t_9;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = y1 * ((x * j) - (z * k))
    t_2 = (t * j) - (y * k)
    t_3 = b * (((a * ((x * y) - (z * t))) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))))
    t_4 = (c * y0) - (a * y1)
    t_5 = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    t_6 = (b * y0) - (i * y1)
    t_7 = z * ((k * t_6) + ((t * ((c * i) - (a * b))) - (y3 * t_4)))
    t_8 = (y * k) - (t * j)
    t_9 = i * (t_1 + ((y5 * t_8) + (c * ((z * t) - (x * y)))))
    if (i <= (-3.3d+243)) then
        tmp = i * t_1
    else if (i <= (-5.6d+200)) then
        tmp = i * (y * ((k * y5) - (x * c)))
    else if (i <= (-1.36d+149)) then
        tmp = t_7
    else if (i <= (-1.4d-45)) then
        tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * t_8) + (y0 * ((j * y3) - (k * y2)))))
    else if (i <= (-1.4d-82)) then
        tmp = t_9
    else if (i <= (-7.8d-143)) then
        tmp = t_3
    else if (i <= (-1.5d-252)) then
        tmp = t_5
    else if (i <= 9.5d-296) then
        tmp = t_7
    else if (i <= 3.6d-63) then
        tmp = t_5
    else if (i <= 7.5d-12) then
        tmp = t_3
    else if (i <= 2.15d+43) then
        tmp = k * ((z * t_6) + (y4 * ((y1 * y2) - (y * b))))
    else if (i <= 1.8d+120) then
        tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_4)) + (t * ((a * y5) - (c * y4))))
    else
        tmp = t_9
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * ((x * j) - (z * k));
	double t_2 = (t * j) - (y * k);
	double t_3 = b * (((a * ((x * y) - (z * t))) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))));
	double t_4 = (c * y0) - (a * y1);
	double t_5 = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double t_6 = (b * y0) - (i * y1);
	double t_7 = z * ((k * t_6) + ((t * ((c * i) - (a * b))) - (y3 * t_4)));
	double t_8 = (y * k) - (t * j);
	double t_9 = i * (t_1 + ((y5 * t_8) + (c * ((z * t) - (x * y)))));
	double tmp;
	if (i <= -3.3e+243) {
		tmp = i * t_1;
	} else if (i <= -5.6e+200) {
		tmp = i * (y * ((k * y5) - (x * c)));
	} else if (i <= -1.36e+149) {
		tmp = t_7;
	} else if (i <= -1.4e-45) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * t_8) + (y0 * ((j * y3) - (k * y2)))));
	} else if (i <= -1.4e-82) {
		tmp = t_9;
	} else if (i <= -7.8e-143) {
		tmp = t_3;
	} else if (i <= -1.5e-252) {
		tmp = t_5;
	} else if (i <= 9.5e-296) {
		tmp = t_7;
	} else if (i <= 3.6e-63) {
		tmp = t_5;
	} else if (i <= 7.5e-12) {
		tmp = t_3;
	} else if (i <= 2.15e+43) {
		tmp = k * ((z * t_6) + (y4 * ((y1 * y2) - (y * b))));
	} else if (i <= 1.8e+120) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_4)) + (t * ((a * y5) - (c * y4))));
	} else {
		tmp = t_9;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y1 * ((x * j) - (z * k))
	t_2 = (t * j) - (y * k)
	t_3 = b * (((a * ((x * y) - (z * t))) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))))
	t_4 = (c * y0) - (a * y1)
	t_5 = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	t_6 = (b * y0) - (i * y1)
	t_7 = z * ((k * t_6) + ((t * ((c * i) - (a * b))) - (y3 * t_4)))
	t_8 = (y * k) - (t * j)
	t_9 = i * (t_1 + ((y5 * t_8) + (c * ((z * t) - (x * y)))))
	tmp = 0
	if i <= -3.3e+243:
		tmp = i * t_1
	elif i <= -5.6e+200:
		tmp = i * (y * ((k * y5) - (x * c)))
	elif i <= -1.36e+149:
		tmp = t_7
	elif i <= -1.4e-45:
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * t_8) + (y0 * ((j * y3) - (k * y2)))))
	elif i <= -1.4e-82:
		tmp = t_9
	elif i <= -7.8e-143:
		tmp = t_3
	elif i <= -1.5e-252:
		tmp = t_5
	elif i <= 9.5e-296:
		tmp = t_7
	elif i <= 3.6e-63:
		tmp = t_5
	elif i <= 7.5e-12:
		tmp = t_3
	elif i <= 2.15e+43:
		tmp = k * ((z * t_6) + (y4 * ((y1 * y2) - (y * b))))
	elif i <= 1.8e+120:
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_4)) + (t * ((a * y5) - (c * y4))))
	else:
		tmp = t_9
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y1 * Float64(Float64(x * j) - Float64(z * k)))
	t_2 = Float64(Float64(t * j) - Float64(y * k))
	t_3 = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * t_2)) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))))
	t_4 = Float64(Float64(c * y0) - Float64(a * y1))
	t_5 = Float64(y4 * Float64(Float64(Float64(b * t_2) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))))
	t_6 = Float64(Float64(b * y0) - Float64(i * y1))
	t_7 = Float64(z * Float64(Float64(k * t_6) + Float64(Float64(t * Float64(Float64(c * i) - Float64(a * b))) - Float64(y3 * t_4))))
	t_8 = Float64(Float64(y * k) - Float64(t * j))
	t_9 = Float64(i * Float64(t_1 + Float64(Float64(y5 * t_8) + Float64(c * Float64(Float64(z * t) - Float64(x * y))))))
	tmp = 0.0
	if (i <= -3.3e+243)
		tmp = Float64(i * t_1);
	elseif (i <= -5.6e+200)
		tmp = Float64(i * Float64(y * Float64(Float64(k * y5) - Float64(x * c))));
	elseif (i <= -1.36e+149)
		tmp = t_7;
	elseif (i <= -1.4e-45)
		tmp = Float64(y5 * Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(Float64(i * t_8) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))))));
	elseif (i <= -1.4e-82)
		tmp = t_9;
	elseif (i <= -7.8e-143)
		tmp = t_3;
	elseif (i <= -1.5e-252)
		tmp = t_5;
	elseif (i <= 9.5e-296)
		tmp = t_7;
	elseif (i <= 3.6e-63)
		tmp = t_5;
	elseif (i <= 7.5e-12)
		tmp = t_3;
	elseif (i <= 2.15e+43)
		tmp = Float64(k * Float64(Float64(z * t_6) + Float64(y4 * Float64(Float64(y1 * y2) - Float64(y * b)))));
	elseif (i <= 1.8e+120)
		tmp = Float64(y2 * Float64(Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(x * t_4)) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	else
		tmp = t_9;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y1 * ((x * j) - (z * k));
	t_2 = (t * j) - (y * k);
	t_3 = b * (((a * ((x * y) - (z * t))) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))));
	t_4 = (c * y0) - (a * y1);
	t_5 = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	t_6 = (b * y0) - (i * y1);
	t_7 = z * ((k * t_6) + ((t * ((c * i) - (a * b))) - (y3 * t_4)));
	t_8 = (y * k) - (t * j);
	t_9 = i * (t_1 + ((y5 * t_8) + (c * ((z * t) - (x * y)))));
	tmp = 0.0;
	if (i <= -3.3e+243)
		tmp = i * t_1;
	elseif (i <= -5.6e+200)
		tmp = i * (y * ((k * y5) - (x * c)));
	elseif (i <= -1.36e+149)
		tmp = t_7;
	elseif (i <= -1.4e-45)
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * t_8) + (y0 * ((j * y3) - (k * y2)))));
	elseif (i <= -1.4e-82)
		tmp = t_9;
	elseif (i <= -7.8e-143)
		tmp = t_3;
	elseif (i <= -1.5e-252)
		tmp = t_5;
	elseif (i <= 9.5e-296)
		tmp = t_7;
	elseif (i <= 3.6e-63)
		tmp = t_5;
	elseif (i <= 7.5e-12)
		tmp = t_3;
	elseif (i <= 2.15e+43)
		tmp = k * ((z * t_6) + (y4 * ((y1 * y2) - (y * b))));
	elseif (i <= 1.8e+120)
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_4)) + (t * ((a * y5) - (c * y4))));
	else
		tmp = t_9;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y4 * N[(N[(N[(b * t$95$2), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(z * N[(N[(k * t$95$6), $MachinePrecision] + N[(N[(t * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y3 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(i * N[(t$95$1 + N[(N[(y5 * t$95$8), $MachinePrecision] + N[(c * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -3.3e+243], N[(i * t$95$1), $MachinePrecision], If[LessEqual[i, -5.6e+200], N[(i * N[(y * N[(N[(k * y5), $MachinePrecision] - N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.36e+149], t$95$7, If[LessEqual[i, -1.4e-45], N[(y5 * N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(i * t$95$8), $MachinePrecision] + N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.4e-82], t$95$9, If[LessEqual[i, -7.8e-143], t$95$3, If[LessEqual[i, -1.5e-252], t$95$5, If[LessEqual[i, 9.5e-296], t$95$7, If[LessEqual[i, 3.6e-63], t$95$5, If[LessEqual[i, 7.5e-12], t$95$3, If[LessEqual[i, 2.15e+43], N[(k * N[(N[(z * t$95$6), $MachinePrecision] + N[(y4 * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.8e+120], N[(y2 * N[(N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$4), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$9]]]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if i < -3.29999999999999994e243

   1. Initial program 28.6%

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

   3. Taylor expanded in y1 around inf 43.6%

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

   4. Taylor expanded in i around inf 78.9%

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

   if -3.29999999999999994e243 < i < -5.59999999999999969e200

   1. Initial program 16.7%

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

   3. Taylor expanded in i around -inf 66.7%

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

   4. Taylor expanded in y around -inf 91.7%

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

      1. mul-1-neg 91.7%

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

      2. *-commutative 91.7%

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

      3. distribute-rgt-neg-in 91.7%

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

      4. +-commutative 91.7%

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

      5. mul-1-neg 91.7%

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

      6. unsub-neg 91.7%

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

      7. *-commutative 91.7%

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

      8. *-commutative 91.7%

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

   6. Simplified 91.7%

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

   if -5.59999999999999969e200 < i < -1.3600000000000001e149 or -1.49999999999999997e-252 < i < 9.50000000000000046e-296

   1. Initial program 27.2%

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

   3. Taylor expanded in z around -inf 77.5%

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

   if -1.3600000000000001e149 < i < -1.4000000000000001e-45

   1. Initial program 48.4%

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

   3. Taylor expanded in y5 around -inf 61.0%

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

   if -1.4000000000000001e-45 < i < -1.40000000000000012e-82 or 1.80000000000000008e120 < i

   1. Initial program 25.6%

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

   3. Taylor expanded in i around -inf 72.8%

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

   if -1.40000000000000012e-82 < i < -7.80000000000000007e-143 or 3.60000000000000008e-63 < i < 7.5e-12

   1. Initial program 29.5%

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

   3. Taylor expanded in b around inf 81.9%

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

   if -7.80000000000000007e-143 < i < -1.49999999999999997e-252 or 9.50000000000000046e-296 < i < 3.60000000000000008e-63

   1. Initial program 43.9%

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

   3. Taylor expanded in y4 around inf 53.1%

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

   if 7.5e-12 < i < 2.15e43

   1. Initial program 37.4%

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

   3. Taylor expanded in k around inf 56.8%

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

   4. Taylor expanded in y5 around 0 63.2%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(b \cdot \left(y \cdot y4\right)\right) + y1 \cdot \left(y2 \cdot y4\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   5. Step-by-step derivation

      1. cancel-sign-sub-inv 63.2%

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

      2. mul-1-neg 63.2%

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

      3. associate-*r* 63.2%

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

      4. distribute-lft-neg-in 63.2%

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

      5. mul-1-neg 63.2%

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

      6. associate-*r* 63.2%

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

      7. distribute-rgt-in 69.4%

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

      8. +-commutative 69.4%

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

      9. mul-1-neg 69.4%

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

      10. unsub-neg 69.4%

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

      11. *-commutative 69.4%

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

      12. metadata-eval 69.4%

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

      13. *-lft-identity 69.4%

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

      14. *-commutative 69.4%

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

      15. *-commutative 69.4%

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

   6. Simplified 69.4%

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

   if 2.15e43 < i < 1.80000000000000008e120

   1. Initial program 16.4%

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

   3. Taylor expanded in y2 around inf 58.2%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.3 \cdot 10^{+243}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;i \leq -5.6 \cdot 10^{+200}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;i \leq -1.36 \cdot 10^{+149}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot \left(c \cdot i - a \cdot b\right) - y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;i \leq -1.4 \cdot 10^{-45}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;i \leq -1.4 \cdot 10^{-82}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) + c \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \mathbf{elif}\;i \leq -7.8 \cdot 10^{-143}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;i \leq -1.5 \cdot 10^{-252}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq 9.5 \cdot 10^{-296}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot \left(c \cdot i - a \cdot b\right) - y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;i \leq 3.6 \cdot 10^{-63}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq 7.5 \cdot 10^{-12}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;i \leq 2.15 \cdot 10^{+43}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right) + y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;i \leq 1.8 \cdot 10^{+120}:\\ \;\;\;\;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}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) + c \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 32.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{if}\;y5 \leq -1.3 \cdot 10^{+118}:\\ \;\;\;\;k \cdot \left(y5 \cdot \left(y \cdot i - y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq -7.6 \cdot 10^{+32}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;y5 \leq -3.4 \cdot 10^{+17}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq -1.32 \cdot 10^{-14}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y5 \leq -5.5 \cdot 10^{-54}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq -1.1 \cdot 10^{-72}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;y5 \leq -8.1 \cdot 10^{-122}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;y5 \leq -3.9 \cdot 10^{-209}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y5 \leq 1.12 \cdot 10^{-299}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 1.1 \cdot 10^{-162}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y5 \leq 3.5 \cdot 10^{+32}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;y5 \leq 9.2 \cdot 10^{+129}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (* z (- (* b y0) (* i y1))))))
   (if (<= y5 -1.3e+118)
     (* k (* y5 (- (* y i) (* y0 y2))))
     (if (<= y5 -7.6e+32)
       (* k (* y1 (- (* y2 y4) (* z i))))
       (if (<= y5 -3.4e+17)
         (* i (* y5 (- (* y k) (* t j))))
         (if (<= y5 -1.32e-14)
           (* b (* y4 (- (* t j) (* y k))))
           (if (<= y5 -5.5e-54)
             (* b (* y0 (- (* z k) (* x j))))
             (if (<= y5 -1.1e-72)
               (* t (* z (- (* c i) (* a b))))
               (if (<= y5 -8.1e-122)
                 (* c (* i (- (* z t) (* x y))))
                 (if (<= y5 -3.9e-209)
                   t_1
                   (if (<= y5 1.12e-299)
                     (* y1 (* y3 (- (* z a) (* j y4))))
                     (if (<= y5 1.1e-162)
                       t_1
                       (if (<= y5 3.5e+32)
                         (* k (* y4 (- (* y1 y2) (* y b))))
                         (if (<= y5 9.2e+129)
                           (* y0 (* y5 (- (* j y3) (* k y2))))
                           (* a (* y5 (- (* 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 = k * (z * ((b * y0) - (i * y1)));
	double tmp;
	if (y5 <= -1.3e+118) {
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	} else if (y5 <= -7.6e+32) {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	} else if (y5 <= -3.4e+17) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (y5 <= -1.32e-14) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y5 <= -5.5e-54) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y5 <= -1.1e-72) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else if (y5 <= -8.1e-122) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (y5 <= -3.9e-209) {
		tmp = t_1;
	} else if (y5 <= 1.12e-299) {
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	} else if (y5 <= 1.1e-162) {
		tmp = t_1;
	} else if (y5 <= 3.5e+32) {
		tmp = k * (y4 * ((y1 * y2) - (y * b)));
	} else if (y5 <= 9.2e+129) {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	} else {
		tmp = a * (y5 * ((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 = k * (z * ((b * y0) - (i * y1)))
    if (y5 <= (-1.3d+118)) then
        tmp = k * (y5 * ((y * i) - (y0 * y2)))
    else if (y5 <= (-7.6d+32)) then
        tmp = k * (y1 * ((y2 * y4) - (z * i)))
    else if (y5 <= (-3.4d+17)) then
        tmp = i * (y5 * ((y * k) - (t * j)))
    else if (y5 <= (-1.32d-14)) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (y5 <= (-5.5d-54)) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (y5 <= (-1.1d-72)) then
        tmp = t * (z * ((c * i) - (a * b)))
    else if (y5 <= (-8.1d-122)) then
        tmp = c * (i * ((z * t) - (x * y)))
    else if (y5 <= (-3.9d-209)) then
        tmp = t_1
    else if (y5 <= 1.12d-299) then
        tmp = y1 * (y3 * ((z * a) - (j * y4)))
    else if (y5 <= 1.1d-162) then
        tmp = t_1
    else if (y5 <= 3.5d+32) then
        tmp = k * (y4 * ((y1 * y2) - (y * b)))
    else if (y5 <= 9.2d+129) then
        tmp = y0 * (y5 * ((j * y3) - (k * y2)))
    else
        tmp = a * (y5 * ((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 = k * (z * ((b * y0) - (i * y1)));
	double tmp;
	if (y5 <= -1.3e+118) {
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	} else if (y5 <= -7.6e+32) {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	} else if (y5 <= -3.4e+17) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (y5 <= -1.32e-14) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y5 <= -5.5e-54) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y5 <= -1.1e-72) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else if (y5 <= -8.1e-122) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (y5 <= -3.9e-209) {
		tmp = t_1;
	} else if (y5 <= 1.12e-299) {
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	} else if (y5 <= 1.1e-162) {
		tmp = t_1;
	} else if (y5 <= 3.5e+32) {
		tmp = k * (y4 * ((y1 * y2) - (y * b)));
	} else if (y5 <= 9.2e+129) {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	} else {
		tmp = a * (y5 * ((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 = k * (z * ((b * y0) - (i * y1)))
	tmp = 0
	if y5 <= -1.3e+118:
		tmp = k * (y5 * ((y * i) - (y0 * y2)))
	elif y5 <= -7.6e+32:
		tmp = k * (y1 * ((y2 * y4) - (z * i)))
	elif y5 <= -3.4e+17:
		tmp = i * (y5 * ((y * k) - (t * j)))
	elif y5 <= -1.32e-14:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif y5 <= -5.5e-54:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif y5 <= -1.1e-72:
		tmp = t * (z * ((c * i) - (a * b)))
	elif y5 <= -8.1e-122:
		tmp = c * (i * ((z * t) - (x * y)))
	elif y5 <= -3.9e-209:
		tmp = t_1
	elif y5 <= 1.12e-299:
		tmp = y1 * (y3 * ((z * a) - (j * y4)))
	elif y5 <= 1.1e-162:
		tmp = t_1
	elif y5 <= 3.5e+32:
		tmp = k * (y4 * ((y1 * y2) - (y * b)))
	elif y5 <= 9.2e+129:
		tmp = y0 * (y5 * ((j * y3) - (k * y2)))
	else:
		tmp = a * (y5 * ((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(k * Float64(z * Float64(Float64(b * y0) - Float64(i * y1))))
	tmp = 0.0
	if (y5 <= -1.3e+118)
		tmp = Float64(k * Float64(y5 * Float64(Float64(y * i) - Float64(y0 * y2))));
	elseif (y5 <= -7.6e+32)
		tmp = Float64(k * Float64(y1 * Float64(Float64(y2 * y4) - Float64(z * i))));
	elseif (y5 <= -3.4e+17)
		tmp = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))));
	elseif (y5 <= -1.32e-14)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (y5 <= -5.5e-54)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (y5 <= -1.1e-72)
		tmp = Float64(t * Float64(z * Float64(Float64(c * i) - Float64(a * b))));
	elseif (y5 <= -8.1e-122)
		tmp = Float64(c * Float64(i * Float64(Float64(z * t) - Float64(x * y))));
	elseif (y5 <= -3.9e-209)
		tmp = t_1;
	elseif (y5 <= 1.12e-299)
		tmp = Float64(y1 * Float64(y3 * Float64(Float64(z * a) - Float64(j * y4))));
	elseif (y5 <= 1.1e-162)
		tmp = t_1;
	elseif (y5 <= 3.5e+32)
		tmp = Float64(k * Float64(y4 * Float64(Float64(y1 * y2) - Float64(y * b))));
	elseif (y5 <= 9.2e+129)
		tmp = Float64(y0 * Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))));
	else
		tmp = Float64(a * Float64(y5 * 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 = k * (z * ((b * y0) - (i * y1)));
	tmp = 0.0;
	if (y5 <= -1.3e+118)
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	elseif (y5 <= -7.6e+32)
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	elseif (y5 <= -3.4e+17)
		tmp = i * (y5 * ((y * k) - (t * j)));
	elseif (y5 <= -1.32e-14)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (y5 <= -5.5e-54)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (y5 <= -1.1e-72)
		tmp = t * (z * ((c * i) - (a * b)));
	elseif (y5 <= -8.1e-122)
		tmp = c * (i * ((z * t) - (x * y)));
	elseif (y5 <= -3.9e-209)
		tmp = t_1;
	elseif (y5 <= 1.12e-299)
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	elseif (y5 <= 1.1e-162)
		tmp = t_1;
	elseif (y5 <= 3.5e+32)
		tmp = k * (y4 * ((y1 * y2) - (y * b)));
	elseif (y5 <= 9.2e+129)
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	else
		tmp = a * (y5 * ((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[(k * N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -1.3e+118], N[(k * N[(y5 * N[(N[(y * i), $MachinePrecision] - N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -7.6e+32], N[(k * N[(y1 * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -3.4e+17], N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.32e-14], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -5.5e-54], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.1e-72], N[(t * N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -8.1e-122], N[(c * N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -3.9e-209], t$95$1, If[LessEqual[y5, 1.12e-299], N[(y1 * N[(y3 * N[(N[(z * a), $MachinePrecision] - N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.1e-162], t$95$1, If[LessEqual[y5, 3.5e+32], N[(k * N[(y4 * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 9.2e+129], N[(y0 * N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 12 regimes

2. if y5 < -1.30000000000000008e118

   1. Initial program 40.6%

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

   3. Taylor expanded in k around inf 50.2%

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

   4. Taylor expanded in y5 around inf 62.7%

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

      1. +-commutative 62.7%

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

      2. mul-1-neg 62.7%

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

      3. unsub-neg 62.7%

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

      4. *-commutative 62.7%

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

   6. Simplified 62.7%

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

   if -1.30000000000000008e118 < y5 < -7.6000000000000006e32

   1. Initial program 35.2%

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

   3. Taylor expanded in y1 around inf 40.9%

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

   4. Taylor expanded in k around inf 50.9%

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

      1. *-commutative 50.9%

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

   6. Simplified 50.9%

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

   if -7.6000000000000006e32 < y5 < -3.4e17

   1. Initial program 20.0%

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

   3. Taylor expanded in i around -inf 40.0%

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

   4. Taylor expanded in y5 around inf 100.0%

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

   if -3.4e17 < y5 < -1.32e-14

   1. Initial program 16.7%

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

   3. Taylor expanded in b around inf 50.4%

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

   4. Taylor expanded in y4 around inf 83.6%

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

   if -1.32e-14 < y5 < -5.50000000000000046e-54

   1. Initial program 50.5%

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

   3. Taylor expanded in b around inf 34.2%

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

   4. Taylor expanded in y0 around inf 50.9%

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

      1. *-commutative 50.9%

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

   6. Simplified 50.9%

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

   if -5.50000000000000046e-54 < y5 < -1.10000000000000001e-72

   1. Initial program 50.0%

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

   3. Taylor expanded in t around inf 66.9%

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

   4. Taylor expanded in z around inf 67.1%

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

      1. associate-*r* 67.1%

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

      2. neg-mul-1 67.1%

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

      3. *-commutative 67.1%

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

   6. Simplified 67.1%

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

   if -1.10000000000000001e-72 < y5 < -8.0999999999999997e-122

   1. Initial program 37.3%

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

   3. Taylor expanded in i around -inf 63.0%

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

   4. Taylor expanded in c around inf 63.4%

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

      1. *-commutative 63.4%

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

   6. Simplified 63.4%

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

   if -8.0999999999999997e-122 < y5 < -3.9e-209 or 1.11999999999999998e-299 < y5 < 1.1e-162

   1. Initial program 44.5%

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

   3. Taylor expanded in k around inf 51.9%

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

   4. Taylor expanded in z around inf 56.4%

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

      1. *-commutative 56.4%

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

      2. *-commutative 56.4%

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

   6. Simplified 56.4%

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

   if -3.9e-209 < y5 < 1.11999999999999998e-299

   1. Initial program 38.3%

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

   3. Taylor expanded in y1 around inf 39.2%

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

   4. Taylor expanded in y3 around inf 48.7%

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

      1. *-commutative 48.7%

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

      2. +-commutative 48.7%

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

      3. mul-1-neg 48.7%

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

      4. unsub-neg 48.7%

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

      5. *-commutative 48.7%

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

   6. Simplified 48.7%

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

   if 1.1e-162 < y5 < 3.5000000000000001e32

   1. Initial program 38.6%

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

   3. Taylor expanded in k around inf 47.1%

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

   4. Taylor expanded in y4 around inf 44.8%

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

      1. +-commutative 44.8%

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

      2. mul-1-neg 44.8%

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

      3. unsub-neg 44.8%

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

      4. *-commutative 44.8%

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

   6. Simplified 44.8%

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

   if 3.5000000000000001e32 < y5 < 9.19999999999999961e129

   1. Initial program 29.8%

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

   3. Taylor expanded in y5 around -inf 55.9%

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

   4. Taylor expanded in y0 around inf 51.2%

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

   if 9.19999999999999961e129 < y5

   1. Initial program 12.2%

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

   3. Taylor expanded in y5 around -inf 66.5%

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

   4. Taylor expanded in a around inf 61.0%

      \[\leadsto -1 \cdot \color{blue}{\left(a \cdot \left(y5 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)} \]
3. Recombined 12 regimes into one program.

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -1.3 \cdot 10^{+118}:\\ \;\;\;\;k \cdot \left(y5 \cdot \left(y \cdot i - y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq -7.6 \cdot 10^{+32}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;y5 \leq -3.4 \cdot 10^{+17}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq -1.32 \cdot 10^{-14}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y5 \leq -5.5 \cdot 10^{-54}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq -1.1 \cdot 10^{-72}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;y5 \leq -8.1 \cdot 10^{-122}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;y5 \leq -3.9 \cdot 10^{-209}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y5 \leq 1.12 \cdot 10^{-299}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 1.1 \cdot 10^{-162}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y5 \leq 3.5 \cdot 10^{+32}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;y5 \leq 9.2 \cdot 10^{+129}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 34.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ t_2 := k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right) + y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ t_3 := b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{if}\;j \leq -7 \cdot 10^{+191}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -1.22 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -7.8 \cdot 10^{-308}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 7.8 \cdot 10^{-233}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{-87}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{+28}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5 - z \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 1.95 \cdot 10^{+102}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.06 \cdot 10^{+213}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* y1 (- (* x j) (* z k)))))
        (t_2
         (* k (+ (* z (- (* b y0) (* i y1))) (* y4 (- (* y1 y2) (* y b))))))
        (t_3
         (*
          b
          (+
           (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
           (* y0 (- (* z k) (* x j)))))))
   (if (<= j -7e+191)
     (* i (* y5 (- (* y k) (* t j))))
     (if (<= j -1.22e+75)
       t_1
       (if (<= j -7.8e-308)
         t_2
         (if (<= j 7.8e-233)
           t_3
           (if (<= j 8.5e-87)
             t_2
             (if (<= j 2.5e+28)
               (* y0 (* y3 (- (* j y5) (* z c))))
               (if (<= j 1.95e+102) t_2 (if (<= j 1.06e+213) t_3 t_1))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (y1 * ((x * j) - (z * k)));
	double t_2 = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))));
	double t_3 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double tmp;
	if (j <= -7e+191) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (j <= -1.22e+75) {
		tmp = t_1;
	} else if (j <= -7.8e-308) {
		tmp = t_2;
	} else if (j <= 7.8e-233) {
		tmp = t_3;
	} else if (j <= 8.5e-87) {
		tmp = t_2;
	} else if (j <= 2.5e+28) {
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	} else if (j <= 1.95e+102) {
		tmp = t_2;
	} else if (j <= 1.06e+213) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = i * (y1 * ((x * j) - (z * k)))
    t_2 = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))))
    t_3 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    if (j <= (-7d+191)) then
        tmp = i * (y5 * ((y * k) - (t * j)))
    else if (j <= (-1.22d+75)) then
        tmp = t_1
    else if (j <= (-7.8d-308)) then
        tmp = t_2
    else if (j <= 7.8d-233) then
        tmp = t_3
    else if (j <= 8.5d-87) then
        tmp = t_2
    else if (j <= 2.5d+28) then
        tmp = y0 * (y3 * ((j * y5) - (z * c)))
    else if (j <= 1.95d+102) then
        tmp = t_2
    else if (j <= 1.06d+213) then
        tmp = t_3
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (y1 * ((x * j) - (z * k)));
	double t_2 = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))));
	double t_3 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double tmp;
	if (j <= -7e+191) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (j <= -1.22e+75) {
		tmp = t_1;
	} else if (j <= -7.8e-308) {
		tmp = t_2;
	} else if (j <= 7.8e-233) {
		tmp = t_3;
	} else if (j <= 8.5e-87) {
		tmp = t_2;
	} else if (j <= 2.5e+28) {
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	} else if (j <= 1.95e+102) {
		tmp = t_2;
	} else if (j <= 1.06e+213) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = i * (y1 * ((x * j) - (z * k)))
	t_2 = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))))
	t_3 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	tmp = 0
	if j <= -7e+191:
		tmp = i * (y5 * ((y * k) - (t * j)))
	elif j <= -1.22e+75:
		tmp = t_1
	elif j <= -7.8e-308:
		tmp = t_2
	elif j <= 7.8e-233:
		tmp = t_3
	elif j <= 8.5e-87:
		tmp = t_2
	elif j <= 2.5e+28:
		tmp = y0 * (y3 * ((j * y5) - (z * c)))
	elif j <= 1.95e+102:
		tmp = t_2
	elif j <= 1.06e+213:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))))
	t_2 = Float64(k * Float64(Float64(z * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(y4 * Float64(Float64(y1 * y2) - Float64(y * b)))))
	t_3 = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))))
	tmp = 0.0
	if (j <= -7e+191)
		tmp = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))));
	elseif (j <= -1.22e+75)
		tmp = t_1;
	elseif (j <= -7.8e-308)
		tmp = t_2;
	elseif (j <= 7.8e-233)
		tmp = t_3;
	elseif (j <= 8.5e-87)
		tmp = t_2;
	elseif (j <= 2.5e+28)
		tmp = Float64(y0 * Float64(y3 * Float64(Float64(j * y5) - Float64(z * c))));
	elseif (j <= 1.95e+102)
		tmp = t_2;
	elseif (j <= 1.06e+213)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = i * (y1 * ((x * j) - (z * k)));
	t_2 = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))));
	t_3 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	tmp = 0.0;
	if (j <= -7e+191)
		tmp = i * (y5 * ((y * k) - (t * j)));
	elseif (j <= -1.22e+75)
		tmp = t_1;
	elseif (j <= -7.8e-308)
		tmp = t_2;
	elseif (j <= 7.8e-233)
		tmp = t_3;
	elseif (j <= 8.5e-87)
		tmp = t_2;
	elseif (j <= 2.5e+28)
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	elseif (j <= 1.95e+102)
		tmp = t_2;
	elseif (j <= 1.06e+213)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -7e+191], N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.22e+75], t$95$1, If[LessEqual[j, -7.8e-308], t$95$2, If[LessEqual[j, 7.8e-233], t$95$3, If[LessEqual[j, 8.5e-87], t$95$2, If[LessEqual[j, 2.5e+28], N[(y0 * N[(y3 * N[(N[(j * y5), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.95e+102], t$95$2, If[LessEqual[j, 1.06e+213], t$95$3, t$95$1]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -6.9999999999999994e191

   1. Initial program 31.0%

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

   3. Taylor expanded in i around -inf 66.5%

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

   4. Taylor expanded in y5 around inf 62.3%

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

   if -6.9999999999999994e191 < j < -1.2199999999999999e75 or 1.05999999999999999e213 < j

   1. Initial program 30.2%

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

   3. Taylor expanded in y1 around inf 47.0%

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

   4. Taylor expanded in i around inf 56.3%

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

   if -1.2199999999999999e75 < j < -7.7999999999999999e-308 or 7.8000000000000002e-233 < j < 8.5000000000000001e-87 or 2.49999999999999979e28 < j < 1.9499999999999999e102

   1. Initial program 34.7%

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

   3. Taylor expanded in k around inf 49.4%

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

   4. Taylor expanded in y5 around 0 48.9%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(b \cdot \left(y \cdot y4\right)\right) + y1 \cdot \left(y2 \cdot y4\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   5. Step-by-step derivation

      1. cancel-sign-sub-inv 48.9%

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

      2. mul-1-neg 48.9%

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

      3. associate-*r* 49.6%

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

      4. distribute-lft-neg-in 49.6%

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

      5. mul-1-neg 49.6%

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

      6. associate-*r* 50.4%

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

      7. distribute-rgt-in 51.9%

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

      8. +-commutative 51.9%

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

      9. mul-1-neg 51.9%

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

      10. unsub-neg 51.9%

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

      11. *-commutative 51.9%

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

      12. metadata-eval 51.9%

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

      13. *-lft-identity 51.9%

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

      14. *-commutative 51.9%

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

      15. *-commutative 51.9%

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

   6. Simplified 51.9%

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

   if -7.7999999999999999e-308 < j < 7.8000000000000002e-233 or 1.9499999999999999e102 < j < 1.05999999999999999e213

   1. Initial program 31.0%

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

   3. Taylor expanded in b around inf 54.8%

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

   if 8.5000000000000001e-87 < j < 2.49999999999999979e28

   1. Initial program 39.2%

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

   3. Taylor expanded in y0 around inf 50.8%

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

   4. Taylor expanded in y3 around inf 50.8%

      \[\leadsto \color{blue}{y0 \cdot \left(y3 \cdot \left(-1 \cdot \left(c \cdot z\right) + j \cdot y5\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -7 \cdot 10^{+191}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -1.22 \cdot 10^{+75}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;j \leq -7.8 \cdot 10^{-308}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right) + y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;j \leq 7.8 \cdot 10^{-233}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{-87}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right) + y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{+28}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5 - z \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 1.95 \cdot 10^{+102}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right) + y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;j \leq 1.06 \cdot 10^{+213}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 33.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ t_2 := k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right) + y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{if}\;j \leq -9 \cdot 10^{+195}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -7.6 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -3.4 \cdot 10^{-231}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 2 \cdot 10^{-142}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 1.05 \cdot 10^{-86}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 1.85 \cdot 10^{+29}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5 - z \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 2.1 \cdot 10^{+102}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 5.5 \cdot 10^{+213}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* y1 (- (* x j) (* z k)))))
        (t_2
         (* k (+ (* z (- (* b y0) (* i y1))) (* y4 (- (* y1 y2) (* y b)))))))
   (if (<= j -9e+195)
     (* i (* y5 (- (* y k) (* t j))))
     (if (<= j -7.6e+73)
       t_1
       (if (<= j -3.4e-231)
         t_2
         (if (<= j 2e-142)
           (*
            y2
            (+
             (+ (* k (- (* y1 y4) (* y0 y5))) (* x (- (* c y0) (* a y1))))
             (* t (- (* a y5) (* c y4)))))
           (if (<= j 1.05e-86)
             (* i (* y (- (* k y5) (* x c))))
             (if (<= j 1.85e+29)
               (* y0 (* y3 (- (* j y5) (* z c))))
               (if (<= j 2.1e+102)
                 t_2
                 (if (<= j 5.5e+213)
                   (*
                    b
                    (+
                     (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
                     (* y0 (- (* z k) (* x 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 = i * (y1 * ((x * j) - (z * k)));
	double t_2 = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))));
	double tmp;
	if (j <= -9e+195) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (j <= -7.6e+73) {
		tmp = t_1;
	} else if (j <= -3.4e-231) {
		tmp = t_2;
	} else if (j <= 2e-142) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else if (j <= 1.05e-86) {
		tmp = i * (y * ((k * y5) - (x * c)));
	} else if (j <= 1.85e+29) {
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	} else if (j <= 2.1e+102) {
		tmp = t_2;
	} else if (j <= 5.5e+213) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * (y1 * ((x * j) - (z * k)))
    t_2 = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))))
    if (j <= (-9d+195)) then
        tmp = i * (y5 * ((y * k) - (t * j)))
    else if (j <= (-7.6d+73)) then
        tmp = t_1
    else if (j <= (-3.4d-231)) then
        tmp = t_2
    else if (j <= 2d-142) then
        tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
    else if (j <= 1.05d-86) then
        tmp = i * (y * ((k * y5) - (x * c)))
    else if (j <= 1.85d+29) then
        tmp = y0 * (y3 * ((j * y5) - (z * c)))
    else if (j <= 2.1d+102) then
        tmp = t_2
    else if (j <= 5.5d+213) then
        tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (y1 * ((x * j) - (z * k)));
	double t_2 = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))));
	double tmp;
	if (j <= -9e+195) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (j <= -7.6e+73) {
		tmp = t_1;
	} else if (j <= -3.4e-231) {
		tmp = t_2;
	} else if (j <= 2e-142) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else if (j <= 1.05e-86) {
		tmp = i * (y * ((k * y5) - (x * c)));
	} else if (j <= 1.85e+29) {
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	} else if (j <= 2.1e+102) {
		tmp = t_2;
	} else if (j <= 5.5e+213) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = i * (y1 * ((x * j) - (z * k)))
	t_2 = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))))
	tmp = 0
	if j <= -9e+195:
		tmp = i * (y5 * ((y * k) - (t * j)))
	elif j <= -7.6e+73:
		tmp = t_1
	elif j <= -3.4e-231:
		tmp = t_2
	elif j <= 2e-142:
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
	elif j <= 1.05e-86:
		tmp = i * (y * ((k * y5) - (x * c)))
	elif j <= 1.85e+29:
		tmp = y0 * (y3 * ((j * y5) - (z * c)))
	elif j <= 2.1e+102:
		tmp = t_2
	elif j <= 5.5e+213:
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))))
	t_2 = Float64(k * Float64(Float64(z * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(y4 * Float64(Float64(y1 * y2) - Float64(y * b)))))
	tmp = 0.0
	if (j <= -9e+195)
		tmp = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))));
	elseif (j <= -7.6e+73)
		tmp = t_1;
	elseif (j <= -3.4e-231)
		tmp = t_2;
	elseif (j <= 2e-142)
		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 (j <= 1.05e-86)
		tmp = Float64(i * Float64(y * Float64(Float64(k * y5) - Float64(x * c))));
	elseif (j <= 1.85e+29)
		tmp = Float64(y0 * Float64(y3 * Float64(Float64(j * y5) - Float64(z * c))));
	elseif (j <= 2.1e+102)
		tmp = t_2;
	elseif (j <= 5.5e+213)
		tmp = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = i * (y1 * ((x * j) - (z * k)));
	t_2 = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))));
	tmp = 0.0;
	if (j <= -9e+195)
		tmp = i * (y5 * ((y * k) - (t * j)));
	elseif (j <= -7.6e+73)
		tmp = t_1;
	elseif (j <= -3.4e-231)
		tmp = t_2;
	elseif (j <= 2e-142)
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	elseif (j <= 1.05e-86)
		tmp = i * (y * ((k * y5) - (x * c)));
	elseif (j <= 1.85e+29)
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	elseif (j <= 2.1e+102)
		tmp = t_2;
	elseif (j <= 5.5e+213)
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -9e+195], N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -7.6e+73], t$95$1, If[LessEqual[j, -3.4e-231], t$95$2, If[LessEqual[j, 2e-142], 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[j, 1.05e-86], N[(i * N[(y * N[(N[(k * y5), $MachinePrecision] - N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.85e+29], N[(y0 * N[(y3 * N[(N[(j * y5), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.1e+102], t$95$2, If[LessEqual[j, 5.5e+213], N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if j < -9.00000000000000018e195

   1. Initial program 31.0%

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

   3. Taylor expanded in i around -inf 66.5%

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

   4. Taylor expanded in y5 around inf 62.3%

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

   if -9.00000000000000018e195 < j < -7.60000000000000044e73 or 5.50000000000000059e213 < j

   1. Initial program 30.2%

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

   3. Taylor expanded in y1 around inf 47.0%

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

   4. Taylor expanded in i around inf 56.3%

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

   if -7.60000000000000044e73 < j < -3.4e-231 or 1.84999999999999987e29 < j < 2.10000000000000001e102

   1. Initial program 33.5%

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

   3. Taylor expanded in k around inf 52.8%

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

   4. Taylor expanded in y5 around 0 51.9%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(b \cdot \left(y \cdot y4\right)\right) + y1 \cdot \left(y2 \cdot y4\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   5. Step-by-step derivation

      1. cancel-sign-sub-inv 51.9%

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

      2. mul-1-neg 51.9%

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

      3. associate-*r* 51.9%

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

      4. distribute-lft-neg-in 51.9%

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

      5. mul-1-neg 51.9%

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

      6. associate-*r* 53.0%

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

      7. distribute-rgt-in 53.0%

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

      8. +-commutative 53.0%

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

      9. mul-1-neg 53.0%

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

      10. unsub-neg 53.0%

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

      11. *-commutative 53.0%

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

      12. metadata-eval 53.0%

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

      13. *-lft-identity 53.0%

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

      14. *-commutative 53.0%

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

      15. *-commutative 53.0%

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

   6. Simplified 53.0%

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

   if -3.4e-231 < j < 2.0000000000000001e-142

   1. Initial program 41.8%

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

   3. Taylor expanded in y2 around inf 50.3%

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

   if 2.0000000000000001e-142 < j < 1.05e-86

   1. Initial program 33.2%

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

   3. Taylor expanded in i around -inf 55.7%

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

   4. Taylor expanded in y around -inf 67.4%

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

      1. mul-1-neg 67.4%

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

      2. *-commutative 67.4%

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

      3. distribute-rgt-neg-in 67.4%

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

      4. +-commutative 67.4%

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

      5. mul-1-neg 67.4%

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

      6. unsub-neg 67.4%

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

      7. *-commutative 67.4%

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

      8. *-commutative 67.4%

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

   6. Simplified 67.4%

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

   if 1.05e-86 < j < 1.84999999999999987e29

   1. Initial program 39.2%

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

   3. Taylor expanded in y0 around inf 50.8%

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

   4. Taylor expanded in y3 around inf 50.8%

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

   if 2.10000000000000001e102 < j < 5.50000000000000059e213

   1. Initial program 21.4%

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

   3. Taylor expanded in b around inf 56.4%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -9 \cdot 10^{+195}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -7.6 \cdot 10^{+73}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;j \leq -3.4 \cdot 10^{-231}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right) + y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;j \leq 2 \cdot 10^{-142}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 1.05 \cdot 10^{-86}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 1.85 \cdot 10^{+29}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5 - z \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 2.1 \cdot 10^{+102}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right) + y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;j \leq 5.5 \cdot 10^{+213}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 39.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot k - t \cdot j\\ t_2 := b \cdot y0 - i \cdot y1\\ t_3 := z \cdot \left(k \cdot t_2 + \left(t \cdot \left(c \cdot i - a \cdot b\right) - y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ t_4 := j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ t_5 := i \cdot y5 - b \cdot y4\\ \mathbf{if}\;y5 \leq -1.5 \cdot 10^{+209}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y5 \leq -6.8 \cdot 10^{+156}:\\ \;\;\;\;y3 \cdot \left(y5 \cdot \left(j \cdot y0 - y \cdot a\right)\right)\\ \mathbf{elif}\;y5 \leq -5.8 \cdot 10^{+30}:\\ \;\;\;\;y \cdot \left(\left(k \cdot t_5 + x \cdot \left(a \cdot b - c \cdot i\right)\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq -4.5 \cdot 10^{-21}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y5 \leq -1.8 \cdot 10^{-196}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot t_1 + c \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 4.8 \cdot 10^{-240}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y5 \leq 6.2 \cdot 10^{-75}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y5 \leq 3.6 \cdot 10^{+42}:\\ \;\;\;\;k \cdot \left(\left(y \cdot t_5 + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + z \cdot t_2\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot t_1 + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y k) (* t j)))
        (t_2 (- (* b y0) (* i y1)))
        (t_3
         (*
          z
          (+
           (* k t_2)
           (- (* t (- (* c i) (* a b))) (* y3 (- (* c y0) (* a y1)))))))
        (t_4
         (*
          j
          (+
           (+ (* y3 (- (* y0 y5) (* y1 y4))) (* t (- (* b y4) (* i y5))))
           (* x (- (* i y1) (* b y0))))))
        (t_5 (- (* i y5) (* b y4))))
   (if (<= y5 -1.5e+209)
     t_3
     (if (<= y5 -6.8e+156)
       (* y3 (* y5 (- (* j y0) (* y a))))
       (if (<= y5 -5.8e+30)
         (*
          y
          (+
           (+ (* k t_5) (* x (- (* a b) (* c i))))
           (* y3 (- (* c y4) (* a y5)))))
         (if (<= y5 -4.5e-21)
           t_4
           (if (<= y5 -1.8e-196)
             (*
              i
              (+
               (* y1 (- (* x j) (* z k)))
               (+ (* y5 t_1) (* c (- (* z t) (* x y))))))
             (if (<= y5 4.8e-240)
               t_3
               (if (<= y5 6.2e-75)
                 t_4
                 (if (<= y5 3.6e+42)
                   (*
                    k
                    (+ (+ (* y t_5) (* y2 (- (* y1 y4) (* y0 y5)))) (* z t_2)))
                   (*
                    y5
                    (+
                     (* a (- (* t y2) (* y y3)))
                     (+ (* i t_1) (* y0 (- (* j y3) (* k 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 = (y * k) - (t * j);
	double t_2 = (b * y0) - (i * y1);
	double t_3 = z * ((k * t_2) + ((t * ((c * i) - (a * b))) - (y3 * ((c * y0) - (a * y1)))));
	double t_4 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))));
	double t_5 = (i * y5) - (b * y4);
	double tmp;
	if (y5 <= -1.5e+209) {
		tmp = t_3;
	} else if (y5 <= -6.8e+156) {
		tmp = y3 * (y5 * ((j * y0) - (y * a)));
	} else if (y5 <= -5.8e+30) {
		tmp = y * (((k * t_5) + (x * ((a * b) - (c * i)))) + (y3 * ((c * y4) - (a * y5))));
	} else if (y5 <= -4.5e-21) {
		tmp = t_4;
	} else if (y5 <= -1.8e-196) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * t_1) + (c * ((z * t) - (x * y)))));
	} else if (y5 <= 4.8e-240) {
		tmp = t_3;
	} else if (y5 <= 6.2e-75) {
		tmp = t_4;
	} else if (y5 <= 3.6e+42) {
		tmp = k * (((y * t_5) + (y2 * ((y1 * y4) - (y0 * y5)))) + (z * t_2));
	} else {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * t_1) + (y0 * ((j * y3) - (k * y2)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = (y * k) - (t * j)
    t_2 = (b * y0) - (i * y1)
    t_3 = z * ((k * t_2) + ((t * ((c * i) - (a * b))) - (y3 * ((c * y0) - (a * y1)))))
    t_4 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))))
    t_5 = (i * y5) - (b * y4)
    if (y5 <= (-1.5d+209)) then
        tmp = t_3
    else if (y5 <= (-6.8d+156)) then
        tmp = y3 * (y5 * ((j * y0) - (y * a)))
    else if (y5 <= (-5.8d+30)) then
        tmp = y * (((k * t_5) + (x * ((a * b) - (c * i)))) + (y3 * ((c * y4) - (a * y5))))
    else if (y5 <= (-4.5d-21)) then
        tmp = t_4
    else if (y5 <= (-1.8d-196)) then
        tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * t_1) + (c * ((z * t) - (x * y)))))
    else if (y5 <= 4.8d-240) then
        tmp = t_3
    else if (y5 <= 6.2d-75) then
        tmp = t_4
    else if (y5 <= 3.6d+42) then
        tmp = k * (((y * t_5) + (y2 * ((y1 * y4) - (y0 * y5)))) + (z * t_2))
    else
        tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * t_1) + (y0 * ((j * y3) - (k * y2)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * k) - (t * j);
	double t_2 = (b * y0) - (i * y1);
	double t_3 = z * ((k * t_2) + ((t * ((c * i) - (a * b))) - (y3 * ((c * y0) - (a * y1)))));
	double t_4 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))));
	double t_5 = (i * y5) - (b * y4);
	double tmp;
	if (y5 <= -1.5e+209) {
		tmp = t_3;
	} else if (y5 <= -6.8e+156) {
		tmp = y3 * (y5 * ((j * y0) - (y * a)));
	} else if (y5 <= -5.8e+30) {
		tmp = y * (((k * t_5) + (x * ((a * b) - (c * i)))) + (y3 * ((c * y4) - (a * y5))));
	} else if (y5 <= -4.5e-21) {
		tmp = t_4;
	} else if (y5 <= -1.8e-196) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * t_1) + (c * ((z * t) - (x * y)))));
	} else if (y5 <= 4.8e-240) {
		tmp = t_3;
	} else if (y5 <= 6.2e-75) {
		tmp = t_4;
	} else if (y5 <= 3.6e+42) {
		tmp = k * (((y * t_5) + (y2 * ((y1 * y4) - (y0 * y5)))) + (z * t_2));
	} else {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * t_1) + (y0 * ((j * y3) - (k * y2)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y * k) - (t * j)
	t_2 = (b * y0) - (i * y1)
	t_3 = z * ((k * t_2) + ((t * ((c * i) - (a * b))) - (y3 * ((c * y0) - (a * y1)))))
	t_4 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))))
	t_5 = (i * y5) - (b * y4)
	tmp = 0
	if y5 <= -1.5e+209:
		tmp = t_3
	elif y5 <= -6.8e+156:
		tmp = y3 * (y5 * ((j * y0) - (y * a)))
	elif y5 <= -5.8e+30:
		tmp = y * (((k * t_5) + (x * ((a * b) - (c * i)))) + (y3 * ((c * y4) - (a * y5))))
	elif y5 <= -4.5e-21:
		tmp = t_4
	elif y5 <= -1.8e-196:
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * t_1) + (c * ((z * t) - (x * y)))))
	elif y5 <= 4.8e-240:
		tmp = t_3
	elif y5 <= 6.2e-75:
		tmp = t_4
	elif y5 <= 3.6e+42:
		tmp = k * (((y * t_5) + (y2 * ((y1 * y4) - (y0 * y5)))) + (z * t_2))
	else:
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * t_1) + (y0 * ((j * y3) - (k * 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(y * k) - Float64(t * j))
	t_2 = Float64(Float64(b * y0) - Float64(i * y1))
	t_3 = Float64(z * Float64(Float64(k * t_2) + Float64(Float64(t * Float64(Float64(c * i) - Float64(a * b))) - Float64(y3 * Float64(Float64(c * y0) - Float64(a * y1))))))
	t_4 = Float64(j * Float64(Float64(Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(t * Float64(Float64(b * y4) - Float64(i * y5)))) + Float64(x * Float64(Float64(i * y1) - Float64(b * y0)))))
	t_5 = Float64(Float64(i * y5) - Float64(b * y4))
	tmp = 0.0
	if (y5 <= -1.5e+209)
		tmp = t_3;
	elseif (y5 <= -6.8e+156)
		tmp = Float64(y3 * Float64(y5 * Float64(Float64(j * y0) - Float64(y * a))));
	elseif (y5 <= -5.8e+30)
		tmp = Float64(y * Float64(Float64(Float64(k * t_5) + Float64(x * Float64(Float64(a * b) - Float64(c * i)))) + Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5)))));
	elseif (y5 <= -4.5e-21)
		tmp = t_4;
	elseif (y5 <= -1.8e-196)
		tmp = Float64(i * Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) + Float64(Float64(y5 * t_1) + Float64(c * Float64(Float64(z * t) - Float64(x * y))))));
	elseif (y5 <= 4.8e-240)
		tmp = t_3;
	elseif (y5 <= 6.2e-75)
		tmp = t_4;
	elseif (y5 <= 3.6e+42)
		tmp = Float64(k * Float64(Float64(Float64(y * t_5) + Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5)))) + Float64(z * t_2)));
	else
		tmp = Float64(y5 * Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(Float64(i * t_1) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * 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 = (y * k) - (t * j);
	t_2 = (b * y0) - (i * y1);
	t_3 = z * ((k * t_2) + ((t * ((c * i) - (a * b))) - (y3 * ((c * y0) - (a * y1)))));
	t_4 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))));
	t_5 = (i * y5) - (b * y4);
	tmp = 0.0;
	if (y5 <= -1.5e+209)
		tmp = t_3;
	elseif (y5 <= -6.8e+156)
		tmp = y3 * (y5 * ((j * y0) - (y * a)));
	elseif (y5 <= -5.8e+30)
		tmp = y * (((k * t_5) + (x * ((a * b) - (c * i)))) + (y3 * ((c * y4) - (a * y5))));
	elseif (y5 <= -4.5e-21)
		tmp = t_4;
	elseif (y5 <= -1.8e-196)
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * t_1) + (c * ((z * t) - (x * y)))));
	elseif (y5 <= 4.8e-240)
		tmp = t_3;
	elseif (y5 <= 6.2e-75)
		tmp = t_4;
	elseif (y5 <= 3.6e+42)
		tmp = k * (((y * t_5) + (y2 * ((y1 * y4) - (y0 * y5)))) + (z * t_2));
	else
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * t_1) + (y0 * ((j * y3) - (k * 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[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(N[(k * t$95$2), $MachinePrecision] + N[(N[(t * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y3 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(j * N[(N[(N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -1.5e+209], t$95$3, If[LessEqual[y5, -6.8e+156], N[(y3 * N[(y5 * N[(N[(j * y0), $MachinePrecision] - N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -5.8e+30], N[(y * N[(N[(N[(k * t$95$5), $MachinePrecision] + N[(x * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -4.5e-21], t$95$4, If[LessEqual[y5, -1.8e-196], N[(i * N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y5 * t$95$1), $MachinePrecision] + N[(c * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 4.8e-240], t$95$3, If[LessEqual[y5, 6.2e-75], t$95$4, If[LessEqual[y5, 3.6e+42], N[(k * N[(N[(N[(y * t$95$5), $MachinePrecision] + N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y5 * N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(i * t$95$1), $MachinePrecision] + N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y5 < -1.49999999999999993e209 or -1.8e-196 < y5 < 4.7999999999999999e-240

   1. Initial program 44.1%

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

   3. Taylor expanded in z around -inf 69.9%

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

   if -1.49999999999999993e209 < y5 < -6.8000000000000002e156

   1. Initial program 30.0%

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

   3. Taylor expanded in y5 around -inf 80.5%

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

   4. Taylor expanded in y3 around inf 80.7%

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

      1. distribute-lft-out-- 80.7%

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

      2. *-commutative 80.7%

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

   6. Simplified 80.7%

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

   if -6.8000000000000002e156 < y5 < -5.7999999999999996e30

   1. Initial program 33.5%

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

   3. Taylor expanded in y around inf 59.2%

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

   if -5.7999999999999996e30 < y5 < -4.49999999999999968e-21 or 4.7999999999999999e-240 < y5 < 6.20000000000000013e-75

   1. Initial program 32.7%

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

   3. Taylor expanded in j around inf 61.5%

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

   if -4.49999999999999968e-21 < y5 < -1.8e-196

   1. Initial program 50.2%

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

   3. Taylor expanded in i around -inf 57.0%

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

   if 6.20000000000000013e-75 < y5 < 3.6000000000000001e42

   1. Initial program 37.8%

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

   3. Taylor expanded in k around inf 67.6%

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

   if 3.6000000000000001e42 < y5

   1. Initial program 16.2%

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

   3. Taylor expanded in y5 around -inf 63.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -1.5 \cdot 10^{+209}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot \left(c \cdot i - a \cdot b\right) - y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;y5 \leq -6.8 \cdot 10^{+156}:\\ \;\;\;\;y3 \cdot \left(y5 \cdot \left(j \cdot y0 - y \cdot a\right)\right)\\ \mathbf{elif}\;y5 \leq -5.8 \cdot 10^{+30}:\\ \;\;\;\;y \cdot \left(\left(k \cdot \left(i \cdot y5 - b \cdot y4\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq -4.5 \cdot 10^{-21}:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq -1.8 \cdot 10^{-196}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) + c \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 4.8 \cdot 10^{-240}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot \left(c \cdot i - a \cdot b\right) - y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 6.2 \cdot 10^{-75}:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 3.6 \cdot 10^{+42}:\\ \;\;\;\;k \cdot \left(\left(y \cdot \left(i \cdot y5 - b \cdot y4\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 38.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot k - t \cdot j\\ t_2 := i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot t_1 + c \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ t_3 := y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot t_1 + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ t_4 := c \cdot i - a \cdot b\\ t_5 := z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot t_4 - y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{if}\;y1 \leq -2.55 \cdot 10^{+123}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y1 \leq -3.2 \cdot 10^{-12}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y1 \leq -1.2 \cdot 10^{-113}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y1 \leq 5.5 \cdot 10^{-301}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y1 \leq 2.32 \cdot 10^{-122}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y1 \leq 1.2 \cdot 10^{-32}:\\ \;\;\;\;t \cdot \left(\left(z \cdot t_4 + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 3.85 \cdot 10^{+180}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y1 \leq 1.28 \cdot 10^{+213}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y k) (* t j)))
        (t_2
         (*
          i
          (+
           (* y1 (- (* x j) (* z k)))
           (+ (* y5 t_1) (* c (- (* z t) (* x y)))))))
        (t_3
         (*
          y5
          (+
           (* a (- (* t y2) (* y y3)))
           (+ (* i t_1) (* y0 (- (* j y3) (* k y2)))))))
        (t_4 (- (* c i) (* a b)))
        (t_5
         (*
          z
          (+
           (* k (- (* b y0) (* i y1)))
           (- (* t t_4) (* y3 (- (* c y0) (* a y1))))))))
   (if (<= y1 -2.55e+123)
     t_2
     (if (<= y1 -3.2e-12)
       t_5
       (if (<= y1 -1.2e-113)
         t_3
         (if (<= y1 5.5e-301)
           t_5
           (if (<= y1 2.32e-122)
             t_3
             (if (<= y1 1.2e-32)
               (*
                t
                (+
                 (+ (* z t_4) (* j (- (* b y4) (* i y5))))
                 (* y2 (- (* a y5) (* c y4)))))
               (if (<= y1 3.85e+180)
                 t_2
                 (if (<= y1 1.28e+213)
                   (* y1 (* y3 (- (* z a) (* j y4))))
                   (* k (* y1 (- (* y2 y4) (* z 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 = (y * k) - (t * j);
	double t_2 = i * ((y1 * ((x * j) - (z * k))) + ((y5 * t_1) + (c * ((z * t) - (x * y)))));
	double t_3 = y5 * ((a * ((t * y2) - (y * y3))) + ((i * t_1) + (y0 * ((j * y3) - (k * y2)))));
	double t_4 = (c * i) - (a * b);
	double t_5 = z * ((k * ((b * y0) - (i * y1))) + ((t * t_4) - (y3 * ((c * y0) - (a * y1)))));
	double tmp;
	if (y1 <= -2.55e+123) {
		tmp = t_2;
	} else if (y1 <= -3.2e-12) {
		tmp = t_5;
	} else if (y1 <= -1.2e-113) {
		tmp = t_3;
	} else if (y1 <= 5.5e-301) {
		tmp = t_5;
	} else if (y1 <= 2.32e-122) {
		tmp = t_3;
	} else if (y1 <= 1.2e-32) {
		tmp = t * (((z * t_4) + (j * ((b * y4) - (i * y5)))) + (y2 * ((a * y5) - (c * y4))));
	} else if (y1 <= 3.85e+180) {
		tmp = t_2;
	} else if (y1 <= 1.28e+213) {
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	} else {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = (y * k) - (t * j)
    t_2 = i * ((y1 * ((x * j) - (z * k))) + ((y5 * t_1) + (c * ((z * t) - (x * y)))))
    t_3 = y5 * ((a * ((t * y2) - (y * y3))) + ((i * t_1) + (y0 * ((j * y3) - (k * y2)))))
    t_4 = (c * i) - (a * b)
    t_5 = z * ((k * ((b * y0) - (i * y1))) + ((t * t_4) - (y3 * ((c * y0) - (a * y1)))))
    if (y1 <= (-2.55d+123)) then
        tmp = t_2
    else if (y1 <= (-3.2d-12)) then
        tmp = t_5
    else if (y1 <= (-1.2d-113)) then
        tmp = t_3
    else if (y1 <= 5.5d-301) then
        tmp = t_5
    else if (y1 <= 2.32d-122) then
        tmp = t_3
    else if (y1 <= 1.2d-32) then
        tmp = t * (((z * t_4) + (j * ((b * y4) - (i * y5)))) + (y2 * ((a * y5) - (c * y4))))
    else if (y1 <= 3.85d+180) then
        tmp = t_2
    else if (y1 <= 1.28d+213) then
        tmp = y1 * (y3 * ((z * a) - (j * y4)))
    else
        tmp = k * (y1 * ((y2 * y4) - (z * 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 = (y * k) - (t * j);
	double t_2 = i * ((y1 * ((x * j) - (z * k))) + ((y5 * t_1) + (c * ((z * t) - (x * y)))));
	double t_3 = y5 * ((a * ((t * y2) - (y * y3))) + ((i * t_1) + (y0 * ((j * y3) - (k * y2)))));
	double t_4 = (c * i) - (a * b);
	double t_5 = z * ((k * ((b * y0) - (i * y1))) + ((t * t_4) - (y3 * ((c * y0) - (a * y1)))));
	double tmp;
	if (y1 <= -2.55e+123) {
		tmp = t_2;
	} else if (y1 <= -3.2e-12) {
		tmp = t_5;
	} else if (y1 <= -1.2e-113) {
		tmp = t_3;
	} else if (y1 <= 5.5e-301) {
		tmp = t_5;
	} else if (y1 <= 2.32e-122) {
		tmp = t_3;
	} else if (y1 <= 1.2e-32) {
		tmp = t * (((z * t_4) + (j * ((b * y4) - (i * y5)))) + (y2 * ((a * y5) - (c * y4))));
	} else if (y1 <= 3.85e+180) {
		tmp = t_2;
	} else if (y1 <= 1.28e+213) {
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	} else {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y * k) - (t * j)
	t_2 = i * ((y1 * ((x * j) - (z * k))) + ((y5 * t_1) + (c * ((z * t) - (x * y)))))
	t_3 = y5 * ((a * ((t * y2) - (y * y3))) + ((i * t_1) + (y0 * ((j * y3) - (k * y2)))))
	t_4 = (c * i) - (a * b)
	t_5 = z * ((k * ((b * y0) - (i * y1))) + ((t * t_4) - (y3 * ((c * y0) - (a * y1)))))
	tmp = 0
	if y1 <= -2.55e+123:
		tmp = t_2
	elif y1 <= -3.2e-12:
		tmp = t_5
	elif y1 <= -1.2e-113:
		tmp = t_3
	elif y1 <= 5.5e-301:
		tmp = t_5
	elif y1 <= 2.32e-122:
		tmp = t_3
	elif y1 <= 1.2e-32:
		tmp = t * (((z * t_4) + (j * ((b * y4) - (i * y5)))) + (y2 * ((a * y5) - (c * y4))))
	elif y1 <= 3.85e+180:
		tmp = t_2
	elif y1 <= 1.28e+213:
		tmp = y1 * (y3 * ((z * a) - (j * y4)))
	else:
		tmp = k * (y1 * ((y2 * y4) - (z * 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(y * k) - Float64(t * j))
	t_2 = Float64(i * Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) + Float64(Float64(y5 * t_1) + Float64(c * Float64(Float64(z * t) - Float64(x * y))))))
	t_3 = Float64(y5 * Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(Float64(i * t_1) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))))))
	t_4 = Float64(Float64(c * i) - Float64(a * b))
	t_5 = Float64(z * Float64(Float64(k * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(Float64(t * t_4) - Float64(y3 * Float64(Float64(c * y0) - Float64(a * y1))))))
	tmp = 0.0
	if (y1 <= -2.55e+123)
		tmp = t_2;
	elseif (y1 <= -3.2e-12)
		tmp = t_5;
	elseif (y1 <= -1.2e-113)
		tmp = t_3;
	elseif (y1 <= 5.5e-301)
		tmp = t_5;
	elseif (y1 <= 2.32e-122)
		tmp = t_3;
	elseif (y1 <= 1.2e-32)
		tmp = Float64(t * Float64(Float64(Float64(z * t_4) + Float64(j * Float64(Float64(b * y4) - Float64(i * y5)))) + Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y1 <= 3.85e+180)
		tmp = t_2;
	elseif (y1 <= 1.28e+213)
		tmp = Float64(y1 * Float64(y3 * Float64(Float64(z * a) - Float64(j * y4))));
	else
		tmp = Float64(k * Float64(y1 * Float64(Float64(y2 * y4) - Float64(z * 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 = (y * k) - (t * j);
	t_2 = i * ((y1 * ((x * j) - (z * k))) + ((y5 * t_1) + (c * ((z * t) - (x * y)))));
	t_3 = y5 * ((a * ((t * y2) - (y * y3))) + ((i * t_1) + (y0 * ((j * y3) - (k * y2)))));
	t_4 = (c * i) - (a * b);
	t_5 = z * ((k * ((b * y0) - (i * y1))) + ((t * t_4) - (y3 * ((c * y0) - (a * y1)))));
	tmp = 0.0;
	if (y1 <= -2.55e+123)
		tmp = t_2;
	elseif (y1 <= -3.2e-12)
		tmp = t_5;
	elseif (y1 <= -1.2e-113)
		tmp = t_3;
	elseif (y1 <= 5.5e-301)
		tmp = t_5;
	elseif (y1 <= 2.32e-122)
		tmp = t_3;
	elseif (y1 <= 1.2e-32)
		tmp = t * (((z * t_4) + (j * ((b * y4) - (i * y5)))) + (y2 * ((a * y5) - (c * y4))));
	elseif (y1 <= 3.85e+180)
		tmp = t_2;
	elseif (y1 <= 1.28e+213)
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	else
		tmp = k * (y1 * ((y2 * y4) - (z * 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[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y5 * t$95$1), $MachinePrecision] + N[(c * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y5 * N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(i * t$95$1), $MachinePrecision] + N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(z * N[(N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t * t$95$4), $MachinePrecision] - N[(y3 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -2.55e+123], t$95$2, If[LessEqual[y1, -3.2e-12], t$95$5, If[LessEqual[y1, -1.2e-113], t$95$3, If[LessEqual[y1, 5.5e-301], t$95$5, If[LessEqual[y1, 2.32e-122], t$95$3, If[LessEqual[y1, 1.2e-32], N[(t * N[(N[(N[(z * t$95$4), $MachinePrecision] + N[(j * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 3.85e+180], t$95$2, If[LessEqual[y1, 1.28e+213], N[(y1 * N[(y3 * N[(N[(z * a), $MachinePrecision] - N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(y1 * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y1 < -2.54999999999999986e123 or 1.2000000000000001e-32 < y1 < 3.8500000000000001e180

   1. Initial program 27.0%

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

   3. Taylor expanded in i around -inf 64.2%

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

   if -2.54999999999999986e123 < y1 < -3.2000000000000001e-12 or -1.20000000000000006e-113 < y1 < 5.50000000000000005e-301

   1. Initial program 34.3%

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

   3. Taylor expanded in z around -inf 63.4%

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

   if -3.2000000000000001e-12 < y1 < -1.20000000000000006e-113 or 5.50000000000000005e-301 < y1 < 2.32000000000000003e-122

   1. Initial program 39.6%

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

   3. Taylor expanded in y5 around -inf 58.9%

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

   if 2.32000000000000003e-122 < y1 < 1.2000000000000001e-32

   1. Initial program 47.8%

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

   3. Taylor expanded in t around inf 58.1%

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

   if 3.8500000000000001e180 < y1 < 1.2799999999999999e213

   1. Initial program 34.2%

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

   3. Taylor expanded in y1 around inf 56.5%

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

   4. Taylor expanded in y3 around inf 67.8%

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

      1. *-commutative 67.8%

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

      2. +-commutative 67.8%

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

      3. mul-1-neg 67.8%

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

      4. unsub-neg 67.8%

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

      5. *-commutative 67.8%

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

   6. Simplified 67.8%

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

   if 1.2799999999999999e213 < y1

   1. Initial program 21.0%

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

   3. Taylor expanded in y1 around inf 73.6%

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

   4. Taylor expanded in k around inf 63.9%

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

      1. *-commutative 63.9%

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

   6. Simplified 63.9%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -2.55 \cdot 10^{+123}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) + c \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -3.2 \cdot 10^{-12}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot \left(c \cdot i - a \cdot b\right) - y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -1.2 \cdot 10^{-113}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 5.5 \cdot 10^{-301}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot \left(c \cdot i - a \cdot b\right) - y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 2.32 \cdot 10^{-122}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 1.2 \cdot 10^{-32}:\\ \;\;\;\;t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 3.85 \cdot 10^{+180}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) + c \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 1.28 \cdot 10^{+213}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 20.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(\left(z \cdot y1\right) \cdot \left(-k\right)\right)\\ t_2 := \left(-t\right) \cdot \left(i \cdot \left(j \cdot y5\right)\right)\\ \mathbf{if}\;y2 \leq -2.5 \cdot 10^{+124}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -2.5 \cdot 10^{+18}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq -3.15 \cdot 10^{-114}:\\ \;\;\;\;a \cdot \left(\left(z \cdot t\right) \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y2 \leq -3.7 \cdot 10^{-187}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y2 \leq 1.4 \cdot 10^{-213}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq 1.15 \cdot 10^{-163}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 3.85 \cdot 10^{-146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq 3.4 \cdot 10^{-60}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y2 \leq 5 \cdot 10^{+55}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(y3 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 2.2 \cdot 10^{+219}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* (* z y1) (- k)))) (t_2 (* (- t) (* i (* j y5)))))
   (if (<= y2 -2.5e+124)
     (* y1 (* y4 (* k y2)))
     (if (<= y2 -2.5e+18)
       (* a (* t (* y2 y5)))
       (if (<= y2 -3.15e-114)
         (* a (* (* z t) (- b)))
         (if (<= y2 -3.7e-187)
           t_2
           (if (<= y2 1.4e-213)
             t_1
             (if (<= y2 1.15e-163)
               (* a (* x (* y b)))
               (if (<= y2 3.85e-146)
                 t_1
                 (if (<= y2 3.4e-60)
                   t_2
                   (if (<= y2 5e+55)
                     (* y1 (* j (* y3 (- y4))))
                     (if (<= y2 2.2e+219)
                       (* k (* y1 (* y2 y4)))
                       (* c (* (* z t) 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 = i * ((z * y1) * -k);
	double t_2 = -t * (i * (j * y5));
	double tmp;
	if (y2 <= -2.5e+124) {
		tmp = y1 * (y4 * (k * y2));
	} else if (y2 <= -2.5e+18) {
		tmp = a * (t * (y2 * y5));
	} else if (y2 <= -3.15e-114) {
		tmp = a * ((z * t) * -b);
	} else if (y2 <= -3.7e-187) {
		tmp = t_2;
	} else if (y2 <= 1.4e-213) {
		tmp = t_1;
	} else if (y2 <= 1.15e-163) {
		tmp = a * (x * (y * b));
	} else if (y2 <= 3.85e-146) {
		tmp = t_1;
	} else if (y2 <= 3.4e-60) {
		tmp = t_2;
	} else if (y2 <= 5e+55) {
		tmp = y1 * (j * (y3 * -y4));
	} else if (y2 <= 2.2e+219) {
		tmp = k * (y1 * (y2 * y4));
	} else {
		tmp = c * ((z * t) * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * ((z * y1) * -k)
    t_2 = -t * (i * (j * y5))
    if (y2 <= (-2.5d+124)) then
        tmp = y1 * (y4 * (k * y2))
    else if (y2 <= (-2.5d+18)) then
        tmp = a * (t * (y2 * y5))
    else if (y2 <= (-3.15d-114)) then
        tmp = a * ((z * t) * -b)
    else if (y2 <= (-3.7d-187)) then
        tmp = t_2
    else if (y2 <= 1.4d-213) then
        tmp = t_1
    else if (y2 <= 1.15d-163) then
        tmp = a * (x * (y * b))
    else if (y2 <= 3.85d-146) then
        tmp = t_1
    else if (y2 <= 3.4d-60) then
        tmp = t_2
    else if (y2 <= 5d+55) then
        tmp = y1 * (j * (y3 * -y4))
    else if (y2 <= 2.2d+219) then
        tmp = k * (y1 * (y2 * y4))
    else
        tmp = c * ((z * t) * 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 = i * ((z * y1) * -k);
	double t_2 = -t * (i * (j * y5));
	double tmp;
	if (y2 <= -2.5e+124) {
		tmp = y1 * (y4 * (k * y2));
	} else if (y2 <= -2.5e+18) {
		tmp = a * (t * (y2 * y5));
	} else if (y2 <= -3.15e-114) {
		tmp = a * ((z * t) * -b);
	} else if (y2 <= -3.7e-187) {
		tmp = t_2;
	} else if (y2 <= 1.4e-213) {
		tmp = t_1;
	} else if (y2 <= 1.15e-163) {
		tmp = a * (x * (y * b));
	} else if (y2 <= 3.85e-146) {
		tmp = t_1;
	} else if (y2 <= 3.4e-60) {
		tmp = t_2;
	} else if (y2 <= 5e+55) {
		tmp = y1 * (j * (y3 * -y4));
	} else if (y2 <= 2.2e+219) {
		tmp = k * (y1 * (y2 * y4));
	} else {
		tmp = c * ((z * t) * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = i * ((z * y1) * -k)
	t_2 = -t * (i * (j * y5))
	tmp = 0
	if y2 <= -2.5e+124:
		tmp = y1 * (y4 * (k * y2))
	elif y2 <= -2.5e+18:
		tmp = a * (t * (y2 * y5))
	elif y2 <= -3.15e-114:
		tmp = a * ((z * t) * -b)
	elif y2 <= -3.7e-187:
		tmp = t_2
	elif y2 <= 1.4e-213:
		tmp = t_1
	elif y2 <= 1.15e-163:
		tmp = a * (x * (y * b))
	elif y2 <= 3.85e-146:
		tmp = t_1
	elif y2 <= 3.4e-60:
		tmp = t_2
	elif y2 <= 5e+55:
		tmp = y1 * (j * (y3 * -y4))
	elif y2 <= 2.2e+219:
		tmp = k * (y1 * (y2 * y4))
	else:
		tmp = c * ((z * t) * 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(i * Float64(Float64(z * y1) * Float64(-k)))
	t_2 = Float64(Float64(-t) * Float64(i * Float64(j * y5)))
	tmp = 0.0
	if (y2 <= -2.5e+124)
		tmp = Float64(y1 * Float64(y4 * Float64(k * y2)));
	elseif (y2 <= -2.5e+18)
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	elseif (y2 <= -3.15e-114)
		tmp = Float64(a * Float64(Float64(z * t) * Float64(-b)));
	elseif (y2 <= -3.7e-187)
		tmp = t_2;
	elseif (y2 <= 1.4e-213)
		tmp = t_1;
	elseif (y2 <= 1.15e-163)
		tmp = Float64(a * Float64(x * Float64(y * b)));
	elseif (y2 <= 3.85e-146)
		tmp = t_1;
	elseif (y2 <= 3.4e-60)
		tmp = t_2;
	elseif (y2 <= 5e+55)
		tmp = Float64(y1 * Float64(j * Float64(y3 * Float64(-y4))));
	elseif (y2 <= 2.2e+219)
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	else
		tmp = Float64(c * Float64(Float64(z * t) * 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 = i * ((z * y1) * -k);
	t_2 = -t * (i * (j * y5));
	tmp = 0.0;
	if (y2 <= -2.5e+124)
		tmp = y1 * (y4 * (k * y2));
	elseif (y2 <= -2.5e+18)
		tmp = a * (t * (y2 * y5));
	elseif (y2 <= -3.15e-114)
		tmp = a * ((z * t) * -b);
	elseif (y2 <= -3.7e-187)
		tmp = t_2;
	elseif (y2 <= 1.4e-213)
		tmp = t_1;
	elseif (y2 <= 1.15e-163)
		tmp = a * (x * (y * b));
	elseif (y2 <= 3.85e-146)
		tmp = t_1;
	elseif (y2 <= 3.4e-60)
		tmp = t_2;
	elseif (y2 <= 5e+55)
		tmp = y1 * (j * (y3 * -y4));
	elseif (y2 <= 2.2e+219)
		tmp = k * (y1 * (y2 * y4));
	else
		tmp = c * ((z * t) * 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[(i * N[(N[(z * y1), $MachinePrecision] * (-k)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[((-t) * N[(i * N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -2.5e+124], N[(y1 * N[(y4 * N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -2.5e+18], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -3.15e-114], N[(a * N[(N[(z * t), $MachinePrecision] * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -3.7e-187], t$95$2, If[LessEqual[y2, 1.4e-213], t$95$1, If[LessEqual[y2, 1.15e-163], N[(a * N[(x * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 3.85e-146], t$95$1, If[LessEqual[y2, 3.4e-60], t$95$2, If[LessEqual[y2, 5e+55], N[(y1 * N[(j * N[(y3 * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.2e+219], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(z * t), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y2 < -2.4999999999999998e124

   1. Initial program 39.5%

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

   3. Taylor expanded in y1 around inf 39.8%

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

   4. Taylor expanded in y4 around inf 40.1%

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

   5. Taylor expanded in k around inf 47.3%

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

   if -2.4999999999999998e124 < y2 < -2.5e18

   1. Initial program 33.3%

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

   3. Taylor expanded in t around inf 33.9%

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

   4. Taylor expanded in y5 around inf 29.0%

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

      1. distribute-lft-out-- 29.0%

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

   6. Simplified 29.0%

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

   7. Taylor expanded in i around 0 40.0%

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

      1. *-commutative 40.0%

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

   9. Simplified 40.0%

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

   if -2.5e18 < y2 < -3.15000000000000007e-114

   1. Initial program 32.0%

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

   3. Taylor expanded in b around inf 50.1%

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

   4. Taylor expanded in a around inf 33.1%

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

      1. *-commutative 33.1%

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

      2. *-commutative 33.1%

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

   6. Simplified 33.1%

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

   7. Taylor expanded in y around 0 29.7%

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

      1. associate-*r* 29.7%

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

      2. neg-mul-1 29.7%

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

      3. *-commutative 29.7%

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

   9. Simplified 29.7%

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

   if -3.15000000000000007e-114 < y2 < -3.7000000000000001e-187 or 3.84999999999999998e-146 < y2 < 3.40000000000000007e-60

   1. Initial program 35.3%

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

   3. Taylor expanded in t around inf 60.6%

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

   4. Taylor expanded in y5 around inf 40.9%

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

      1. distribute-lft-out-- 40.9%

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

   6. Simplified 40.9%

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

   7. Taylor expanded in i around inf 41.1%

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

      1. mul-1-neg 41.1%

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

      2. distribute-rgt-neg-in 41.1%

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

      3. *-commutative 41.1%

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

   9. Simplified 41.1%

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

   if -3.7000000000000001e-187 < y2 < 1.4e-213 or 1.15e-163 < y2 < 3.84999999999999998e-146

   1. Initial program 36.7%

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

   3. Taylor expanded in y1 around inf 42.8%

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

   4. Taylor expanded in i around inf 44.8%

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

   5. Taylor expanded in j around 0 37.9%

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

      1. mul-1-neg 37.9%

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

      2. distribute-rgt-neg-in 37.9%

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

      3. distribute-rgt-neg-in 37.9%

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

   7. Simplified 37.9%

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

   if 1.4e-213 < y2 < 1.15e-163

   1. Initial program 50.0%

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

   3. Taylor expanded in b around inf 39.2%

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

   4. Taylor expanded in a around inf 27.3%

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

      1. *-commutative 27.3%

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

      2. *-commutative 27.3%

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

   6. Simplified 27.3%

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

   7. Taylor expanded in y around inf 27.5%

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

      1. *-commutative 27.5%

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

   9. Simplified 27.5%

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

   10. Taylor expanded in y around 0 27.5%

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

       1. associate-*r* 27.6%

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

       2. *-commutative 27.6%

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

       3. associate-*l* 33.5%

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

   12. Simplified 33.5%

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

   if 3.40000000000000007e-60 < y2 < 5.00000000000000046e55

   1. Initial program 40.8%

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

   3. Taylor expanded in y1 around inf 27.9%

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

   4. Taylor expanded in y4 around inf 46.0%

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

   5. Taylor expanded in k around 0 46.1%

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

      1. mul-1-neg 46.1%

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

      2. *-commutative 46.1%

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

      3. distribute-rgt-neg-in 46.1%

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

      4. *-commutative 46.1%

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

   7. Simplified 46.1%

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

   if 5.00000000000000046e55 < y2 < 2.2000000000000001e219

   1. Initial program 17.1%

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

   3. Taylor expanded in y1 around inf 49.2%

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

   4. Taylor expanded in y4 around inf 46.6%

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

   5. Taylor expanded in k around inf 41.4%

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

   if 2.2000000000000001e219 < y2

   1. Initial program 14.3%

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

   3. Taylor expanded in t around inf 64.3%

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

   4. Taylor expanded in z around inf 52.4%

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

      1. associate-*r* 52.4%

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

      2. neg-mul-1 52.4%

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

      3. *-commutative 52.4%

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

   6. Simplified 52.4%

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

   7. Taylor expanded in a around 0 65.0%

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

      1. *-commutative 65.0%

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

   9. Simplified 65.0%

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

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -2.5 \cdot 10^{+124}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -2.5 \cdot 10^{+18}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq -3.15 \cdot 10^{-114}:\\ \;\;\;\;a \cdot \left(\left(z \cdot t\right) \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y2 \leq -3.7 \cdot 10^{-187}:\\ \;\;\;\;\left(-t\right) \cdot \left(i \cdot \left(j \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 1.4 \cdot 10^{-213}:\\ \;\;\;\;i \cdot \left(\left(z \cdot y1\right) \cdot \left(-k\right)\right)\\ \mathbf{elif}\;y2 \leq 1.15 \cdot 10^{-163}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 3.85 \cdot 10^{-146}:\\ \;\;\;\;i \cdot \left(\left(z \cdot y1\right) \cdot \left(-k\right)\right)\\ \mathbf{elif}\;y2 \leq 3.4 \cdot 10^{-60}:\\ \;\;\;\;\left(-t\right) \cdot \left(i \cdot \left(j \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 5 \cdot 10^{+55}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(y3 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 2.2 \cdot 10^{+219}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 20.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(\left(z \cdot y1\right) \cdot \left(-k\right)\right)\\ t_2 := \left(-t\right) \cdot \left(i \cdot \left(j \cdot y5\right)\right)\\ \mathbf{if}\;y2 \leq -1.6 \cdot 10^{+124}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -5 \cdot 10^{+23}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq -2.8 \cdot 10^{-113}:\\ \;\;\;\;t \cdot \left(z \cdot \left(a \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -1.5 \cdot 10^{-188}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y2 \leq 7 \cdot 10^{-214}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq 7.6 \cdot 10^{-164}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 2.32 \cdot 10^{-144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq 2.8 \cdot 10^{-60}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y2 \leq 8 \cdot 10^{+55}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(y3 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 5.5 \cdot 10^{+219}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* (* z y1) (- k)))) (t_2 (* (- t) (* i (* j y5)))))
   (if (<= y2 -1.6e+124)
     (* y1 (* y4 (* k y2)))
     (if (<= y2 -5e+23)
       (* a (* t (* y2 y5)))
       (if (<= y2 -2.8e-113)
         (* t (* z (* a (- b))))
         (if (<= y2 -1.5e-188)
           t_2
           (if (<= y2 7e-214)
             t_1
             (if (<= y2 7.6e-164)
               (* a (* x (* y b)))
               (if (<= y2 2.32e-144)
                 t_1
                 (if (<= y2 2.8e-60)
                   t_2
                   (if (<= y2 8e+55)
                     (* y1 (* j (* y3 (- y4))))
                     (if (<= y2 5.5e+219)
                       (* k (* y1 (* y2 y4)))
                       (* c (* (* z t) 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 = i * ((z * y1) * -k);
	double t_2 = -t * (i * (j * y5));
	double tmp;
	if (y2 <= -1.6e+124) {
		tmp = y1 * (y4 * (k * y2));
	} else if (y2 <= -5e+23) {
		tmp = a * (t * (y2 * y5));
	} else if (y2 <= -2.8e-113) {
		tmp = t * (z * (a * -b));
	} else if (y2 <= -1.5e-188) {
		tmp = t_2;
	} else if (y2 <= 7e-214) {
		tmp = t_1;
	} else if (y2 <= 7.6e-164) {
		tmp = a * (x * (y * b));
	} else if (y2 <= 2.32e-144) {
		tmp = t_1;
	} else if (y2 <= 2.8e-60) {
		tmp = t_2;
	} else if (y2 <= 8e+55) {
		tmp = y1 * (j * (y3 * -y4));
	} else if (y2 <= 5.5e+219) {
		tmp = k * (y1 * (y2 * y4));
	} else {
		tmp = c * ((z * t) * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * ((z * y1) * -k)
    t_2 = -t * (i * (j * y5))
    if (y2 <= (-1.6d+124)) then
        tmp = y1 * (y4 * (k * y2))
    else if (y2 <= (-5d+23)) then
        tmp = a * (t * (y2 * y5))
    else if (y2 <= (-2.8d-113)) then
        tmp = t * (z * (a * -b))
    else if (y2 <= (-1.5d-188)) then
        tmp = t_2
    else if (y2 <= 7d-214) then
        tmp = t_1
    else if (y2 <= 7.6d-164) then
        tmp = a * (x * (y * b))
    else if (y2 <= 2.32d-144) then
        tmp = t_1
    else if (y2 <= 2.8d-60) then
        tmp = t_2
    else if (y2 <= 8d+55) then
        tmp = y1 * (j * (y3 * -y4))
    else if (y2 <= 5.5d+219) then
        tmp = k * (y1 * (y2 * y4))
    else
        tmp = c * ((z * t) * 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 = i * ((z * y1) * -k);
	double t_2 = -t * (i * (j * y5));
	double tmp;
	if (y2 <= -1.6e+124) {
		tmp = y1 * (y4 * (k * y2));
	} else if (y2 <= -5e+23) {
		tmp = a * (t * (y2 * y5));
	} else if (y2 <= -2.8e-113) {
		tmp = t * (z * (a * -b));
	} else if (y2 <= -1.5e-188) {
		tmp = t_2;
	} else if (y2 <= 7e-214) {
		tmp = t_1;
	} else if (y2 <= 7.6e-164) {
		tmp = a * (x * (y * b));
	} else if (y2 <= 2.32e-144) {
		tmp = t_1;
	} else if (y2 <= 2.8e-60) {
		tmp = t_2;
	} else if (y2 <= 8e+55) {
		tmp = y1 * (j * (y3 * -y4));
	} else if (y2 <= 5.5e+219) {
		tmp = k * (y1 * (y2 * y4));
	} else {
		tmp = c * ((z * t) * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = i * ((z * y1) * -k)
	t_2 = -t * (i * (j * y5))
	tmp = 0
	if y2 <= -1.6e+124:
		tmp = y1 * (y4 * (k * y2))
	elif y2 <= -5e+23:
		tmp = a * (t * (y2 * y5))
	elif y2 <= -2.8e-113:
		tmp = t * (z * (a * -b))
	elif y2 <= -1.5e-188:
		tmp = t_2
	elif y2 <= 7e-214:
		tmp = t_1
	elif y2 <= 7.6e-164:
		tmp = a * (x * (y * b))
	elif y2 <= 2.32e-144:
		tmp = t_1
	elif y2 <= 2.8e-60:
		tmp = t_2
	elif y2 <= 8e+55:
		tmp = y1 * (j * (y3 * -y4))
	elif y2 <= 5.5e+219:
		tmp = k * (y1 * (y2 * y4))
	else:
		tmp = c * ((z * t) * 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(i * Float64(Float64(z * y1) * Float64(-k)))
	t_2 = Float64(Float64(-t) * Float64(i * Float64(j * y5)))
	tmp = 0.0
	if (y2 <= -1.6e+124)
		tmp = Float64(y1 * Float64(y4 * Float64(k * y2)));
	elseif (y2 <= -5e+23)
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	elseif (y2 <= -2.8e-113)
		tmp = Float64(t * Float64(z * Float64(a * Float64(-b))));
	elseif (y2 <= -1.5e-188)
		tmp = t_2;
	elseif (y2 <= 7e-214)
		tmp = t_1;
	elseif (y2 <= 7.6e-164)
		tmp = Float64(a * Float64(x * Float64(y * b)));
	elseif (y2 <= 2.32e-144)
		tmp = t_1;
	elseif (y2 <= 2.8e-60)
		tmp = t_2;
	elseif (y2 <= 8e+55)
		tmp = Float64(y1 * Float64(j * Float64(y3 * Float64(-y4))));
	elseif (y2 <= 5.5e+219)
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	else
		tmp = Float64(c * Float64(Float64(z * t) * 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 = i * ((z * y1) * -k);
	t_2 = -t * (i * (j * y5));
	tmp = 0.0;
	if (y2 <= -1.6e+124)
		tmp = y1 * (y4 * (k * y2));
	elseif (y2 <= -5e+23)
		tmp = a * (t * (y2 * y5));
	elseif (y2 <= -2.8e-113)
		tmp = t * (z * (a * -b));
	elseif (y2 <= -1.5e-188)
		tmp = t_2;
	elseif (y2 <= 7e-214)
		tmp = t_1;
	elseif (y2 <= 7.6e-164)
		tmp = a * (x * (y * b));
	elseif (y2 <= 2.32e-144)
		tmp = t_1;
	elseif (y2 <= 2.8e-60)
		tmp = t_2;
	elseif (y2 <= 8e+55)
		tmp = y1 * (j * (y3 * -y4));
	elseif (y2 <= 5.5e+219)
		tmp = k * (y1 * (y2 * y4));
	else
		tmp = c * ((z * t) * 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[(i * N[(N[(z * y1), $MachinePrecision] * (-k)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[((-t) * N[(i * N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -1.6e+124], N[(y1 * N[(y4 * N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -5e+23], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -2.8e-113], N[(t * N[(z * N[(a * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1.5e-188], t$95$2, If[LessEqual[y2, 7e-214], t$95$1, If[LessEqual[y2, 7.6e-164], N[(a * N[(x * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.32e-144], t$95$1, If[LessEqual[y2, 2.8e-60], t$95$2, If[LessEqual[y2, 8e+55], N[(y1 * N[(j * N[(y3 * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 5.5e+219], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(z * t), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y2 < -1.59999999999999996e124

   1. Initial program 39.5%

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

   3. Taylor expanded in y1 around inf 39.8%

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

   4. Taylor expanded in y4 around inf 40.1%

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

   5. Taylor expanded in k around inf 47.3%

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

   if -1.59999999999999996e124 < y2 < -4.9999999999999999e23

   1. Initial program 33.3%

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

   3. Taylor expanded in t around inf 33.9%

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

   4. Taylor expanded in y5 around inf 29.0%

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

      1. distribute-lft-out-- 29.0%

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

   6. Simplified 29.0%

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

   7. Taylor expanded in i around 0 40.0%

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

      1. *-commutative 40.0%

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

   9. Simplified 40.0%

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

   if -4.9999999999999999e23 < y2 < -2.8e-113

   1. Initial program 32.0%

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

   3. Taylor expanded in t around inf 47.2%

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

   4. Taylor expanded in z around inf 36.5%

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

      1. associate-*r* 36.5%

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

      2. neg-mul-1 36.5%

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

      3. *-commutative 36.5%

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

   6. Simplified 36.5%

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

   7. Taylor expanded in a around inf 36.5%

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

      1. *-commutative 36.5%

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

   9. Simplified 36.5%

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

   if -2.8e-113 < y2 < -1.50000000000000008e-188 or 2.31999999999999987e-144 < y2 < 2.8000000000000002e-60

   1. Initial program 35.3%

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

   3. Taylor expanded in t around inf 60.6%

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

   4. Taylor expanded in y5 around inf 40.9%

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

      1. distribute-lft-out-- 40.9%

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

   6. Simplified 40.9%

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

   7. Taylor expanded in i around inf 41.1%

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

      1. mul-1-neg 41.1%

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

      2. distribute-rgt-neg-in 41.1%

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

      3. *-commutative 41.1%

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

   9. Simplified 41.1%

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

   if -1.50000000000000008e-188 < y2 < 7e-214 or 7.59999999999999979e-164 < y2 < 2.31999999999999987e-144

   1. Initial program 36.7%

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

   3. Taylor expanded in y1 around inf 42.8%

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

   4. Taylor expanded in i around inf 44.8%

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

   5. Taylor expanded in j around 0 37.9%

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

      1. mul-1-neg 37.9%

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

      2. distribute-rgt-neg-in 37.9%

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

      3. distribute-rgt-neg-in 37.9%

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

   7. Simplified 37.9%

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

   if 7e-214 < y2 < 7.59999999999999979e-164

   1. Initial program 50.0%

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

   3. Taylor expanded in b around inf 39.2%

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

   4. Taylor expanded in a around inf 27.3%

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

      1. *-commutative 27.3%

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

      2. *-commutative 27.3%

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

   6. Simplified 27.3%

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

   7. Taylor expanded in y around inf 27.5%

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

      1. *-commutative 27.5%

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

   9. Simplified 27.5%

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

   10. Taylor expanded in y around 0 27.5%

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

       1. associate-*r* 27.6%

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

       2. *-commutative 27.6%

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

       3. associate-*l* 33.5%

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

   12. Simplified 33.5%

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

   if 2.8000000000000002e-60 < y2 < 8.00000000000000008e55

   1. Initial program 40.8%

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

   3. Taylor expanded in y1 around inf 27.9%

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

   4. Taylor expanded in y4 around inf 46.0%

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

   5. Taylor expanded in k around 0 46.1%

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

      1. mul-1-neg 46.1%

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

      2. *-commutative 46.1%

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

      3. distribute-rgt-neg-in 46.1%

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

      4. *-commutative 46.1%

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

   7. Simplified 46.1%

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

   if 8.00000000000000008e55 < y2 < 5.49999999999999973e219

   1. Initial program 17.1%

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

   3. Taylor expanded in y1 around inf 49.2%

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

   4. Taylor expanded in y4 around inf 46.6%

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

   5. Taylor expanded in k around inf 41.4%

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

   if 5.49999999999999973e219 < y2

   1. Initial program 14.3%

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

   3. Taylor expanded in t around inf 64.3%

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

   4. Taylor expanded in z around inf 52.4%

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

      1. associate-*r* 52.4%

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

      2. neg-mul-1 52.4%

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

      3. *-commutative 52.4%

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

   6. Simplified 52.4%

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

   7. Taylor expanded in a around 0 65.0%

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

      1. *-commutative 65.0%

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

   9. Simplified 65.0%

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

4. Final simplification 41.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.6 \cdot 10^{+124}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -5 \cdot 10^{+23}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq -2.8 \cdot 10^{-113}:\\ \;\;\;\;t \cdot \left(z \cdot \left(a \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -1.5 \cdot 10^{-188}:\\ \;\;\;\;\left(-t\right) \cdot \left(i \cdot \left(j \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 7 \cdot 10^{-214}:\\ \;\;\;\;i \cdot \left(\left(z \cdot y1\right) \cdot \left(-k\right)\right)\\ \mathbf{elif}\;y2 \leq 7.6 \cdot 10^{-164}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 2.32 \cdot 10^{-144}:\\ \;\;\;\;i \cdot \left(\left(z \cdot y1\right) \cdot \left(-k\right)\right)\\ \mathbf{elif}\;y2 \leq 2.8 \cdot 10^{-60}:\\ \;\;\;\;\left(-t\right) \cdot \left(i \cdot \left(j \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 8 \cdot 10^{+55}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(y3 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 5.5 \cdot 10^{+219}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 20.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(\left(z \cdot y1\right) \cdot \left(-k\right)\right)\\ \mathbf{if}\;y2 \leq -1.8 \cdot 10^{+129}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -1.12 \cdot 10^{+23}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq -4.4 \cdot 10^{-115}:\\ \;\;\;\;t \cdot \left(z \cdot \left(a \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -1.45 \cdot 10^{-148}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;y2 \leq 2.8 \cdot 10^{-215}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq 1.25 \cdot 10^{-163}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 3.2 \cdot 10^{-145}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq 1.05 \cdot 10^{-63}:\\ \;\;\;\;\left(-t\right) \cdot \left(i \cdot \left(j \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 7.5 \cdot 10^{+55}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(y3 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 5 \cdot 10^{+219}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* (* z y1) (- k)))))
   (if (<= y2 -1.8e+129)
     (* y1 (* y4 (* k y2)))
     (if (<= y2 -1.12e+23)
       (* a (* t (* y2 y5)))
       (if (<= y2 -4.4e-115)
         (* t (* z (* a (- b))))
         (if (<= y2 -1.45e-148)
           (* t (* z (* c i)))
           (if (<= y2 2.8e-215)
             t_1
             (if (<= y2 1.25e-163)
               (* a (* x (* y b)))
               (if (<= y2 3.2e-145)
                 t_1
                 (if (<= y2 1.05e-63)
                   (* (- t) (* i (* j y5)))
                   (if (<= y2 7.5e+55)
                     (* y1 (* j (* y3 (- y4))))
                     (if (<= y2 5e+219)
                       (* k (* y1 (* y2 y4)))
                       (* c (* (* z t) 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 = i * ((z * y1) * -k);
	double tmp;
	if (y2 <= -1.8e+129) {
		tmp = y1 * (y4 * (k * y2));
	} else if (y2 <= -1.12e+23) {
		tmp = a * (t * (y2 * y5));
	} else if (y2 <= -4.4e-115) {
		tmp = t * (z * (a * -b));
	} else if (y2 <= -1.45e-148) {
		tmp = t * (z * (c * i));
	} else if (y2 <= 2.8e-215) {
		tmp = t_1;
	} else if (y2 <= 1.25e-163) {
		tmp = a * (x * (y * b));
	} else if (y2 <= 3.2e-145) {
		tmp = t_1;
	} else if (y2 <= 1.05e-63) {
		tmp = -t * (i * (j * y5));
	} else if (y2 <= 7.5e+55) {
		tmp = y1 * (j * (y3 * -y4));
	} else if (y2 <= 5e+219) {
		tmp = k * (y1 * (y2 * y4));
	} else {
		tmp = c * ((z * t) * 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) :: tmp
    t_1 = i * ((z * y1) * -k)
    if (y2 <= (-1.8d+129)) then
        tmp = y1 * (y4 * (k * y2))
    else if (y2 <= (-1.12d+23)) then
        tmp = a * (t * (y2 * y5))
    else if (y2 <= (-4.4d-115)) then
        tmp = t * (z * (a * -b))
    else if (y2 <= (-1.45d-148)) then
        tmp = t * (z * (c * i))
    else if (y2 <= 2.8d-215) then
        tmp = t_1
    else if (y2 <= 1.25d-163) then
        tmp = a * (x * (y * b))
    else if (y2 <= 3.2d-145) then
        tmp = t_1
    else if (y2 <= 1.05d-63) then
        tmp = -t * (i * (j * y5))
    else if (y2 <= 7.5d+55) then
        tmp = y1 * (j * (y3 * -y4))
    else if (y2 <= 5d+219) then
        tmp = k * (y1 * (y2 * y4))
    else
        tmp = c * ((z * t) * 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 = i * ((z * y1) * -k);
	double tmp;
	if (y2 <= -1.8e+129) {
		tmp = y1 * (y4 * (k * y2));
	} else if (y2 <= -1.12e+23) {
		tmp = a * (t * (y2 * y5));
	} else if (y2 <= -4.4e-115) {
		tmp = t * (z * (a * -b));
	} else if (y2 <= -1.45e-148) {
		tmp = t * (z * (c * i));
	} else if (y2 <= 2.8e-215) {
		tmp = t_1;
	} else if (y2 <= 1.25e-163) {
		tmp = a * (x * (y * b));
	} else if (y2 <= 3.2e-145) {
		tmp = t_1;
	} else if (y2 <= 1.05e-63) {
		tmp = -t * (i * (j * y5));
	} else if (y2 <= 7.5e+55) {
		tmp = y1 * (j * (y3 * -y4));
	} else if (y2 <= 5e+219) {
		tmp = k * (y1 * (y2 * y4));
	} else {
		tmp = c * ((z * t) * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = i * ((z * y1) * -k)
	tmp = 0
	if y2 <= -1.8e+129:
		tmp = y1 * (y4 * (k * y2))
	elif y2 <= -1.12e+23:
		tmp = a * (t * (y2 * y5))
	elif y2 <= -4.4e-115:
		tmp = t * (z * (a * -b))
	elif y2 <= -1.45e-148:
		tmp = t * (z * (c * i))
	elif y2 <= 2.8e-215:
		tmp = t_1
	elif y2 <= 1.25e-163:
		tmp = a * (x * (y * b))
	elif y2 <= 3.2e-145:
		tmp = t_1
	elif y2 <= 1.05e-63:
		tmp = -t * (i * (j * y5))
	elif y2 <= 7.5e+55:
		tmp = y1 * (j * (y3 * -y4))
	elif y2 <= 5e+219:
		tmp = k * (y1 * (y2 * y4))
	else:
		tmp = c * ((z * t) * 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(i * Float64(Float64(z * y1) * Float64(-k)))
	tmp = 0.0
	if (y2 <= -1.8e+129)
		tmp = Float64(y1 * Float64(y4 * Float64(k * y2)));
	elseif (y2 <= -1.12e+23)
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	elseif (y2 <= -4.4e-115)
		tmp = Float64(t * Float64(z * Float64(a * Float64(-b))));
	elseif (y2 <= -1.45e-148)
		tmp = Float64(t * Float64(z * Float64(c * i)));
	elseif (y2 <= 2.8e-215)
		tmp = t_1;
	elseif (y2 <= 1.25e-163)
		tmp = Float64(a * Float64(x * Float64(y * b)));
	elseif (y2 <= 3.2e-145)
		tmp = t_1;
	elseif (y2 <= 1.05e-63)
		tmp = Float64(Float64(-t) * Float64(i * Float64(j * y5)));
	elseif (y2 <= 7.5e+55)
		tmp = Float64(y1 * Float64(j * Float64(y3 * Float64(-y4))));
	elseif (y2 <= 5e+219)
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	else
		tmp = Float64(c * Float64(Float64(z * t) * 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 = i * ((z * y1) * -k);
	tmp = 0.0;
	if (y2 <= -1.8e+129)
		tmp = y1 * (y4 * (k * y2));
	elseif (y2 <= -1.12e+23)
		tmp = a * (t * (y2 * y5));
	elseif (y2 <= -4.4e-115)
		tmp = t * (z * (a * -b));
	elseif (y2 <= -1.45e-148)
		tmp = t * (z * (c * i));
	elseif (y2 <= 2.8e-215)
		tmp = t_1;
	elseif (y2 <= 1.25e-163)
		tmp = a * (x * (y * b));
	elseif (y2 <= 3.2e-145)
		tmp = t_1;
	elseif (y2 <= 1.05e-63)
		tmp = -t * (i * (j * y5));
	elseif (y2 <= 7.5e+55)
		tmp = y1 * (j * (y3 * -y4));
	elseif (y2 <= 5e+219)
		tmp = k * (y1 * (y2 * y4));
	else
		tmp = c * ((z * t) * 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[(i * N[(N[(z * y1), $MachinePrecision] * (-k)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -1.8e+129], N[(y1 * N[(y4 * N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1.12e+23], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -4.4e-115], N[(t * N[(z * N[(a * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1.45e-148], N[(t * N[(z * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.8e-215], t$95$1, If[LessEqual[y2, 1.25e-163], N[(a * N[(x * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 3.2e-145], t$95$1, If[LessEqual[y2, 1.05e-63], N[((-t) * N[(i * N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 7.5e+55], N[(y1 * N[(j * N[(y3 * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 5e+219], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(z * t), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if y2 < -1.8000000000000001e129

   1. Initial program 39.5%

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

   3. Taylor expanded in y1 around inf 39.8%

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

   4. Taylor expanded in y4 around inf 40.1%

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

   5. Taylor expanded in k around inf 47.3%

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

   if -1.8000000000000001e129 < y2 < -1.12e23

   1. Initial program 33.3%

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

   3. Taylor expanded in t around inf 33.9%

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

   4. Taylor expanded in y5 around inf 29.0%

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

      1. distribute-lft-out-- 29.0%

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

   6. Simplified 29.0%

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

   7. Taylor expanded in i around 0 40.0%

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

      1. *-commutative 40.0%

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

   9. Simplified 40.0%

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

   if -1.12e23 < y2 < -4.3999999999999999e-115

   1. Initial program 32.0%

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

   3. Taylor expanded in t around inf 47.2%

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

   4. Taylor expanded in z around inf 36.5%

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

      1. associate-*r* 36.5%

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

      2. neg-mul-1 36.5%

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

      3. *-commutative 36.5%

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

   6. Simplified 36.5%

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

   7. Taylor expanded in a around inf 36.5%

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

      1. *-commutative 36.5%

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

   9. Simplified 36.5%

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

   if -4.3999999999999999e-115 < y2 < -1.4499999999999999e-148

   1. Initial program 42.7%

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

   3. Taylor expanded in t around inf 65.0%

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

   4. Taylor expanded in z around inf 30.1%

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

      1. associate-*r* 30.1%

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

      2. neg-mul-1 30.1%

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

      3. *-commutative 30.1%

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

   6. Simplified 30.1%

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

   7. Taylor expanded in a around 0 37.5%

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

      1. mul-1-neg 37.5%

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

      2. *-commutative 37.5%

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

      3. distribute-rgt-neg-in 37.5%

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

   9. Simplified 37.5%

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

   if -1.4499999999999999e-148 < y2 < 2.79999999999999986e-215 or 1.24999999999999994e-163 < y2 < 3.20000000000000008e-145

   1. Initial program 32.7%

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

   3. Taylor expanded in y1 around inf 43.9%

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

   4. Taylor expanded in i around inf 44.1%

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

   5. Taylor expanded in j around 0 35.3%

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

      1. mul-1-neg 35.3%

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

      2. distribute-rgt-neg-in 35.3%

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

      3. distribute-rgt-neg-in 35.3%

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

   7. Simplified 35.3%

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

   if 2.79999999999999986e-215 < y2 < 1.24999999999999994e-163

   1. Initial program 50.0%

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

   3. Taylor expanded in b around inf 39.2%

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

   4. Taylor expanded in a around inf 27.3%

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

      1. *-commutative 27.3%

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

      2. *-commutative 27.3%

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

   6. Simplified 27.3%

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

   7. Taylor expanded in y around inf 27.5%

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

      1. *-commutative 27.5%

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

   9. Simplified 27.5%

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

   10. Taylor expanded in y around 0 27.5%

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

       1. associate-*r* 27.6%

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

       2. *-commutative 27.6%

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

       3. associate-*l* 33.5%

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

   12. Simplified 33.5%

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

   if 3.20000000000000008e-145 < y2 < 1.05e-63

   1. Initial program 44.3%

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

   3. Taylor expanded in t around inf 69.2%

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

   4. Taylor expanded in y5 around inf 56.9%

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

      1. distribute-lft-out-- 56.9%

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

   6. Simplified 56.9%

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

   7. Taylor expanded in i around inf 56.6%

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

      1. mul-1-neg 56.6%

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

      2. distribute-rgt-neg-in 56.6%

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

      3. *-commutative 56.6%

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

   9. Simplified 56.6%

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

   if 1.05e-63 < y2 < 7.50000000000000014e55

   1. Initial program 40.8%

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

   3. Taylor expanded in y1 around inf 27.9%

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

   4. Taylor expanded in y4 around inf 46.0%

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

   5. Taylor expanded in k around 0 46.1%

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

      1. mul-1-neg 46.1%

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

      2. *-commutative 46.1%

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

      3. distribute-rgt-neg-in 46.1%

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

      4. *-commutative 46.1%

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

   7. Simplified 46.1%

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

   if 7.50000000000000014e55 < y2 < 5e219

   1. Initial program 17.1%

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

   3. Taylor expanded in y1 around inf 49.2%

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

   4. Taylor expanded in y4 around inf 46.6%

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

   5. Taylor expanded in k around inf 41.4%

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

   if 5e219 < y2

   1. Initial program 14.3%

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

   3. Taylor expanded in t around inf 64.3%

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

   4. Taylor expanded in z around inf 52.4%

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

      1. associate-*r* 52.4%

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

      2. neg-mul-1 52.4%

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

      3. *-commutative 52.4%

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

   6. Simplified 52.4%

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

   7. Taylor expanded in a around 0 65.0%

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

      1. *-commutative 65.0%

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

   9. Simplified 65.0%

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

4. Final simplification 41.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.8 \cdot 10^{+129}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -1.12 \cdot 10^{+23}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq -4.4 \cdot 10^{-115}:\\ \;\;\;\;t \cdot \left(z \cdot \left(a \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -1.45 \cdot 10^{-148}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;y2 \leq 2.8 \cdot 10^{-215}:\\ \;\;\;\;i \cdot \left(\left(z \cdot y1\right) \cdot \left(-k\right)\right)\\ \mathbf{elif}\;y2 \leq 1.25 \cdot 10^{-163}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 3.2 \cdot 10^{-145}:\\ \;\;\;\;i \cdot \left(\left(z \cdot y1\right) \cdot \left(-k\right)\right)\\ \mathbf{elif}\;y2 \leq 1.05 \cdot 10^{-63}:\\ \;\;\;\;\left(-t\right) \cdot \left(i \cdot \left(j \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 7.5 \cdot 10^{+55}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(y3 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 5 \cdot 10^{+219}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 31.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{if}\;y0 \leq -8.2 \cdot 10^{+93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y0 \leq -1.55 \cdot 10^{-42}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq -3.6 \cdot 10^{-290}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;y0 \leq 3.15 \cdot 10^{-273}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y0 \leq 2 \cdot 10^{-200}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq 1.75 \cdot 10^{-146}:\\ \;\;\;\;c \cdot \left(\left(x \cdot y\right) \cdot \left(-i\right)\right)\\ \mathbf{elif}\;y0 \leq 7.5 \cdot 10^{-100}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(y1 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 6.8 \cdot 10^{-49}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y0 \leq 9.5 \cdot 10^{+60}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* y0 (- (* z k) (* x j))))))
   (if (<= y0 -8.2e+93)
     t_1
     (if (<= y0 -1.55e-42)
       (* j (* t (- (* b y4) (* i y5))))
       (if (<= y0 -3.6e-290)
         (* k (* i (- (* y y5) (* z y1))))
         (if (<= y0 3.15e-273)
           (* b (* y4 (- (* t j) (* y k))))
           (if (<= y0 2e-200)
             (* t (* c (* z i)))
             (if (<= y0 1.75e-146)
               (* c (* (* x y) (- i)))
               (if (<= y0 7.5e-100)
                 (* j (* y4 (* y1 (- y3))))
                 (if (<= y0 6.8e-49)
                   (* i (* y1 (- (* x j) (* z k))))
                   (if (<= y0 9.5e+60)
                     (* a (* b (- (* x y) (* z t))))
                     t_1)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (y0 * ((z * k) - (x * j)));
	double tmp;
	if (y0 <= -8.2e+93) {
		tmp = t_1;
	} else if (y0 <= -1.55e-42) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (y0 <= -3.6e-290) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (y0 <= 3.15e-273) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y0 <= 2e-200) {
		tmp = t * (c * (z * i));
	} else if (y0 <= 1.75e-146) {
		tmp = c * ((x * y) * -i);
	} else if (y0 <= 7.5e-100) {
		tmp = j * (y4 * (y1 * -y3));
	} else if (y0 <= 6.8e-49) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (y0 <= 9.5e+60) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (y0 * ((z * k) - (x * j)))
    if (y0 <= (-8.2d+93)) then
        tmp = t_1
    else if (y0 <= (-1.55d-42)) then
        tmp = j * (t * ((b * y4) - (i * y5)))
    else if (y0 <= (-3.6d-290)) then
        tmp = k * (i * ((y * y5) - (z * y1)))
    else if (y0 <= 3.15d-273) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (y0 <= 2d-200) then
        tmp = t * (c * (z * i))
    else if (y0 <= 1.75d-146) then
        tmp = c * ((x * y) * -i)
    else if (y0 <= 7.5d-100) then
        tmp = j * (y4 * (y1 * -y3))
    else if (y0 <= 6.8d-49) then
        tmp = i * (y1 * ((x * j) - (z * k)))
    else if (y0 <= 9.5d+60) then
        tmp = a * (b * ((x * y) - (z * t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (y0 * ((z * k) - (x * j)));
	double tmp;
	if (y0 <= -8.2e+93) {
		tmp = t_1;
	} else if (y0 <= -1.55e-42) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (y0 <= -3.6e-290) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (y0 <= 3.15e-273) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y0 <= 2e-200) {
		tmp = t * (c * (z * i));
	} else if (y0 <= 1.75e-146) {
		tmp = c * ((x * y) * -i);
	} else if (y0 <= 7.5e-100) {
		tmp = j * (y4 * (y1 * -y3));
	} else if (y0 <= 6.8e-49) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (y0 <= 9.5e+60) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (y0 * ((z * k) - (x * j)))
	tmp = 0
	if y0 <= -8.2e+93:
		tmp = t_1
	elif y0 <= -1.55e-42:
		tmp = j * (t * ((b * y4) - (i * y5)))
	elif y0 <= -3.6e-290:
		tmp = k * (i * ((y * y5) - (z * y1)))
	elif y0 <= 3.15e-273:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif y0 <= 2e-200:
		tmp = t * (c * (z * i))
	elif y0 <= 1.75e-146:
		tmp = c * ((x * y) * -i)
	elif y0 <= 7.5e-100:
		tmp = j * (y4 * (y1 * -y3))
	elif y0 <= 6.8e-49:
		tmp = i * (y1 * ((x * j) - (z * k)))
	elif y0 <= 9.5e+60:
		tmp = a * (b * ((x * y) - (z * t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))))
	tmp = 0.0
	if (y0 <= -8.2e+93)
		tmp = t_1;
	elseif (y0 <= -1.55e-42)
		tmp = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))));
	elseif (y0 <= -3.6e-290)
		tmp = Float64(k * Float64(i * Float64(Float64(y * y5) - Float64(z * y1))));
	elseif (y0 <= 3.15e-273)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (y0 <= 2e-200)
		tmp = Float64(t * Float64(c * Float64(z * i)));
	elseif (y0 <= 1.75e-146)
		tmp = Float64(c * Float64(Float64(x * y) * Float64(-i)));
	elseif (y0 <= 7.5e-100)
		tmp = Float64(j * Float64(y4 * Float64(y1 * Float64(-y3))));
	elseif (y0 <= 6.8e-49)
		tmp = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))));
	elseif (y0 <= 9.5e+60)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (y0 * ((z * k) - (x * j)));
	tmp = 0.0;
	if (y0 <= -8.2e+93)
		tmp = t_1;
	elseif (y0 <= -1.55e-42)
		tmp = j * (t * ((b * y4) - (i * y5)));
	elseif (y0 <= -3.6e-290)
		tmp = k * (i * ((y * y5) - (z * y1)));
	elseif (y0 <= 3.15e-273)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (y0 <= 2e-200)
		tmp = t * (c * (z * i));
	elseif (y0 <= 1.75e-146)
		tmp = c * ((x * y) * -i);
	elseif (y0 <= 7.5e-100)
		tmp = j * (y4 * (y1 * -y3));
	elseif (y0 <= 6.8e-49)
		tmp = i * (y1 * ((x * j) - (z * k)));
	elseif (y0 <= 9.5e+60)
		tmp = a * (b * ((x * y) - (z * t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -8.2e+93], t$95$1, If[LessEqual[y0, -1.55e-42], N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -3.6e-290], N[(k * N[(i * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 3.15e-273], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 2e-200], N[(t * N[(c * N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.75e-146], N[(c * N[(N[(x * y), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 7.5e-100], N[(j * N[(y4 * N[(y1 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 6.8e-49], N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 9.5e+60], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y0 < -8.2000000000000002e93 or 9.49999999999999988e60 < y0

   1. Initial program 27.7%

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

   3. Taylor expanded in b around inf 48.8%

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

   4. Taylor expanded in y0 around inf 48.6%

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

      1. *-commutative 48.6%

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

   6. Simplified 48.6%

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

   if -8.2000000000000002e93 < y0 < -1.5500000000000001e-42

   1. Initial program 41.3%

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

   3. Taylor expanded in t around inf 42.1%

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

   4. Taylor expanded in j around inf 39.7%

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

   if -1.5500000000000001e-42 < y0 < -3.59999999999999979e-290

   1. Initial program 50.2%

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

   3. Taylor expanded in k around inf 47.0%

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

   4. Taylor expanded in i around inf 44.6%

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

      1. *-commutative 44.6%

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

   6. Simplified 44.6%

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

   if -3.59999999999999979e-290 < y0 < 3.14999999999999989e-273

   1. Initial program 0.0%

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

   3. Taylor expanded in b around inf 28.6%

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

   4. Taylor expanded in y4 around inf 72.6%

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

   if 3.14999999999999989e-273 < y0 < 2e-200

   1. Initial program 20.7%

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

   3. Taylor expanded in t around inf 27.4%

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

   4. Taylor expanded in z around inf 34.3%

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

      1. associate-*r* 34.3%

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

      2. neg-mul-1 34.3%

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

      3. *-commutative 34.3%

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

   6. Simplified 34.3%

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

   7. Taylor expanded in a around 0 41.0%

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

      1. mul-1-neg 41.0%

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

      2. *-commutative 41.0%

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

      3. distribute-rgt-neg-in 41.0%

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

      4. *-commutative 41.0%

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

   9. Simplified 41.0%

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

   if 2e-200 < y0 < 1.7500000000000001e-146

   1. Initial program 25.4%

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

   3. Taylor expanded in i around -inf 42.4%

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

   4. Taylor expanded in c around inf 58.9%

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

      1. *-commutative 58.9%

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

   6. Simplified 58.9%

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

   7. Taylor expanded in y around inf 51.2%

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

      1. *-commutative 51.2%

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

   9. Simplified 51.2%

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

   if 1.7500000000000001e-146 < y0 < 7.50000000000000015e-100

   1. Initial program 39.8%

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

   3. Taylor expanded in y1 around inf 51.0%

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

   4. Taylor expanded in y4 around inf 51.9%

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

   5. Taylor expanded in k around 0 51.5%

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

      1. mul-1-neg 51.5%

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

      2. *-commutative 51.5%

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

      3. distribute-rgt-neg-in 51.5%

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

      4. associate-*r* 61.0%

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

   7. Simplified 61.0%

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

   if 7.50000000000000015e-100 < y0 < 6.8000000000000001e-49

   1. Initial program 23.1%

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

   3. Taylor expanded in y1 around inf 46.2%

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

   4. Taylor expanded in i around inf 77.2%

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

   if 6.8000000000000001e-49 < y0 < 9.49999999999999988e60

   1. Initial program 31.1%

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

   3. Taylor expanded in b around inf 31.7%

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

   4. Taylor expanded in a around inf 50.8%

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

      1. *-commutative 50.8%

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

      2. *-commutative 50.8%

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

   6. Simplified 50.8%

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

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -8.2 \cdot 10^{+93}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -1.55 \cdot 10^{-42}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq -3.6 \cdot 10^{-290}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;y0 \leq 3.15 \cdot 10^{-273}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y0 \leq 2 \cdot 10^{-200}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq 1.75 \cdot 10^{-146}:\\ \;\;\;\;c \cdot \left(\left(x \cdot y\right) \cdot \left(-i\right)\right)\\ \mathbf{elif}\;y0 \leq 7.5 \cdot 10^{-100}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(y1 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 6.8 \cdot 10^{-49}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y0 \leq 9.5 \cdot 10^{+60}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 28.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(j \cdot y0\right) \cdot \left(y3 \cdot y5 - x \cdot b\right)\\ t_2 := k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{if}\;b \leq -5 \cdot 10^{+207}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;b \leq -1.85 \cdot 10^{+139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -4.3 \cdot 10^{+113}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{-56}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{-77}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-101}:\\ \;\;\;\;k \cdot \left(y5 \cdot \left(y \cdot i - y0 \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-248}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+24}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+169}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* j y0) (- (* y3 y5) (* x b))))
        (t_2 (* k (* z (- (* b y0) (* i y1))))))
   (if (<= b -5e+207)
     (* k (* y4 (- (* y1 y2) (* y b))))
     (if (<= b -1.85e+139)
       t_1
       (if (<= b -4.3e+113)
         t_2
         (if (<= b -1.45e-56)
           (* k (* i (- (* y y5) (* z y1))))
           (if (<= b -1.35e-77)
             (* t (* z (- (* c i) (* a b))))
             (if (<= b -3e-101)
               (* k (* y5 (- (* y i) (* y0 y2))))
               (if (<= b -2e-248)
                 t_1
                 (if (<= b 7.5e+24)
                   (* k (* y1 (- (* y2 y4) (* z i))))
                   (if (<= b 5.8e+169)
                     (* a (* b (- (* x y) (* z t))))
                     t_2)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (j * y0) * ((y3 * y5) - (x * b));
	double t_2 = k * (z * ((b * y0) - (i * y1)));
	double tmp;
	if (b <= -5e+207) {
		tmp = k * (y4 * ((y1 * y2) - (y * b)));
	} else if (b <= -1.85e+139) {
		tmp = t_1;
	} else if (b <= -4.3e+113) {
		tmp = t_2;
	} else if (b <= -1.45e-56) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (b <= -1.35e-77) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else if (b <= -3e-101) {
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	} else if (b <= -2e-248) {
		tmp = t_1;
	} else if (b <= 7.5e+24) {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	} else if (b <= 5.8e+169) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (j * y0) * ((y3 * y5) - (x * b))
    t_2 = k * (z * ((b * y0) - (i * y1)))
    if (b <= (-5d+207)) then
        tmp = k * (y4 * ((y1 * y2) - (y * b)))
    else if (b <= (-1.85d+139)) then
        tmp = t_1
    else if (b <= (-4.3d+113)) then
        tmp = t_2
    else if (b <= (-1.45d-56)) then
        tmp = k * (i * ((y * y5) - (z * y1)))
    else if (b <= (-1.35d-77)) then
        tmp = t * (z * ((c * i) - (a * b)))
    else if (b <= (-3d-101)) then
        tmp = k * (y5 * ((y * i) - (y0 * y2)))
    else if (b <= (-2d-248)) then
        tmp = t_1
    else if (b <= 7.5d+24) then
        tmp = k * (y1 * ((y2 * y4) - (z * i)))
    else if (b <= 5.8d+169) then
        tmp = a * (b * ((x * y) - (z * t)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (j * y0) * ((y3 * y5) - (x * b));
	double t_2 = k * (z * ((b * y0) - (i * y1)));
	double tmp;
	if (b <= -5e+207) {
		tmp = k * (y4 * ((y1 * y2) - (y * b)));
	} else if (b <= -1.85e+139) {
		tmp = t_1;
	} else if (b <= -4.3e+113) {
		tmp = t_2;
	} else if (b <= -1.45e-56) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (b <= -1.35e-77) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else if (b <= -3e-101) {
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	} else if (b <= -2e-248) {
		tmp = t_1;
	} else if (b <= 7.5e+24) {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	} else if (b <= 5.8e+169) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (j * y0) * ((y3 * y5) - (x * b))
	t_2 = k * (z * ((b * y0) - (i * y1)))
	tmp = 0
	if b <= -5e+207:
		tmp = k * (y4 * ((y1 * y2) - (y * b)))
	elif b <= -1.85e+139:
		tmp = t_1
	elif b <= -4.3e+113:
		tmp = t_2
	elif b <= -1.45e-56:
		tmp = k * (i * ((y * y5) - (z * y1)))
	elif b <= -1.35e-77:
		tmp = t * (z * ((c * i) - (a * b)))
	elif b <= -3e-101:
		tmp = k * (y5 * ((y * i) - (y0 * y2)))
	elif b <= -2e-248:
		tmp = t_1
	elif b <= 7.5e+24:
		tmp = k * (y1 * ((y2 * y4) - (z * i)))
	elif b <= 5.8e+169:
		tmp = a * (b * ((x * y) - (z * t)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(j * y0) * Float64(Float64(y3 * y5) - Float64(x * b)))
	t_2 = Float64(k * Float64(z * Float64(Float64(b * y0) - Float64(i * y1))))
	tmp = 0.0
	if (b <= -5e+207)
		tmp = Float64(k * Float64(y4 * Float64(Float64(y1 * y2) - Float64(y * b))));
	elseif (b <= -1.85e+139)
		tmp = t_1;
	elseif (b <= -4.3e+113)
		tmp = t_2;
	elseif (b <= -1.45e-56)
		tmp = Float64(k * Float64(i * Float64(Float64(y * y5) - Float64(z * y1))));
	elseif (b <= -1.35e-77)
		tmp = Float64(t * Float64(z * Float64(Float64(c * i) - Float64(a * b))));
	elseif (b <= -3e-101)
		tmp = Float64(k * Float64(y5 * Float64(Float64(y * i) - Float64(y0 * y2))));
	elseif (b <= -2e-248)
		tmp = t_1;
	elseif (b <= 7.5e+24)
		tmp = Float64(k * Float64(y1 * Float64(Float64(y2 * y4) - Float64(z * i))));
	elseif (b <= 5.8e+169)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (j * y0) * ((y3 * y5) - (x * b));
	t_2 = k * (z * ((b * y0) - (i * y1)));
	tmp = 0.0;
	if (b <= -5e+207)
		tmp = k * (y4 * ((y1 * y2) - (y * b)));
	elseif (b <= -1.85e+139)
		tmp = t_1;
	elseif (b <= -4.3e+113)
		tmp = t_2;
	elseif (b <= -1.45e-56)
		tmp = k * (i * ((y * y5) - (z * y1)));
	elseif (b <= -1.35e-77)
		tmp = t * (z * ((c * i) - (a * b)));
	elseif (b <= -3e-101)
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	elseif (b <= -2e-248)
		tmp = t_1;
	elseif (b <= 7.5e+24)
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	elseif (b <= 5.8e+169)
		tmp = a * (b * ((x * y) - (z * t)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(j * y0), $MachinePrecision] * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5e+207], N[(k * N[(y4 * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.85e+139], t$95$1, If[LessEqual[b, -4.3e+113], t$95$2, If[LessEqual[b, -1.45e-56], N[(k * N[(i * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.35e-77], N[(t * N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3e-101], N[(k * N[(y5 * N[(N[(y * i), $MachinePrecision] - N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2e-248], t$95$1, If[LessEqual[b, 7.5e+24], N[(k * N[(y1 * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.8e+169], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if b < -4.9999999999999999e207

   1. Initial program 25.0%

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

   3. Taylor expanded in k around inf 55.0%

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

   4. Taylor expanded in y4 around inf 60.4%

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

      1. +-commutative 60.4%

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

      2. mul-1-neg 60.4%

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

      3. unsub-neg 60.4%

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

      4. *-commutative 60.4%

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

   6. Simplified 60.4%

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

   if -4.9999999999999999e207 < b < -1.84999999999999996e139 or -3.0000000000000003e-101 < b < -1.99999999999999996e-248

   1. Initial program 43.9%

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

   3. Taylor expanded in y0 around inf 48.4%

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

   4. Taylor expanded in j around inf 58.6%

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

      1. associate-*r* 56.5%

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

      2. *-commutative 56.5%

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

   6. Simplified 56.5%

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

   if -1.84999999999999996e139 < b < -4.3000000000000003e113 or 5.8000000000000001e169 < b

   1. Initial program 21.2%

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

   3. Taylor expanded in k around inf 39.5%

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

   4. Taylor expanded in z around inf 70.0%

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

      1. *-commutative 70.0%

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

      2. *-commutative 70.0%

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

   6. Simplified 70.0%

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

   if -4.3000000000000003e113 < b < -1.44999999999999996e-56

   1. Initial program 45.2%

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

   3. Taylor expanded in k around inf 53.8%

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

   4. Taylor expanded in i around inf 45.1%

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

      1. *-commutative 45.1%

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

   6. Simplified 45.1%

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

   if -1.44999999999999996e-56 < b < -1.35e-77

   1. Initial program 33.3%

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

   3. Taylor expanded in t around inf 17.1%

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

   4. Taylor expanded in z around inf 51.0%

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

      1. associate-*r* 51.0%

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

      2. neg-mul-1 51.0%

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

      3. *-commutative 51.0%

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

   6. Simplified 51.0%

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

   if -1.35e-77 < b < -3.0000000000000003e-101

   1. Initial program 0.0%

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

   3. Taylor expanded in k around inf 25.0%

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

   4. Taylor expanded in y5 around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. *-commutative 100.0%

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

   6. Simplified 100.0%

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

   if -1.99999999999999996e-248 < b < 7.50000000000000014e24

   1. Initial program 30.6%

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

   3. Taylor expanded in y1 around inf 45.4%

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

   4. Taylor expanded in k around inf 44.2%

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

      1. *-commutative 44.2%

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

   6. Simplified 44.2%

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

   if 7.50000000000000014e24 < b < 5.8000000000000001e169

   1. Initial program 35.1%

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

   3. Taylor expanded in b around inf 43.3%

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

   4. Taylor expanded in a around inf 41.9%

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

      1. *-commutative 41.9%

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

      2. *-commutative 41.9%

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

   6. Simplified 41.9%

      \[\leadsto \color{blue}{a \cdot \left(\left(y \cdot x - t \cdot z\right) \cdot b\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+207}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;b \leq -1.85 \cdot 10^{+139}:\\ \;\;\;\;\left(j \cdot y0\right) \cdot \left(y3 \cdot y5 - x \cdot b\right)\\ \mathbf{elif}\;b \leq -4.3 \cdot 10^{+113}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{-56}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{-77}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-101}:\\ \;\;\;\;k \cdot \left(y5 \cdot \left(y \cdot i - y0 \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-248}:\\ \;\;\;\;\left(j \cdot y0\right) \cdot \left(y3 \cdot y5 - x \cdot b\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+24}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+169}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 27.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(j \cdot y0\right) \cdot \left(y3 \cdot y5 - x \cdot b\right)\\ t_2 := k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{if}\;b \leq -3 \cdot 10^{+209}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{+136}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{+114}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -4.3 \cdot 10^{-54}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{-75}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-99}:\\ \;\;\;\;k \cdot \left(y5 \cdot \left(y \cdot i - y0 \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq -2.25 \cdot 10^{-248}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+17}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;b \leq 4.7 \cdot 10^{+167}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* j y0) (- (* y3 y5) (* x b))))
        (t_2 (* k (* z (- (* b y0) (* i y1))))))
   (if (<= b -3e+209)
     (* k (* y4 (- (* y1 y2) (* y b))))
     (if (<= b -1.1e+136)
       t_1
       (if (<= b -8.2e+114)
         t_2
         (if (<= b -4.3e-54)
           (* k (* i (- (* y y5) (* z y1))))
           (if (<= b -1.05e-75)
             (* t (* z (- (* c i) (* a b))))
             (if (<= b -1.2e-99)
               (* k (* y5 (- (* y i) (* y0 y2))))
               (if (<= b -2.25e-248)
                 t_1
                 (if (<= b 4e+17)
                   (* k (* y1 (- (* y2 y4) (* z i))))
                   (if (<= b 4.7e+167)
                     (* i (* y5 (- (* y k) (* t j))))
                     t_2)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (j * y0) * ((y3 * y5) - (x * b));
	double t_2 = k * (z * ((b * y0) - (i * y1)));
	double tmp;
	if (b <= -3e+209) {
		tmp = k * (y4 * ((y1 * y2) - (y * b)));
	} else if (b <= -1.1e+136) {
		tmp = t_1;
	} else if (b <= -8.2e+114) {
		tmp = t_2;
	} else if (b <= -4.3e-54) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (b <= -1.05e-75) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else if (b <= -1.2e-99) {
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	} else if (b <= -2.25e-248) {
		tmp = t_1;
	} else if (b <= 4e+17) {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	} else if (b <= 4.7e+167) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (j * y0) * ((y3 * y5) - (x * b))
    t_2 = k * (z * ((b * y0) - (i * y1)))
    if (b <= (-3d+209)) then
        tmp = k * (y4 * ((y1 * y2) - (y * b)))
    else if (b <= (-1.1d+136)) then
        tmp = t_1
    else if (b <= (-8.2d+114)) then
        tmp = t_2
    else if (b <= (-4.3d-54)) then
        tmp = k * (i * ((y * y5) - (z * y1)))
    else if (b <= (-1.05d-75)) then
        tmp = t * (z * ((c * i) - (a * b)))
    else if (b <= (-1.2d-99)) then
        tmp = k * (y5 * ((y * i) - (y0 * y2)))
    else if (b <= (-2.25d-248)) then
        tmp = t_1
    else if (b <= 4d+17) then
        tmp = k * (y1 * ((y2 * y4) - (z * i)))
    else if (b <= 4.7d+167) then
        tmp = i * (y5 * ((y * k) - (t * j)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (j * y0) * ((y3 * y5) - (x * b));
	double t_2 = k * (z * ((b * y0) - (i * y1)));
	double tmp;
	if (b <= -3e+209) {
		tmp = k * (y4 * ((y1 * y2) - (y * b)));
	} else if (b <= -1.1e+136) {
		tmp = t_1;
	} else if (b <= -8.2e+114) {
		tmp = t_2;
	} else if (b <= -4.3e-54) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (b <= -1.05e-75) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else if (b <= -1.2e-99) {
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	} else if (b <= -2.25e-248) {
		tmp = t_1;
	} else if (b <= 4e+17) {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	} else if (b <= 4.7e+167) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (j * y0) * ((y3 * y5) - (x * b))
	t_2 = k * (z * ((b * y0) - (i * y1)))
	tmp = 0
	if b <= -3e+209:
		tmp = k * (y4 * ((y1 * y2) - (y * b)))
	elif b <= -1.1e+136:
		tmp = t_1
	elif b <= -8.2e+114:
		tmp = t_2
	elif b <= -4.3e-54:
		tmp = k * (i * ((y * y5) - (z * y1)))
	elif b <= -1.05e-75:
		tmp = t * (z * ((c * i) - (a * b)))
	elif b <= -1.2e-99:
		tmp = k * (y5 * ((y * i) - (y0 * y2)))
	elif b <= -2.25e-248:
		tmp = t_1
	elif b <= 4e+17:
		tmp = k * (y1 * ((y2 * y4) - (z * i)))
	elif b <= 4.7e+167:
		tmp = i * (y5 * ((y * k) - (t * j)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(j * y0) * Float64(Float64(y3 * y5) - Float64(x * b)))
	t_2 = Float64(k * Float64(z * Float64(Float64(b * y0) - Float64(i * y1))))
	tmp = 0.0
	if (b <= -3e+209)
		tmp = Float64(k * Float64(y4 * Float64(Float64(y1 * y2) - Float64(y * b))));
	elseif (b <= -1.1e+136)
		tmp = t_1;
	elseif (b <= -8.2e+114)
		tmp = t_2;
	elseif (b <= -4.3e-54)
		tmp = Float64(k * Float64(i * Float64(Float64(y * y5) - Float64(z * y1))));
	elseif (b <= -1.05e-75)
		tmp = Float64(t * Float64(z * Float64(Float64(c * i) - Float64(a * b))));
	elseif (b <= -1.2e-99)
		tmp = Float64(k * Float64(y5 * Float64(Float64(y * i) - Float64(y0 * y2))));
	elseif (b <= -2.25e-248)
		tmp = t_1;
	elseif (b <= 4e+17)
		tmp = Float64(k * Float64(y1 * Float64(Float64(y2 * y4) - Float64(z * i))));
	elseif (b <= 4.7e+167)
		tmp = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (j * y0) * ((y3 * y5) - (x * b));
	t_2 = k * (z * ((b * y0) - (i * y1)));
	tmp = 0.0;
	if (b <= -3e+209)
		tmp = k * (y4 * ((y1 * y2) - (y * b)));
	elseif (b <= -1.1e+136)
		tmp = t_1;
	elseif (b <= -8.2e+114)
		tmp = t_2;
	elseif (b <= -4.3e-54)
		tmp = k * (i * ((y * y5) - (z * y1)));
	elseif (b <= -1.05e-75)
		tmp = t * (z * ((c * i) - (a * b)));
	elseif (b <= -1.2e-99)
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	elseif (b <= -2.25e-248)
		tmp = t_1;
	elseif (b <= 4e+17)
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	elseif (b <= 4.7e+167)
		tmp = i * (y5 * ((y * k) - (t * j)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(j * y0), $MachinePrecision] * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3e+209], N[(k * N[(y4 * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.1e+136], t$95$1, If[LessEqual[b, -8.2e+114], t$95$2, If[LessEqual[b, -4.3e-54], N[(k * N[(i * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.05e-75], N[(t * N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.2e-99], N[(k * N[(y5 * N[(N[(y * i), $MachinePrecision] - N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.25e-248], t$95$1, If[LessEqual[b, 4e+17], N[(k * N[(y1 * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.7e+167], N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if b < -2.99999999999999985e209

   1. Initial program 25.0%

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

   3. Taylor expanded in k around inf 55.0%

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

   4. Taylor expanded in y4 around inf 60.4%

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

      1. +-commutative 60.4%

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

      2. mul-1-neg 60.4%

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

      3. unsub-neg 60.4%

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

      4. *-commutative 60.4%

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

   6. Simplified 60.4%

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

   if -2.99999999999999985e209 < b < -1.1e136 or -1.2e-99 < b < -2.2499999999999998e-248

   1. Initial program 43.9%

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

   3. Taylor expanded in y0 around inf 48.4%

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

   4. Taylor expanded in j around inf 58.6%

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

      1. associate-*r* 56.5%

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

      2. *-commutative 56.5%

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

   6. Simplified 56.5%

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

   if -1.1e136 < b < -8.2000000000000001e114 or 4.70000000000000013e167 < b

   1. Initial program 21.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 39.5%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   4. Taylor expanded in z around inf 70.0%

      \[\leadsto \color{blue}{k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 70.0%

         \[\leadsto k \cdot \left(z \cdot \left(\color{blue}{y0 \cdot b} - i \cdot y1\right)\right) \]

      2. *-commutative 70.0%

         \[\leadsto k \cdot \left(z \cdot \left(y0 \cdot b - \color{blue}{y1 \cdot i}\right)\right) \]

   6. Simplified 70.0%

      \[\leadsto \color{blue}{k \cdot \left(z \cdot \left(y0 \cdot b - y1 \cdot i\right)\right)} \]

   if -8.2000000000000001e114 < b < -4.3e-54

   1. Initial program 45.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 53.8%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   4. Taylor expanded in i around inf 45.1%

      \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 45.1%

         \[\leadsto k \cdot \left(i \cdot \left(\color{blue}{y5 \cdot y} - y1 \cdot z\right)\right) \]

   6. Simplified 45.1%

      \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(y5 \cdot y - y1 \cdot z\right)\right)} \]

   if -4.3e-54 < b < -1.0500000000000001e-75

   1. Initial program 33.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 17.1%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in z around inf 51.0%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 51.0%

         \[\leadsto \color{blue}{\left(-1 \cdot t\right) \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

      2. neg-mul-1 51.0%

         \[\leadsto \color{blue}{\left(-t\right)} \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) \]

      3. *-commutative 51.0%

         \[\leadsto \left(-t\right) \cdot \left(z \cdot \left(a \cdot b - \color{blue}{i \cdot c}\right)\right) \]

   6. Simplified 51.0%

      \[\leadsto \color{blue}{\left(-t\right) \cdot \left(z \cdot \left(a \cdot b - i \cdot c\right)\right)} \]

   if -1.0500000000000001e-75 < b < -1.2e-99

   1. Initial program 0.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 25.0%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 100.0%

      \[\leadsto k \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto k \cdot \left(y5 \cdot \color{blue}{\left(i \cdot y + -1 \cdot \left(y0 \cdot y2\right)\right)}\right) \]

      2. mul-1-neg 100.0%

         \[\leadsto k \cdot \left(y5 \cdot \left(i \cdot y + \color{blue}{\left(-y0 \cdot y2\right)}\right)\right) \]

      3. unsub-neg 100.0%

         \[\leadsto k \cdot \left(y5 \cdot \color{blue}{\left(i \cdot y - y0 \cdot y2\right)}\right) \]

      4. *-commutative 100.0%

         \[\leadsto k \cdot \left(y5 \cdot \left(i \cdot y - \color{blue}{y2 \cdot y0}\right)\right) \]

   6. Simplified 100.0%

      \[\leadsto k \cdot \color{blue}{\left(y5 \cdot \left(i \cdot y - y2 \cdot y0\right)\right)} \]

   if -2.2499999999999998e-248 < b < 4e17

   1. Initial program 28.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 45.6%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in k around inf 45.7%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4 - i \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 45.7%

         \[\leadsto k \cdot \left(y1 \cdot \left(\color{blue}{y4 \cdot y2} - i \cdot z\right)\right) \]

   6. Simplified 45.7%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y4 \cdot y2 - i \cdot z\right)\right)} \]

   if 4e17 < b < 4.70000000000000013e167

   1. Initial program 38.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around -inf 51.2%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 39.6%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+209}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{+136}:\\ \;\;\;\;\left(j \cdot y0\right) \cdot \left(y3 \cdot y5 - x \cdot b\right)\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{+114}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq -4.3 \cdot 10^{-54}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{-75}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-99}:\\ \;\;\;\;k \cdot \left(y5 \cdot \left(y \cdot i - y0 \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq -2.25 \cdot 10^{-248}:\\ \;\;\;\;\left(j \cdot y0\right) \cdot \left(y3 \cdot y5 - x \cdot b\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+17}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;b \leq 4.7 \cdot 10^{+167}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 29.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ t_2 := k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{if}\;b \leq -6.5 \cdot 10^{+206}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{+136}:\\ \;\;\;\;\left(j \cdot y0\right) \cdot \left(y3 \cdot y5 - x \cdot b\right)\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{+115}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-56}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{-78}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5 - z \cdot c\right)\right)\\ \mathbf{elif}\;b \leq -1.32 \cdot 10^{-135}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -3.9 \cdot 10^{-249}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{+19}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+167}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* y (- (* k y5) (* x c)))))
        (t_2 (* k (* z (- (* b y0) (* i y1))))))
   (if (<= b -6.5e+206)
     (* k (* y4 (- (* y1 y2) (* y b))))
     (if (<= b -1.3e+136)
       (* (* j y0) (- (* y3 y5) (* x b)))
       (if (<= b -1.75e+115)
         t_2
         (if (<= b -2.5e-56)
           (* k (* i (- (* y y5) (* z y1))))
           (if (<= b -1.35e-78)
             (* y0 (* y3 (- (* j y5) (* z c))))
             (if (<= b -1.32e-135)
               t_1
               (if (<= b -3.9e-249)
                 (* y0 (* y5 (- (* j y3) (* k y2))))
                 (if (<= b 1.65e+19)
                   (* k (* y1 (- (* y2 y4) (* z i))))
                   (if (<= b 3.2e+167) t_1 t_2)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (y * ((k * y5) - (x * c)));
	double t_2 = k * (z * ((b * y0) - (i * y1)));
	double tmp;
	if (b <= -6.5e+206) {
		tmp = k * (y4 * ((y1 * y2) - (y * b)));
	} else if (b <= -1.3e+136) {
		tmp = (j * y0) * ((y3 * y5) - (x * b));
	} else if (b <= -1.75e+115) {
		tmp = t_2;
	} else if (b <= -2.5e-56) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (b <= -1.35e-78) {
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	} else if (b <= -1.32e-135) {
		tmp = t_1;
	} else if (b <= -3.9e-249) {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	} else if (b <= 1.65e+19) {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	} else if (b <= 3.2e+167) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * (y * ((k * y5) - (x * c)))
    t_2 = k * (z * ((b * y0) - (i * y1)))
    if (b <= (-6.5d+206)) then
        tmp = k * (y4 * ((y1 * y2) - (y * b)))
    else if (b <= (-1.3d+136)) then
        tmp = (j * y0) * ((y3 * y5) - (x * b))
    else if (b <= (-1.75d+115)) then
        tmp = t_2
    else if (b <= (-2.5d-56)) then
        tmp = k * (i * ((y * y5) - (z * y1)))
    else if (b <= (-1.35d-78)) then
        tmp = y0 * (y3 * ((j * y5) - (z * c)))
    else if (b <= (-1.32d-135)) then
        tmp = t_1
    else if (b <= (-3.9d-249)) then
        tmp = y0 * (y5 * ((j * y3) - (k * y2)))
    else if (b <= 1.65d+19) then
        tmp = k * (y1 * ((y2 * y4) - (z * i)))
    else if (b <= 3.2d+167) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (y * ((k * y5) - (x * c)));
	double t_2 = k * (z * ((b * y0) - (i * y1)));
	double tmp;
	if (b <= -6.5e+206) {
		tmp = k * (y4 * ((y1 * y2) - (y * b)));
	} else if (b <= -1.3e+136) {
		tmp = (j * y0) * ((y3 * y5) - (x * b));
	} else if (b <= -1.75e+115) {
		tmp = t_2;
	} else if (b <= -2.5e-56) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (b <= -1.35e-78) {
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	} else if (b <= -1.32e-135) {
		tmp = t_1;
	} else if (b <= -3.9e-249) {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	} else if (b <= 1.65e+19) {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	} else if (b <= 3.2e+167) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = i * (y * ((k * y5) - (x * c)))
	t_2 = k * (z * ((b * y0) - (i * y1)))
	tmp = 0
	if b <= -6.5e+206:
		tmp = k * (y4 * ((y1 * y2) - (y * b)))
	elif b <= -1.3e+136:
		tmp = (j * y0) * ((y3 * y5) - (x * b))
	elif b <= -1.75e+115:
		tmp = t_2
	elif b <= -2.5e-56:
		tmp = k * (i * ((y * y5) - (z * y1)))
	elif b <= -1.35e-78:
		tmp = y0 * (y3 * ((j * y5) - (z * c)))
	elif b <= -1.32e-135:
		tmp = t_1
	elif b <= -3.9e-249:
		tmp = y0 * (y5 * ((j * y3) - (k * y2)))
	elif b <= 1.65e+19:
		tmp = k * (y1 * ((y2 * y4) - (z * i)))
	elif b <= 3.2e+167:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(i * Float64(y * Float64(Float64(k * y5) - Float64(x * c))))
	t_2 = Float64(k * Float64(z * Float64(Float64(b * y0) - Float64(i * y1))))
	tmp = 0.0
	if (b <= -6.5e+206)
		tmp = Float64(k * Float64(y4 * Float64(Float64(y1 * y2) - Float64(y * b))));
	elseif (b <= -1.3e+136)
		tmp = Float64(Float64(j * y0) * Float64(Float64(y3 * y5) - Float64(x * b)));
	elseif (b <= -1.75e+115)
		tmp = t_2;
	elseif (b <= -2.5e-56)
		tmp = Float64(k * Float64(i * Float64(Float64(y * y5) - Float64(z * y1))));
	elseif (b <= -1.35e-78)
		tmp = Float64(y0 * Float64(y3 * Float64(Float64(j * y5) - Float64(z * c))));
	elseif (b <= -1.32e-135)
		tmp = t_1;
	elseif (b <= -3.9e-249)
		tmp = Float64(y0 * Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))));
	elseif (b <= 1.65e+19)
		tmp = Float64(k * Float64(y1 * Float64(Float64(y2 * y4) - Float64(z * i))));
	elseif (b <= 3.2e+167)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = i * (y * ((k * y5) - (x * c)));
	t_2 = k * (z * ((b * y0) - (i * y1)));
	tmp = 0.0;
	if (b <= -6.5e+206)
		tmp = k * (y4 * ((y1 * y2) - (y * b)));
	elseif (b <= -1.3e+136)
		tmp = (j * y0) * ((y3 * y5) - (x * b));
	elseif (b <= -1.75e+115)
		tmp = t_2;
	elseif (b <= -2.5e-56)
		tmp = k * (i * ((y * y5) - (z * y1)));
	elseif (b <= -1.35e-78)
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	elseif (b <= -1.32e-135)
		tmp = t_1;
	elseif (b <= -3.9e-249)
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	elseif (b <= 1.65e+19)
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	elseif (b <= 3.2e+167)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(i * N[(y * N[(N[(k * y5), $MachinePrecision] - N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.5e+206], N[(k * N[(y4 * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.3e+136], N[(N[(j * y0), $MachinePrecision] * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.75e+115], t$95$2, If[LessEqual[b, -2.5e-56], N[(k * N[(i * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.35e-78], N[(y0 * N[(y3 * N[(N[(j * y5), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.32e-135], t$95$1, If[LessEqual[b, -3.9e-249], N[(y0 * N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.65e+19], N[(k * N[(y1 * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.2e+167], t$95$1, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if b < -6.4999999999999995e206

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 55.0%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   4. Taylor expanded in y4 around inf 60.4%

      \[\leadsto k \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(b \cdot y\right) + y1 \cdot y2\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 60.4%

         \[\leadsto k \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(b \cdot y\right)\right)}\right) \]

      2. mul-1-neg 60.4%

         \[\leadsto k \cdot \left(y4 \cdot \left(y1 \cdot y2 + \color{blue}{\left(-b \cdot y\right)}\right)\right) \]

      3. unsub-neg 60.4%

         \[\leadsto k \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot y2 - b \cdot y\right)}\right) \]

      4. *-commutative 60.4%

         \[\leadsto k \cdot \left(y4 \cdot \left(\color{blue}{y2 \cdot y1} - b \cdot y\right)\right) \]

   6. Simplified 60.4%

      \[\leadsto k \cdot \color{blue}{\left(y4 \cdot \left(y2 \cdot y1 - b \cdot y\right)\right)} \]

   if -6.4999999999999995e206 < b < -1.3000000000000001e136

   1. Initial program 35.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 41.7%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in j around inf 65.2%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 59.3%

         \[\leadsto \color{blue}{\left(j \cdot y0\right) \cdot \left(y3 \cdot y5 - b \cdot x\right)} \]

      2. *-commutative 59.3%

         \[\leadsto \left(j \cdot y0\right) \cdot \left(y3 \cdot y5 - \color{blue}{x \cdot b}\right) \]

   6. Simplified 59.3%

      \[\leadsto \color{blue}{\left(j \cdot y0\right) \cdot \left(y3 \cdot y5 - x \cdot b\right)} \]

   if -1.3000000000000001e136 < b < -1.75000000000000003e115 or 3.19999999999999981e167 < b

   1. Initial program 21.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 39.5%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   4. Taylor expanded in z around inf 70.0%

      \[\leadsto \color{blue}{k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 70.0%

         \[\leadsto k \cdot \left(z \cdot \left(\color{blue}{y0 \cdot b} - i \cdot y1\right)\right) \]

      2. *-commutative 70.0%

         \[\leadsto k \cdot \left(z \cdot \left(y0 \cdot b - \color{blue}{y1 \cdot i}\right)\right) \]

   6. Simplified 70.0%

      \[\leadsto \color{blue}{k \cdot \left(z \cdot \left(y0 \cdot b - y1 \cdot i\right)\right)} \]

   if -1.75000000000000003e115 < b < -2.49999999999999999e-56

   1. Initial program 45.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 53.8%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   4. Taylor expanded in i around inf 45.1%

      \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 45.1%

         \[\leadsto k \cdot \left(i \cdot \left(\color{blue}{y5 \cdot y} - y1 \cdot z\right)\right) \]

   6. Simplified 45.1%

      \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(y5 \cdot y - y1 \cdot z\right)\right)} \]

   if -2.49999999999999999e-56 < b < -1.34999999999999997e-78

   1. Initial program 33.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 17.4%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y3 around inf 51.1%

      \[\leadsto \color{blue}{y0 \cdot \left(y3 \cdot \left(-1 \cdot \left(c \cdot z\right) + j \cdot y5\right)\right)} \]

   if -1.34999999999999997e-78 < b < -1.32000000000000007e-135 or 1.65e19 < b < 3.19999999999999981e167

   1. Initial program 40.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around -inf 51.8%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in y around -inf 46.9%

      \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 46.9%

         \[\leadsto -1 \cdot \color{blue}{\left(-i \cdot \left(y \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right)\right)} \]

      2. *-commutative 46.9%

         \[\leadsto -1 \cdot \left(-\color{blue}{\left(y \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right) \cdot i}\right) \]

      3. distribute-rgt-neg-in 46.9%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(y \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right) \cdot \left(-i\right)\right)} \]

      4. +-commutative 46.9%

         \[\leadsto -1 \cdot \left(\left(y \cdot \color{blue}{\left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right)}\right) \cdot \left(-i\right)\right) \]

      5. mul-1-neg 46.9%

         \[\leadsto -1 \cdot \left(\left(y \cdot \left(k \cdot y5 + \color{blue}{\left(-c \cdot x\right)}\right)\right) \cdot \left(-i\right)\right) \]

      6. unsub-neg 46.9%

         \[\leadsto -1 \cdot \left(\left(y \cdot \color{blue}{\left(k \cdot y5 - c \cdot x\right)}\right) \cdot \left(-i\right)\right) \]

      7. *-commutative 46.9%

         \[\leadsto -1 \cdot \left(\left(y \cdot \left(\color{blue}{y5 \cdot k} - c \cdot x\right)\right) \cdot \left(-i\right)\right) \]

      8. *-commutative 46.9%

         \[\leadsto -1 \cdot \left(\left(y \cdot \left(y5 \cdot k - \color{blue}{x \cdot c}\right)\right) \cdot \left(-i\right)\right) \]

   6. Simplified 46.9%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(y \cdot \left(y5 \cdot k - x \cdot c\right)\right) \cdot \left(-i\right)\right)} \]

   if -1.32000000000000007e-135 < b < -3.8999999999999999e-249

   1. Initial program 40.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around -inf 85.1%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 70.3%

      \[\leadsto -1 \cdot \color{blue}{\left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]

   if -3.8999999999999999e-249 < b < 1.65e19

   1. Initial program 28.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 45.6%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in k around inf 45.7%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4 - i \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 45.7%

         \[\leadsto k \cdot \left(y1 \cdot \left(\color{blue}{y4 \cdot y2} - i \cdot z\right)\right) \]

   6. Simplified 45.7%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y4 \cdot y2 - i \cdot z\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{+206}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{+136}:\\ \;\;\;\;\left(j \cdot y0\right) \cdot \left(y3 \cdot y5 - x \cdot b\right)\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{+115}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-56}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{-78}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5 - z \cdot c\right)\right)\\ \mathbf{elif}\;b \leq -1.32 \cdot 10^{-135}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;b \leq -3.9 \cdot 10^{-249}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{+19}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+167}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 28.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ t_2 := k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{if}\;b \leq -1.02 \cdot 10^{+207}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{+135}:\\ \;\;\;\;\left(j \cdot y0\right) \cdot \left(y3 \cdot y5 - x \cdot b\right)\\ \mathbf{elif}\;b \leq -4.4 \cdot 10^{+113}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{-54}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-79}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5 - z \cdot c\right)\right)\\ \mathbf{elif}\;b \leq -9.5 \cdot 10^{-136}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.85 \cdot 10^{-248}:\\ \;\;\;\;y3 \cdot \left(y5 \cdot \left(j \cdot y0 - y \cdot a\right)\right)\\ \mathbf{elif}\;b \leq 1.04 \cdot 10^{+21}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+167}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* y (- (* k y5) (* x c)))))
        (t_2 (* k (* z (- (* b y0) (* i y1))))))
   (if (<= b -1.02e+207)
     (* k (* y4 (- (* y1 y2) (* y b))))
     (if (<= b -2.4e+135)
       (* (* j y0) (- (* y3 y5) (* x b)))
       (if (<= b -4.4e+113)
         t_2
         (if (<= b -2.2e-54)
           (* k (* i (- (* y y5) (* z y1))))
           (if (<= b -2.7e-79)
             (* y0 (* y3 (- (* j y5) (* z c))))
             (if (<= b -9.5e-136)
               t_1
               (if (<= b -1.85e-248)
                 (* y3 (* y5 (- (* j y0) (* y a))))
                 (if (<= b 1.04e+21)
                   (* k (* y1 (- (* y2 y4) (* z i))))
                   (if (<= b 9.5e+167) t_1 t_2)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (y * ((k * y5) - (x * c)));
	double t_2 = k * (z * ((b * y0) - (i * y1)));
	double tmp;
	if (b <= -1.02e+207) {
		tmp = k * (y4 * ((y1 * y2) - (y * b)));
	} else if (b <= -2.4e+135) {
		tmp = (j * y0) * ((y3 * y5) - (x * b));
	} else if (b <= -4.4e+113) {
		tmp = t_2;
	} else if (b <= -2.2e-54) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (b <= -2.7e-79) {
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	} else if (b <= -9.5e-136) {
		tmp = t_1;
	} else if (b <= -1.85e-248) {
		tmp = y3 * (y5 * ((j * y0) - (y * a)));
	} else if (b <= 1.04e+21) {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	} else if (b <= 9.5e+167) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * (y * ((k * y5) - (x * c)))
    t_2 = k * (z * ((b * y0) - (i * y1)))
    if (b <= (-1.02d+207)) then
        tmp = k * (y4 * ((y1 * y2) - (y * b)))
    else if (b <= (-2.4d+135)) then
        tmp = (j * y0) * ((y3 * y5) - (x * b))
    else if (b <= (-4.4d+113)) then
        tmp = t_2
    else if (b <= (-2.2d-54)) then
        tmp = k * (i * ((y * y5) - (z * y1)))
    else if (b <= (-2.7d-79)) then
        tmp = y0 * (y3 * ((j * y5) - (z * c)))
    else if (b <= (-9.5d-136)) then
        tmp = t_1
    else if (b <= (-1.85d-248)) then
        tmp = y3 * (y5 * ((j * y0) - (y * a)))
    else if (b <= 1.04d+21) then
        tmp = k * (y1 * ((y2 * y4) - (z * i)))
    else if (b <= 9.5d+167) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (y * ((k * y5) - (x * c)));
	double t_2 = k * (z * ((b * y0) - (i * y1)));
	double tmp;
	if (b <= -1.02e+207) {
		tmp = k * (y4 * ((y1 * y2) - (y * b)));
	} else if (b <= -2.4e+135) {
		tmp = (j * y0) * ((y3 * y5) - (x * b));
	} else if (b <= -4.4e+113) {
		tmp = t_2;
	} else if (b <= -2.2e-54) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (b <= -2.7e-79) {
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	} else if (b <= -9.5e-136) {
		tmp = t_1;
	} else if (b <= -1.85e-248) {
		tmp = y3 * (y5 * ((j * y0) - (y * a)));
	} else if (b <= 1.04e+21) {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	} else if (b <= 9.5e+167) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = i * (y * ((k * y5) - (x * c)))
	t_2 = k * (z * ((b * y0) - (i * y1)))
	tmp = 0
	if b <= -1.02e+207:
		tmp = k * (y4 * ((y1 * y2) - (y * b)))
	elif b <= -2.4e+135:
		tmp = (j * y0) * ((y3 * y5) - (x * b))
	elif b <= -4.4e+113:
		tmp = t_2
	elif b <= -2.2e-54:
		tmp = k * (i * ((y * y5) - (z * y1)))
	elif b <= -2.7e-79:
		tmp = y0 * (y3 * ((j * y5) - (z * c)))
	elif b <= -9.5e-136:
		tmp = t_1
	elif b <= -1.85e-248:
		tmp = y3 * (y5 * ((j * y0) - (y * a)))
	elif b <= 1.04e+21:
		tmp = k * (y1 * ((y2 * y4) - (z * i)))
	elif b <= 9.5e+167:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(i * Float64(y * Float64(Float64(k * y5) - Float64(x * c))))
	t_2 = Float64(k * Float64(z * Float64(Float64(b * y0) - Float64(i * y1))))
	tmp = 0.0
	if (b <= -1.02e+207)
		tmp = Float64(k * Float64(y4 * Float64(Float64(y1 * y2) - Float64(y * b))));
	elseif (b <= -2.4e+135)
		tmp = Float64(Float64(j * y0) * Float64(Float64(y3 * y5) - Float64(x * b)));
	elseif (b <= -4.4e+113)
		tmp = t_2;
	elseif (b <= -2.2e-54)
		tmp = Float64(k * Float64(i * Float64(Float64(y * y5) - Float64(z * y1))));
	elseif (b <= -2.7e-79)
		tmp = Float64(y0 * Float64(y3 * Float64(Float64(j * y5) - Float64(z * c))));
	elseif (b <= -9.5e-136)
		tmp = t_1;
	elseif (b <= -1.85e-248)
		tmp = Float64(y3 * Float64(y5 * Float64(Float64(j * y0) - Float64(y * a))));
	elseif (b <= 1.04e+21)
		tmp = Float64(k * Float64(y1 * Float64(Float64(y2 * y4) - Float64(z * i))));
	elseif (b <= 9.5e+167)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = i * (y * ((k * y5) - (x * c)));
	t_2 = k * (z * ((b * y0) - (i * y1)));
	tmp = 0.0;
	if (b <= -1.02e+207)
		tmp = k * (y4 * ((y1 * y2) - (y * b)));
	elseif (b <= -2.4e+135)
		tmp = (j * y0) * ((y3 * y5) - (x * b));
	elseif (b <= -4.4e+113)
		tmp = t_2;
	elseif (b <= -2.2e-54)
		tmp = k * (i * ((y * y5) - (z * y1)));
	elseif (b <= -2.7e-79)
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	elseif (b <= -9.5e-136)
		tmp = t_1;
	elseif (b <= -1.85e-248)
		tmp = y3 * (y5 * ((j * y0) - (y * a)));
	elseif (b <= 1.04e+21)
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	elseif (b <= 9.5e+167)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(i * N[(y * N[(N[(k * y5), $MachinePrecision] - N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.02e+207], N[(k * N[(y4 * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.4e+135], N[(N[(j * y0), $MachinePrecision] * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.4e+113], t$95$2, If[LessEqual[b, -2.2e-54], N[(k * N[(i * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.7e-79], N[(y0 * N[(y3 * N[(N[(j * y5), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -9.5e-136], t$95$1, If[LessEqual[b, -1.85e-248], N[(y3 * N[(y5 * N[(N[(j * y0), $MachinePrecision] - N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.04e+21], N[(k * N[(y1 * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.5e+167], t$95$1, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if b < -1.0200000000000001e207

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 55.0%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   4. Taylor expanded in y4 around inf 60.4%

      \[\leadsto k \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(b \cdot y\right) + y1 \cdot y2\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 60.4%

         \[\leadsto k \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(b \cdot y\right)\right)}\right) \]

      2. mul-1-neg 60.4%

         \[\leadsto k \cdot \left(y4 \cdot \left(y1 \cdot y2 + \color{blue}{\left(-b \cdot y\right)}\right)\right) \]

      3. unsub-neg 60.4%

         \[\leadsto k \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot y2 - b \cdot y\right)}\right) \]

      4. *-commutative 60.4%

         \[\leadsto k \cdot \left(y4 \cdot \left(\color{blue}{y2 \cdot y1} - b \cdot y\right)\right) \]

   6. Simplified 60.4%

      \[\leadsto k \cdot \color{blue}{\left(y4 \cdot \left(y2 \cdot y1 - b \cdot y\right)\right)} \]

   if -1.0200000000000001e207 < b < -2.39999999999999997e135

   1. Initial program 35.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 41.7%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in j around inf 65.2%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 59.3%

         \[\leadsto \color{blue}{\left(j \cdot y0\right) \cdot \left(y3 \cdot y5 - b \cdot x\right)} \]

      2. *-commutative 59.3%

         \[\leadsto \left(j \cdot y0\right) \cdot \left(y3 \cdot y5 - \color{blue}{x \cdot b}\right) \]

   6. Simplified 59.3%

      \[\leadsto \color{blue}{\left(j \cdot y0\right) \cdot \left(y3 \cdot y5 - x \cdot b\right)} \]

   if -2.39999999999999997e135 < b < -4.40000000000000021e113 or 9.5000000000000006e167 < b

   1. Initial program 21.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 39.5%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   4. Taylor expanded in z around inf 70.0%

      \[\leadsto \color{blue}{k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 70.0%

         \[\leadsto k \cdot \left(z \cdot \left(\color{blue}{y0 \cdot b} - i \cdot y1\right)\right) \]

      2. *-commutative 70.0%

         \[\leadsto k \cdot \left(z \cdot \left(y0 \cdot b - \color{blue}{y1 \cdot i}\right)\right) \]

   6. Simplified 70.0%

      \[\leadsto \color{blue}{k \cdot \left(z \cdot \left(y0 \cdot b - y1 \cdot i\right)\right)} \]

   if -4.40000000000000021e113 < b < -2.2e-54

   1. Initial program 45.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 53.8%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   4. Taylor expanded in i around inf 45.1%

      \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 45.1%

         \[\leadsto k \cdot \left(i \cdot \left(\color{blue}{y5 \cdot y} - y1 \cdot z\right)\right) \]

   6. Simplified 45.1%

      \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(y5 \cdot y - y1 \cdot z\right)\right)} \]

   if -2.2e-54 < b < -2.7000000000000002e-79

   1. Initial program 33.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 17.4%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y3 around inf 51.1%

      \[\leadsto \color{blue}{y0 \cdot \left(y3 \cdot \left(-1 \cdot \left(c \cdot z\right) + j \cdot y5\right)\right)} \]

   if -2.7000000000000002e-79 < b < -9.5000000000000007e-136 or 1.04e21 < b < 9.5000000000000006e167

   1. Initial program 40.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around -inf 51.8%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in y around -inf 46.9%

      \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 46.9%

         \[\leadsto -1 \cdot \color{blue}{\left(-i \cdot \left(y \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right)\right)} \]

      2. *-commutative 46.9%

         \[\leadsto -1 \cdot \left(-\color{blue}{\left(y \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right) \cdot i}\right) \]

      3. distribute-rgt-neg-in 46.9%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(y \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right) \cdot \left(-i\right)\right)} \]

      4. +-commutative 46.9%

         \[\leadsto -1 \cdot \left(\left(y \cdot \color{blue}{\left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right)}\right) \cdot \left(-i\right)\right) \]

      5. mul-1-neg 46.9%

         \[\leadsto -1 \cdot \left(\left(y \cdot \left(k \cdot y5 + \color{blue}{\left(-c \cdot x\right)}\right)\right) \cdot \left(-i\right)\right) \]

      6. unsub-neg 46.9%

         \[\leadsto -1 \cdot \left(\left(y \cdot \color{blue}{\left(k \cdot y5 - c \cdot x\right)}\right) \cdot \left(-i\right)\right) \]

      7. *-commutative 46.9%

         \[\leadsto -1 \cdot \left(\left(y \cdot \left(\color{blue}{y5 \cdot k} - c \cdot x\right)\right) \cdot \left(-i\right)\right) \]

      8. *-commutative 46.9%

         \[\leadsto -1 \cdot \left(\left(y \cdot \left(y5 \cdot k - \color{blue}{x \cdot c}\right)\right) \cdot \left(-i\right)\right) \]

   6. Simplified 46.9%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(y \cdot \left(y5 \cdot k - x \cdot c\right)\right) \cdot \left(-i\right)\right)} \]

   if -9.5000000000000007e-136 < b < -1.85000000000000013e-248

   1. Initial program 40.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around -inf 85.1%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   4. Taylor expanded in y3 around inf 70.5%

      \[\leadsto -1 \cdot \color{blue}{\left(y3 \cdot \left(y5 \cdot \left(-1 \cdot \left(j \cdot y0\right) - -1 \cdot \left(a \cdot y\right)\right)\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 70.5%

         \[\leadsto -1 \cdot \left(y3 \cdot \left(y5 \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y0 - a \cdot y\right)\right)}\right)\right) \]

      2. *-commutative 70.5%

         \[\leadsto -1 \cdot \left(y3 \cdot \left(y5 \cdot \left(-1 \cdot \left(j \cdot y0 - \color{blue}{y \cdot a}\right)\right)\right)\right) \]

   6. Simplified 70.5%

      \[\leadsto -1 \cdot \color{blue}{\left(y3 \cdot \left(y5 \cdot \left(-1 \cdot \left(j \cdot y0 - y \cdot a\right)\right)\right)\right)} \]

   if -1.85000000000000013e-248 < b < 1.04e21

   1. Initial program 28.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 45.6%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in k around inf 45.7%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4 - i \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 45.7%

         \[\leadsto k \cdot \left(y1 \cdot \left(\color{blue}{y4 \cdot y2} - i \cdot z\right)\right) \]

   6. Simplified 45.7%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y4 \cdot y2 - i \cdot z\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.02 \cdot 10^{+207}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{+135}:\\ \;\;\;\;\left(j \cdot y0\right) \cdot \left(y3 \cdot y5 - x \cdot b\right)\\ \mathbf{elif}\;b \leq -4.4 \cdot 10^{+113}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{-54}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-79}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5 - z \cdot c\right)\right)\\ \mathbf{elif}\;b \leq -9.5 \cdot 10^{-136}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;b \leq -1.85 \cdot 10^{-248}:\\ \;\;\;\;y3 \cdot \left(y5 \cdot \left(j \cdot y0 - y \cdot a\right)\right)\\ \mathbf{elif}\;b \leq 1.04 \cdot 10^{+21}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+167}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 33.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ t_2 := k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right) + y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{if}\;j \leq -9.8 \cdot 10^{+194}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -1.22 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -2.4 \cdot 10^{-274}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 5.6 \cdot 10^{-175}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq 1.05 \cdot 10^{-86}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.85 \cdot 10^{+29}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5 - z \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 6.8 \cdot 10^{+99}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.9 \cdot 10^{+196}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 7.3 \cdot 10^{+294}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* y1 (- (* x j) (* z k)))))
        (t_2
         (* k (+ (* z (- (* b y0) (* i y1))) (* y4 (- (* y1 y2) (* y b)))))))
   (if (<= j -9.8e+194)
     (* i (* y5 (- (* y k) (* t j))))
     (if (<= j -1.22e+75)
       t_1
       (if (<= j -2.4e-274)
         t_2
         (if (<= j 5.6e-175)
           (* k (* i (- (* y y5) (* z y1))))
           (if (<= j 1.05e-86)
             t_2
             (if (<= j 1.85e+29)
               (* y0 (* y3 (- (* j y5) (* z c))))
               (if (<= j 6.8e+99)
                 t_2
                 (if (<= j 1.9e+196)
                   (* y0 (* y5 (- (* j y3) (* k y2))))
                   (if (<= j 7.3e+294)
                     t_1
                     (* b (* y0 (- (* z k) (* x j)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (y1 * ((x * j) - (z * k)));
	double t_2 = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))));
	double tmp;
	if (j <= -9.8e+194) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (j <= -1.22e+75) {
		tmp = t_1;
	} else if (j <= -2.4e-274) {
		tmp = t_2;
	} else if (j <= 5.6e-175) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (j <= 1.05e-86) {
		tmp = t_2;
	} else if (j <= 1.85e+29) {
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	} else if (j <= 6.8e+99) {
		tmp = t_2;
	} else if (j <= 1.9e+196) {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	} else if (j <= 7.3e+294) {
		tmp = t_1;
	} else {
		tmp = b * (y0 * ((z * k) - (x * j)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * (y1 * ((x * j) - (z * k)))
    t_2 = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))))
    if (j <= (-9.8d+194)) then
        tmp = i * (y5 * ((y * k) - (t * j)))
    else if (j <= (-1.22d+75)) then
        tmp = t_1
    else if (j <= (-2.4d-274)) then
        tmp = t_2
    else if (j <= 5.6d-175) then
        tmp = k * (i * ((y * y5) - (z * y1)))
    else if (j <= 1.05d-86) then
        tmp = t_2
    else if (j <= 1.85d+29) then
        tmp = y0 * (y3 * ((j * y5) - (z * c)))
    else if (j <= 6.8d+99) then
        tmp = t_2
    else if (j <= 1.9d+196) then
        tmp = y0 * (y5 * ((j * y3) - (k * y2)))
    else if (j <= 7.3d+294) then
        tmp = t_1
    else
        tmp = b * (y0 * ((z * k) - (x * j)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (y1 * ((x * j) - (z * k)));
	double t_2 = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))));
	double tmp;
	if (j <= -9.8e+194) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (j <= -1.22e+75) {
		tmp = t_1;
	} else if (j <= -2.4e-274) {
		tmp = t_2;
	} else if (j <= 5.6e-175) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (j <= 1.05e-86) {
		tmp = t_2;
	} else if (j <= 1.85e+29) {
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	} else if (j <= 6.8e+99) {
		tmp = t_2;
	} else if (j <= 1.9e+196) {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	} else if (j <= 7.3e+294) {
		tmp = t_1;
	} else {
		tmp = b * (y0 * ((z * k) - (x * j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = i * (y1 * ((x * j) - (z * k)))
	t_2 = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))))
	tmp = 0
	if j <= -9.8e+194:
		tmp = i * (y5 * ((y * k) - (t * j)))
	elif j <= -1.22e+75:
		tmp = t_1
	elif j <= -2.4e-274:
		tmp = t_2
	elif j <= 5.6e-175:
		tmp = k * (i * ((y * y5) - (z * y1)))
	elif j <= 1.05e-86:
		tmp = t_2
	elif j <= 1.85e+29:
		tmp = y0 * (y3 * ((j * y5) - (z * c)))
	elif j <= 6.8e+99:
		tmp = t_2
	elif j <= 1.9e+196:
		tmp = y0 * (y5 * ((j * y3) - (k * y2)))
	elif j <= 7.3e+294:
		tmp = t_1
	else:
		tmp = b * (y0 * ((z * k) - (x * j)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))))
	t_2 = Float64(k * Float64(Float64(z * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(y4 * Float64(Float64(y1 * y2) - Float64(y * b)))))
	tmp = 0.0
	if (j <= -9.8e+194)
		tmp = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))));
	elseif (j <= -1.22e+75)
		tmp = t_1;
	elseif (j <= -2.4e-274)
		tmp = t_2;
	elseif (j <= 5.6e-175)
		tmp = Float64(k * Float64(i * Float64(Float64(y * y5) - Float64(z * y1))));
	elseif (j <= 1.05e-86)
		tmp = t_2;
	elseif (j <= 1.85e+29)
		tmp = Float64(y0 * Float64(y3 * Float64(Float64(j * y5) - Float64(z * c))));
	elseif (j <= 6.8e+99)
		tmp = t_2;
	elseif (j <= 1.9e+196)
		tmp = Float64(y0 * Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))));
	elseif (j <= 7.3e+294)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = i * (y1 * ((x * j) - (z * k)));
	t_2 = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))));
	tmp = 0.0;
	if (j <= -9.8e+194)
		tmp = i * (y5 * ((y * k) - (t * j)));
	elseif (j <= -1.22e+75)
		tmp = t_1;
	elseif (j <= -2.4e-274)
		tmp = t_2;
	elseif (j <= 5.6e-175)
		tmp = k * (i * ((y * y5) - (z * y1)));
	elseif (j <= 1.05e-86)
		tmp = t_2;
	elseif (j <= 1.85e+29)
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	elseif (j <= 6.8e+99)
		tmp = t_2;
	elseif (j <= 1.9e+196)
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	elseif (j <= 7.3e+294)
		tmp = t_1;
	else
		tmp = b * (y0 * ((z * k) - (x * j)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -9.8e+194], N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.22e+75], t$95$1, If[LessEqual[j, -2.4e-274], t$95$2, If[LessEqual[j, 5.6e-175], N[(k * N[(i * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.05e-86], t$95$2, If[LessEqual[j, 1.85e+29], N[(y0 * N[(y3 * N[(N[(j * y5), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6.8e+99], t$95$2, If[LessEqual[j, 1.9e+196], N[(y0 * N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7.3e+294], t$95$1, N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if j < -9.80000000000000053e194

   1. Initial program 31.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around -inf 66.5%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 62.3%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} \]

   if -9.80000000000000053e194 < j < -1.2199999999999999e75 or 1.9000000000000001e196 < j < 7.2999999999999996e294

   1. Initial program 28.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 47.1%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in i around inf 56.0%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   if -1.2199999999999999e75 < j < -2.4e-274 or 5.6e-175 < j < 1.05e-86 or 1.84999999999999987e29 < j < 6.79999999999999968e99

   1. Initial program 34.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 50.2%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   4. Taylor expanded in y5 around 0 51.2%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(b \cdot \left(y \cdot y4\right)\right) + y1 \cdot \left(y2 \cdot y4\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   5. Step-by-step derivation

      1. cancel-sign-sub-inv 51.2%

         \[\leadsto k \cdot \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(y \cdot y4\right)\right) + y1 \cdot \left(y2 \cdot y4\right)\right) + \left(--1\right) \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. mul-1-neg 51.2%

         \[\leadsto k \cdot \left(\left(\color{blue}{\left(-b \cdot \left(y \cdot y4\right)\right)} + y1 \cdot \left(y2 \cdot y4\right)\right) + \left(--1\right) \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. associate-*r* 52.1%

         \[\leadsto k \cdot \left(\left(\left(-\color{blue}{\left(b \cdot y\right) \cdot y4}\right) + y1 \cdot \left(y2 \cdot y4\right)\right) + \left(--1\right) \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. distribute-lft-neg-in 52.1%

         \[\leadsto k \cdot \left(\left(\color{blue}{\left(-b \cdot y\right) \cdot y4} + y1 \cdot \left(y2 \cdot y4\right)\right) + \left(--1\right) \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. mul-1-neg 52.1%

         \[\leadsto k \cdot \left(\left(\color{blue}{\left(-1 \cdot \left(b \cdot y\right)\right)} \cdot y4 + y1 \cdot \left(y2 \cdot y4\right)\right) + \left(--1\right) \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      6. associate-*r* 52.2%

         \[\leadsto k \cdot \left(\left(\left(-1 \cdot \left(b \cdot y\right)\right) \cdot y4 + \color{blue}{\left(y1 \cdot y2\right) \cdot y4}\right) + \left(--1\right) \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      7. distribute-rgt-in 53.1%

         \[\leadsto k \cdot \left(\color{blue}{y4 \cdot \left(-1 \cdot \left(b \cdot y\right) + y1 \cdot y2\right)} + \left(--1\right) \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      8. +-commutative 53.1%

         \[\leadsto k \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(b \cdot y\right)\right)} + \left(--1\right) \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      9. mul-1-neg 53.1%

         \[\leadsto k \cdot \left(y4 \cdot \left(y1 \cdot y2 + \color{blue}{\left(-b \cdot y\right)}\right) + \left(--1\right) \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      10. unsub-neg 53.1%

          \[\leadsto k \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot y2 - b \cdot y\right)} + \left(--1\right) \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      11. *-commutative 53.1%

          \[\leadsto k \cdot \left(y4 \cdot \left(\color{blue}{y2 \cdot y1} - b \cdot y\right) + \left(--1\right) \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      12. metadata-eval 53.1%

          \[\leadsto k \cdot \left(y4 \cdot \left(y2 \cdot y1 - b \cdot y\right) + \color{blue}{1} \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      13. *-lft-identity 53.1%

          \[\leadsto k \cdot \left(y4 \cdot \left(y2 \cdot y1 - b \cdot y\right) + \color{blue}{z \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      14. *-commutative 53.1%

          \[\leadsto k \cdot \left(y4 \cdot \left(y2 \cdot y1 - b \cdot y\right) + z \cdot \left(\color{blue}{y0 \cdot b} - i \cdot y1\right)\right) \]

      15. *-commutative 53.1%

          \[\leadsto k \cdot \left(y4 \cdot \left(y2 \cdot y1 - b \cdot y\right) + z \cdot \left(y0 \cdot b - \color{blue}{y1 \cdot i}\right)\right) \]

   6. Simplified 53.1%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y2 \cdot y1 - b \cdot y\right) + z \cdot \left(y0 \cdot b - y1 \cdot i\right)\right)} \]

   if -2.4e-274 < j < 5.6e-175

   1. Initial program 43.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 34.9%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   4. Taylor expanded in i around inf 44.5%

      \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 44.5%

         \[\leadsto k \cdot \left(i \cdot \left(\color{blue}{y5 \cdot y} - y1 \cdot z\right)\right) \]

   6. Simplified 44.5%

      \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(y5 \cdot y - y1 \cdot z\right)\right)} \]

   if 1.05e-86 < j < 1.84999999999999987e29

   1. Initial program 39.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 50.8%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y3 around inf 50.8%

      \[\leadsto \color{blue}{y0 \cdot \left(y3 \cdot \left(-1 \cdot \left(c \cdot z\right) + j \cdot y5\right)\right)} \]

   if 6.79999999999999968e99 < j < 1.9000000000000001e196

   1. Initial program 23.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around -inf 54.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 54.7%

      \[\leadsto -1 \cdot \color{blue}{\left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]

   if 7.2999999999999996e294 < j

   1. Initial program 0.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 0.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y0 around inf 100.0%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto b \cdot \color{blue}{\left(\left(k \cdot z - j \cdot x\right) \cdot y0\right)} \]

   6. Simplified 100.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot y0\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -9.8 \cdot 10^{+194}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -1.22 \cdot 10^{+75}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;j \leq -2.4 \cdot 10^{-274}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right) + y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;j \leq 5.6 \cdot 10^{-175}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq 1.05 \cdot 10^{-86}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right) + y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;j \leq 1.85 \cdot 10^{+29}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5 - z \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 6.8 \cdot 10^{+99}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right) + y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;j \leq 1.9 \cdot 10^{+196}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 7.3 \cdot 10^{+294}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 35.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{if}\;k \leq -6.8 \cdot 10^{-47}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right) + y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;k \leq -2.8 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq -2.8 \cdot 10^{-143}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 3.2 \cdot 10^{-181}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + j \cdot \left(y3 \cdot y5\right)\right) - b \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;k \leq 2.3 \cdot 10^{-122}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 2.02 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 8.6 \cdot 10^{+41}:\\ \;\;\;\;k \cdot \left(y5 \cdot \left(y \cdot i - y0 \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 3 \cdot 10^{+69}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 2.9 \cdot 10^{+222}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* t (* z (- (* c i) (* a b))))))
   (if (<= k -6.8e-47)
     (* k (+ (* z (- (* b y0) (* i y1))) (* y4 (- (* y1 y2) (* y b)))))
     (if (<= k -2.8e-70)
       t_1
       (if (<= k -2.8e-143)
         (* j (* t (- (* b y4) (* i y5))))
         (if (<= k 3.2e-181)
           (*
            y0
            (- (+ (* c (- (* x y2) (* z y3))) (* j (* y3 y5))) (* b (* x j))))
           (if (<= k 2.3e-122)
             (* b (* j (- (* t y4) (* x y0))))
             (if (<= k 2.02e-66)
               t_1
               (if (<= k 8.6e+41)
                 (* k (* y5 (- (* y i) (* y0 y2))))
                 (if (<= k 3e+69)
                   (* b (* x (- (* y a) (* j y0))))
                   (if (<= k 2.9e+222)
                     (* k (* i (- (* y y5) (* z y1))))
                     (* b (* k (- (* z y0) (* y y4)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * (z * ((c * i) - (a * b)));
	double tmp;
	if (k <= -6.8e-47) {
		tmp = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))));
	} else if (k <= -2.8e-70) {
		tmp = t_1;
	} else if (k <= -2.8e-143) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (k <= 3.2e-181) {
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (j * (y3 * y5))) - (b * (x * j)));
	} else if (k <= 2.3e-122) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (k <= 2.02e-66) {
		tmp = t_1;
	} else if (k <= 8.6e+41) {
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	} else if (k <= 3e+69) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (k <= 2.9e+222) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else {
		tmp = b * (k * ((z * y0) - (y * y4)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (z * ((c * i) - (a * b)))
    if (k <= (-6.8d-47)) then
        tmp = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))))
    else if (k <= (-2.8d-70)) then
        tmp = t_1
    else if (k <= (-2.8d-143)) then
        tmp = j * (t * ((b * y4) - (i * y5)))
    else if (k <= 3.2d-181) then
        tmp = y0 * (((c * ((x * y2) - (z * y3))) + (j * (y3 * y5))) - (b * (x * j)))
    else if (k <= 2.3d-122) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (k <= 2.02d-66) then
        tmp = t_1
    else if (k <= 8.6d+41) then
        tmp = k * (y5 * ((y * i) - (y0 * y2)))
    else if (k <= 3d+69) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (k <= 2.9d+222) then
        tmp = k * (i * ((y * y5) - (z * y1)))
    else
        tmp = b * (k * ((z * y0) - (y * y4)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * (z * ((c * i) - (a * b)));
	double tmp;
	if (k <= -6.8e-47) {
		tmp = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))));
	} else if (k <= -2.8e-70) {
		tmp = t_1;
	} else if (k <= -2.8e-143) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (k <= 3.2e-181) {
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (j * (y3 * y5))) - (b * (x * j)));
	} else if (k <= 2.3e-122) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (k <= 2.02e-66) {
		tmp = t_1;
	} else if (k <= 8.6e+41) {
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	} else if (k <= 3e+69) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (k <= 2.9e+222) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else {
		tmp = b * (k * ((z * y0) - (y * y4)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = t * (z * ((c * i) - (a * b)))
	tmp = 0
	if k <= -6.8e-47:
		tmp = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))))
	elif k <= -2.8e-70:
		tmp = t_1
	elif k <= -2.8e-143:
		tmp = j * (t * ((b * y4) - (i * y5)))
	elif k <= 3.2e-181:
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (j * (y3 * y5))) - (b * (x * j)))
	elif k <= 2.3e-122:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif k <= 2.02e-66:
		tmp = t_1
	elif k <= 8.6e+41:
		tmp = k * (y5 * ((y * i) - (y0 * y2)))
	elif k <= 3e+69:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif k <= 2.9e+222:
		tmp = k * (i * ((y * y5) - (z * y1)))
	else:
		tmp = b * (k * ((z * y0) - (y * y4)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(t * Float64(z * Float64(Float64(c * i) - Float64(a * b))))
	tmp = 0.0
	if (k <= -6.8e-47)
		tmp = Float64(k * Float64(Float64(z * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(y4 * Float64(Float64(y1 * y2) - Float64(y * b)))));
	elseif (k <= -2.8e-70)
		tmp = t_1;
	elseif (k <= -2.8e-143)
		tmp = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))));
	elseif (k <= 3.2e-181)
		tmp = Float64(y0 * Float64(Float64(Float64(c * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(j * Float64(y3 * y5))) - Float64(b * Float64(x * j))));
	elseif (k <= 2.3e-122)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (k <= 2.02e-66)
		tmp = t_1;
	elseif (k <= 8.6e+41)
		tmp = Float64(k * Float64(y5 * Float64(Float64(y * i) - Float64(y0 * y2))));
	elseif (k <= 3e+69)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (k <= 2.9e+222)
		tmp = Float64(k * Float64(i * Float64(Float64(y * y5) - Float64(z * y1))));
	else
		tmp = Float64(b * Float64(k * Float64(Float64(z * y0) - Float64(y * y4))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = t * (z * ((c * i) - (a * b)));
	tmp = 0.0;
	if (k <= -6.8e-47)
		tmp = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))));
	elseif (k <= -2.8e-70)
		tmp = t_1;
	elseif (k <= -2.8e-143)
		tmp = j * (t * ((b * y4) - (i * y5)));
	elseif (k <= 3.2e-181)
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (j * (y3 * y5))) - (b * (x * j)));
	elseif (k <= 2.3e-122)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (k <= 2.02e-66)
		tmp = t_1;
	elseif (k <= 8.6e+41)
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	elseif (k <= 3e+69)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (k <= 2.9e+222)
		tmp = k * (i * ((y * y5) - (z * y1)));
	else
		tmp = b * (k * ((z * y0) - (y * y4)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(t * N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -6.8e-47], N[(k * N[(N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -2.8e-70], t$95$1, If[LessEqual[k, -2.8e-143], N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 3.2e-181], N[(y0 * N[(N[(N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.3e-122], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.02e-66], t$95$1, If[LessEqual[k, 8.6e+41], N[(k * N[(y5 * N[(N[(y * i), $MachinePrecision] - N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 3e+69], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.9e+222], N[(k * N[(i * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if k < -6.8000000000000003e-47

   1. Initial program 25.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 62.1%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   4. Taylor expanded in y5 around 0 47.2%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(b \cdot \left(y \cdot y4\right)\right) + y1 \cdot \left(y2 \cdot y4\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   5. Step-by-step derivation

      1. cancel-sign-sub-inv 47.2%

         \[\leadsto k \cdot \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(y \cdot y4\right)\right) + y1 \cdot \left(y2 \cdot y4\right)\right) + \left(--1\right) \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. mul-1-neg 47.2%

         \[\leadsto k \cdot \left(\left(\color{blue}{\left(-b \cdot \left(y \cdot y4\right)\right)} + y1 \cdot \left(y2 \cdot y4\right)\right) + \left(--1\right) \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. associate-*r* 50.3%

         \[\leadsto k \cdot \left(\left(\left(-\color{blue}{\left(b \cdot y\right) \cdot y4}\right) + y1 \cdot \left(y2 \cdot y4\right)\right) + \left(--1\right) \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. distribute-lft-neg-in 50.3%

         \[\leadsto k \cdot \left(\left(\color{blue}{\left(-b \cdot y\right) \cdot y4} + y1 \cdot \left(y2 \cdot y4\right)\right) + \left(--1\right) \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. mul-1-neg 50.3%

         \[\leadsto k \cdot \left(\left(\color{blue}{\left(-1 \cdot \left(b \cdot y\right)\right)} \cdot y4 + y1 \cdot \left(y2 \cdot y4\right)\right) + \left(--1\right) \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      6. associate-*r* 51.8%

         \[\leadsto k \cdot \left(\left(\left(-1 \cdot \left(b \cdot y\right)\right) \cdot y4 + \color{blue}{\left(y1 \cdot y2\right) \cdot y4}\right) + \left(--1\right) \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      7. distribute-rgt-in 53.3%

         \[\leadsto k \cdot \left(\color{blue}{y4 \cdot \left(-1 \cdot \left(b \cdot y\right) + y1 \cdot y2\right)} + \left(--1\right) \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      8. +-commutative 53.3%

         \[\leadsto k \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(b \cdot y\right)\right)} + \left(--1\right) \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      9. mul-1-neg 53.3%

         \[\leadsto k \cdot \left(y4 \cdot \left(y1 \cdot y2 + \color{blue}{\left(-b \cdot y\right)}\right) + \left(--1\right) \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      10. unsub-neg 53.3%

          \[\leadsto k \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot y2 - b \cdot y\right)} + \left(--1\right) \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      11. *-commutative 53.3%

          \[\leadsto k \cdot \left(y4 \cdot \left(\color{blue}{y2 \cdot y1} - b \cdot y\right) + \left(--1\right) \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      12. metadata-eval 53.3%

          \[\leadsto k \cdot \left(y4 \cdot \left(y2 \cdot y1 - b \cdot y\right) + \color{blue}{1} \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      13. *-lft-identity 53.3%

          \[\leadsto k \cdot \left(y4 \cdot \left(y2 \cdot y1 - b \cdot y\right) + \color{blue}{z \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      14. *-commutative 53.3%

          \[\leadsto k \cdot \left(y4 \cdot \left(y2 \cdot y1 - b \cdot y\right) + z \cdot \left(\color{blue}{y0 \cdot b} - i \cdot y1\right)\right) \]

      15. *-commutative 53.3%

          \[\leadsto k \cdot \left(y4 \cdot \left(y2 \cdot y1 - b \cdot y\right) + z \cdot \left(y0 \cdot b - \color{blue}{y1 \cdot i}\right)\right) \]

   6. Simplified 53.3%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y2 \cdot y1 - b \cdot y\right) + z \cdot \left(y0 \cdot b - y1 \cdot i\right)\right)} \]

   if -6.8000000000000003e-47 < k < -2.7999999999999999e-70 or 2.30000000000000007e-122 < k < 2.0200000000000001e-66

   1. Initial program 36.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 41.9%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in z around inf 60.0%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 60.0%

         \[\leadsto \color{blue}{\left(-1 \cdot t\right) \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

      2. neg-mul-1 60.0%

         \[\leadsto \color{blue}{\left(-t\right)} \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) \]

      3. *-commutative 60.0%

         \[\leadsto \left(-t\right) \cdot \left(z \cdot \left(a \cdot b - \color{blue}{i \cdot c}\right)\right) \]

   6. Simplified 60.0%

      \[\leadsto \color{blue}{\left(-t\right) \cdot \left(z \cdot \left(a \cdot b - i \cdot c\right)\right)} \]

   if -2.7999999999999999e-70 < k < -2.7999999999999999e-143

   1. Initial program 41.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 59.6%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 59.5%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]

   if -2.7999999999999999e-143 < k < 3.2000000000000002e-181

   1. Initial program 48.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 57.2%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in k around 0 55.6%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + j \cdot \left(y3 \cdot y5\right)\right) - b \cdot \left(j \cdot x\right)\right)} \]

   if 3.2000000000000002e-181 < k < 2.30000000000000007e-122

   1. Initial program 33.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 34.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in j around inf 51.4%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if 2.0200000000000001e-66 < k < 8.60000000000000048e41

   1. Initial program 41.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 45.2%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 45.8%

      \[\leadsto k \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 45.8%

         \[\leadsto k \cdot \left(y5 \cdot \color{blue}{\left(i \cdot y + -1 \cdot \left(y0 \cdot y2\right)\right)}\right) \]

      2. mul-1-neg 45.8%

         \[\leadsto k \cdot \left(y5 \cdot \left(i \cdot y + \color{blue}{\left(-y0 \cdot y2\right)}\right)\right) \]

      3. unsub-neg 45.8%

         \[\leadsto k \cdot \left(y5 \cdot \color{blue}{\left(i \cdot y - y0 \cdot y2\right)}\right) \]

      4. *-commutative 45.8%

         \[\leadsto k \cdot \left(y5 \cdot \left(i \cdot y - \color{blue}{y2 \cdot y0}\right)\right) \]

   6. Simplified 45.8%

      \[\leadsto k \cdot \color{blue}{\left(y5 \cdot \left(i \cdot y - y2 \cdot y0\right)\right)} \]

   if 8.60000000000000048e41 < k < 2.99999999999999983e69

   1. Initial program 42.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 71.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in x around inf 85.7%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 85.7%

         \[\leadsto b \cdot \left(x \cdot \left(\color{blue}{y \cdot a} - j \cdot y0\right)\right) \]

   6. Simplified 85.7%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)} \]

   if 2.99999999999999983e69 < k < 2.89999999999999981e222

   1. Initial program 11.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 44.5%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   4. Taylor expanded in i around inf 56.1%

      \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 56.1%

         \[\leadsto k \cdot \left(i \cdot \left(\color{blue}{y5 \cdot y} - y1 \cdot z\right)\right) \]

   6. Simplified 56.1%

      \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(y5 \cdot y - y1 \cdot z\right)\right)} \]

   if 2.89999999999999981e222 < k

   1. Initial program 20.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 55.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in k around inf 80.3%

      \[\leadsto \color{blue}{b \cdot \left(k \cdot \left(-1 \cdot \left(y \cdot y4\right) - -1 \cdot \left(y0 \cdot z\right)\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 80.3%

         \[\leadsto b \cdot \left(k \cdot \color{blue}{\left(-1 \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)}\right) \]

      2. *-commutative 80.3%

         \[\leadsto b \cdot \left(k \cdot \left(-1 \cdot \left(y \cdot y4 - \color{blue}{z \cdot y0}\right)\right)\right) \]

   6. Simplified 80.3%

      \[\leadsto \color{blue}{b \cdot \left(k \cdot \left(-1 \cdot \left(y \cdot y4 - z \cdot y0\right)\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -6.8 \cdot 10^{-47}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right) + y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;k \leq -2.8 \cdot 10^{-70}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;k \leq -2.8 \cdot 10^{-143}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 3.2 \cdot 10^{-181}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + j \cdot \left(y3 \cdot y5\right)\right) - b \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;k \leq 2.3 \cdot 10^{-122}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 2.02 \cdot 10^{-66}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;k \leq 8.6 \cdot 10^{+41}:\\ \;\;\;\;k \cdot \left(y5 \cdot \left(y \cdot i - y0 \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 3 \cdot 10^{+69}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 2.9 \cdot 10^{+222}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 28.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ t_2 := k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{if}\;y2 \leq -3 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq -1.62 \cdot 10^{+16}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -8.8 \cdot 10^{-23}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y2 \leq -7.2 \cdot 10^{-128}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq -8 \cdot 10^{-151}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 2.65 \cdot 10^{-76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y2 \leq 2.1 \cdot 10^{+90}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y2 \leq 5.3 \cdot 10^{+219}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (* y1 (- (* y2 y4) (* z i)))))
        (t_2 (* k (* i (- (* y y5) (* z y1))))))
   (if (<= y2 -3e+36)
     t_1
     (if (<= y2 -1.62e+16)
       (* t (* y5 (* a y2)))
       (if (<= y2 -8.8e-23)
         t_2
         (if (<= y2 -7.2e-128)
           (* b (* y0 (- (* z k) (* x j))))
           (if (<= y2 -8e-151)
             (* b (* j (- (* t y4) (* x y0))))
             (if (<= y2 2.65e-76)
               t_2
               (if (<= y2 2.1e+90)
                 (* i (* y1 (- (* x j) (* z k))))
                 (if (<= y2 5.3e+219) t_1 (* c (* (* z t) 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 = k * (y1 * ((y2 * y4) - (z * i)));
	double t_2 = k * (i * ((y * y5) - (z * y1)));
	double tmp;
	if (y2 <= -3e+36) {
		tmp = t_1;
	} else if (y2 <= -1.62e+16) {
		tmp = t * (y5 * (a * y2));
	} else if (y2 <= -8.8e-23) {
		tmp = t_2;
	} else if (y2 <= -7.2e-128) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y2 <= -8e-151) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y2 <= 2.65e-76) {
		tmp = t_2;
	} else if (y2 <= 2.1e+90) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (y2 <= 5.3e+219) {
		tmp = t_1;
	} else {
		tmp = c * ((z * t) * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = k * (y1 * ((y2 * y4) - (z * i)))
    t_2 = k * (i * ((y * y5) - (z * y1)))
    if (y2 <= (-3d+36)) then
        tmp = t_1
    else if (y2 <= (-1.62d+16)) then
        tmp = t * (y5 * (a * y2))
    else if (y2 <= (-8.8d-23)) then
        tmp = t_2
    else if (y2 <= (-7.2d-128)) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (y2 <= (-8d-151)) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (y2 <= 2.65d-76) then
        tmp = t_2
    else if (y2 <= 2.1d+90) then
        tmp = i * (y1 * ((x * j) - (z * k)))
    else if (y2 <= 5.3d+219) then
        tmp = t_1
    else
        tmp = c * ((z * t) * 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 = k * (y1 * ((y2 * y4) - (z * i)));
	double t_2 = k * (i * ((y * y5) - (z * y1)));
	double tmp;
	if (y2 <= -3e+36) {
		tmp = t_1;
	} else if (y2 <= -1.62e+16) {
		tmp = t * (y5 * (a * y2));
	} else if (y2 <= -8.8e-23) {
		tmp = t_2;
	} else if (y2 <= -7.2e-128) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y2 <= -8e-151) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y2 <= 2.65e-76) {
		tmp = t_2;
	} else if (y2 <= 2.1e+90) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (y2 <= 5.3e+219) {
		tmp = t_1;
	} else {
		tmp = c * ((z * t) * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = k * (y1 * ((y2 * y4) - (z * i)))
	t_2 = k * (i * ((y * y5) - (z * y1)))
	tmp = 0
	if y2 <= -3e+36:
		tmp = t_1
	elif y2 <= -1.62e+16:
		tmp = t * (y5 * (a * y2))
	elif y2 <= -8.8e-23:
		tmp = t_2
	elif y2 <= -7.2e-128:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif y2 <= -8e-151:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif y2 <= 2.65e-76:
		tmp = t_2
	elif y2 <= 2.1e+90:
		tmp = i * (y1 * ((x * j) - (z * k)))
	elif y2 <= 5.3e+219:
		tmp = t_1
	else:
		tmp = c * ((z * t) * 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(k * Float64(y1 * Float64(Float64(y2 * y4) - Float64(z * i))))
	t_2 = Float64(k * Float64(i * Float64(Float64(y * y5) - Float64(z * y1))))
	tmp = 0.0
	if (y2 <= -3e+36)
		tmp = t_1;
	elseif (y2 <= -1.62e+16)
		tmp = Float64(t * Float64(y5 * Float64(a * y2)));
	elseif (y2 <= -8.8e-23)
		tmp = t_2;
	elseif (y2 <= -7.2e-128)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (y2 <= -8e-151)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (y2 <= 2.65e-76)
		tmp = t_2;
	elseif (y2 <= 2.1e+90)
		tmp = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))));
	elseif (y2 <= 5.3e+219)
		tmp = t_1;
	else
		tmp = Float64(c * Float64(Float64(z * t) * 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 = k * (y1 * ((y2 * y4) - (z * i)));
	t_2 = k * (i * ((y * y5) - (z * y1)));
	tmp = 0.0;
	if (y2 <= -3e+36)
		tmp = t_1;
	elseif (y2 <= -1.62e+16)
		tmp = t * (y5 * (a * y2));
	elseif (y2 <= -8.8e-23)
		tmp = t_2;
	elseif (y2 <= -7.2e-128)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (y2 <= -8e-151)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (y2 <= 2.65e-76)
		tmp = t_2;
	elseif (y2 <= 2.1e+90)
		tmp = i * (y1 * ((x * j) - (z * k)));
	elseif (y2 <= 5.3e+219)
		tmp = t_1;
	else
		tmp = c * ((z * t) * 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[(k * N[(y1 * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(i * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -3e+36], t$95$1, If[LessEqual[y2, -1.62e+16], N[(t * N[(y5 * N[(a * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -8.8e-23], t$95$2, If[LessEqual[y2, -7.2e-128], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -8e-151], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.65e-76], t$95$2, If[LessEqual[y2, 2.1e+90], N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 5.3e+219], t$95$1, N[(c * N[(N[(z * t), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y2 < -3e36 or 2.09999999999999981e90 < y2 < 5.29999999999999983e219

   1. Initial program 32.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 44.7%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in k around inf 46.4%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4 - i \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 46.4%

         \[\leadsto k \cdot \left(y1 \cdot \left(\color{blue}{y4 \cdot y2} - i \cdot z\right)\right) \]

   6. Simplified 46.4%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y4 \cdot y2 - i \cdot z\right)\right)} \]

   if -3e36 < y2 < -1.62e16

   1. Initial program 0.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 67.0%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in y5 around inf 67.0%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot j\right) - -1 \cdot \left(a \cdot y2\right)\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 67.0%

         \[\leadsto t \cdot \left(y5 \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j - a \cdot y2\right)\right)}\right) \]

   6. Simplified 67.0%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\right)} \]

   7. Taylor expanded in i around 0 83.7%

      \[\leadsto t \cdot \left(y5 \cdot \left(-1 \cdot \color{blue}{\left(-1 \cdot \left(a \cdot y2\right)\right)}\right)\right) \]
   8. Step-by-step derivation

      1. mul-1-neg 83.7%

         \[\leadsto t \cdot \left(y5 \cdot \left(-1 \cdot \color{blue}{\left(-a \cdot y2\right)}\right)\right) \]

      2. distribute-lft-neg-out 83.7%

         \[\leadsto t \cdot \left(y5 \cdot \left(-1 \cdot \color{blue}{\left(\left(-a\right) \cdot y2\right)}\right)\right) \]

      3. *-commutative 83.7%

         \[\leadsto t \cdot \left(y5 \cdot \left(-1 \cdot \color{blue}{\left(y2 \cdot \left(-a\right)\right)}\right)\right) \]

   9. Simplified 83.7%

      \[\leadsto t \cdot \left(y5 \cdot \left(-1 \cdot \color{blue}{\left(y2 \cdot \left(-a\right)\right)}\right)\right) \]

   if -1.62e16 < y2 < -8.7999999999999998e-23 or -7.9999999999999995e-151 < y2 < 2.65e-76

   1. Initial program 38.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 43.6%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   4. Taylor expanded in i around inf 47.8%

      \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 47.8%

         \[\leadsto k \cdot \left(i \cdot \left(\color{blue}{y5 \cdot y} - y1 \cdot z\right)\right) \]

   6. Simplified 47.8%

      \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(y5 \cdot y - y1 \cdot z\right)\right)} \]

   if -8.7999999999999998e-23 < y2 < -7.20000000000000049e-128

   1. Initial program 37.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 52.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y0 around inf 49.0%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 49.0%

         \[\leadsto b \cdot \color{blue}{\left(\left(k \cdot z - j \cdot x\right) \cdot y0\right)} \]

   6. Simplified 49.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot y0\right)} \]

   if -7.20000000000000049e-128 < y2 < -7.9999999999999995e-151

   1. Initial program 22.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 44.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in j around inf 56.6%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if 2.65e-76 < y2 < 2.09999999999999981e90

   1. Initial program 34.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 38.0%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in i around inf 41.5%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   if 5.29999999999999983e219 < y2

   1. Initial program 14.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 64.3%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in z around inf 52.4%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 52.4%

         \[\leadsto \color{blue}{\left(-1 \cdot t\right) \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

      2. neg-mul-1 52.4%

         \[\leadsto \color{blue}{\left(-t\right)} \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) \]

      3. *-commutative 52.4%

         \[\leadsto \left(-t\right) \cdot \left(z \cdot \left(a \cdot b - \color{blue}{i \cdot c}\right)\right) \]

   6. Simplified 52.4%

      \[\leadsto \color{blue}{\left(-t\right) \cdot \left(z \cdot \left(a \cdot b - i \cdot c\right)\right)} \]

   7. Taylor expanded in a around 0 65.0%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 65.0%

         \[\leadsto c \cdot \left(i \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

   9. Simplified 65.0%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(z \cdot t\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -3 \cdot 10^{+36}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;y2 \leq -1.62 \cdot 10^{+16}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -8.8 \cdot 10^{-23}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq -7.2 \cdot 10^{-128}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq -8 \cdot 10^{-151}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 2.65 \cdot 10^{-76}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq 2.1 \cdot 10^{+90}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y2 \leq 5.3 \cdot 10^{+219}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 20.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ t_2 := i \cdot \left(\left(z \cdot y1\right) \cdot \left(-k\right)\right)\\ t_3 := \left(-t\right) \cdot \left(i \cdot \left(j \cdot y5\right)\right)\\ \mathbf{if}\;y2 \leq -7 \cdot 10^{+36}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -2.08 \cdot 10^{-187}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y2 \leq 2.3 \cdot 10^{-214}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y2 \leq 8 \cdot 10^{-164}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq 1.35 \cdot 10^{-145}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y2 \leq 4.5 \cdot 10^{-62}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y2 \leq 4.2 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq 5.5 \cdot 10^{+219}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* x (* y b))))
        (t_2 (* i (* (* z y1) (- k))))
        (t_3 (* (- t) (* i (* j y5)))))
   (if (<= y2 -7e+36)
     (* y1 (* y4 (* k y2)))
     (if (<= y2 -2.08e-187)
       t_3
       (if (<= y2 2.3e-214)
         t_2
         (if (<= y2 8e-164)
           t_1
           (if (<= y2 1.35e-145)
             t_2
             (if (<= y2 4.5e-62)
               t_3
               (if (<= y2 4.2e+55)
                 t_1
                 (if (<= y2 5.5e+219)
                   (* k (* y1 (* y2 y4)))
                   (* c (* (* z t) i))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (x * (y * b));
	double t_2 = i * ((z * y1) * -k);
	double t_3 = -t * (i * (j * y5));
	double tmp;
	if (y2 <= -7e+36) {
		tmp = y1 * (y4 * (k * y2));
	} else if (y2 <= -2.08e-187) {
		tmp = t_3;
	} else if (y2 <= 2.3e-214) {
		tmp = t_2;
	} else if (y2 <= 8e-164) {
		tmp = t_1;
	} else if (y2 <= 1.35e-145) {
		tmp = t_2;
	} else if (y2 <= 4.5e-62) {
		tmp = t_3;
	} else if (y2 <= 4.2e+55) {
		tmp = t_1;
	} else if (y2 <= 5.5e+219) {
		tmp = k * (y1 * (y2 * y4));
	} else {
		tmp = c * ((z * t) * 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 = a * (x * (y * b))
    t_2 = i * ((z * y1) * -k)
    t_3 = -t * (i * (j * y5))
    if (y2 <= (-7d+36)) then
        tmp = y1 * (y4 * (k * y2))
    else if (y2 <= (-2.08d-187)) then
        tmp = t_3
    else if (y2 <= 2.3d-214) then
        tmp = t_2
    else if (y2 <= 8d-164) then
        tmp = t_1
    else if (y2 <= 1.35d-145) then
        tmp = t_2
    else if (y2 <= 4.5d-62) then
        tmp = t_3
    else if (y2 <= 4.2d+55) then
        tmp = t_1
    else if (y2 <= 5.5d+219) then
        tmp = k * (y1 * (y2 * y4))
    else
        tmp = c * ((z * t) * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (x * (y * b));
	double t_2 = i * ((z * y1) * -k);
	double t_3 = -t * (i * (j * y5));
	double tmp;
	if (y2 <= -7e+36) {
		tmp = y1 * (y4 * (k * y2));
	} else if (y2 <= -2.08e-187) {
		tmp = t_3;
	} else if (y2 <= 2.3e-214) {
		tmp = t_2;
	} else if (y2 <= 8e-164) {
		tmp = t_1;
	} else if (y2 <= 1.35e-145) {
		tmp = t_2;
	} else if (y2 <= 4.5e-62) {
		tmp = t_3;
	} else if (y2 <= 4.2e+55) {
		tmp = t_1;
	} else if (y2 <= 5.5e+219) {
		tmp = k * (y1 * (y2 * y4));
	} else {
		tmp = c * ((z * t) * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (x * (y * b))
	t_2 = i * ((z * y1) * -k)
	t_3 = -t * (i * (j * y5))
	tmp = 0
	if y2 <= -7e+36:
		tmp = y1 * (y4 * (k * y2))
	elif y2 <= -2.08e-187:
		tmp = t_3
	elif y2 <= 2.3e-214:
		tmp = t_2
	elif y2 <= 8e-164:
		tmp = t_1
	elif y2 <= 1.35e-145:
		tmp = t_2
	elif y2 <= 4.5e-62:
		tmp = t_3
	elif y2 <= 4.2e+55:
		tmp = t_1
	elif y2 <= 5.5e+219:
		tmp = k * (y1 * (y2 * y4))
	else:
		tmp = c * ((z * t) * 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(a * Float64(x * Float64(y * b)))
	t_2 = Float64(i * Float64(Float64(z * y1) * Float64(-k)))
	t_3 = Float64(Float64(-t) * Float64(i * Float64(j * y5)))
	tmp = 0.0
	if (y2 <= -7e+36)
		tmp = Float64(y1 * Float64(y4 * Float64(k * y2)));
	elseif (y2 <= -2.08e-187)
		tmp = t_3;
	elseif (y2 <= 2.3e-214)
		tmp = t_2;
	elseif (y2 <= 8e-164)
		tmp = t_1;
	elseif (y2 <= 1.35e-145)
		tmp = t_2;
	elseif (y2 <= 4.5e-62)
		tmp = t_3;
	elseif (y2 <= 4.2e+55)
		tmp = t_1;
	elseif (y2 <= 5.5e+219)
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	else
		tmp = Float64(c * Float64(Float64(z * t) * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (x * (y * b));
	t_2 = i * ((z * y1) * -k);
	t_3 = -t * (i * (j * y5));
	tmp = 0.0;
	if (y2 <= -7e+36)
		tmp = y1 * (y4 * (k * y2));
	elseif (y2 <= -2.08e-187)
		tmp = t_3;
	elseif (y2 <= 2.3e-214)
		tmp = t_2;
	elseif (y2 <= 8e-164)
		tmp = t_1;
	elseif (y2 <= 1.35e-145)
		tmp = t_2;
	elseif (y2 <= 4.5e-62)
		tmp = t_3;
	elseif (y2 <= 4.2e+55)
		tmp = t_1;
	elseif (y2 <= 5.5e+219)
		tmp = k * (y1 * (y2 * y4));
	else
		tmp = c * ((z * t) * 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[(a * N[(x * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(z * y1), $MachinePrecision] * (-k)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[((-t) * N[(i * N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -7e+36], N[(y1 * N[(y4 * N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -2.08e-187], t$95$3, If[LessEqual[y2, 2.3e-214], t$95$2, If[LessEqual[y2, 8e-164], t$95$1, If[LessEqual[y2, 1.35e-145], t$95$2, If[LessEqual[y2, 4.5e-62], t$95$3, If[LessEqual[y2, 4.2e+55], t$95$1, If[LessEqual[y2, 5.5e+219], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(z * t), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y2 < -6.9999999999999996e36

   1. Initial program 41.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 44.5%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in y4 around inf 32.7%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 37.5%

      \[\leadsto y1 \cdot \left(y4 \cdot \color{blue}{\left(k \cdot y2\right)}\right) \]

   if -6.9999999999999996e36 < y2 < -2.08e-187 or 1.35e-145 < y2 < 4.50000000000000018e-62

   1. Initial program 31.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 55.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in y5 around inf 39.2%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot j\right) - -1 \cdot \left(a \cdot y2\right)\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 39.2%

         \[\leadsto t \cdot \left(y5 \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j - a \cdot y2\right)\right)}\right) \]

   6. Simplified 39.2%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\right)} \]

   7. Taylor expanded in i around inf 35.4%

      \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y5\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 35.4%

         \[\leadsto t \cdot \color{blue}{\left(-i \cdot \left(j \cdot y5\right)\right)} \]

      2. distribute-rgt-neg-in 35.4%

         \[\leadsto t \cdot \color{blue}{\left(i \cdot \left(-j \cdot y5\right)\right)} \]

      3. *-commutative 35.4%

         \[\leadsto t \cdot \left(i \cdot \left(-\color{blue}{y5 \cdot j}\right)\right) \]

   9. Simplified 35.4%

      \[\leadsto t \cdot \color{blue}{\left(i \cdot \left(-y5 \cdot j\right)\right)} \]

   if -2.08e-187 < y2 < 2.30000000000000011e-214 or 7.99999999999999969e-164 < y2 < 1.35e-145

   1. Initial program 36.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 42.8%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in i around inf 44.8%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in j around 0 37.9%

      \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y1 \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 37.9%

         \[\leadsto i \cdot \color{blue}{\left(-k \cdot \left(y1 \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 37.9%

         \[\leadsto i \cdot \color{blue}{\left(k \cdot \left(-y1 \cdot z\right)\right)} \]

      3. distribute-rgt-neg-in 37.9%

         \[\leadsto i \cdot \left(k \cdot \color{blue}{\left(y1 \cdot \left(-z\right)\right)}\right) \]

   7. Simplified 37.9%

      \[\leadsto i \cdot \color{blue}{\left(k \cdot \left(y1 \cdot \left(-z\right)\right)\right)} \]

   if 2.30000000000000011e-214 < y2 < 7.99999999999999969e-164 or 4.50000000000000018e-62 < y2 < 4.2000000000000001e55

   1. Initial program 44.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 40.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 28.1%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 28.1%

         \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y - t \cdot z\right) \cdot b\right)} \]

      2. *-commutative 28.1%

         \[\leadsto a \cdot \left(\left(\color{blue}{y \cdot x} - t \cdot z\right) \cdot b\right) \]

   6. Simplified 28.1%

      \[\leadsto \color{blue}{a \cdot \left(\left(y \cdot x - t \cdot z\right) \cdot b\right)} \]

   7. Taylor expanded in y around inf 25.6%

      \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot y\right)} \cdot b\right) \]
   8. Step-by-step derivation

      1. *-commutative 25.6%

         \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot b\right) \]

   9. Simplified 25.6%

      \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot b\right) \]

   10. Taylor expanded in y around 0 25.6%

       \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 23.0%

          \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot x\right) \cdot y\right)} \]

       2. *-commutative 23.0%

          \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot b\right)} \cdot y\right) \]

       3. associate-*l* 30.6%

          \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

   12. Simplified 30.6%

       \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

   if 4.2000000000000001e55 < y2 < 5.49999999999999973e219

   1. Initial program 17.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 49.2%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in y4 around inf 46.6%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 41.4%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)} \]

   if 5.49999999999999973e219 < y2

   1. Initial program 14.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 64.3%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in z around inf 52.4%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 52.4%

         \[\leadsto \color{blue}{\left(-1 \cdot t\right) \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

      2. neg-mul-1 52.4%

         \[\leadsto \color{blue}{\left(-t\right)} \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) \]

      3. *-commutative 52.4%

         \[\leadsto \left(-t\right) \cdot \left(z \cdot \left(a \cdot b - \color{blue}{i \cdot c}\right)\right) \]

   6. Simplified 52.4%

      \[\leadsto \color{blue}{\left(-t\right) \cdot \left(z \cdot \left(a \cdot b - i \cdot c\right)\right)} \]

   7. Taylor expanded in a around 0 65.0%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 65.0%

         \[\leadsto c \cdot \left(i \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

   9. Simplified 65.0%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(z \cdot t\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 38.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -7 \cdot 10^{+36}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -2.08 \cdot 10^{-187}:\\ \;\;\;\;\left(-t\right) \cdot \left(i \cdot \left(j \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 2.3 \cdot 10^{-214}:\\ \;\;\;\;i \cdot \left(\left(z \cdot y1\right) \cdot \left(-k\right)\right)\\ \mathbf{elif}\;y2 \leq 8 \cdot 10^{-164}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 1.35 \cdot 10^{-145}:\\ \;\;\;\;i \cdot \left(\left(z \cdot y1\right) \cdot \left(-k\right)\right)\\ \mathbf{elif}\;y2 \leq 4.5 \cdot 10^{-62}:\\ \;\;\;\;\left(-t\right) \cdot \left(i \cdot \left(j \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 4.2 \cdot 10^{+55}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 5.5 \cdot 10^{+219}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 20.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(\left(z \cdot y1\right) \cdot \left(-k\right)\right)\\ t_2 := \left(-t\right) \cdot \left(i \cdot \left(j \cdot y5\right)\right)\\ \mathbf{if}\;y2 \leq -4.6 \cdot 10^{+36}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -1.7 \cdot 10^{-189}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y2 \leq 1.25 \cdot 10^{-213}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq 8 \cdot 10^{-164}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 6.1 \cdot 10^{-146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq 7.6 \cdot 10^{-62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y2 \leq 10^{+56}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(j \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 2.7 \cdot 10^{+218}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* (* z y1) (- k)))) (t_2 (* (- t) (* i (* j y5)))))
   (if (<= y2 -4.6e+36)
     (* y1 (* y4 (* k y2)))
     (if (<= y2 -1.7e-189)
       t_2
       (if (<= y2 1.25e-213)
         t_1
         (if (<= y2 8e-164)
           (* a (* x (* y b)))
           (if (<= y2 6.1e-146)
             t_1
             (if (<= y2 7.6e-62)
               t_2
               (if (<= y2 1e+56)
                 (* y1 (* y4 (* j (- y3))))
                 (if (<= y2 2.7e+218)
                   (* k (* y1 (* y2 y4)))
                   (* c (* (* z t) 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 = i * ((z * y1) * -k);
	double t_2 = -t * (i * (j * y5));
	double tmp;
	if (y2 <= -4.6e+36) {
		tmp = y1 * (y4 * (k * y2));
	} else if (y2 <= -1.7e-189) {
		tmp = t_2;
	} else if (y2 <= 1.25e-213) {
		tmp = t_1;
	} else if (y2 <= 8e-164) {
		tmp = a * (x * (y * b));
	} else if (y2 <= 6.1e-146) {
		tmp = t_1;
	} else if (y2 <= 7.6e-62) {
		tmp = t_2;
	} else if (y2 <= 1e+56) {
		tmp = y1 * (y4 * (j * -y3));
	} else if (y2 <= 2.7e+218) {
		tmp = k * (y1 * (y2 * y4));
	} else {
		tmp = c * ((z * t) * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * ((z * y1) * -k)
    t_2 = -t * (i * (j * y5))
    if (y2 <= (-4.6d+36)) then
        tmp = y1 * (y4 * (k * y2))
    else if (y2 <= (-1.7d-189)) then
        tmp = t_2
    else if (y2 <= 1.25d-213) then
        tmp = t_1
    else if (y2 <= 8d-164) then
        tmp = a * (x * (y * b))
    else if (y2 <= 6.1d-146) then
        tmp = t_1
    else if (y2 <= 7.6d-62) then
        tmp = t_2
    else if (y2 <= 1d+56) then
        tmp = y1 * (y4 * (j * -y3))
    else if (y2 <= 2.7d+218) then
        tmp = k * (y1 * (y2 * y4))
    else
        tmp = c * ((z * t) * 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 = i * ((z * y1) * -k);
	double t_2 = -t * (i * (j * y5));
	double tmp;
	if (y2 <= -4.6e+36) {
		tmp = y1 * (y4 * (k * y2));
	} else if (y2 <= -1.7e-189) {
		tmp = t_2;
	} else if (y2 <= 1.25e-213) {
		tmp = t_1;
	} else if (y2 <= 8e-164) {
		tmp = a * (x * (y * b));
	} else if (y2 <= 6.1e-146) {
		tmp = t_1;
	} else if (y2 <= 7.6e-62) {
		tmp = t_2;
	} else if (y2 <= 1e+56) {
		tmp = y1 * (y4 * (j * -y3));
	} else if (y2 <= 2.7e+218) {
		tmp = k * (y1 * (y2 * y4));
	} else {
		tmp = c * ((z * t) * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = i * ((z * y1) * -k)
	t_2 = -t * (i * (j * y5))
	tmp = 0
	if y2 <= -4.6e+36:
		tmp = y1 * (y4 * (k * y2))
	elif y2 <= -1.7e-189:
		tmp = t_2
	elif y2 <= 1.25e-213:
		tmp = t_1
	elif y2 <= 8e-164:
		tmp = a * (x * (y * b))
	elif y2 <= 6.1e-146:
		tmp = t_1
	elif y2 <= 7.6e-62:
		tmp = t_2
	elif y2 <= 1e+56:
		tmp = y1 * (y4 * (j * -y3))
	elif y2 <= 2.7e+218:
		tmp = k * (y1 * (y2 * y4))
	else:
		tmp = c * ((z * t) * 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(i * Float64(Float64(z * y1) * Float64(-k)))
	t_2 = Float64(Float64(-t) * Float64(i * Float64(j * y5)))
	tmp = 0.0
	if (y2 <= -4.6e+36)
		tmp = Float64(y1 * Float64(y4 * Float64(k * y2)));
	elseif (y2 <= -1.7e-189)
		tmp = t_2;
	elseif (y2 <= 1.25e-213)
		tmp = t_1;
	elseif (y2 <= 8e-164)
		tmp = Float64(a * Float64(x * Float64(y * b)));
	elseif (y2 <= 6.1e-146)
		tmp = t_1;
	elseif (y2 <= 7.6e-62)
		tmp = t_2;
	elseif (y2 <= 1e+56)
		tmp = Float64(y1 * Float64(y4 * Float64(j * Float64(-y3))));
	elseif (y2 <= 2.7e+218)
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	else
		tmp = Float64(c * Float64(Float64(z * t) * 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 = i * ((z * y1) * -k);
	t_2 = -t * (i * (j * y5));
	tmp = 0.0;
	if (y2 <= -4.6e+36)
		tmp = y1 * (y4 * (k * y2));
	elseif (y2 <= -1.7e-189)
		tmp = t_2;
	elseif (y2 <= 1.25e-213)
		tmp = t_1;
	elseif (y2 <= 8e-164)
		tmp = a * (x * (y * b));
	elseif (y2 <= 6.1e-146)
		tmp = t_1;
	elseif (y2 <= 7.6e-62)
		tmp = t_2;
	elseif (y2 <= 1e+56)
		tmp = y1 * (y4 * (j * -y3));
	elseif (y2 <= 2.7e+218)
		tmp = k * (y1 * (y2 * y4));
	else
		tmp = c * ((z * t) * 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[(i * N[(N[(z * y1), $MachinePrecision] * (-k)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[((-t) * N[(i * N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -4.6e+36], N[(y1 * N[(y4 * N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1.7e-189], t$95$2, If[LessEqual[y2, 1.25e-213], t$95$1, If[LessEqual[y2, 8e-164], N[(a * N[(x * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 6.1e-146], t$95$1, If[LessEqual[y2, 7.6e-62], t$95$2, If[LessEqual[y2, 1e+56], N[(y1 * N[(y4 * N[(j * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.7e+218], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(z * t), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y2 < -4.59999999999999993e36

   1. Initial program 41.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 44.5%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in y4 around inf 32.7%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 37.5%

      \[\leadsto y1 \cdot \left(y4 \cdot \color{blue}{\left(k \cdot y2\right)}\right) \]

   if -4.59999999999999993e36 < y2 < -1.7000000000000001e-189 or 6.0999999999999996e-146 < y2 < 7.60000000000000013e-62

   1. Initial program 31.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 55.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in y5 around inf 39.2%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot j\right) - -1 \cdot \left(a \cdot y2\right)\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 39.2%

         \[\leadsto t \cdot \left(y5 \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j - a \cdot y2\right)\right)}\right) \]

   6. Simplified 39.2%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\right)} \]

   7. Taylor expanded in i around inf 35.4%

      \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y5\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 35.4%

         \[\leadsto t \cdot \color{blue}{\left(-i \cdot \left(j \cdot y5\right)\right)} \]

      2. distribute-rgt-neg-in 35.4%

         \[\leadsto t \cdot \color{blue}{\left(i \cdot \left(-j \cdot y5\right)\right)} \]

      3. *-commutative 35.4%

         \[\leadsto t \cdot \left(i \cdot \left(-\color{blue}{y5 \cdot j}\right)\right) \]

   9. Simplified 35.4%

      \[\leadsto t \cdot \color{blue}{\left(i \cdot \left(-y5 \cdot j\right)\right)} \]

   if -1.7000000000000001e-189 < y2 < 1.24999999999999994e-213 or 7.99999999999999969e-164 < y2 < 6.0999999999999996e-146

   1. Initial program 36.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 42.8%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in i around inf 44.8%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in j around 0 37.9%

      \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y1 \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 37.9%

         \[\leadsto i \cdot \color{blue}{\left(-k \cdot \left(y1 \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 37.9%

         \[\leadsto i \cdot \color{blue}{\left(k \cdot \left(-y1 \cdot z\right)\right)} \]

      3. distribute-rgt-neg-in 37.9%

         \[\leadsto i \cdot \left(k \cdot \color{blue}{\left(y1 \cdot \left(-z\right)\right)}\right) \]

   7. Simplified 37.9%

      \[\leadsto i \cdot \color{blue}{\left(k \cdot \left(y1 \cdot \left(-z\right)\right)\right)} \]

   if 1.24999999999999994e-213 < y2 < 7.99999999999999969e-164

   1. Initial program 50.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 39.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 27.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 27.3%

         \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y - t \cdot z\right) \cdot b\right)} \]

      2. *-commutative 27.3%

         \[\leadsto a \cdot \left(\left(\color{blue}{y \cdot x} - t \cdot z\right) \cdot b\right) \]

   6. Simplified 27.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(y \cdot x - t \cdot z\right) \cdot b\right)} \]

   7. Taylor expanded in y around inf 27.5%

      \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot y\right)} \cdot b\right) \]
   8. Step-by-step derivation

      1. *-commutative 27.5%

         \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot b\right) \]

   9. Simplified 27.5%

      \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot b\right) \]

   10. Taylor expanded in y around 0 27.5%

       \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 27.6%

          \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot x\right) \cdot y\right)} \]

       2. *-commutative 27.6%

          \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot b\right)} \cdot y\right) \]

       3. associate-*l* 33.5%

          \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

   12. Simplified 33.5%

       \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

   if 7.60000000000000013e-62 < y2 < 1.00000000000000009e56

   1. Initial program 40.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 27.9%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in y4 around inf 46.0%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   5. Taylor expanded in k around 0 46.1%

      \[\leadsto y1 \cdot \left(y4 \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y3\right)\right)}\right) \]
   6. Step-by-step derivation

      1. neg-mul-1 46.1%

         \[\leadsto y1 \cdot \left(y4 \cdot \color{blue}{\left(-j \cdot y3\right)}\right) \]

      2. distribute-rgt-neg-in 46.1%

         \[\leadsto y1 \cdot \left(y4 \cdot \color{blue}{\left(j \cdot \left(-y3\right)\right)}\right) \]

   7. Simplified 46.1%

      \[\leadsto y1 \cdot \left(y4 \cdot \color{blue}{\left(j \cdot \left(-y3\right)\right)}\right) \]

   if 1.00000000000000009e56 < y2 < 2.70000000000000013e218

   1. Initial program 17.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 49.2%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in y4 around inf 46.6%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 41.4%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)} \]

   if 2.70000000000000013e218 < y2

   1. Initial program 14.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 64.3%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in z around inf 52.4%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 52.4%

         \[\leadsto \color{blue}{\left(-1 \cdot t\right) \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

      2. neg-mul-1 52.4%

         \[\leadsto \color{blue}{\left(-t\right)} \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) \]

      3. *-commutative 52.4%

         \[\leadsto \left(-t\right) \cdot \left(z \cdot \left(a \cdot b - \color{blue}{i \cdot c}\right)\right) \]

   6. Simplified 52.4%

      \[\leadsto \color{blue}{\left(-t\right) \cdot \left(z \cdot \left(a \cdot b - i \cdot c\right)\right)} \]

   7. Taylor expanded in a around 0 65.0%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 65.0%

         \[\leadsto c \cdot \left(i \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

   9. Simplified 65.0%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(z \cdot t\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 39.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -4.6 \cdot 10^{+36}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -1.7 \cdot 10^{-189}:\\ \;\;\;\;\left(-t\right) \cdot \left(i \cdot \left(j \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 1.25 \cdot 10^{-213}:\\ \;\;\;\;i \cdot \left(\left(z \cdot y1\right) \cdot \left(-k\right)\right)\\ \mathbf{elif}\;y2 \leq 8 \cdot 10^{-164}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 6.1 \cdot 10^{-146}:\\ \;\;\;\;i \cdot \left(\left(z \cdot y1\right) \cdot \left(-k\right)\right)\\ \mathbf{elif}\;y2 \leq 7.6 \cdot 10^{-62}:\\ \;\;\;\;\left(-t\right) \cdot \left(i \cdot \left(j \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 10^{+56}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(j \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 2.7 \cdot 10^{+218}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 20.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(\left(z \cdot y1\right) \cdot \left(-k\right)\right)\\ t_2 := \left(-t\right) \cdot \left(i \cdot \left(j \cdot y5\right)\right)\\ \mathbf{if}\;y2 \leq -5.6 \cdot 10^{+36}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -5.7 \cdot 10^{-187}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y2 \leq 8.5 \cdot 10^{-215}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq 2.1 \cdot 10^{-163}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 2.35 \cdot 10^{-144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq 1.35 \cdot 10^{-60}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y2 \leq 7.4 \cdot 10^{+55}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(y3 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 5.3 \cdot 10^{+219}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* (* z y1) (- k)))) (t_2 (* (- t) (* i (* j y5)))))
   (if (<= y2 -5.6e+36)
     (* y1 (* y4 (* k y2)))
     (if (<= y2 -5.7e-187)
       t_2
       (if (<= y2 8.5e-215)
         t_1
         (if (<= y2 2.1e-163)
           (* a (* x (* y b)))
           (if (<= y2 2.35e-144)
             t_1
             (if (<= y2 1.35e-60)
               t_2
               (if (<= y2 7.4e+55)
                 (* y1 (* j (* y3 (- y4))))
                 (if (<= y2 5.3e+219)
                   (* k (* y1 (* y2 y4)))
                   (* c (* (* z t) 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 = i * ((z * y1) * -k);
	double t_2 = -t * (i * (j * y5));
	double tmp;
	if (y2 <= -5.6e+36) {
		tmp = y1 * (y4 * (k * y2));
	} else if (y2 <= -5.7e-187) {
		tmp = t_2;
	} else if (y2 <= 8.5e-215) {
		tmp = t_1;
	} else if (y2 <= 2.1e-163) {
		tmp = a * (x * (y * b));
	} else if (y2 <= 2.35e-144) {
		tmp = t_1;
	} else if (y2 <= 1.35e-60) {
		tmp = t_2;
	} else if (y2 <= 7.4e+55) {
		tmp = y1 * (j * (y3 * -y4));
	} else if (y2 <= 5.3e+219) {
		tmp = k * (y1 * (y2 * y4));
	} else {
		tmp = c * ((z * t) * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * ((z * y1) * -k)
    t_2 = -t * (i * (j * y5))
    if (y2 <= (-5.6d+36)) then
        tmp = y1 * (y4 * (k * y2))
    else if (y2 <= (-5.7d-187)) then
        tmp = t_2
    else if (y2 <= 8.5d-215) then
        tmp = t_1
    else if (y2 <= 2.1d-163) then
        tmp = a * (x * (y * b))
    else if (y2 <= 2.35d-144) then
        tmp = t_1
    else if (y2 <= 1.35d-60) then
        tmp = t_2
    else if (y2 <= 7.4d+55) then
        tmp = y1 * (j * (y3 * -y4))
    else if (y2 <= 5.3d+219) then
        tmp = k * (y1 * (y2 * y4))
    else
        tmp = c * ((z * t) * 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 = i * ((z * y1) * -k);
	double t_2 = -t * (i * (j * y5));
	double tmp;
	if (y2 <= -5.6e+36) {
		tmp = y1 * (y4 * (k * y2));
	} else if (y2 <= -5.7e-187) {
		tmp = t_2;
	} else if (y2 <= 8.5e-215) {
		tmp = t_1;
	} else if (y2 <= 2.1e-163) {
		tmp = a * (x * (y * b));
	} else if (y2 <= 2.35e-144) {
		tmp = t_1;
	} else if (y2 <= 1.35e-60) {
		tmp = t_2;
	} else if (y2 <= 7.4e+55) {
		tmp = y1 * (j * (y3 * -y4));
	} else if (y2 <= 5.3e+219) {
		tmp = k * (y1 * (y2 * y4));
	} else {
		tmp = c * ((z * t) * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = i * ((z * y1) * -k)
	t_2 = -t * (i * (j * y5))
	tmp = 0
	if y2 <= -5.6e+36:
		tmp = y1 * (y4 * (k * y2))
	elif y2 <= -5.7e-187:
		tmp = t_2
	elif y2 <= 8.5e-215:
		tmp = t_1
	elif y2 <= 2.1e-163:
		tmp = a * (x * (y * b))
	elif y2 <= 2.35e-144:
		tmp = t_1
	elif y2 <= 1.35e-60:
		tmp = t_2
	elif y2 <= 7.4e+55:
		tmp = y1 * (j * (y3 * -y4))
	elif y2 <= 5.3e+219:
		tmp = k * (y1 * (y2 * y4))
	else:
		tmp = c * ((z * t) * 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(i * Float64(Float64(z * y1) * Float64(-k)))
	t_2 = Float64(Float64(-t) * Float64(i * Float64(j * y5)))
	tmp = 0.0
	if (y2 <= -5.6e+36)
		tmp = Float64(y1 * Float64(y4 * Float64(k * y2)));
	elseif (y2 <= -5.7e-187)
		tmp = t_2;
	elseif (y2 <= 8.5e-215)
		tmp = t_1;
	elseif (y2 <= 2.1e-163)
		tmp = Float64(a * Float64(x * Float64(y * b)));
	elseif (y2 <= 2.35e-144)
		tmp = t_1;
	elseif (y2 <= 1.35e-60)
		tmp = t_2;
	elseif (y2 <= 7.4e+55)
		tmp = Float64(y1 * Float64(j * Float64(y3 * Float64(-y4))));
	elseif (y2 <= 5.3e+219)
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	else
		tmp = Float64(c * Float64(Float64(z * t) * 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 = i * ((z * y1) * -k);
	t_2 = -t * (i * (j * y5));
	tmp = 0.0;
	if (y2 <= -5.6e+36)
		tmp = y1 * (y4 * (k * y2));
	elseif (y2 <= -5.7e-187)
		tmp = t_2;
	elseif (y2 <= 8.5e-215)
		tmp = t_1;
	elseif (y2 <= 2.1e-163)
		tmp = a * (x * (y * b));
	elseif (y2 <= 2.35e-144)
		tmp = t_1;
	elseif (y2 <= 1.35e-60)
		tmp = t_2;
	elseif (y2 <= 7.4e+55)
		tmp = y1 * (j * (y3 * -y4));
	elseif (y2 <= 5.3e+219)
		tmp = k * (y1 * (y2 * y4));
	else
		tmp = c * ((z * t) * 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[(i * N[(N[(z * y1), $MachinePrecision] * (-k)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[((-t) * N[(i * N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -5.6e+36], N[(y1 * N[(y4 * N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -5.7e-187], t$95$2, If[LessEqual[y2, 8.5e-215], t$95$1, If[LessEqual[y2, 2.1e-163], N[(a * N[(x * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.35e-144], t$95$1, If[LessEqual[y2, 1.35e-60], t$95$2, If[LessEqual[y2, 7.4e+55], N[(y1 * N[(j * N[(y3 * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 5.3e+219], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(z * t), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y2 < -5.6000000000000001e36

   1. Initial program 41.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 44.5%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in y4 around inf 32.7%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 37.5%

      \[\leadsto y1 \cdot \left(y4 \cdot \color{blue}{\left(k \cdot y2\right)}\right) \]

   if -5.6000000000000001e36 < y2 < -5.6999999999999996e-187 or 2.3500000000000001e-144 < y2 < 1.35e-60

   1. Initial program 31.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 55.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in y5 around inf 39.2%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot j\right) - -1 \cdot \left(a \cdot y2\right)\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 39.2%

         \[\leadsto t \cdot \left(y5 \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j - a \cdot y2\right)\right)}\right) \]

   6. Simplified 39.2%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\right)} \]

   7. Taylor expanded in i around inf 35.4%

      \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y5\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 35.4%

         \[\leadsto t \cdot \color{blue}{\left(-i \cdot \left(j \cdot y5\right)\right)} \]

      2. distribute-rgt-neg-in 35.4%

         \[\leadsto t \cdot \color{blue}{\left(i \cdot \left(-j \cdot y5\right)\right)} \]

      3. *-commutative 35.4%

         \[\leadsto t \cdot \left(i \cdot \left(-\color{blue}{y5 \cdot j}\right)\right) \]

   9. Simplified 35.4%

      \[\leadsto t \cdot \color{blue}{\left(i \cdot \left(-y5 \cdot j\right)\right)} \]

   if -5.6999999999999996e-187 < y2 < 8.4999999999999998e-215 or 2.09999999999999998e-163 < y2 < 2.3500000000000001e-144

   1. Initial program 36.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 42.8%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in i around inf 44.8%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in j around 0 37.9%

      \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y1 \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 37.9%

         \[\leadsto i \cdot \color{blue}{\left(-k \cdot \left(y1 \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 37.9%

         \[\leadsto i \cdot \color{blue}{\left(k \cdot \left(-y1 \cdot z\right)\right)} \]

      3. distribute-rgt-neg-in 37.9%

         \[\leadsto i \cdot \left(k \cdot \color{blue}{\left(y1 \cdot \left(-z\right)\right)}\right) \]

   7. Simplified 37.9%

      \[\leadsto i \cdot \color{blue}{\left(k \cdot \left(y1 \cdot \left(-z\right)\right)\right)} \]

   if 8.4999999999999998e-215 < y2 < 2.09999999999999998e-163

   1. Initial program 50.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 39.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 27.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 27.3%

         \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y - t \cdot z\right) \cdot b\right)} \]

      2. *-commutative 27.3%

         \[\leadsto a \cdot \left(\left(\color{blue}{y \cdot x} - t \cdot z\right) \cdot b\right) \]

   6. Simplified 27.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(y \cdot x - t \cdot z\right) \cdot b\right)} \]

   7. Taylor expanded in y around inf 27.5%

      \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot y\right)} \cdot b\right) \]
   8. Step-by-step derivation

      1. *-commutative 27.5%

         \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot b\right) \]

   9. Simplified 27.5%

      \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot b\right) \]

   10. Taylor expanded in y around 0 27.5%

       \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 27.6%

          \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot x\right) \cdot y\right)} \]

       2. *-commutative 27.6%

          \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot b\right)} \cdot y\right) \]

       3. associate-*l* 33.5%

          \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

   12. Simplified 33.5%

       \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

   if 1.35e-60 < y2 < 7.4000000000000004e55

   1. Initial program 40.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 27.9%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in y4 around inf 46.0%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   5. Taylor expanded in k around 0 46.1%

      \[\leadsto y1 \cdot \color{blue}{\left(-1 \cdot \left(j \cdot \left(y3 \cdot y4\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 46.1%

         \[\leadsto y1 \cdot \color{blue}{\left(-j \cdot \left(y3 \cdot y4\right)\right)} \]

      2. *-commutative 46.1%

         \[\leadsto y1 \cdot \left(-\color{blue}{\left(y3 \cdot y4\right) \cdot j}\right) \]

      3. distribute-rgt-neg-in 46.1%

         \[\leadsto y1 \cdot \color{blue}{\left(\left(y3 \cdot y4\right) \cdot \left(-j\right)\right)} \]

      4. *-commutative 46.1%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot y3\right)} \cdot \left(-j\right)\right) \]

   7. Simplified 46.1%

      \[\leadsto y1 \cdot \color{blue}{\left(\left(y4 \cdot y3\right) \cdot \left(-j\right)\right)} \]

   if 7.4000000000000004e55 < y2 < 5.29999999999999983e219

   1. Initial program 17.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 49.2%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in y4 around inf 46.6%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 41.4%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)} \]

   if 5.29999999999999983e219 < y2

   1. Initial program 14.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 64.3%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in z around inf 52.4%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 52.4%

         \[\leadsto \color{blue}{\left(-1 \cdot t\right) \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

      2. neg-mul-1 52.4%

         \[\leadsto \color{blue}{\left(-t\right)} \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) \]

      3. *-commutative 52.4%

         \[\leadsto \left(-t\right) \cdot \left(z \cdot \left(a \cdot b - \color{blue}{i \cdot c}\right)\right) \]

   6. Simplified 52.4%

      \[\leadsto \color{blue}{\left(-t\right) \cdot \left(z \cdot \left(a \cdot b - i \cdot c\right)\right)} \]

   7. Taylor expanded in a around 0 65.0%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 65.0%

         \[\leadsto c \cdot \left(i \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

   9. Simplified 65.0%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(z \cdot t\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 39.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -5.6 \cdot 10^{+36}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -5.7 \cdot 10^{-187}:\\ \;\;\;\;\left(-t\right) \cdot \left(i \cdot \left(j \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 8.5 \cdot 10^{-215}:\\ \;\;\;\;i \cdot \left(\left(z \cdot y1\right) \cdot \left(-k\right)\right)\\ \mathbf{elif}\;y2 \leq 2.1 \cdot 10^{-163}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 2.35 \cdot 10^{-144}:\\ \;\;\;\;i \cdot \left(\left(z \cdot y1\right) \cdot \left(-k\right)\right)\\ \mathbf{elif}\;y2 \leq 1.35 \cdot 10^{-60}:\\ \;\;\;\;\left(-t\right) \cdot \left(i \cdot \left(j \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 7.4 \cdot 10^{+55}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(y3 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 5.3 \cdot 10^{+219}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 27.2% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{+158}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y \leq -1650000000:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq -1.16 \cdot 10^{-92}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(y3 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-259}:\\ \;\;\;\;j \cdot \left(i \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y \leq 3.89 \cdot 10^{-44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 180000:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+181}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(x \cdot y\right) \cdot \left(-i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* j (- (* t y4) (* x y0))))))
   (if (<= y -2.8e+158)
     (* a (* b (- (* x y) (* z t))))
     (if (<= y -1650000000.0)
       (* b (* x (- (* y a) (* j y0))))
       (if (<= y -1.16e-92)
         (* y1 (* j (* y3 (- y4))))
         (if (<= y -7e-259)
           (* j (* i (* x y1)))
           (if (<= y 3.89e-44)
             t_1
             (if (<= y 180000.0)
               (* t (* a (* y2 y5)))
               (if (<= y 2.5e+181) t_1 (* c (* (* x 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 = b * (j * ((t * y4) - (x * y0)));
	double tmp;
	if (y <= -2.8e+158) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y <= -1650000000.0) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y <= -1.16e-92) {
		tmp = y1 * (j * (y3 * -y4));
	} else if (y <= -7e-259) {
		tmp = j * (i * (x * y1));
	} else if (y <= 3.89e-44) {
		tmp = t_1;
	} else if (y <= 180000.0) {
		tmp = t * (a * (y2 * y5));
	} else if (y <= 2.5e+181) {
		tmp = t_1;
	} else {
		tmp = c * ((x * 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) :: tmp
    t_1 = b * (j * ((t * y4) - (x * y0)))
    if (y <= (-2.8d+158)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (y <= (-1650000000.0d0)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (y <= (-1.16d-92)) then
        tmp = y1 * (j * (y3 * -y4))
    else if (y <= (-7d-259)) then
        tmp = j * (i * (x * y1))
    else if (y <= 3.89d-44) then
        tmp = t_1
    else if (y <= 180000.0d0) then
        tmp = t * (a * (y2 * y5))
    else if (y <= 2.5d+181) then
        tmp = t_1
    else
        tmp = c * ((x * 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 = b * (j * ((t * y4) - (x * y0)));
	double tmp;
	if (y <= -2.8e+158) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y <= -1650000000.0) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y <= -1.16e-92) {
		tmp = y1 * (j * (y3 * -y4));
	} else if (y <= -7e-259) {
		tmp = j * (i * (x * y1));
	} else if (y <= 3.89e-44) {
		tmp = t_1;
	} else if (y <= 180000.0) {
		tmp = t * (a * (y2 * y5));
	} else if (y <= 2.5e+181) {
		tmp = t_1;
	} else {
		tmp = c * ((x * 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 = b * (j * ((t * y4) - (x * y0)))
	tmp = 0
	if y <= -2.8e+158:
		tmp = a * (b * ((x * y) - (z * t)))
	elif y <= -1650000000.0:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif y <= -1.16e-92:
		tmp = y1 * (j * (y3 * -y4))
	elif y <= -7e-259:
		tmp = j * (i * (x * y1))
	elif y <= 3.89e-44:
		tmp = t_1
	elif y <= 180000.0:
		tmp = t * (a * (y2 * y5))
	elif y <= 2.5e+181:
		tmp = t_1
	else:
		tmp = c * ((x * 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(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))))
	tmp = 0.0
	if (y <= -2.8e+158)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y <= -1650000000.0)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (y <= -1.16e-92)
		tmp = Float64(y1 * Float64(j * Float64(y3 * Float64(-y4))));
	elseif (y <= -7e-259)
		tmp = Float64(j * Float64(i * Float64(x * y1)));
	elseif (y <= 3.89e-44)
		tmp = t_1;
	elseif (y <= 180000.0)
		tmp = Float64(t * Float64(a * Float64(y2 * y5)));
	elseif (y <= 2.5e+181)
		tmp = t_1;
	else
		tmp = Float64(c * Float64(Float64(x * y) * Float64(-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 = b * (j * ((t * y4) - (x * y0)));
	tmp = 0.0;
	if (y <= -2.8e+158)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (y <= -1650000000.0)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (y <= -1.16e-92)
		tmp = y1 * (j * (y3 * -y4));
	elseif (y <= -7e-259)
		tmp = j * (i * (x * y1));
	elseif (y <= 3.89e-44)
		tmp = t_1;
	elseif (y <= 180000.0)
		tmp = t * (a * (y2 * y5));
	elseif (y <= 2.5e+181)
		tmp = t_1;
	else
		tmp = c * ((x * 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[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.8e+158], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1650000000.0], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.16e-92], N[(y1 * N[(j * N[(y3 * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7e-259], N[(j * N[(i * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.89e-44], t$95$1, If[LessEqual[y, 180000.0], N[(t * N[(a * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e+181], t$95$1, N[(c * N[(N[(x * y), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -2.80000000000000001e158

   1. Initial program 22.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 41.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 56.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 56.9%

         \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y - t \cdot z\right) \cdot b\right)} \]

      2. *-commutative 56.9%

         \[\leadsto a \cdot \left(\left(\color{blue}{y \cdot x} - t \cdot z\right) \cdot b\right) \]

   6. Simplified 56.9%

      \[\leadsto \color{blue}{a \cdot \left(\left(y \cdot x - t \cdot z\right) \cdot b\right)} \]

   if -2.80000000000000001e158 < y < -1.65e9

   1. Initial program 44.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 36.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in x around inf 42.9%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 42.9%

         \[\leadsto b \cdot \left(x \cdot \left(\color{blue}{y \cdot a} - j \cdot y0\right)\right) \]

   6. Simplified 42.9%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)} \]

   if -1.65e9 < y < -1.1599999999999999e-92

   1. Initial program 33.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 33.5%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in y4 around inf 34.2%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   5. Taylor expanded in k around 0 30.5%

      \[\leadsto y1 \cdot \color{blue}{\left(-1 \cdot \left(j \cdot \left(y3 \cdot y4\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 30.5%

         \[\leadsto y1 \cdot \color{blue}{\left(-j \cdot \left(y3 \cdot y4\right)\right)} \]

      2. *-commutative 30.5%

         \[\leadsto y1 \cdot \left(-\color{blue}{\left(y3 \cdot y4\right) \cdot j}\right) \]

      3. distribute-rgt-neg-in 30.5%

         \[\leadsto y1 \cdot \color{blue}{\left(\left(y3 \cdot y4\right) \cdot \left(-j\right)\right)} \]

      4. *-commutative 30.5%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot y3\right)} \cdot \left(-j\right)\right) \]

   7. Simplified 30.5%

      \[\leadsto y1 \cdot \color{blue}{\left(\left(y4 \cdot y3\right) \cdot \left(-j\right)\right)} \]

   if -1.1599999999999999e-92 < y < -7.0000000000000005e-259

   1. Initial program 19.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 43.3%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in i around inf 47.2%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in j around inf 35.9%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 35.9%

         \[\leadsto \color{blue}{\left(j \cdot \left(x \cdot y1\right)\right) \cdot i} \]

      2. associate-*l* 43.2%

         \[\leadsto \color{blue}{j \cdot \left(\left(x \cdot y1\right) \cdot i\right)} \]

   7. Simplified 43.2%

      \[\leadsto \color{blue}{j \cdot \left(\left(x \cdot y1\right) \cdot i\right)} \]

   if -7.0000000000000005e-259 < y < 3.8899999999999999e-44 or 1.8e5 < y < 2.5000000000000002e181

   1. Initial program 35.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 39.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in j around inf 35.1%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if 3.8899999999999999e-44 < y < 1.8e5

   1. Initial program 73.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 60.8%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in y5 around inf 41.3%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot j\right) - -1 \cdot \left(a \cdot y2\right)\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 41.3%

         \[\leadsto t \cdot \left(y5 \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j - a \cdot y2\right)\right)}\right) \]

   6. Simplified 41.3%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\right)} \]

   7. Taylor expanded in i around 0 41.3%

      \[\leadsto t \cdot \color{blue}{\left(a \cdot \left(y2 \cdot y5\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 41.3%

         \[\leadsto t \cdot \color{blue}{\left(\left(y2 \cdot y5\right) \cdot a\right)} \]

   9. Simplified 41.3%

      \[\leadsto t \cdot \color{blue}{\left(\left(y2 \cdot y5\right) \cdot a\right)} \]

   if 2.5000000000000002e181 < y

   1. Initial program 16.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around -inf 50.6%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in c around inf 51.0%

      \[\leadsto -1 \cdot \color{blue}{\left(c \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 51.0%

         \[\leadsto -1 \cdot \left(c \cdot \left(i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right)\right) \]

   6. Simplified 51.0%

      \[\leadsto -1 \cdot \color{blue}{\left(c \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right)\right)} \]

   7. Taylor expanded in y around inf 47.7%

      \[\leadsto -1 \cdot \left(c \cdot \color{blue}{\left(i \cdot \left(x \cdot y\right)\right)}\right) \]
   8. Step-by-step derivation

      1. *-commutative 47.7%

         \[\leadsto -1 \cdot \left(c \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot i\right)}\right) \]

   9. Simplified 47.7%

      \[\leadsto -1 \cdot \left(c \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot i\right)}\right) \]
3. Recombined 7 regimes into one program.

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+158}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y \leq -1650000000:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq -1.16 \cdot 10^{-92}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(y3 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-259}:\\ \;\;\;\;j \cdot \left(i \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y \leq 3.89 \cdot 10^{-44}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq 180000:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+181}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(x \cdot y\right) \cdot \left(-i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 27.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{if}\;y0 \leq -9.6 \cdot 10^{-24}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq 5.6 \cdot 10^{-186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y0 \leq 4 \cdot 10^{-145}:\\ \;\;\;\;c \cdot \left(\left(x \cdot y\right) \cdot \left(-i\right)\right)\\ \mathbf{elif}\;y0 \leq 2.2 \cdot 10^{-100}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(y1 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 1.65 \cdot 10^{-57}:\\ \;\;\;\;i \cdot \left(\left(z \cdot y1\right) \cdot \left(-k\right)\right)\\ \mathbf{elif}\;y0 \leq 2.85 \cdot 10^{+107}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y0 \leq 7.5 \cdot 10^{+227}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* y4 (- (* t j) (* y k))))))
   (if (<= y0 -9.6e-24)
     (* b (* j (- (* t y4) (* x y0))))
     (if (<= y0 5.6e-186)
       t_1
       (if (<= y0 4e-145)
         (* c (* (* x y) (- i)))
         (if (<= y0 2.2e-100)
           (* j (* y4 (* y1 (- y3))))
           (if (<= y0 1.65e-57)
             (* i (* (* z y1) (- k)))
             (if (<= y0 2.85e+107)
               (* a (* b (- (* x y) (* z t))))
               (if (<= y0 7.5e+227)
                 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 = b * (y4 * ((t * j) - (y * k)));
	double tmp;
	if (y0 <= -9.6e-24) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y0 <= 5.6e-186) {
		tmp = t_1;
	} else if (y0 <= 4e-145) {
		tmp = c * ((x * y) * -i);
	} else if (y0 <= 2.2e-100) {
		tmp = j * (y4 * (y1 * -y3));
	} else if (y0 <= 1.65e-57) {
		tmp = i * ((z * y1) * -k);
	} else if (y0 <= 2.85e+107) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y0 <= 7.5e+227) {
		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 = b * (y4 * ((t * j) - (y * k)))
    if (y0 <= (-9.6d-24)) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (y0 <= 5.6d-186) then
        tmp = t_1
    else if (y0 <= 4d-145) then
        tmp = c * ((x * y) * -i)
    else if (y0 <= 2.2d-100) then
        tmp = j * (y4 * (y1 * -y3))
    else if (y0 <= 1.65d-57) then
        tmp = i * ((z * y1) * -k)
    else if (y0 <= 2.85d+107) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (y0 <= 7.5d+227) 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 = b * (y4 * ((t * j) - (y * k)));
	double tmp;
	if (y0 <= -9.6e-24) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y0 <= 5.6e-186) {
		tmp = t_1;
	} else if (y0 <= 4e-145) {
		tmp = c * ((x * y) * -i);
	} else if (y0 <= 2.2e-100) {
		tmp = j * (y4 * (y1 * -y3));
	} else if (y0 <= 1.65e-57) {
		tmp = i * ((z * y1) * -k);
	} else if (y0 <= 2.85e+107) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y0 <= 7.5e+227) {
		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 = b * (y4 * ((t * j) - (y * k)))
	tmp = 0
	if y0 <= -9.6e-24:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif y0 <= 5.6e-186:
		tmp = t_1
	elif y0 <= 4e-145:
		tmp = c * ((x * y) * -i)
	elif y0 <= 2.2e-100:
		tmp = j * (y4 * (y1 * -y3))
	elif y0 <= 1.65e-57:
		tmp = i * ((z * y1) * -k)
	elif y0 <= 2.85e+107:
		tmp = a * (b * ((x * y) - (z * t)))
	elif y0 <= 7.5e+227:
		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(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))))
	tmp = 0.0
	if (y0 <= -9.6e-24)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (y0 <= 5.6e-186)
		tmp = t_1;
	elseif (y0 <= 4e-145)
		tmp = Float64(c * Float64(Float64(x * y) * Float64(-i)));
	elseif (y0 <= 2.2e-100)
		tmp = Float64(j * Float64(y4 * Float64(y1 * Float64(-y3))));
	elseif (y0 <= 1.65e-57)
		tmp = Float64(i * Float64(Float64(z * y1) * Float64(-k)));
	elseif (y0 <= 2.85e+107)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y0 <= 7.5e+227)
		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 = b * (y4 * ((t * j) - (y * k)));
	tmp = 0.0;
	if (y0 <= -9.6e-24)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (y0 <= 5.6e-186)
		tmp = t_1;
	elseif (y0 <= 4e-145)
		tmp = c * ((x * y) * -i);
	elseif (y0 <= 2.2e-100)
		tmp = j * (y4 * (y1 * -y3));
	elseif (y0 <= 1.65e-57)
		tmp = i * ((z * y1) * -k);
	elseif (y0 <= 2.85e+107)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (y0 <= 7.5e+227)
		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[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -9.6e-24], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 5.6e-186], t$95$1, If[LessEqual[y0, 4e-145], N[(c * N[(N[(x * y), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 2.2e-100], N[(j * N[(y4 * N[(y1 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.65e-57], N[(i * N[(N[(z * y1), $MachinePrecision] * (-k)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 2.85e+107], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 7.5e+227], t$95$1, N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y0 < -9.5999999999999993e-24

   1. Initial program 37.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 40.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in j around inf 35.8%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if -9.5999999999999993e-24 < y0 < 5.59999999999999966e-186 or 2.84999999999999986e107 < y0 < 7.5000000000000003e227

   1. Initial program 34.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 31.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y4 around inf 35.6%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   if 5.59999999999999966e-186 < y0 < 3.99999999999999966e-145

   1. Initial program 27.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around -inf 46.1%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in c around inf 64.1%

      \[\leadsto -1 \cdot \color{blue}{\left(c \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 64.1%

         \[\leadsto -1 \cdot \left(c \cdot \left(i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right)\right) \]

   6. Simplified 64.1%

      \[\leadsto -1 \cdot \color{blue}{\left(c \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right)\right)} \]

   7. Taylor expanded in y around inf 55.7%

      \[\leadsto -1 \cdot \left(c \cdot \color{blue}{\left(i \cdot \left(x \cdot y\right)\right)}\right) \]
   8. Step-by-step derivation

      1. *-commutative 55.7%

         \[\leadsto -1 \cdot \left(c \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot i\right)}\right) \]

   9. Simplified 55.7%

      \[\leadsto -1 \cdot \left(c \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot i\right)}\right) \]

   if 3.99999999999999966e-145 < y0 < 2.19999999999999989e-100

   1. Initial program 44.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 56.7%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in y4 around inf 46.6%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   5. Taylor expanded in k around 0 46.1%

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(y1 \cdot \left(y3 \cdot y4\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 46.1%

         \[\leadsto \color{blue}{-j \cdot \left(y1 \cdot \left(y3 \cdot y4\right)\right)} \]

      2. *-commutative 46.1%

         \[\leadsto -\color{blue}{\left(y1 \cdot \left(y3 \cdot y4\right)\right) \cdot j} \]

      3. distribute-rgt-neg-in 46.1%

         \[\leadsto \color{blue}{\left(y1 \cdot \left(y3 \cdot y4\right)\right) \cdot \left(-j\right)} \]

      4. associate-*r* 56.6%

         \[\leadsto \color{blue}{\left(\left(y1 \cdot y3\right) \cdot y4\right)} \cdot \left(-j\right) \]

   7. Simplified 56.6%

      \[\leadsto \color{blue}{\left(\left(y1 \cdot y3\right) \cdot y4\right) \cdot \left(-j\right)} \]

   if 2.19999999999999989e-100 < y0 < 1.6499999999999999e-57

   1. Initial program 16.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 41.7%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in i around inf 67.0%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in j around 0 75.4%

      \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y1 \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 75.4%

         \[\leadsto i \cdot \color{blue}{\left(-k \cdot \left(y1 \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 75.4%

         \[\leadsto i \cdot \color{blue}{\left(k \cdot \left(-y1 \cdot z\right)\right)} \]

      3. distribute-rgt-neg-in 75.4%

         \[\leadsto i \cdot \left(k \cdot \color{blue}{\left(y1 \cdot \left(-z\right)\right)}\right) \]

   7. Simplified 75.4%

      \[\leadsto i \cdot \color{blue}{\left(k \cdot \left(y1 \cdot \left(-z\right)\right)\right)} \]

   if 1.6499999999999999e-57 < y0 < 2.84999999999999986e107

   1. Initial program 32.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 32.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 39.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 39.9%

         \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y - t \cdot z\right) \cdot b\right)} \]

      2. *-commutative 39.9%

         \[\leadsto a \cdot \left(\left(\color{blue}{y \cdot x} - t \cdot z\right) \cdot b\right) \]

   6. Simplified 39.9%

      \[\leadsto \color{blue}{a \cdot \left(\left(y \cdot x - t \cdot z\right) \cdot b\right)} \]

   if 7.5000000000000003e227 < y0

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 60.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in x around inf 51.1%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 51.1%

         \[\leadsto b \cdot \left(x \cdot \left(\color{blue}{y \cdot a} - j \cdot y0\right)\right) \]

   6. Simplified 51.1%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -9.6 \cdot 10^{-24}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq 5.6 \cdot 10^{-186}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y0 \leq 4 \cdot 10^{-145}:\\ \;\;\;\;c \cdot \left(\left(x \cdot y\right) \cdot \left(-i\right)\right)\\ \mathbf{elif}\;y0 \leq 2.2 \cdot 10^{-100}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(y1 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 1.65 \cdot 10^{-57}:\\ \;\;\;\;i \cdot \left(\left(z \cdot y1\right) \cdot \left(-k\right)\right)\\ \mathbf{elif}\;y0 \leq 2.85 \cdot 10^{+107}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y0 \leq 7.5 \cdot 10^{+227}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 28.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{if}\;y2 \leq -2.2 \cdot 10^{+36}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;y2 \leq -7 \cdot 10^{+15}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -4.1 \cdot 10^{-23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq -1.66 \cdot 10^{-127}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq -6 \cdot 10^{-151}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 5.3 \cdot 10^{-76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq 5.4 \cdot 10^{+219}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (* i (- (* y y5) (* z y1))))))
   (if (<= y2 -2.2e+36)
     (* k (* y1 (- (* y2 y4) (* z i))))
     (if (<= y2 -7e+15)
       (* t (* y5 (* a y2)))
       (if (<= y2 -4.1e-23)
         t_1
         (if (<= y2 -1.66e-127)
           (* b (* y0 (- (* z k) (* x j))))
           (if (<= y2 -6e-151)
             (* b (* j (- (* t y4) (* x y0))))
             (if (<= y2 5.3e-76)
               t_1
               (if (<= y2 5.4e+219)
                 (* k (* y4 (- (* y1 y2) (* y b))))
                 (* c (* (* z t) 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 = k * (i * ((y * y5) - (z * y1)));
	double tmp;
	if (y2 <= -2.2e+36) {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	} else if (y2 <= -7e+15) {
		tmp = t * (y5 * (a * y2));
	} else if (y2 <= -4.1e-23) {
		tmp = t_1;
	} else if (y2 <= -1.66e-127) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y2 <= -6e-151) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y2 <= 5.3e-76) {
		tmp = t_1;
	} else if (y2 <= 5.4e+219) {
		tmp = k * (y4 * ((y1 * y2) - (y * b)));
	} else {
		tmp = c * ((z * t) * 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) :: tmp
    t_1 = k * (i * ((y * y5) - (z * y1)))
    if (y2 <= (-2.2d+36)) then
        tmp = k * (y1 * ((y2 * y4) - (z * i)))
    else if (y2 <= (-7d+15)) then
        tmp = t * (y5 * (a * y2))
    else if (y2 <= (-4.1d-23)) then
        tmp = t_1
    else if (y2 <= (-1.66d-127)) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (y2 <= (-6d-151)) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (y2 <= 5.3d-76) then
        tmp = t_1
    else if (y2 <= 5.4d+219) then
        tmp = k * (y4 * ((y1 * y2) - (y * b)))
    else
        tmp = c * ((z * t) * 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 = k * (i * ((y * y5) - (z * y1)));
	double tmp;
	if (y2 <= -2.2e+36) {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	} else if (y2 <= -7e+15) {
		tmp = t * (y5 * (a * y2));
	} else if (y2 <= -4.1e-23) {
		tmp = t_1;
	} else if (y2 <= -1.66e-127) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y2 <= -6e-151) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y2 <= 5.3e-76) {
		tmp = t_1;
	} else if (y2 <= 5.4e+219) {
		tmp = k * (y4 * ((y1 * y2) - (y * b)));
	} else {
		tmp = c * ((z * t) * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = k * (i * ((y * y5) - (z * y1)))
	tmp = 0
	if y2 <= -2.2e+36:
		tmp = k * (y1 * ((y2 * y4) - (z * i)))
	elif y2 <= -7e+15:
		tmp = t * (y5 * (a * y2))
	elif y2 <= -4.1e-23:
		tmp = t_1
	elif y2 <= -1.66e-127:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif y2 <= -6e-151:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif y2 <= 5.3e-76:
		tmp = t_1
	elif y2 <= 5.4e+219:
		tmp = k * (y4 * ((y1 * y2) - (y * b)))
	else:
		tmp = c * ((z * t) * 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(k * Float64(i * Float64(Float64(y * y5) - Float64(z * y1))))
	tmp = 0.0
	if (y2 <= -2.2e+36)
		tmp = Float64(k * Float64(y1 * Float64(Float64(y2 * y4) - Float64(z * i))));
	elseif (y2 <= -7e+15)
		tmp = Float64(t * Float64(y5 * Float64(a * y2)));
	elseif (y2 <= -4.1e-23)
		tmp = t_1;
	elseif (y2 <= -1.66e-127)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (y2 <= -6e-151)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (y2 <= 5.3e-76)
		tmp = t_1;
	elseif (y2 <= 5.4e+219)
		tmp = Float64(k * Float64(y4 * Float64(Float64(y1 * y2) - Float64(y * b))));
	else
		tmp = Float64(c * Float64(Float64(z * t) * 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 = k * (i * ((y * y5) - (z * y1)));
	tmp = 0.0;
	if (y2 <= -2.2e+36)
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	elseif (y2 <= -7e+15)
		tmp = t * (y5 * (a * y2));
	elseif (y2 <= -4.1e-23)
		tmp = t_1;
	elseif (y2 <= -1.66e-127)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (y2 <= -6e-151)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (y2 <= 5.3e-76)
		tmp = t_1;
	elseif (y2 <= 5.4e+219)
		tmp = k * (y4 * ((y1 * y2) - (y * b)));
	else
		tmp = c * ((z * t) * 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[(k * N[(i * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -2.2e+36], N[(k * N[(y1 * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -7e+15], N[(t * N[(y5 * N[(a * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -4.1e-23], t$95$1, If[LessEqual[y2, -1.66e-127], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -6e-151], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 5.3e-76], t$95$1, If[LessEqual[y2, 5.4e+219], N[(k * N[(y4 * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(z * t), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y2 < -2.2e36

   1. Initial program 41.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 44.5%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in k around inf 44.7%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4 - i \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 44.7%

         \[\leadsto k \cdot \left(y1 \cdot \left(\color{blue}{y4 \cdot y2} - i \cdot z\right)\right) \]

   6. Simplified 44.7%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y4 \cdot y2 - i \cdot z\right)\right)} \]

   if -2.2e36 < y2 < -7e15

   1. Initial program 0.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 67.0%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in y5 around inf 67.0%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot j\right) - -1 \cdot \left(a \cdot y2\right)\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 67.0%

         \[\leadsto t \cdot \left(y5 \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j - a \cdot y2\right)\right)}\right) \]

   6. Simplified 67.0%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\right)} \]

   7. Taylor expanded in i around 0 83.7%

      \[\leadsto t \cdot \left(y5 \cdot \left(-1 \cdot \color{blue}{\left(-1 \cdot \left(a \cdot y2\right)\right)}\right)\right) \]
   8. Step-by-step derivation

      1. mul-1-neg 83.7%

         \[\leadsto t \cdot \left(y5 \cdot \left(-1 \cdot \color{blue}{\left(-a \cdot y2\right)}\right)\right) \]

      2. distribute-lft-neg-out 83.7%

         \[\leadsto t \cdot \left(y5 \cdot \left(-1 \cdot \color{blue}{\left(\left(-a\right) \cdot y2\right)}\right)\right) \]

      3. *-commutative 83.7%

         \[\leadsto t \cdot \left(y5 \cdot \left(-1 \cdot \color{blue}{\left(y2 \cdot \left(-a\right)\right)}\right)\right) \]

   9. Simplified 83.7%

      \[\leadsto t \cdot \left(y5 \cdot \left(-1 \cdot \color{blue}{\left(y2 \cdot \left(-a\right)\right)}\right)\right) \]

   if -7e15 < y2 < -4.10000000000000029e-23 or -6e-151 < y2 < 5.3e-76

   1. Initial program 38.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 43.6%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   4. Taylor expanded in i around inf 47.8%

      \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 47.8%

         \[\leadsto k \cdot \left(i \cdot \left(\color{blue}{y5 \cdot y} - y1 \cdot z\right)\right) \]

   6. Simplified 47.8%

      \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(y5 \cdot y - y1 \cdot z\right)\right)} \]

   if -4.10000000000000029e-23 < y2 < -1.66000000000000003e-127

   1. Initial program 37.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 52.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y0 around inf 49.0%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 49.0%

         \[\leadsto b \cdot \color{blue}{\left(\left(k \cdot z - j \cdot x\right) \cdot y0\right)} \]

   6. Simplified 49.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot y0\right)} \]

   if -1.66000000000000003e-127 < y2 < -6e-151

   1. Initial program 22.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 44.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in j around inf 56.6%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if 5.3e-76 < y2 < 5.3999999999999998e219

   1. Initial program 27.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 37.7%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   4. Taylor expanded in y4 around inf 43.5%

      \[\leadsto k \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(b \cdot y\right) + y1 \cdot y2\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 43.5%

         \[\leadsto k \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(b \cdot y\right)\right)}\right) \]

      2. mul-1-neg 43.5%

         \[\leadsto k \cdot \left(y4 \cdot \left(y1 \cdot y2 + \color{blue}{\left(-b \cdot y\right)}\right)\right) \]

      3. unsub-neg 43.5%

         \[\leadsto k \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot y2 - b \cdot y\right)}\right) \]

      4. *-commutative 43.5%

         \[\leadsto k \cdot \left(y4 \cdot \left(\color{blue}{y2 \cdot y1} - b \cdot y\right)\right) \]

   6. Simplified 43.5%

      \[\leadsto k \cdot \color{blue}{\left(y4 \cdot \left(y2 \cdot y1 - b \cdot y\right)\right)} \]

   if 5.3999999999999998e219 < y2

   1. Initial program 14.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 64.3%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in z around inf 52.4%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 52.4%

         \[\leadsto \color{blue}{\left(-1 \cdot t\right) \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

      2. neg-mul-1 52.4%

         \[\leadsto \color{blue}{\left(-t\right)} \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) \]

      3. *-commutative 52.4%

         \[\leadsto \left(-t\right) \cdot \left(z \cdot \left(a \cdot b - \color{blue}{i \cdot c}\right)\right) \]

   6. Simplified 52.4%

      \[\leadsto \color{blue}{\left(-t\right) \cdot \left(z \cdot \left(a \cdot b - i \cdot c\right)\right)} \]

   7. Taylor expanded in a around 0 65.0%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 65.0%

         \[\leadsto c \cdot \left(i \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

   9. Simplified 65.0%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(z \cdot t\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 48.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -2.2 \cdot 10^{+36}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;y2 \leq -7 \cdot 10^{+15}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -4.1 \cdot 10^{-23}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq -1.66 \cdot 10^{-127}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq -6 \cdot 10^{-151}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 5.3 \cdot 10^{-76}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq 5.4 \cdot 10^{+219}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 28.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(j \cdot y0\right) \cdot \left(y3 \cdot y5 - x \cdot b\right)\\ t_2 := k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{if}\;b \leq -1.15 \cdot 10^{+209}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{+138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{+114}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -6 \cdot 10^{-91}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq -1.46 \cdot 10^{-248}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+25}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+169}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* j y0) (- (* y3 y5) (* x b))))
        (t_2 (* k (* z (- (* b y0) (* i y1))))))
   (if (<= b -1.15e+209)
     (* k (* y4 (- (* y1 y2) (* y b))))
     (if (<= b -1.15e+138)
       t_1
       (if (<= b -5.2e+114)
         t_2
         (if (<= b -6e-91)
           (* k (* i (- (* y y5) (* z y1))))
           (if (<= b -1.46e-248)
             t_1
             (if (<= b 1.8e+25)
               (* k (* y1 (- (* y2 y4) (* z i))))
               (if (<= b 2.5e+169) (* a (* b (- (* x y) (* z t)))) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (j * y0) * ((y3 * y5) - (x * b));
	double t_2 = k * (z * ((b * y0) - (i * y1)));
	double tmp;
	if (b <= -1.15e+209) {
		tmp = k * (y4 * ((y1 * y2) - (y * b)));
	} else if (b <= -1.15e+138) {
		tmp = t_1;
	} else if (b <= -5.2e+114) {
		tmp = t_2;
	} else if (b <= -6e-91) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (b <= -1.46e-248) {
		tmp = t_1;
	} else if (b <= 1.8e+25) {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	} else if (b <= 2.5e+169) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (j * y0) * ((y3 * y5) - (x * b))
    t_2 = k * (z * ((b * y0) - (i * y1)))
    if (b <= (-1.15d+209)) then
        tmp = k * (y4 * ((y1 * y2) - (y * b)))
    else if (b <= (-1.15d+138)) then
        tmp = t_1
    else if (b <= (-5.2d+114)) then
        tmp = t_2
    else if (b <= (-6d-91)) then
        tmp = k * (i * ((y * y5) - (z * y1)))
    else if (b <= (-1.46d-248)) then
        tmp = t_1
    else if (b <= 1.8d+25) then
        tmp = k * (y1 * ((y2 * y4) - (z * i)))
    else if (b <= 2.5d+169) then
        tmp = a * (b * ((x * y) - (z * t)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (j * y0) * ((y3 * y5) - (x * b));
	double t_2 = k * (z * ((b * y0) - (i * y1)));
	double tmp;
	if (b <= -1.15e+209) {
		tmp = k * (y4 * ((y1 * y2) - (y * b)));
	} else if (b <= -1.15e+138) {
		tmp = t_1;
	} else if (b <= -5.2e+114) {
		tmp = t_2;
	} else if (b <= -6e-91) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (b <= -1.46e-248) {
		tmp = t_1;
	} else if (b <= 1.8e+25) {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	} else if (b <= 2.5e+169) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (j * y0) * ((y3 * y5) - (x * b))
	t_2 = k * (z * ((b * y0) - (i * y1)))
	tmp = 0
	if b <= -1.15e+209:
		tmp = k * (y4 * ((y1 * y2) - (y * b)))
	elif b <= -1.15e+138:
		tmp = t_1
	elif b <= -5.2e+114:
		tmp = t_2
	elif b <= -6e-91:
		tmp = k * (i * ((y * y5) - (z * y1)))
	elif b <= -1.46e-248:
		tmp = t_1
	elif b <= 1.8e+25:
		tmp = k * (y1 * ((y2 * y4) - (z * i)))
	elif b <= 2.5e+169:
		tmp = a * (b * ((x * y) - (z * t)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(j * y0) * Float64(Float64(y3 * y5) - Float64(x * b)))
	t_2 = Float64(k * Float64(z * Float64(Float64(b * y0) - Float64(i * y1))))
	tmp = 0.0
	if (b <= -1.15e+209)
		tmp = Float64(k * Float64(y4 * Float64(Float64(y1 * y2) - Float64(y * b))));
	elseif (b <= -1.15e+138)
		tmp = t_1;
	elseif (b <= -5.2e+114)
		tmp = t_2;
	elseif (b <= -6e-91)
		tmp = Float64(k * Float64(i * Float64(Float64(y * y5) - Float64(z * y1))));
	elseif (b <= -1.46e-248)
		tmp = t_1;
	elseif (b <= 1.8e+25)
		tmp = Float64(k * Float64(y1 * Float64(Float64(y2 * y4) - Float64(z * i))));
	elseif (b <= 2.5e+169)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (j * y0) * ((y3 * y5) - (x * b));
	t_2 = k * (z * ((b * y0) - (i * y1)));
	tmp = 0.0;
	if (b <= -1.15e+209)
		tmp = k * (y4 * ((y1 * y2) - (y * b)));
	elseif (b <= -1.15e+138)
		tmp = t_1;
	elseif (b <= -5.2e+114)
		tmp = t_2;
	elseif (b <= -6e-91)
		tmp = k * (i * ((y * y5) - (z * y1)));
	elseif (b <= -1.46e-248)
		tmp = t_1;
	elseif (b <= 1.8e+25)
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	elseif (b <= 2.5e+169)
		tmp = a * (b * ((x * y) - (z * t)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(j * y0), $MachinePrecision] * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.15e+209], N[(k * N[(y4 * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.15e+138], t$95$1, If[LessEqual[b, -5.2e+114], t$95$2, If[LessEqual[b, -6e-91], N[(k * N[(i * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.46e-248], t$95$1, If[LessEqual[b, 1.8e+25], N[(k * N[(y1 * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.5e+169], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -1.15000000000000005e209

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 55.0%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   4. Taylor expanded in y4 around inf 60.4%

      \[\leadsto k \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(b \cdot y\right) + y1 \cdot y2\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 60.4%

         \[\leadsto k \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(b \cdot y\right)\right)}\right) \]

      2. mul-1-neg 60.4%

         \[\leadsto k \cdot \left(y4 \cdot \left(y1 \cdot y2 + \color{blue}{\left(-b \cdot y\right)}\right)\right) \]

      3. unsub-neg 60.4%

         \[\leadsto k \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot y2 - b \cdot y\right)}\right) \]

      4. *-commutative 60.4%

         \[\leadsto k \cdot \left(y4 \cdot \left(\color{blue}{y2 \cdot y1} - b \cdot y\right)\right) \]

   6. Simplified 60.4%

      \[\leadsto k \cdot \color{blue}{\left(y4 \cdot \left(y2 \cdot y1 - b \cdot y\right)\right)} \]

   if -1.15000000000000005e209 < b < -1.15000000000000004e138 or -6.0000000000000004e-91 < b < -1.4599999999999999e-248

   1. Initial program 43.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 49.5%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in j around inf 57.5%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 55.4%

         \[\leadsto \color{blue}{\left(j \cdot y0\right) \cdot \left(y3 \cdot y5 - b \cdot x\right)} \]

      2. *-commutative 55.4%

         \[\leadsto \left(j \cdot y0\right) \cdot \left(y3 \cdot y5 - \color{blue}{x \cdot b}\right) \]

   6. Simplified 55.4%

      \[\leadsto \color{blue}{\left(j \cdot y0\right) \cdot \left(y3 \cdot y5 - x \cdot b\right)} \]

   if -1.15000000000000004e138 < b < -5.2000000000000001e114 or 2.50000000000000009e169 < b

   1. Initial program 21.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 39.5%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   4. Taylor expanded in z around inf 70.0%

      \[\leadsto \color{blue}{k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 70.0%

         \[\leadsto k \cdot \left(z \cdot \left(\color{blue}{y0 \cdot b} - i \cdot y1\right)\right) \]

      2. *-commutative 70.0%

         \[\leadsto k \cdot \left(z \cdot \left(y0 \cdot b - \color{blue}{y1 \cdot i}\right)\right) \]

   6. Simplified 70.0%

      \[\leadsto \color{blue}{k \cdot \left(z \cdot \left(y0 \cdot b - y1 \cdot i\right)\right)} \]

   if -5.2000000000000001e114 < b < -6.0000000000000004e-91

   1. Initial program 39.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 43.7%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   4. Taylor expanded in i around inf 39.9%

      \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 39.9%

         \[\leadsto k \cdot \left(i \cdot \left(\color{blue}{y5 \cdot y} - y1 \cdot z\right)\right) \]

   6. Simplified 39.9%

      \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(y5 \cdot y - y1 \cdot z\right)\right)} \]

   if -1.4599999999999999e-248 < b < 1.80000000000000008e25

   1. Initial program 30.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 45.4%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in k around inf 44.2%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4 - i \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 44.2%

         \[\leadsto k \cdot \left(y1 \cdot \left(\color{blue}{y4 \cdot y2} - i \cdot z\right)\right) \]

   6. Simplified 44.2%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y4 \cdot y2 - i \cdot z\right)\right)} \]

   if 1.80000000000000008e25 < b < 2.50000000000000009e169

   1. Initial program 35.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 43.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 41.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 41.9%

         \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y - t \cdot z\right) \cdot b\right)} \]

      2. *-commutative 41.9%

         \[\leadsto a \cdot \left(\left(\color{blue}{y \cdot x} - t \cdot z\right) \cdot b\right) \]

   6. Simplified 41.9%

      \[\leadsto \color{blue}{a \cdot \left(\left(y \cdot x - t \cdot z\right) \cdot b\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+209}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{+138}:\\ \;\;\;\;\left(j \cdot y0\right) \cdot \left(y3 \cdot y5 - x \cdot b\right)\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{+114}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq -6 \cdot 10^{-91}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq -1.46 \cdot 10^{-248}:\\ \;\;\;\;\left(j \cdot y0\right) \cdot \left(y3 \cdot y5 - x \cdot b\right)\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+25}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+169}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 29.7% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{if}\;y \leq -6.4 \cdot 10^{+158}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{+46}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-160}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-25}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+181}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+183}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(x \cdot y\right) \cdot \left(-i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* t (- (* b y4) (* i y5))))))
   (if (<= y -6.4e+158)
     (* a (* b (- (* x y) (* z t))))
     (if (<= y -3.9e+46)
       (* b (* x (- (* y a) (* j y0))))
       (if (<= y -3.6e-60)
         t_1
         (if (<= y 4.5e-160)
           (* i (* y1 (- (* x j) (* z k))))
           (if (<= y 6.5e-25)
             (* b (* y0 (- (* z k) (* x j))))
             (if (<= y 1.2e+181)
               t_1
               (if (<= y 7e+183)
                 (* a (* x (* y b)))
                 (* c (* (* x 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 = j * (t * ((b * y4) - (i * y5)));
	double tmp;
	if (y <= -6.4e+158) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y <= -3.9e+46) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y <= -3.6e-60) {
		tmp = t_1;
	} else if (y <= 4.5e-160) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (y <= 6.5e-25) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y <= 1.2e+181) {
		tmp = t_1;
	} else if (y <= 7e+183) {
		tmp = a * (x * (y * b));
	} else {
		tmp = c * ((x * 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) :: tmp
    t_1 = j * (t * ((b * y4) - (i * y5)))
    if (y <= (-6.4d+158)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (y <= (-3.9d+46)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (y <= (-3.6d-60)) then
        tmp = t_1
    else if (y <= 4.5d-160) then
        tmp = i * (y1 * ((x * j) - (z * k)))
    else if (y <= 6.5d-25) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (y <= 1.2d+181) then
        tmp = t_1
    else if (y <= 7d+183) then
        tmp = a * (x * (y * b))
    else
        tmp = c * ((x * 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 = j * (t * ((b * y4) - (i * y5)));
	double tmp;
	if (y <= -6.4e+158) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y <= -3.9e+46) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y <= -3.6e-60) {
		tmp = t_1;
	} else if (y <= 4.5e-160) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (y <= 6.5e-25) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y <= 1.2e+181) {
		tmp = t_1;
	} else if (y <= 7e+183) {
		tmp = a * (x * (y * b));
	} else {
		tmp = c * ((x * 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 = j * (t * ((b * y4) - (i * y5)))
	tmp = 0
	if y <= -6.4e+158:
		tmp = a * (b * ((x * y) - (z * t)))
	elif y <= -3.9e+46:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif y <= -3.6e-60:
		tmp = t_1
	elif y <= 4.5e-160:
		tmp = i * (y1 * ((x * j) - (z * k)))
	elif y <= 6.5e-25:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif y <= 1.2e+181:
		tmp = t_1
	elif y <= 7e+183:
		tmp = a * (x * (y * b))
	else:
		tmp = c * ((x * 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(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))))
	tmp = 0.0
	if (y <= -6.4e+158)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y <= -3.9e+46)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (y <= -3.6e-60)
		tmp = t_1;
	elseif (y <= 4.5e-160)
		tmp = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))));
	elseif (y <= 6.5e-25)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (y <= 1.2e+181)
		tmp = t_1;
	elseif (y <= 7e+183)
		tmp = Float64(a * Float64(x * Float64(y * b)));
	else
		tmp = Float64(c * Float64(Float64(x * y) * Float64(-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 = j * (t * ((b * y4) - (i * y5)));
	tmp = 0.0;
	if (y <= -6.4e+158)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (y <= -3.9e+46)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (y <= -3.6e-60)
		tmp = t_1;
	elseif (y <= 4.5e-160)
		tmp = i * (y1 * ((x * j) - (z * k)));
	elseif (y <= 6.5e-25)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (y <= 1.2e+181)
		tmp = t_1;
	elseif (y <= 7e+183)
		tmp = a * (x * (y * b));
	else
		tmp = c * ((x * 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[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.4e+158], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.9e+46], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.6e-60], t$95$1, If[LessEqual[y, 4.5e-160], N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e-25], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+181], t$95$1, If[LessEqual[y, 7e+183], N[(a * N[(x * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(x * y), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -6.39999999999999989e158

   1. Initial program 22.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 41.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 56.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 56.9%

         \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y - t \cdot z\right) \cdot b\right)} \]

      2. *-commutative 56.9%

         \[\leadsto a \cdot \left(\left(\color{blue}{y \cdot x} - t \cdot z\right) \cdot b\right) \]

   6. Simplified 56.9%

      \[\leadsto \color{blue}{a \cdot \left(\left(y \cdot x - t \cdot z\right) \cdot b\right)} \]

   if -6.39999999999999989e158 < y < -3.89999999999999995e46

   1. Initial program 50.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 39.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in x around inf 47.1%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 47.1%

         \[\leadsto b \cdot \left(x \cdot \left(\color{blue}{y \cdot a} - j \cdot y0\right)\right) \]

   6. Simplified 47.1%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)} \]

   if -3.89999999999999995e46 < y < -3.6e-60 or 6.5e-25 < y < 1.20000000000000001e181

   1. Initial program 37.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 51.5%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. 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 -3.6e-60 < y < 4.50000000000000026e-160

   1. Initial program 34.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 44.0%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in i around inf 41.7%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   if 4.50000000000000026e-160 < y < 6.5e-25

   1. Initial program 35.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 45.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y0 around inf 43.5%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 43.5%

         \[\leadsto b \cdot \color{blue}{\left(\left(k \cdot z - j \cdot x\right) \cdot y0\right)} \]

   6. Simplified 43.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot y0\right)} \]

   if 1.20000000000000001e181 < y < 6.99999999999999974e183

   1. Initial program 0.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 50.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 50.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 50.5%

         \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y - t \cdot z\right) \cdot b\right)} \]

      2. *-commutative 50.5%

         \[\leadsto a \cdot \left(\left(\color{blue}{y \cdot x} - t \cdot z\right) \cdot b\right) \]

   6. Simplified 50.5%

      \[\leadsto \color{blue}{a \cdot \left(\left(y \cdot x - t \cdot z\right) \cdot b\right)} \]

   7. Taylor expanded in y around inf 51.1%

      \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot y\right)} \cdot b\right) \]
   8. Step-by-step derivation

      1. *-commutative 51.1%

         \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot b\right) \]

   9. Simplified 51.1%

      \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot b\right) \]

   10. Taylor expanded in y around 0 51.1%

       \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 51.1%

          \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot x\right) \cdot y\right)} \]

       2. *-commutative 51.1%

          \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot b\right)} \cdot y\right) \]

       3. associate-*l* 57.1%

          \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

   12. Simplified 57.1%

       \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

   if 6.99999999999999974e183 < y

   1. Initial program 18.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around -inf 50.1%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in c around inf 51.0%

      \[\leadsto -1 \cdot \color{blue}{\left(c \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 51.0%

         \[\leadsto -1 \cdot \left(c \cdot \left(i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right)\right) \]

   6. Simplified 51.0%

      \[\leadsto -1 \cdot \color{blue}{\left(c \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right)\right)} \]

   7. Taylor expanded in y around inf 47.5%

      \[\leadsto -1 \cdot \left(c \cdot \color{blue}{\left(i \cdot \left(x \cdot y\right)\right)}\right) \]
   8. Step-by-step derivation

      1. *-commutative 47.5%

         \[\leadsto -1 \cdot \left(c \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot i\right)}\right) \]

   9. Simplified 47.5%

      \[\leadsto -1 \cdot \left(c \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot i\right)}\right) \]
3. Recombined 7 regimes into one program.

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+158}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{+46}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-60}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-160}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-25}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+181}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+183}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(x \cdot y\right) \cdot \left(-i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 24.3% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{if}\;y0 \leq -1.1 \cdot 10^{-15}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -7.2 \cdot 10^{-72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y0 \leq -3.9 \cdot 10^{-103}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq -3.4 \cdot 10^{-299}:\\ \;\;\;\;\left(-t\right) \cdot \left(i \cdot \left(j \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 1.7 \cdot 10^{-166}:\\ \;\;\;\;c \cdot \left(\left(x \cdot y\right) \cdot \left(-i\right)\right)\\ \mathbf{elif}\;y0 \leq 9.5 \cdot 10^{-60}:\\ \;\;\;\;i \cdot \left(\left(z \cdot y1\right) \cdot \left(-k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* b (- (* x y) (* z t))))))
   (if (<= y0 -1.1e-15)
     (* b (* j (- (* t y4) (* x y0))))
     (if (<= y0 -7.2e-72)
       t_1
       (if (<= y0 -3.9e-103)
         (* k (* y4 (* y1 y2)))
         (if (<= y0 -3.4e-299)
           (* (- t) (* i (* j y5)))
           (if (<= y0 1.7e-166)
             (* c (* (* x y) (- i)))
             (if (<= y0 9.5e-60) (* i (* (* z y1) (- k))) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (b * ((x * y) - (z * t)));
	double tmp;
	if (y0 <= -1.1e-15) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y0 <= -7.2e-72) {
		tmp = t_1;
	} else if (y0 <= -3.9e-103) {
		tmp = k * (y4 * (y1 * y2));
	} else if (y0 <= -3.4e-299) {
		tmp = -t * (i * (j * y5));
	} else if (y0 <= 1.7e-166) {
		tmp = c * ((x * y) * -i);
	} else if (y0 <= 9.5e-60) {
		tmp = i * ((z * y1) * -k);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (b * ((x * y) - (z * t)))
    if (y0 <= (-1.1d-15)) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (y0 <= (-7.2d-72)) then
        tmp = t_1
    else if (y0 <= (-3.9d-103)) then
        tmp = k * (y4 * (y1 * y2))
    else if (y0 <= (-3.4d-299)) then
        tmp = -t * (i * (j * y5))
    else if (y0 <= 1.7d-166) then
        tmp = c * ((x * y) * -i)
    else if (y0 <= 9.5d-60) then
        tmp = i * ((z * y1) * -k)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (b * ((x * y) - (z * t)));
	double tmp;
	if (y0 <= -1.1e-15) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y0 <= -7.2e-72) {
		tmp = t_1;
	} else if (y0 <= -3.9e-103) {
		tmp = k * (y4 * (y1 * y2));
	} else if (y0 <= -3.4e-299) {
		tmp = -t * (i * (j * y5));
	} else if (y0 <= 1.7e-166) {
		tmp = c * ((x * y) * -i);
	} else if (y0 <= 9.5e-60) {
		tmp = i * ((z * y1) * -k);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (b * ((x * y) - (z * t)))
	tmp = 0
	if y0 <= -1.1e-15:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif y0 <= -7.2e-72:
		tmp = t_1
	elif y0 <= -3.9e-103:
		tmp = k * (y4 * (y1 * y2))
	elif y0 <= -3.4e-299:
		tmp = -t * (i * (j * y5))
	elif y0 <= 1.7e-166:
		tmp = c * ((x * y) * -i)
	elif y0 <= 9.5e-60:
		tmp = i * ((z * y1) * -k)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))))
	tmp = 0.0
	if (y0 <= -1.1e-15)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (y0 <= -7.2e-72)
		tmp = t_1;
	elseif (y0 <= -3.9e-103)
		tmp = Float64(k * Float64(y4 * Float64(y1 * y2)));
	elseif (y0 <= -3.4e-299)
		tmp = Float64(Float64(-t) * Float64(i * Float64(j * y5)));
	elseif (y0 <= 1.7e-166)
		tmp = Float64(c * Float64(Float64(x * y) * Float64(-i)));
	elseif (y0 <= 9.5e-60)
		tmp = Float64(i * Float64(Float64(z * y1) * Float64(-k)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (b * ((x * y) - (z * t)));
	tmp = 0.0;
	if (y0 <= -1.1e-15)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (y0 <= -7.2e-72)
		tmp = t_1;
	elseif (y0 <= -3.9e-103)
		tmp = k * (y4 * (y1 * y2));
	elseif (y0 <= -3.4e-299)
		tmp = -t * (i * (j * y5));
	elseif (y0 <= 1.7e-166)
		tmp = c * ((x * y) * -i);
	elseif (y0 <= 9.5e-60)
		tmp = i * ((z * y1) * -k);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -1.1e-15], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -7.2e-72], t$95$1, If[LessEqual[y0, -3.9e-103], N[(k * N[(y4 * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -3.4e-299], N[((-t) * N[(i * N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.7e-166], N[(c * N[(N[(x * y), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 9.5e-60], N[(i * N[(N[(z * y1), $MachinePrecision] * (-k)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y0 < -1.09999999999999993e-15

   1. Initial program 37.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 41.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in j around inf 36.3%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if -1.09999999999999993e-15 < y0 < -7.2e-72 or 9.49999999999999958e-60 < y0

   1. Initial program 26.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 43.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 37.4%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 37.4%

         \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y - t \cdot z\right) \cdot b\right)} \]

      2. *-commutative 37.4%

         \[\leadsto a \cdot \left(\left(\color{blue}{y \cdot x} - t \cdot z\right) \cdot b\right) \]

   6. Simplified 37.4%

      \[\leadsto \color{blue}{a \cdot \left(\left(y \cdot x - t \cdot z\right) \cdot b\right)} \]

   if -7.2e-72 < y0 < -3.9000000000000002e-103

   1. Initial program 29.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 16.6%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in y4 around inf 29.8%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 29.8%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 43.8%

         \[\leadsto k \cdot \color{blue}{\left(\left(y1 \cdot y2\right) \cdot y4\right)} \]

      2. *-commutative 43.8%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot y1\right)} \cdot y4\right) \]

   7. Simplified 43.8%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot y1\right) \cdot y4\right)} \]

   if -3.9000000000000002e-103 < y0 < -3.3999999999999998e-299

   1. Initial program 53.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 51.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in y5 around inf 35.4%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot j\right) - -1 \cdot \left(a \cdot y2\right)\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 35.4%

         \[\leadsto t \cdot \left(y5 \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j - a \cdot y2\right)\right)}\right) \]

   6. Simplified 35.4%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\right)} \]

   7. Taylor expanded in i around inf 32.7%

      \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y5\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 32.7%

         \[\leadsto t \cdot \color{blue}{\left(-i \cdot \left(j \cdot y5\right)\right)} \]

      2. distribute-rgt-neg-in 32.7%

         \[\leadsto t \cdot \color{blue}{\left(i \cdot \left(-j \cdot y5\right)\right)} \]

      3. *-commutative 32.7%

         \[\leadsto t \cdot \left(i \cdot \left(-\color{blue}{y5 \cdot j}\right)\right) \]

   9. Simplified 32.7%

      \[\leadsto t \cdot \color{blue}{\left(i \cdot \left(-y5 \cdot j\right)\right)} \]

   if -3.3999999999999998e-299 < y0 < 1.6999999999999999e-166

   1. Initial program 21.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around -inf 46.0%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in c around inf 52.6%

      \[\leadsto -1 \cdot \color{blue}{\left(c \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 52.6%

         \[\leadsto -1 \cdot \left(c \cdot \left(i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right)\right) \]

   6. Simplified 52.6%

      \[\leadsto -1 \cdot \color{blue}{\left(c \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right)\right)} \]

   7. Taylor expanded in y around inf 32.4%

      \[\leadsto -1 \cdot \left(c \cdot \color{blue}{\left(i \cdot \left(x \cdot y\right)\right)}\right) \]
   8. Step-by-step derivation

      1. *-commutative 32.4%

         \[\leadsto -1 \cdot \left(c \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot i\right)}\right) \]

   9. Simplified 32.4%

      \[\leadsto -1 \cdot \left(c \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot i\right)}\right) \]

   if 1.6999999999999999e-166 < y0 < 9.49999999999999958e-60

   1. Initial program 24.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 50.4%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in i around inf 51.0%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in j around 0 51.0%

      \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y1 \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 51.0%

         \[\leadsto i \cdot \color{blue}{\left(-k \cdot \left(y1 \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 51.0%

         \[\leadsto i \cdot \color{blue}{\left(k \cdot \left(-y1 \cdot z\right)\right)} \]

      3. distribute-rgt-neg-in 51.0%

         \[\leadsto i \cdot \left(k \cdot \color{blue}{\left(y1 \cdot \left(-z\right)\right)}\right) \]

   7. Simplified 51.0%

      \[\leadsto i \cdot \color{blue}{\left(k \cdot \left(y1 \cdot \left(-z\right)\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 37.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -1.1 \cdot 10^{-15}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -7.2 \cdot 10^{-72}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y0 \leq -3.9 \cdot 10^{-103}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq -3.4 \cdot 10^{-299}:\\ \;\;\;\;\left(-t\right) \cdot \left(i \cdot \left(j \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 1.7 \cdot 10^{-166}:\\ \;\;\;\;c \cdot \left(\left(x \cdot y\right) \cdot \left(-i\right)\right)\\ \mathbf{elif}\;y0 \leq 9.5 \cdot 10^{-60}:\\ \;\;\;\;i \cdot \left(\left(z \cdot y1\right) \cdot \left(-k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 31: 27.2% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+159}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y \leq -6600000:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-97}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(y3 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-253}:\\ \;\;\;\;j \cdot \left(i \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{-89}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+118}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(x \cdot y\right) \cdot \left(-i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y -2e+159)
   (* a (* b (- (* x y) (* z t))))
   (if (<= y -6600000.0)
     (* b (* x (- (* y a) (* j y0))))
     (if (<= y -6.8e-97)
       (* y1 (* j (* y3 (- y4))))
       (if (<= y -1.3e-253)
         (* j (* i (* x y1)))
         (if (<= y 5.1e-89)
           (* b (* j (- (* t y4) (* x y0))))
           (if (<= y 4.8e+118)
             (* b (* y0 (- (* z k) (* x j))))
             (* c (* (* x 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 (y <= -2e+159) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y <= -6600000.0) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y <= -6.8e-97) {
		tmp = y1 * (j * (y3 * -y4));
	} else if (y <= -1.3e-253) {
		tmp = j * (i * (x * y1));
	} else if (y <= 5.1e-89) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y <= 4.8e+118) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else {
		tmp = c * ((x * 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 (y <= (-2d+159)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (y <= (-6600000.0d0)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (y <= (-6.8d-97)) then
        tmp = y1 * (j * (y3 * -y4))
    else if (y <= (-1.3d-253)) then
        tmp = j * (i * (x * y1))
    else if (y <= 5.1d-89) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (y <= 4.8d+118) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else
        tmp = c * ((x * 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 (y <= -2e+159) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y <= -6600000.0) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y <= -6.8e-97) {
		tmp = y1 * (j * (y3 * -y4));
	} else if (y <= -1.3e-253) {
		tmp = j * (i * (x * y1));
	} else if (y <= 5.1e-89) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y <= 4.8e+118) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else {
		tmp = c * ((x * 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 y <= -2e+159:
		tmp = a * (b * ((x * y) - (z * t)))
	elif y <= -6600000.0:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif y <= -6.8e-97:
		tmp = y1 * (j * (y3 * -y4))
	elif y <= -1.3e-253:
		tmp = j * (i * (x * y1))
	elif y <= 5.1e-89:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif y <= 4.8e+118:
		tmp = b * (y0 * ((z * k) - (x * j)))
	else:
		tmp = c * ((x * 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 (y <= -2e+159)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y <= -6600000.0)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (y <= -6.8e-97)
		tmp = Float64(y1 * Float64(j * Float64(y3 * Float64(-y4))));
	elseif (y <= -1.3e-253)
		tmp = Float64(j * Float64(i * Float64(x * y1)));
	elseif (y <= 5.1e-89)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (y <= 4.8e+118)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	else
		tmp = Float64(c * Float64(Float64(x * y) * Float64(-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 (y <= -2e+159)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (y <= -6600000.0)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (y <= -6.8e-97)
		tmp = y1 * (j * (y3 * -y4));
	elseif (y <= -1.3e-253)
		tmp = j * (i * (x * y1));
	elseif (y <= 5.1e-89)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (y <= 4.8e+118)
		tmp = b * (y0 * ((z * k) - (x * j)));
	else
		tmp = c * ((x * 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[y, -2e+159], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6600000.0], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.8e-97], N[(y1 * N[(j * N[(y3 * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.3e-253], N[(j * N[(i * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.1e-89], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e+118], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(x * y), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -1.9999999999999999e159

   1. Initial program 22.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 41.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 56.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 56.9%

         \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y - t \cdot z\right) \cdot b\right)} \]

      2. *-commutative 56.9%

         \[\leadsto a \cdot \left(\left(\color{blue}{y \cdot x} - t \cdot z\right) \cdot b\right) \]

   6. Simplified 56.9%

      \[\leadsto \color{blue}{a \cdot \left(\left(y \cdot x - t \cdot z\right) \cdot b\right)} \]

   if -1.9999999999999999e159 < y < -6.6e6

   1. Initial program 44.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 36.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in x around inf 42.9%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 42.9%

         \[\leadsto b \cdot \left(x \cdot \left(\color{blue}{y \cdot a} - j \cdot y0\right)\right) \]

   6. Simplified 42.9%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)} \]

   if -6.6e6 < y < -6.7999999999999998e-97

   1. Initial program 33.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 33.5%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in y4 around inf 34.2%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   5. Taylor expanded in k around 0 30.5%

      \[\leadsto y1 \cdot \color{blue}{\left(-1 \cdot \left(j \cdot \left(y3 \cdot y4\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 30.5%

         \[\leadsto y1 \cdot \color{blue}{\left(-j \cdot \left(y3 \cdot y4\right)\right)} \]

      2. *-commutative 30.5%

         \[\leadsto y1 \cdot \left(-\color{blue}{\left(y3 \cdot y4\right) \cdot j}\right) \]

      3. distribute-rgt-neg-in 30.5%

         \[\leadsto y1 \cdot \color{blue}{\left(\left(y3 \cdot y4\right) \cdot \left(-j\right)\right)} \]

      4. *-commutative 30.5%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot y3\right)} \cdot \left(-j\right)\right) \]

   7. Simplified 30.5%

      \[\leadsto y1 \cdot \color{blue}{\left(\left(y4 \cdot y3\right) \cdot \left(-j\right)\right)} \]

   if -6.7999999999999998e-97 < y < -1.3e-253

   1. Initial program 19.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 43.3%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in i around inf 47.2%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in j around inf 35.9%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 35.9%

         \[\leadsto \color{blue}{\left(j \cdot \left(x \cdot y1\right)\right) \cdot i} \]

      2. associate-*l* 43.2%

         \[\leadsto \color{blue}{j \cdot \left(\left(x \cdot y1\right) \cdot i\right)} \]

   7. Simplified 43.2%

      \[\leadsto \color{blue}{j \cdot \left(\left(x \cdot y1\right) \cdot i\right)} \]

   if -1.3e-253 < y < 5.10000000000000004e-89

   1. Initial program 37.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 38.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in j around inf 35.7%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if 5.10000000000000004e-89 < y < 4.8e118

   1. Initial program 46.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 44.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y0 around inf 36.4%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 36.4%

         \[\leadsto b \cdot \color{blue}{\left(\left(k \cdot z - j \cdot x\right) \cdot y0\right)} \]

   6. Simplified 36.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot y0\right)} \]

   if 4.8e118 < y

   1. Initial program 20.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around -inf 49.4%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in c around inf 47.2%

      \[\leadsto -1 \cdot \color{blue}{\left(c \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 47.2%

         \[\leadsto -1 \cdot \left(c \cdot \left(i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right)\right) \]

   6. Simplified 47.2%

      \[\leadsto -1 \cdot \color{blue}{\left(c \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right)\right)} \]

   7. Taylor expanded in y around inf 44.6%

      \[\leadsto -1 \cdot \left(c \cdot \color{blue}{\left(i \cdot \left(x \cdot y\right)\right)}\right) \]
   8. Step-by-step derivation

      1. *-commutative 44.6%

         \[\leadsto -1 \cdot \left(c \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot i\right)}\right) \]

   9. Simplified 44.6%

      \[\leadsto -1 \cdot \left(c \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot i\right)}\right) \]
3. Recombined 7 regimes into one program.

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+159}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y \leq -6600000:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-97}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(y3 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-253}:\\ \;\;\;\;j \cdot \left(i \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{-89}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+118}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(x \cdot y\right) \cdot \left(-i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 32: 28.4% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -1.26 \cdot 10^{+14}:\\ \;\;\;\;k \cdot \left(y5 \cdot \left(y \cdot i - y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -2.8 \cdot 10^{-127}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq -6.8 \cdot 10^{-151}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq -1.9 \cdot 10^{-185}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 3.2 \cdot 10^{-74}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq 2.2 \cdot 10^{+219}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -1.26e+14)
   (* k (* y5 (- (* y i) (* y0 y2))))
   (if (<= y2 -2.8e-127)
     (* b (* y0 (- (* z k) (* x j))))
     (if (<= y2 -6.8e-151)
       (* b (* j (- (* t y4) (* x y0))))
       (if (<= y2 -1.9e-185)
         (* j (* t (- (* b y4) (* i y5))))
         (if (<= y2 3.2e-74)
           (* k (* i (- (* y y5) (* z y1))))
           (if (<= y2 2.2e+219)
             (* k (* y4 (- (* y1 y2) (* y b))))
             (* c (* (* z t) 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 (y2 <= -1.26e+14) {
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	} else if (y2 <= -2.8e-127) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y2 <= -6.8e-151) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y2 <= -1.9e-185) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (y2 <= 3.2e-74) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (y2 <= 2.2e+219) {
		tmp = k * (y4 * ((y1 * y2) - (y * b)));
	} else {
		tmp = c * ((z * t) * 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 (y2 <= (-1.26d+14)) then
        tmp = k * (y5 * ((y * i) - (y0 * y2)))
    else if (y2 <= (-2.8d-127)) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (y2 <= (-6.8d-151)) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (y2 <= (-1.9d-185)) then
        tmp = j * (t * ((b * y4) - (i * y5)))
    else if (y2 <= 3.2d-74) then
        tmp = k * (i * ((y * y5) - (z * y1)))
    else if (y2 <= 2.2d+219) then
        tmp = k * (y4 * ((y1 * y2) - (y * b)))
    else
        tmp = c * ((z * t) * 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 (y2 <= -1.26e+14) {
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	} else if (y2 <= -2.8e-127) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y2 <= -6.8e-151) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y2 <= -1.9e-185) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (y2 <= 3.2e-74) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (y2 <= 2.2e+219) {
		tmp = k * (y4 * ((y1 * y2) - (y * b)));
	} else {
		tmp = c * ((z * t) * 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 y2 <= -1.26e+14:
		tmp = k * (y5 * ((y * i) - (y0 * y2)))
	elif y2 <= -2.8e-127:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif y2 <= -6.8e-151:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif y2 <= -1.9e-185:
		tmp = j * (t * ((b * y4) - (i * y5)))
	elif y2 <= 3.2e-74:
		tmp = k * (i * ((y * y5) - (z * y1)))
	elif y2 <= 2.2e+219:
		tmp = k * (y4 * ((y1 * y2) - (y * b)))
	else:
		tmp = c * ((z * t) * 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 (y2 <= -1.26e+14)
		tmp = Float64(k * Float64(y5 * Float64(Float64(y * i) - Float64(y0 * y2))));
	elseif (y2 <= -2.8e-127)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (y2 <= -6.8e-151)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (y2 <= -1.9e-185)
		tmp = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))));
	elseif (y2 <= 3.2e-74)
		tmp = Float64(k * Float64(i * Float64(Float64(y * y5) - Float64(z * y1))));
	elseif (y2 <= 2.2e+219)
		tmp = Float64(k * Float64(y4 * Float64(Float64(y1 * y2) - Float64(y * b))));
	else
		tmp = Float64(c * Float64(Float64(z * t) * 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 (y2 <= -1.26e+14)
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	elseif (y2 <= -2.8e-127)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (y2 <= -6.8e-151)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (y2 <= -1.9e-185)
		tmp = j * (t * ((b * y4) - (i * y5)));
	elseif (y2 <= 3.2e-74)
		tmp = k * (i * ((y * y5) - (z * y1)));
	elseif (y2 <= 2.2e+219)
		tmp = k * (y4 * ((y1 * y2) - (y * b)));
	else
		tmp = c * ((z * t) * 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[y2, -1.26e+14], N[(k * N[(y5 * N[(N[(y * i), $MachinePrecision] - N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -2.8e-127], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -6.8e-151], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1.9e-185], N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 3.2e-74], N[(k * N[(i * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.2e+219], N[(k * N[(y4 * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(z * t), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y2 < -1.26e14

   1. Initial program 36.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 49.2%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 49.8%

      \[\leadsto k \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 49.8%

         \[\leadsto k \cdot \left(y5 \cdot \color{blue}{\left(i \cdot y + -1 \cdot \left(y0 \cdot y2\right)\right)}\right) \]

      2. mul-1-neg 49.8%

         \[\leadsto k \cdot \left(y5 \cdot \left(i \cdot y + \color{blue}{\left(-y0 \cdot y2\right)}\right)\right) \]

      3. unsub-neg 49.8%

         \[\leadsto k \cdot \left(y5 \cdot \color{blue}{\left(i \cdot y - y0 \cdot y2\right)}\right) \]

      4. *-commutative 49.8%

         \[\leadsto k \cdot \left(y5 \cdot \left(i \cdot y - \color{blue}{y2 \cdot y0}\right)\right) \]

   6. Simplified 49.8%

      \[\leadsto k \cdot \color{blue}{\left(y5 \cdot \left(i \cdot y - y2 \cdot y0\right)\right)} \]

   if -1.26e14 < y2 < -2.8e-127

   1. Initial program 38.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 50.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y0 around inf 47.8%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 47.8%

         \[\leadsto b \cdot \color{blue}{\left(\left(k \cdot z - j \cdot x\right) \cdot y0\right)} \]

   6. Simplified 47.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot y0\right)} \]

   if -2.8e-127 < y2 < -6.8000000000000005e-151

   1. Initial program 22.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 44.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in j around inf 56.6%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if -6.8000000000000005e-151 < y2 < -1.9e-185

   1. Initial program 14.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 42.9%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 72.3%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]

   if -1.9e-185 < y2 < 3.1999999999999999e-74

   1. Initial program 39.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 43.8%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   4. Taylor expanded in i around inf 46.5%

      \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 46.5%

         \[\leadsto k \cdot \left(i \cdot \left(\color{blue}{y5 \cdot y} - y1 \cdot z\right)\right) \]

   6. Simplified 46.5%

      \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(y5 \cdot y - y1 \cdot z\right)\right)} \]

   if 3.1999999999999999e-74 < y2 < 2.2000000000000001e219

   1. Initial program 27.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 37.7%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   4. Taylor expanded in y4 around inf 43.5%

      \[\leadsto k \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(b \cdot y\right) + y1 \cdot y2\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 43.5%

         \[\leadsto k \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(b \cdot y\right)\right)}\right) \]

      2. mul-1-neg 43.5%

         \[\leadsto k \cdot \left(y4 \cdot \left(y1 \cdot y2 + \color{blue}{\left(-b \cdot y\right)}\right)\right) \]

      3. unsub-neg 43.5%

         \[\leadsto k \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot y2 - b \cdot y\right)}\right) \]

      4. *-commutative 43.5%

         \[\leadsto k \cdot \left(y4 \cdot \left(\color{blue}{y2 \cdot y1} - b \cdot y\right)\right) \]

   6. Simplified 43.5%

      \[\leadsto k \cdot \color{blue}{\left(y4 \cdot \left(y2 \cdot y1 - b \cdot y\right)\right)} \]

   if 2.2000000000000001e219 < y2

   1. Initial program 14.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 64.3%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in z around inf 52.4%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 52.4%

         \[\leadsto \color{blue}{\left(-1 \cdot t\right) \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

      2. neg-mul-1 52.4%

         \[\leadsto \color{blue}{\left(-t\right)} \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) \]

      3. *-commutative 52.4%

         \[\leadsto \left(-t\right) \cdot \left(z \cdot \left(a \cdot b - \color{blue}{i \cdot c}\right)\right) \]

   6. Simplified 52.4%

      \[\leadsto \color{blue}{\left(-t\right) \cdot \left(z \cdot \left(a \cdot b - i \cdot c\right)\right)} \]

   7. Taylor expanded in a around 0 65.0%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 65.0%

         \[\leadsto c \cdot \left(i \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

   9. Simplified 65.0%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(z \cdot t\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 48.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.26 \cdot 10^{+14}:\\ \;\;\;\;k \cdot \left(y5 \cdot \left(y \cdot i - y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -2.8 \cdot 10^{-127}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq -6.8 \cdot 10^{-151}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq -1.9 \cdot 10^{-185}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 3.2 \cdot 10^{-74}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq 2.2 \cdot 10^{+219}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 33: 28.3% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -52000000000000:\\ \;\;\;\;k \cdot \left(y5 \cdot \left(y \cdot i - y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -1.85 \cdot 10^{-127}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq -8.5 \cdot 10^{-151}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq -6.6 \cdot 10^{-186}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 3.5 \cdot 10^{-66}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq 5.5 \cdot 10^{+219}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -52000000000000.0)
   (* k (* y5 (- (* y i) (* y0 y2))))
   (if (<= y2 -1.85e-127)
     (* b (* y0 (- (* z k) (* x j))))
     (if (<= y2 -8.5e-151)
       (* b (* j (- (* t y4) (* x y0))))
       (if (<= y2 -6.6e-186)
         (* j (* t (- (* b y4) (* i y5))))
         (if (<= y2 3.5e-66)
           (* k (* i (- (* y y5) (* z y1))))
           (if (<= y2 5.5e+219)
             (* y1 (* y4 (- (* k y2) (* j y3))))
             (* c (* (* z t) 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 (y2 <= -52000000000000.0) {
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	} else if (y2 <= -1.85e-127) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y2 <= -8.5e-151) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y2 <= -6.6e-186) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (y2 <= 3.5e-66) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (y2 <= 5.5e+219) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else {
		tmp = c * ((z * t) * 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 (y2 <= (-52000000000000.0d0)) then
        tmp = k * (y5 * ((y * i) - (y0 * y2)))
    else if (y2 <= (-1.85d-127)) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (y2 <= (-8.5d-151)) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (y2 <= (-6.6d-186)) then
        tmp = j * (t * ((b * y4) - (i * y5)))
    else if (y2 <= 3.5d-66) then
        tmp = k * (i * ((y * y5) - (z * y1)))
    else if (y2 <= 5.5d+219) then
        tmp = y1 * (y4 * ((k * y2) - (j * y3)))
    else
        tmp = c * ((z * t) * 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 (y2 <= -52000000000000.0) {
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	} else if (y2 <= -1.85e-127) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y2 <= -8.5e-151) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y2 <= -6.6e-186) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (y2 <= 3.5e-66) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (y2 <= 5.5e+219) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else {
		tmp = c * ((z * t) * 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 y2 <= -52000000000000.0:
		tmp = k * (y5 * ((y * i) - (y0 * y2)))
	elif y2 <= -1.85e-127:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif y2 <= -8.5e-151:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif y2 <= -6.6e-186:
		tmp = j * (t * ((b * y4) - (i * y5)))
	elif y2 <= 3.5e-66:
		tmp = k * (i * ((y * y5) - (z * y1)))
	elif y2 <= 5.5e+219:
		tmp = y1 * (y4 * ((k * y2) - (j * y3)))
	else:
		tmp = c * ((z * t) * 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 (y2 <= -52000000000000.0)
		tmp = Float64(k * Float64(y5 * Float64(Float64(y * i) - Float64(y0 * y2))));
	elseif (y2 <= -1.85e-127)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (y2 <= -8.5e-151)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (y2 <= -6.6e-186)
		tmp = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))));
	elseif (y2 <= 3.5e-66)
		tmp = Float64(k * Float64(i * Float64(Float64(y * y5) - Float64(z * y1))));
	elseif (y2 <= 5.5e+219)
		tmp = Float64(y1 * Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))));
	else
		tmp = Float64(c * Float64(Float64(z * t) * 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 (y2 <= -52000000000000.0)
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	elseif (y2 <= -1.85e-127)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (y2 <= -8.5e-151)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (y2 <= -6.6e-186)
		tmp = j * (t * ((b * y4) - (i * y5)));
	elseif (y2 <= 3.5e-66)
		tmp = k * (i * ((y * y5) - (z * y1)));
	elseif (y2 <= 5.5e+219)
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	else
		tmp = c * ((z * t) * 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[y2, -52000000000000.0], N[(k * N[(y5 * N[(N[(y * i), $MachinePrecision] - N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1.85e-127], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -8.5e-151], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -6.6e-186], N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 3.5e-66], N[(k * N[(i * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 5.5e+219], N[(y1 * N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(z * t), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y2 < -5.2e13

   1. Initial program 36.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 49.2%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 49.8%

      \[\leadsto k \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 49.8%

         \[\leadsto k \cdot \left(y5 \cdot \color{blue}{\left(i \cdot y + -1 \cdot \left(y0 \cdot y2\right)\right)}\right) \]

      2. mul-1-neg 49.8%

         \[\leadsto k \cdot \left(y5 \cdot \left(i \cdot y + \color{blue}{\left(-y0 \cdot y2\right)}\right)\right) \]

      3. unsub-neg 49.8%

         \[\leadsto k \cdot \left(y5 \cdot \color{blue}{\left(i \cdot y - y0 \cdot y2\right)}\right) \]

      4. *-commutative 49.8%

         \[\leadsto k \cdot \left(y5 \cdot \left(i \cdot y - \color{blue}{y2 \cdot y0}\right)\right) \]

   6. Simplified 49.8%

      \[\leadsto k \cdot \color{blue}{\left(y5 \cdot \left(i \cdot y - y2 \cdot y0\right)\right)} \]

   if -5.2e13 < y2 < -1.8500000000000002e-127

   1. Initial program 38.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 50.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y0 around inf 47.8%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 47.8%

         \[\leadsto b \cdot \color{blue}{\left(\left(k \cdot z - j \cdot x\right) \cdot y0\right)} \]

   6. Simplified 47.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot y0\right)} \]

   if -1.8500000000000002e-127 < y2 < -8.49999999999999999e-151

   1. Initial program 22.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 44.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in j around inf 56.6%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if -8.49999999999999999e-151 < y2 < -6.59999999999999998e-186

   1. Initial program 14.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 42.9%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 72.3%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]

   if -6.59999999999999998e-186 < y2 < 3.5e-66

   1. Initial program 39.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 44.5%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   4. Taylor expanded in i around inf 46.0%

      \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 46.0%

         \[\leadsto k \cdot \left(i \cdot \left(\color{blue}{y5 \cdot y} - y1 \cdot z\right)\right) \]

   6. Simplified 46.0%

      \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(y5 \cdot y - y1 \cdot z\right)\right)} \]

   if 3.5e-66 < y2 < 5.49999999999999973e219

   1. Initial program 27.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 42.0%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in y4 around inf 45.6%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   if 5.49999999999999973e219 < y2

   1. Initial program 14.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 64.3%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in z around inf 52.4%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 52.4%

         \[\leadsto \color{blue}{\left(-1 \cdot t\right) \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

      2. neg-mul-1 52.4%

         \[\leadsto \color{blue}{\left(-t\right)} \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) \]

      3. *-commutative 52.4%

         \[\leadsto \left(-t\right) \cdot \left(z \cdot \left(a \cdot b - \color{blue}{i \cdot c}\right)\right) \]

   6. Simplified 52.4%

      \[\leadsto \color{blue}{\left(-t\right) \cdot \left(z \cdot \left(a \cdot b - i \cdot c\right)\right)} \]

   7. Taylor expanded in a around 0 65.0%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 65.0%

         \[\leadsto c \cdot \left(i \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

   9. Simplified 65.0%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(z \cdot t\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 49.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -52000000000000:\\ \;\;\;\;k \cdot \left(y5 \cdot \left(y \cdot i - y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -1.85 \cdot 10^{-127}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq -8.5 \cdot 10^{-151}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq -6.6 \cdot 10^{-186}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 3.5 \cdot 10^{-66}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq 5.5 \cdot 10^{+219}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 34: 25.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(i \cdot \left(x \cdot y1\right)\right)\\ t_2 := a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{if}\;i \leq -1.2 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -1.1 \cdot 10^{-267}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 1.22 \cdot 10^{-175}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(y3 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;i \leq 1.25 \cdot 10^{+96}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{+205}:\\ \;\;\;\;\left(t \cdot y5\right) \cdot \left(j \cdot \left(-i\right)\right)\\ \mathbf{elif}\;i \leq 1.26 \cdot 10^{+247}:\\ \;\;\;\;i \cdot \left(\left(z \cdot y1\right) \cdot \left(-k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* i (* x y1)))) (t_2 (* a (* b (- (* x y) (* z t))))))
   (if (<= i -1.2e+103)
     t_1
     (if (<= i -1.1e-267)
       t_2
       (if (<= i 1.22e-175)
         (* y1 (* j (* y3 (- y4))))
         (if (<= i 1.25e+96)
           t_2
           (if (<= i 4.8e+205)
             (* (* t y5) (* j (- i)))
             (if (<= i 1.26e+247) (* i (* (* z y1) (- k))) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (i * (x * y1));
	double t_2 = a * (b * ((x * y) - (z * t)));
	double tmp;
	if (i <= -1.2e+103) {
		tmp = t_1;
	} else if (i <= -1.1e-267) {
		tmp = t_2;
	} else if (i <= 1.22e-175) {
		tmp = y1 * (j * (y3 * -y4));
	} else if (i <= 1.25e+96) {
		tmp = t_2;
	} else if (i <= 4.8e+205) {
		tmp = (t * y5) * (j * -i);
	} else if (i <= 1.26e+247) {
		tmp = i * ((z * y1) * -k);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (i * (x * y1))
    t_2 = a * (b * ((x * y) - (z * t)))
    if (i <= (-1.2d+103)) then
        tmp = t_1
    else if (i <= (-1.1d-267)) then
        tmp = t_2
    else if (i <= 1.22d-175) then
        tmp = y1 * (j * (y3 * -y4))
    else if (i <= 1.25d+96) then
        tmp = t_2
    else if (i <= 4.8d+205) then
        tmp = (t * y5) * (j * -i)
    else if (i <= 1.26d+247) then
        tmp = i * ((z * y1) * -k)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (i * (x * y1));
	double t_2 = a * (b * ((x * y) - (z * t)));
	double tmp;
	if (i <= -1.2e+103) {
		tmp = t_1;
	} else if (i <= -1.1e-267) {
		tmp = t_2;
	} else if (i <= 1.22e-175) {
		tmp = y1 * (j * (y3 * -y4));
	} else if (i <= 1.25e+96) {
		tmp = t_2;
	} else if (i <= 4.8e+205) {
		tmp = (t * y5) * (j * -i);
	} else if (i <= 1.26e+247) {
		tmp = i * ((z * y1) * -k);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = j * (i * (x * y1))
	t_2 = a * (b * ((x * y) - (z * t)))
	tmp = 0
	if i <= -1.2e+103:
		tmp = t_1
	elif i <= -1.1e-267:
		tmp = t_2
	elif i <= 1.22e-175:
		tmp = y1 * (j * (y3 * -y4))
	elif i <= 1.25e+96:
		tmp = t_2
	elif i <= 4.8e+205:
		tmp = (t * y5) * (j * -i)
	elif i <= 1.26e+247:
		tmp = i * ((z * y1) * -k)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(j * Float64(i * Float64(x * y1)))
	t_2 = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))))
	tmp = 0.0
	if (i <= -1.2e+103)
		tmp = t_1;
	elseif (i <= -1.1e-267)
		tmp = t_2;
	elseif (i <= 1.22e-175)
		tmp = Float64(y1 * Float64(j * Float64(y3 * Float64(-y4))));
	elseif (i <= 1.25e+96)
		tmp = t_2;
	elseif (i <= 4.8e+205)
		tmp = Float64(Float64(t * y5) * Float64(j * Float64(-i)));
	elseif (i <= 1.26e+247)
		tmp = Float64(i * Float64(Float64(z * y1) * Float64(-k)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = j * (i * (x * y1));
	t_2 = a * (b * ((x * y) - (z * t)));
	tmp = 0.0;
	if (i <= -1.2e+103)
		tmp = t_1;
	elseif (i <= -1.1e-267)
		tmp = t_2;
	elseif (i <= 1.22e-175)
		tmp = y1 * (j * (y3 * -y4));
	elseif (i <= 1.25e+96)
		tmp = t_2;
	elseif (i <= 4.8e+205)
		tmp = (t * y5) * (j * -i);
	elseif (i <= 1.26e+247)
		tmp = i * ((z * y1) * -k);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(j * N[(i * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.2e+103], t$95$1, If[LessEqual[i, -1.1e-267], t$95$2, If[LessEqual[i, 1.22e-175], N[(y1 * N[(j * N[(y3 * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.25e+96], t$95$2, If[LessEqual[i, 4.8e+205], N[(N[(t * y5), $MachinePrecision] * N[(j * (-i)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.26e+247], N[(i * N[(N[(z * y1), $MachinePrecision] * (-k)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -1.1999999999999999e103 or 1.26e247 < i

   1. Initial program 24.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 32.8%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in i around inf 45.9%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in j around inf 38.1%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 38.1%

         \[\leadsto \color{blue}{\left(j \cdot \left(x \cdot y1\right)\right) \cdot i} \]

      2. associate-*l* 46.8%

         \[\leadsto \color{blue}{j \cdot \left(\left(x \cdot y1\right) \cdot i\right)} \]

   7. Simplified 46.8%

      \[\leadsto \color{blue}{j \cdot \left(\left(x \cdot y1\right) \cdot i\right)} \]

   if -1.1999999999999999e103 < i < -1.09999999999999994e-267 or 1.2200000000000001e-175 < i < 1.2500000000000001e96

   1. Initial program 37.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 40.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 28.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 28.9%

         \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y - t \cdot z\right) \cdot b\right)} \]

      2. *-commutative 28.9%

         \[\leadsto a \cdot \left(\left(\color{blue}{y \cdot x} - t \cdot z\right) \cdot b\right) \]

   6. Simplified 28.9%

      \[\leadsto \color{blue}{a \cdot \left(\left(y \cdot x - t \cdot z\right) \cdot b\right)} \]

   if -1.09999999999999994e-267 < i < 1.2200000000000001e-175

   1. Initial program 46.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 57.1%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in y4 around inf 47.6%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   5. Taylor expanded in k around 0 37.5%

      \[\leadsto y1 \cdot \color{blue}{\left(-1 \cdot \left(j \cdot \left(y3 \cdot y4\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 37.5%

         \[\leadsto y1 \cdot \color{blue}{\left(-j \cdot \left(y3 \cdot y4\right)\right)} \]

      2. *-commutative 37.5%

         \[\leadsto y1 \cdot \left(-\color{blue}{\left(y3 \cdot y4\right) \cdot j}\right) \]

      3. distribute-rgt-neg-in 37.5%

         \[\leadsto y1 \cdot \color{blue}{\left(\left(y3 \cdot y4\right) \cdot \left(-j\right)\right)} \]

      4. *-commutative 37.5%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot y3\right)} \cdot \left(-j\right)\right) \]

   7. Simplified 37.5%

      \[\leadsto y1 \cdot \color{blue}{\left(\left(y4 \cdot y3\right) \cdot \left(-j\right)\right)} \]

   if 1.2500000000000001e96 < i < 4.79999999999999972e205

   1. Initial program 12.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 39.0%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in y5 around inf 47.2%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot j\right) - -1 \cdot \left(a \cdot y2\right)\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 47.2%

         \[\leadsto t \cdot \left(y5 \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j - a \cdot y2\right)\right)}\right) \]

   6. Simplified 47.2%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\right)} \]

   7. Taylor expanded in i around inf 43.3%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot \left(t \cdot y5\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 43.3%

         \[\leadsto \color{blue}{-i \cdot \left(j \cdot \left(t \cdot y5\right)\right)} \]

      2. associate-*r* 43.7%

         \[\leadsto -\color{blue}{\left(i \cdot j\right) \cdot \left(t \cdot y5\right)} \]

      3. distribute-rgt-neg-in 43.7%

         \[\leadsto \color{blue}{\left(i \cdot j\right) \cdot \left(-t \cdot y5\right)} \]

      4. *-commutative 43.7%

         \[\leadsto \left(i \cdot j\right) \cdot \left(-\color{blue}{y5 \cdot t}\right) \]

   9. Simplified 43.7%

      \[\leadsto \color{blue}{\left(i \cdot j\right) \cdot \left(-y5 \cdot t\right)} \]

   if 4.79999999999999972e205 < i < 1.26e247

   1. Initial program 50.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 75.8%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in i around inf 75.8%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in j around 0 75.9%

      \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y1 \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 75.9%

         \[\leadsto i \cdot \color{blue}{\left(-k \cdot \left(y1 \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 75.9%

         \[\leadsto i \cdot \color{blue}{\left(k \cdot \left(-y1 \cdot z\right)\right)} \]

      3. distribute-rgt-neg-in 75.9%

         \[\leadsto i \cdot \left(k \cdot \color{blue}{\left(y1 \cdot \left(-z\right)\right)}\right) \]

   7. Simplified 75.9%

      \[\leadsto i \cdot \color{blue}{\left(k \cdot \left(y1 \cdot \left(-z\right)\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.2 \cdot 10^{+103}:\\ \;\;\;\;j \cdot \left(i \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;i \leq -1.1 \cdot 10^{-267}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;i \leq 1.22 \cdot 10^{-175}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(y3 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;i \leq 1.25 \cdot 10^{+96}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{+205}:\\ \;\;\;\;\left(t \cdot y5\right) \cdot \left(j \cdot \left(-i\right)\right)\\ \mathbf{elif}\;i \leq 1.26 \cdot 10^{+247}:\\ \;\;\;\;i \cdot \left(\left(z \cdot y1\right) \cdot \left(-k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(i \cdot \left(x \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 35: 21.7% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{+137}:\\ \;\;\;\;j \cdot \left(i \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{+45}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-196}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{elif}\;x \leq 8.4 \cdot 10^{+156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+246}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* t (* y2 y5)))))
   (if (<= x -2.6e+137)
     (* j (* i (* x y1)))
     (if (<= x -6.2e+45)
       (* a (* x (* y b)))
       (if (<= x -1.75e-68)
         t_1
         (if (<= x 5.5e-196)
           (* c (* (* z t) i))
           (if (<= x 8.4e+156)
             t_1
             (if (<= x 5.5e+246)
               (* b (* (* x y) a))
               (* i (* j (* x y1)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (t * (y2 * y5));
	double tmp;
	if (x <= -2.6e+137) {
		tmp = j * (i * (x * y1));
	} else if (x <= -6.2e+45) {
		tmp = a * (x * (y * b));
	} else if (x <= -1.75e-68) {
		tmp = t_1;
	} else if (x <= 5.5e-196) {
		tmp = c * ((z * t) * i);
	} else if (x <= 8.4e+156) {
		tmp = t_1;
	} else if (x <= 5.5e+246) {
		tmp = b * ((x * y) * a);
	} else {
		tmp = i * (j * (x * y1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (t * (y2 * y5))
    if (x <= (-2.6d+137)) then
        tmp = j * (i * (x * y1))
    else if (x <= (-6.2d+45)) then
        tmp = a * (x * (y * b))
    else if (x <= (-1.75d-68)) then
        tmp = t_1
    else if (x <= 5.5d-196) then
        tmp = c * ((z * t) * i)
    else if (x <= 8.4d+156) then
        tmp = t_1
    else if (x <= 5.5d+246) then
        tmp = b * ((x * y) * a)
    else
        tmp = i * (j * (x * y1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (t * (y2 * y5));
	double tmp;
	if (x <= -2.6e+137) {
		tmp = j * (i * (x * y1));
	} else if (x <= -6.2e+45) {
		tmp = a * (x * (y * b));
	} else if (x <= -1.75e-68) {
		tmp = t_1;
	} else if (x <= 5.5e-196) {
		tmp = c * ((z * t) * i);
	} else if (x <= 8.4e+156) {
		tmp = t_1;
	} else if (x <= 5.5e+246) {
		tmp = b * ((x * y) * a);
	} else {
		tmp = i * (j * (x * y1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (t * (y2 * y5))
	tmp = 0
	if x <= -2.6e+137:
		tmp = j * (i * (x * y1))
	elif x <= -6.2e+45:
		tmp = a * (x * (y * b))
	elif x <= -1.75e-68:
		tmp = t_1
	elif x <= 5.5e-196:
		tmp = c * ((z * t) * i)
	elif x <= 8.4e+156:
		tmp = t_1
	elif x <= 5.5e+246:
		tmp = b * ((x * y) * a)
	else:
		tmp = i * (j * (x * y1))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(t * Float64(y2 * y5)))
	tmp = 0.0
	if (x <= -2.6e+137)
		tmp = Float64(j * Float64(i * Float64(x * y1)));
	elseif (x <= -6.2e+45)
		tmp = Float64(a * Float64(x * Float64(y * b)));
	elseif (x <= -1.75e-68)
		tmp = t_1;
	elseif (x <= 5.5e-196)
		tmp = Float64(c * Float64(Float64(z * t) * i));
	elseif (x <= 8.4e+156)
		tmp = t_1;
	elseif (x <= 5.5e+246)
		tmp = Float64(b * Float64(Float64(x * y) * a));
	else
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (t * (y2 * y5));
	tmp = 0.0;
	if (x <= -2.6e+137)
		tmp = j * (i * (x * y1));
	elseif (x <= -6.2e+45)
		tmp = a * (x * (y * b));
	elseif (x <= -1.75e-68)
		tmp = t_1;
	elseif (x <= 5.5e-196)
		tmp = c * ((z * t) * i);
	elseif (x <= 8.4e+156)
		tmp = t_1;
	elseif (x <= 5.5e+246)
		tmp = b * ((x * y) * a);
	else
		tmp = i * (j * (x * y1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.6e+137], N[(j * N[(i * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.2e+45], N[(a * N[(x * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.75e-68], t$95$1, If[LessEqual[x, 5.5e-196], N[(c * N[(N[(z * t), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.4e+156], t$95$1, If[LessEqual[x, 5.5e+246], N[(b * N[(N[(x * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -2.5999999999999999e137

   1. Initial program 20.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 60.2%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in i around inf 50.3%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in j around inf 44.1%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 44.1%

         \[\leadsto \color{blue}{\left(j \cdot \left(x \cdot y1\right)\right) \cdot i} \]

      2. associate-*l* 47.3%

         \[\leadsto \color{blue}{j \cdot \left(\left(x \cdot y1\right) \cdot i\right)} \]

   7. Simplified 47.3%

      \[\leadsto \color{blue}{j \cdot \left(\left(x \cdot y1\right) \cdot i\right)} \]

   if -2.5999999999999999e137 < x < -6.19999999999999975e45

   1. Initial program 24.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 34.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 39.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 39.0%

         \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y - t \cdot z\right) \cdot b\right)} \]

      2. *-commutative 39.0%

         \[\leadsto a \cdot \left(\left(\color{blue}{y \cdot x} - t \cdot z\right) \cdot b\right) \]

   6. Simplified 39.0%

      \[\leadsto \color{blue}{a \cdot \left(\left(y \cdot x - t \cdot z\right) \cdot b\right)} \]

   7. Taylor expanded in y around inf 34.4%

      \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot y\right)} \cdot b\right) \]
   8. Step-by-step derivation

      1. *-commutative 34.4%

         \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot b\right) \]

   9. Simplified 34.4%

      \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot b\right) \]

   10. Taylor expanded in y around 0 34.4%

       \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 39.1%

          \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot x\right) \cdot y\right)} \]

       2. *-commutative 39.1%

          \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot b\right)} \cdot y\right) \]

       3. associate-*l* 34.4%

          \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

   12. Simplified 34.4%

       \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

   if -6.19999999999999975e45 < x < -1.75000000000000006e-68 or 5.50000000000000014e-196 < x < 8.39999999999999925e156

   1. Initial program 34.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 44.6%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in y5 around inf 27.5%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot j\right) - -1 \cdot \left(a \cdot y2\right)\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 27.5%

         \[\leadsto t \cdot \left(y5 \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j - a \cdot y2\right)\right)}\right) \]

   6. Simplified 27.5%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\right)} \]

   7. Taylor expanded in i around 0 21.2%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 21.2%

         \[\leadsto a \cdot \color{blue}{\left(\left(y2 \cdot y5\right) \cdot t\right)} \]

   9. Simplified 21.2%

      \[\leadsto \color{blue}{a \cdot \left(\left(y2 \cdot y5\right) \cdot t\right)} \]

   if -1.75000000000000006e-68 < x < 5.50000000000000014e-196

   1. Initial program 39.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 42.3%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in z around inf 39.6%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 39.6%

         \[\leadsto \color{blue}{\left(-1 \cdot t\right) \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

      2. neg-mul-1 39.6%

         \[\leadsto \color{blue}{\left(-t\right)} \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) \]

      3. *-commutative 39.6%

         \[\leadsto \left(-t\right) \cdot \left(z \cdot \left(a \cdot b - \color{blue}{i \cdot c}\right)\right) \]

   6. Simplified 39.6%

      \[\leadsto \color{blue}{\left(-t\right) \cdot \left(z \cdot \left(a \cdot b - i \cdot c\right)\right)} \]

   7. Taylor expanded in a around 0 24.6%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 24.6%

         \[\leadsto c \cdot \left(i \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

   9. Simplified 24.6%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(z \cdot t\right)\right)} \]

   if 8.39999999999999925e156 < x < 5.50000000000000028e246

   1. Initial program 33.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 44.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 56.7%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 56.7%

         \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y - t \cdot z\right) \cdot b\right)} \]

      2. *-commutative 56.7%

         \[\leadsto a \cdot \left(\left(\color{blue}{y \cdot x} - t \cdot z\right) \cdot b\right) \]

   6. Simplified 56.7%

      \[\leadsto \color{blue}{a \cdot \left(\left(y \cdot x - t \cdot z\right) \cdot b\right)} \]

   7. Taylor expanded in y around inf 51.6%

      \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot y\right)} \cdot b\right) \]
   8. Step-by-step derivation

      1. *-commutative 51.6%

         \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot b\right) \]

   9. Simplified 51.6%

      \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot b\right) \]

   10. Taylor expanded in a around 0 51.6%

       \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative 51.6%

          \[\leadsto \color{blue}{\left(b \cdot \left(x \cdot y\right)\right) \cdot a} \]

       2. associate-*l* 61.8%

          \[\leadsto \color{blue}{b \cdot \left(\left(x \cdot y\right) \cdot a\right)} \]

   12. Simplified 61.8%

       \[\leadsto \color{blue}{b \cdot \left(\left(x \cdot y\right) \cdot a\right)} \]

   if 5.50000000000000028e246 < x

   1. Initial program 22.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 44.4%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in i around inf 78.0%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in j around inf 67.1%

      \[\leadsto i \cdot \color{blue}{\left(j \cdot \left(x \cdot y1\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 67.1%

         \[\leadsto i \cdot \left(j \cdot \color{blue}{\left(y1 \cdot x\right)}\right) \]

   7. Simplified 67.1%

      \[\leadsto i \cdot \color{blue}{\left(j \cdot \left(y1 \cdot x\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 31.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+137}:\\ \;\;\;\;j \cdot \left(i \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{+45}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-68}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-196}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{elif}\;x \leq 8.4 \cdot 10^{+156}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+246}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 36: 19.8% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ t_2 := c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{if}\;y2 \leq -6 \cdot 10^{+143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq -2.2 \cdot 10^{-89}:\\ \;\;\;\;j \cdot \left(i \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq -1.45 \cdot 10^{-148}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y2 \leq 3.5 \cdot 10^{-203}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq 4.5 \cdot 10^{+55}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 2.2 \cdot 10^{+219}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (* y1 (* y2 y4)))) (t_2 (* c (* (* z t) i))))
   (if (<= y2 -6e+143)
     t_1
     (if (<= y2 -2.2e-89)
       (* j (* i (* x y1)))
       (if (<= y2 -1.45e-148)
         t_2
         (if (<= y2 3.5e-203)
           (* i (* j (* x y1)))
           (if (<= y2 4.5e+55)
             (* a (* x (* y b)))
             (if (<= y2 2.2e+219) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (y1 * (y2 * y4));
	double t_2 = c * ((z * t) * i);
	double tmp;
	if (y2 <= -6e+143) {
		tmp = t_1;
	} else if (y2 <= -2.2e-89) {
		tmp = j * (i * (x * y1));
	} else if (y2 <= -1.45e-148) {
		tmp = t_2;
	} else if (y2 <= 3.5e-203) {
		tmp = i * (j * (x * y1));
	} else if (y2 <= 4.5e+55) {
		tmp = a * (x * (y * b));
	} else if (y2 <= 2.2e+219) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = k * (y1 * (y2 * y4))
    t_2 = c * ((z * t) * i)
    if (y2 <= (-6d+143)) then
        tmp = t_1
    else if (y2 <= (-2.2d-89)) then
        tmp = j * (i * (x * y1))
    else if (y2 <= (-1.45d-148)) then
        tmp = t_2
    else if (y2 <= 3.5d-203) then
        tmp = i * (j * (x * y1))
    else if (y2 <= 4.5d+55) then
        tmp = a * (x * (y * b))
    else if (y2 <= 2.2d+219) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (y1 * (y2 * y4));
	double t_2 = c * ((z * t) * i);
	double tmp;
	if (y2 <= -6e+143) {
		tmp = t_1;
	} else if (y2 <= -2.2e-89) {
		tmp = j * (i * (x * y1));
	} else if (y2 <= -1.45e-148) {
		tmp = t_2;
	} else if (y2 <= 3.5e-203) {
		tmp = i * (j * (x * y1));
	} else if (y2 <= 4.5e+55) {
		tmp = a * (x * (y * b));
	} else if (y2 <= 2.2e+219) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = k * (y1 * (y2 * y4))
	t_2 = c * ((z * t) * i)
	tmp = 0
	if y2 <= -6e+143:
		tmp = t_1
	elif y2 <= -2.2e-89:
		tmp = j * (i * (x * y1))
	elif y2 <= -1.45e-148:
		tmp = t_2
	elif y2 <= 3.5e-203:
		tmp = i * (j * (x * y1))
	elif y2 <= 4.5e+55:
		tmp = a * (x * (y * b))
	elif y2 <= 2.2e+219:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(k * Float64(y1 * Float64(y2 * y4)))
	t_2 = Float64(c * Float64(Float64(z * t) * i))
	tmp = 0.0
	if (y2 <= -6e+143)
		tmp = t_1;
	elseif (y2 <= -2.2e-89)
		tmp = Float64(j * Float64(i * Float64(x * y1)));
	elseif (y2 <= -1.45e-148)
		tmp = t_2;
	elseif (y2 <= 3.5e-203)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (y2 <= 4.5e+55)
		tmp = Float64(a * Float64(x * Float64(y * b)));
	elseif (y2 <= 2.2e+219)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = k * (y1 * (y2 * y4));
	t_2 = c * ((z * t) * i);
	tmp = 0.0;
	if (y2 <= -6e+143)
		tmp = t_1;
	elseif (y2 <= -2.2e-89)
		tmp = j * (i * (x * y1));
	elseif (y2 <= -1.45e-148)
		tmp = t_2;
	elseif (y2 <= 3.5e-203)
		tmp = i * (j * (x * y1));
	elseif (y2 <= 4.5e+55)
		tmp = a * (x * (y * b));
	elseif (y2 <= 2.2e+219)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(z * t), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -6e+143], t$95$1, If[LessEqual[y2, -2.2e-89], N[(j * N[(i * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1.45e-148], t$95$2, If[LessEqual[y2, 3.5e-203], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 4.5e+55], N[(a * N[(x * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.2e+219], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y2 < -6.0000000000000001e143 or 4.49999999999999998e55 < y2 < 2.2000000000000001e219

   1. Initial program 26.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 47.8%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in y4 around inf 46.5%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 43.4%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)} \]

   if -6.0000000000000001e143 < y2 < -2.20000000000000012e-89

   1. Initial program 27.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 34.8%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in i around inf 30.7%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in j around inf 22.8%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 22.8%

         \[\leadsto \color{blue}{\left(j \cdot \left(x \cdot y1\right)\right) \cdot i} \]

      2. associate-*l* 24.8%

         \[\leadsto \color{blue}{j \cdot \left(\left(x \cdot y1\right) \cdot i\right)} \]

   7. Simplified 24.8%

      \[\leadsto \color{blue}{j \cdot \left(\left(x \cdot y1\right) \cdot i\right)} \]

   if -2.20000000000000012e-89 < y2 < -1.4499999999999999e-148 or 2.2000000000000001e219 < y2

   1. Initial program 36.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 67.0%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in z around inf 44.2%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 44.2%

         \[\leadsto \color{blue}{\left(-1 \cdot t\right) \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

      2. neg-mul-1 44.2%

         \[\leadsto \color{blue}{\left(-t\right)} \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) \]

      3. *-commutative 44.2%

         \[\leadsto \left(-t\right) \cdot \left(z \cdot \left(a \cdot b - \color{blue}{i \cdot c}\right)\right) \]

   6. Simplified 44.2%

      \[\leadsto \color{blue}{\left(-t\right) \cdot \left(z \cdot \left(a \cdot b - i \cdot c\right)\right)} \]

   7. Taylor expanded in a around 0 43.8%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 43.8%

         \[\leadsto c \cdot \left(i \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

   9. Simplified 43.8%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(z \cdot t\right)\right)} \]

   if -1.4499999999999999e-148 < y2 < 3.5000000000000001e-203

   1. Initial program 32.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 42.8%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in i around inf 44.7%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in j around inf 25.5%

      \[\leadsto i \cdot \color{blue}{\left(j \cdot \left(x \cdot y1\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 25.5%

         \[\leadsto i \cdot \left(j \cdot \color{blue}{\left(y1 \cdot x\right)}\right) \]

   7. Simplified 25.5%

      \[\leadsto i \cdot \color{blue}{\left(j \cdot \left(y1 \cdot x\right)\right)} \]

   if 3.5000000000000001e-203 < y2 < 4.49999999999999998e55

   1. Initial program 43.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 44.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 26.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 26.2%

         \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y - t \cdot z\right) \cdot b\right)} \]

      2. *-commutative 26.2%

         \[\leadsto a \cdot \left(\left(\color{blue}{y \cdot x} - t \cdot z\right) \cdot b\right) \]

   6. Simplified 26.2%

      \[\leadsto \color{blue}{a \cdot \left(\left(y \cdot x - t \cdot z\right) \cdot b\right)} \]

   7. Taylor expanded in y around inf 19.4%

      \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot y\right)} \cdot b\right) \]
   8. Step-by-step derivation

      1. *-commutative 19.4%

         \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot b\right) \]

   9. Simplified 19.4%

      \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot b\right) \]

   10. Taylor expanded in y around 0 19.4%

       \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 17.7%

          \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot x\right) \cdot y\right)} \]

       2. *-commutative 17.7%

          \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot b\right)} \cdot y\right) \]

       3. associate-*l* 24.4%

          \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

   12. Simplified 24.4%

       \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 31.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -6 \cdot 10^{+143}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -2.2 \cdot 10^{-89}:\\ \;\;\;\;j \cdot \left(i \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq -1.45 \cdot 10^{-148}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{elif}\;y2 \leq 3.5 \cdot 10^{-203}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq 4.5 \cdot 10^{+55}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 2.2 \cdot 10^{+219}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 37: 29.3% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.52 \cdot 10^{+159}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{+23}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-58}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-160}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+117}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(x \cdot y\right) \cdot \left(-i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y -1.52e+159)
   (* a (* b (- (* x y) (* z t))))
   (if (<= y -4.7e+23)
     (* b (* x (- (* y a) (* j y0))))
     (if (<= y -3e-58)
       (* b (* y4 (- (* t j) (* y k))))
       (if (<= y 2.05e-160)
         (* i (* y1 (- (* x j) (* z k))))
         (if (<= y 2.2e+117)
           (* b (* y0 (- (* z k) (* x j))))
           (* c (* (* x 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 (y <= -1.52e+159) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y <= -4.7e+23) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y <= -3e-58) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y <= 2.05e-160) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (y <= 2.2e+117) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else {
		tmp = c * ((x * 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 (y <= (-1.52d+159)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (y <= (-4.7d+23)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (y <= (-3d-58)) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (y <= 2.05d-160) then
        tmp = i * (y1 * ((x * j) - (z * k)))
    else if (y <= 2.2d+117) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else
        tmp = c * ((x * 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 (y <= -1.52e+159) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y <= -4.7e+23) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y <= -3e-58) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y <= 2.05e-160) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (y <= 2.2e+117) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else {
		tmp = c * ((x * 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 y <= -1.52e+159:
		tmp = a * (b * ((x * y) - (z * t)))
	elif y <= -4.7e+23:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif y <= -3e-58:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif y <= 2.05e-160:
		tmp = i * (y1 * ((x * j) - (z * k)))
	elif y <= 2.2e+117:
		tmp = b * (y0 * ((z * k) - (x * j)))
	else:
		tmp = c * ((x * 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 (y <= -1.52e+159)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y <= -4.7e+23)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (y <= -3e-58)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (y <= 2.05e-160)
		tmp = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))));
	elseif (y <= 2.2e+117)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	else
		tmp = Float64(c * Float64(Float64(x * y) * Float64(-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 (y <= -1.52e+159)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (y <= -4.7e+23)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (y <= -3e-58)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (y <= 2.05e-160)
		tmp = i * (y1 * ((x * j) - (z * k)));
	elseif (y <= 2.2e+117)
		tmp = b * (y0 * ((z * k) - (x * j)));
	else
		tmp = c * ((x * 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[y, -1.52e+159], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.7e+23], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3e-58], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.05e-160], N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.2e+117], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(x * y), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1.5199999999999999e159

   1. Initial program 22.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 41.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 56.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 56.9%

         \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y - t \cdot z\right) \cdot b\right)} \]

      2. *-commutative 56.9%

         \[\leadsto a \cdot \left(\left(\color{blue}{y \cdot x} - t \cdot z\right) \cdot b\right) \]

   6. Simplified 56.9%

      \[\leadsto \color{blue}{a \cdot \left(\left(y \cdot x - t \cdot z\right) \cdot b\right)} \]

   if -1.5199999999999999e159 < y < -4.6999999999999997e23

   1. Initial program 47.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 35.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in x around inf 44.8%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 44.8%

         \[\leadsto b \cdot \left(x \cdot \left(\color{blue}{y \cdot a} - j \cdot y0\right)\right) \]

   6. Simplified 44.8%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)} \]

   if -4.6999999999999997e23 < y < -3.00000000000000008e-58

   1. Initial program 26.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 40.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y4 around inf 36.5%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   if -3.00000000000000008e-58 < y < 2.05000000000000001e-160

   1. Initial program 34.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 44.0%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in i around inf 41.7%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   if 2.05000000000000001e-160 < y < 2.20000000000000014e117

   1. Initial program 41.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 43.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y0 around inf 35.9%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 35.9%

         \[\leadsto b \cdot \color{blue}{\left(\left(k \cdot z - j \cdot x\right) \cdot y0\right)} \]

   6. Simplified 35.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot y0\right)} \]

   if 2.20000000000000014e117 < y

   1. Initial program 20.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around -inf 49.4%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in c around inf 47.2%

      \[\leadsto -1 \cdot \color{blue}{\left(c \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 47.2%

         \[\leadsto -1 \cdot \left(c \cdot \left(i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right)\right) \]

   6. Simplified 47.2%

      \[\leadsto -1 \cdot \color{blue}{\left(c \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right)\right)} \]

   7. Taylor expanded in y around inf 44.6%

      \[\leadsto -1 \cdot \left(c \cdot \color{blue}{\left(i \cdot \left(x \cdot y\right)\right)}\right) \]
   8. Step-by-step derivation

      1. *-commutative 44.6%

         \[\leadsto -1 \cdot \left(c \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot i\right)}\right) \]

   9. Simplified 44.6%

      \[\leadsto -1 \cdot \left(c \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot i\right)}\right) \]
3. Recombined 6 regimes into one program.

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.52 \cdot 10^{+159}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{+23}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-58}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-160}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+117}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(x \cdot y\right) \cdot \left(-i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 38: 21.1% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{if}\;y5 \leq -2.5 \cdot 10^{+119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y5 \leq -1.5 \cdot 10^{-128}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y5 \leq 3.4 \cdot 10^{-213}:\\ \;\;\;\;j \cdot \left(i \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y5 \leq 4.5 \cdot 10^{-149}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{elif}\;y5 \leq 2.3 \cdot 10^{+72}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* t (* a (* y2 y5)))))
   (if (<= y5 -2.5e+119)
     t_1
     (if (<= y5 -1.5e-128)
       (* a (* (* x y) b))
       (if (<= y5 3.4e-213)
         (* j (* i (* x y1)))
         (if (<= y5 4.5e-149)
           (* c (* (* z t) i))
           (if (<= y5 2.3e+72) (* k (* y1 (* y2 y4))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * (a * (y2 * y5));
	double tmp;
	if (y5 <= -2.5e+119) {
		tmp = t_1;
	} else if (y5 <= -1.5e-128) {
		tmp = a * ((x * y) * b);
	} else if (y5 <= 3.4e-213) {
		tmp = j * (i * (x * y1));
	} else if (y5 <= 4.5e-149) {
		tmp = c * ((z * t) * i);
	} else if (y5 <= 2.3e+72) {
		tmp = k * (y1 * (y2 * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (a * (y2 * y5))
    if (y5 <= (-2.5d+119)) then
        tmp = t_1
    else if (y5 <= (-1.5d-128)) then
        tmp = a * ((x * y) * b)
    else if (y5 <= 3.4d-213) then
        tmp = j * (i * (x * y1))
    else if (y5 <= 4.5d-149) then
        tmp = c * ((z * t) * i)
    else if (y5 <= 2.3d+72) then
        tmp = k * (y1 * (y2 * y4))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * (a * (y2 * y5));
	double tmp;
	if (y5 <= -2.5e+119) {
		tmp = t_1;
	} else if (y5 <= -1.5e-128) {
		tmp = a * ((x * y) * b);
	} else if (y5 <= 3.4e-213) {
		tmp = j * (i * (x * y1));
	} else if (y5 <= 4.5e-149) {
		tmp = c * ((z * t) * i);
	} else if (y5 <= 2.3e+72) {
		tmp = k * (y1 * (y2 * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = t * (a * (y2 * y5))
	tmp = 0
	if y5 <= -2.5e+119:
		tmp = t_1
	elif y5 <= -1.5e-128:
		tmp = a * ((x * y) * b)
	elif y5 <= 3.4e-213:
		tmp = j * (i * (x * y1))
	elif y5 <= 4.5e-149:
		tmp = c * ((z * t) * i)
	elif y5 <= 2.3e+72:
		tmp = k * (y1 * (y2 * y4))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(t * Float64(a * Float64(y2 * y5)))
	tmp = 0.0
	if (y5 <= -2.5e+119)
		tmp = t_1;
	elseif (y5 <= -1.5e-128)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	elseif (y5 <= 3.4e-213)
		tmp = Float64(j * Float64(i * Float64(x * y1)));
	elseif (y5 <= 4.5e-149)
		tmp = Float64(c * Float64(Float64(z * t) * i));
	elseif (y5 <= 2.3e+72)
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = t * (a * (y2 * y5));
	tmp = 0.0;
	if (y5 <= -2.5e+119)
		tmp = t_1;
	elseif (y5 <= -1.5e-128)
		tmp = a * ((x * y) * b);
	elseif (y5 <= 3.4e-213)
		tmp = j * (i * (x * y1));
	elseif (y5 <= 4.5e-149)
		tmp = c * ((z * t) * i);
	elseif (y5 <= 2.3e+72)
		tmp = k * (y1 * (y2 * y4));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(t * N[(a * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -2.5e+119], t$95$1, If[LessEqual[y5, -1.5e-128], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 3.4e-213], N[(j * N[(i * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 4.5e-149], N[(c * N[(N[(z * t), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 2.3e+72], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y5 < -2.5e119 or 2.3e72 < y5

   1. Initial program 24.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 41.0%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in y5 around inf 44.7%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot j\right) - -1 \cdot \left(a \cdot y2\right)\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 44.7%

         \[\leadsto t \cdot \left(y5 \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j - a \cdot y2\right)\right)}\right) \]

   6. Simplified 44.7%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\right)} \]

   7. Taylor expanded in i around 0 34.8%

      \[\leadsto t \cdot \color{blue}{\left(a \cdot \left(y2 \cdot y5\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 34.8%

         \[\leadsto t \cdot \color{blue}{\left(\left(y2 \cdot y5\right) \cdot a\right)} \]

   9. Simplified 34.8%

      \[\leadsto t \cdot \color{blue}{\left(\left(y2 \cdot y5\right) \cdot a\right)} \]

   if -2.5e119 < y5 < -1.49999999999999989e-128

   1. Initial program 35.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 33.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 27.4%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 27.4%

         \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y - t \cdot z\right) \cdot b\right)} \]

      2. *-commutative 27.4%

         \[\leadsto a \cdot \left(\left(\color{blue}{y \cdot x} - t \cdot z\right) \cdot b\right) \]

   6. Simplified 27.4%

      \[\leadsto \color{blue}{a \cdot \left(\left(y \cdot x - t \cdot z\right) \cdot b\right)} \]

   7. Taylor expanded in y around inf 18.5%

      \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot y\right)} \cdot b\right) \]
   8. Step-by-step derivation

      1. *-commutative 18.5%

         \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot b\right) \]

   9. Simplified 18.5%

      \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot b\right) \]

   if -1.49999999999999989e-128 < y5 < 3.4000000000000002e-213

   1. Initial program 43.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 41.7%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in i around inf 46.1%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in j around inf 25.2%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 25.2%

         \[\leadsto \color{blue}{\left(j \cdot \left(x \cdot y1\right)\right) \cdot i} \]

      2. associate-*l* 27.0%

         \[\leadsto \color{blue}{j \cdot \left(\left(x \cdot y1\right) \cdot i\right)} \]

   7. Simplified 27.0%

      \[\leadsto \color{blue}{j \cdot \left(\left(x \cdot y1\right) \cdot i\right)} \]

   if 3.4000000000000002e-213 < y5 < 4.4999999999999998e-149

   1. Initial program 37.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 56.8%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in z around inf 44.9%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 44.9%

         \[\leadsto \color{blue}{\left(-1 \cdot t\right) \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

      2. neg-mul-1 44.9%

         \[\leadsto \color{blue}{\left(-t\right)} \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) \]

      3. *-commutative 44.9%

         \[\leadsto \left(-t\right) \cdot \left(z \cdot \left(a \cdot b - \color{blue}{i \cdot c}\right)\right) \]

   6. Simplified 44.9%

      \[\leadsto \color{blue}{\left(-t\right) \cdot \left(z \cdot \left(a \cdot b - i \cdot c\right)\right)} \]

   7. Taylor expanded in a around 0 38.6%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 38.6%

         \[\leadsto c \cdot \left(i \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

   9. Simplified 38.6%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(z \cdot t\right)\right)} \]

   if 4.4999999999999998e-149 < y5 < 2.3e72

   1. Initial program 38.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 44.8%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in y4 around inf 34.8%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 34.7%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 30.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -2.5 \cdot 10^{+119}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq -1.5 \cdot 10^{-128}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y5 \leq 3.4 \cdot 10^{-213}:\\ \;\;\;\;j \cdot \left(i \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y5 \leq 4.5 \cdot 10^{-149}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{elif}\;y5 \leq 2.3 \cdot 10^{+72}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 39: 20.2% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -1.05 \cdot 10^{+122}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -5.2 \cdot 10^{-60}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 1.45 \cdot 10^{-213}:\\ \;\;\;\;i \cdot \left(\left(z \cdot y1\right) \cdot \left(-k\right)\right)\\ \mathbf{elif}\;y2 \leq 2.4 \cdot 10^{+56}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 2.2 \cdot 10^{+219}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -1.05e+122)
   (* y1 (* y4 (* k y2)))
   (if (<= y2 -5.2e-60)
     (* a (* t (* y2 y5)))
     (if (<= y2 1.45e-213)
       (* i (* (* z y1) (- k)))
       (if (<= y2 2.4e+56)
         (* a (* x (* y b)))
         (if (<= y2 2.2e+219) (* k (* y1 (* y2 y4))) (* c (* (* z t) 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 (y2 <= -1.05e+122) {
		tmp = y1 * (y4 * (k * y2));
	} else if (y2 <= -5.2e-60) {
		tmp = a * (t * (y2 * y5));
	} else if (y2 <= 1.45e-213) {
		tmp = i * ((z * y1) * -k);
	} else if (y2 <= 2.4e+56) {
		tmp = a * (x * (y * b));
	} else if (y2 <= 2.2e+219) {
		tmp = k * (y1 * (y2 * y4));
	} else {
		tmp = c * ((z * t) * 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 (y2 <= (-1.05d+122)) then
        tmp = y1 * (y4 * (k * y2))
    else if (y2 <= (-5.2d-60)) then
        tmp = a * (t * (y2 * y5))
    else if (y2 <= 1.45d-213) then
        tmp = i * ((z * y1) * -k)
    else if (y2 <= 2.4d+56) then
        tmp = a * (x * (y * b))
    else if (y2 <= 2.2d+219) then
        tmp = k * (y1 * (y2 * y4))
    else
        tmp = c * ((z * t) * 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 (y2 <= -1.05e+122) {
		tmp = y1 * (y4 * (k * y2));
	} else if (y2 <= -5.2e-60) {
		tmp = a * (t * (y2 * y5));
	} else if (y2 <= 1.45e-213) {
		tmp = i * ((z * y1) * -k);
	} else if (y2 <= 2.4e+56) {
		tmp = a * (x * (y * b));
	} else if (y2 <= 2.2e+219) {
		tmp = k * (y1 * (y2 * y4));
	} else {
		tmp = c * ((z * t) * 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 y2 <= -1.05e+122:
		tmp = y1 * (y4 * (k * y2))
	elif y2 <= -5.2e-60:
		tmp = a * (t * (y2 * y5))
	elif y2 <= 1.45e-213:
		tmp = i * ((z * y1) * -k)
	elif y2 <= 2.4e+56:
		tmp = a * (x * (y * b))
	elif y2 <= 2.2e+219:
		tmp = k * (y1 * (y2 * y4))
	else:
		tmp = c * ((z * t) * 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 (y2 <= -1.05e+122)
		tmp = Float64(y1 * Float64(y4 * Float64(k * y2)));
	elseif (y2 <= -5.2e-60)
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	elseif (y2 <= 1.45e-213)
		tmp = Float64(i * Float64(Float64(z * y1) * Float64(-k)));
	elseif (y2 <= 2.4e+56)
		tmp = Float64(a * Float64(x * Float64(y * b)));
	elseif (y2 <= 2.2e+219)
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	else
		tmp = Float64(c * Float64(Float64(z * t) * 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 (y2 <= -1.05e+122)
		tmp = y1 * (y4 * (k * y2));
	elseif (y2 <= -5.2e-60)
		tmp = a * (t * (y2 * y5));
	elseif (y2 <= 1.45e-213)
		tmp = i * ((z * y1) * -k);
	elseif (y2 <= 2.4e+56)
		tmp = a * (x * (y * b));
	elseif (y2 <= 2.2e+219)
		tmp = k * (y1 * (y2 * y4));
	else
		tmp = c * ((z * t) * 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[y2, -1.05e+122], N[(y1 * N[(y4 * N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -5.2e-60], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.45e-213], N[(i * N[(N[(z * y1), $MachinePrecision] * (-k)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.4e+56], N[(a * N[(x * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.2e+219], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(z * t), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y2 < -1.05000000000000008e122

   1. Initial program 39.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 39.8%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in y4 around inf 40.1%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 47.3%

      \[\leadsto y1 \cdot \left(y4 \cdot \color{blue}{\left(k \cdot y2\right)}\right) \]

   if -1.05000000000000008e122 < y2 < -5.1999999999999995e-60

   1. Initial program 28.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 37.8%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in y5 around inf 35.4%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot j\right) - -1 \cdot \left(a \cdot y2\right)\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 35.4%

         \[\leadsto t \cdot \left(y5 \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j - a \cdot y2\right)\right)}\right) \]

   6. Simplified 35.4%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\right)} \]

   7. Taylor expanded in i around 0 27.2%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 27.2%

         \[\leadsto a \cdot \color{blue}{\left(\left(y2 \cdot y5\right) \cdot t\right)} \]

   9. Simplified 27.2%

      \[\leadsto \color{blue}{a \cdot \left(\left(y2 \cdot y5\right) \cdot t\right)} \]

   if -5.1999999999999995e-60 < y2 < 1.45e-213

   1. Initial program 35.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 38.5%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in i around inf 38.8%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in j around 0 29.8%

      \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y1 \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 29.8%

         \[\leadsto i \cdot \color{blue}{\left(-k \cdot \left(y1 \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 29.8%

         \[\leadsto i \cdot \color{blue}{\left(k \cdot \left(-y1 \cdot z\right)\right)} \]

      3. distribute-rgt-neg-in 29.8%

         \[\leadsto i \cdot \left(k \cdot \color{blue}{\left(y1 \cdot \left(-z\right)\right)}\right) \]

   7. Simplified 29.8%

      \[\leadsto i \cdot \color{blue}{\left(k \cdot \left(y1 \cdot \left(-z\right)\right)\right)} \]

   if 1.45e-213 < y2 < 2.40000000000000013e56

   1. Initial program 44.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 43.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 27.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 27.0%

         \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y - t \cdot z\right) \cdot b\right)} \]

      2. *-commutative 27.0%

         \[\leadsto a \cdot \left(\left(\color{blue}{y \cdot x} - t \cdot z\right) \cdot b\right) \]

   6. Simplified 27.0%

      \[\leadsto \color{blue}{a \cdot \left(\left(y \cdot x - t \cdot z\right) \cdot b\right)} \]

   7. Taylor expanded in y around inf 20.5%

      \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot y\right)} \cdot b\right) \]
   8. Step-by-step derivation

      1. *-commutative 20.5%

         \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot b\right) \]

   9. Simplified 20.5%

      \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot b\right) \]

   10. Taylor expanded in y around 0 20.5%

       \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 18.8%

          \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot x\right) \cdot y\right)} \]

       2. *-commutative 18.8%

          \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot b\right)} \cdot y\right) \]

       3. associate-*l* 25.3%

          \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

   12. Simplified 25.3%

       \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

   if 2.40000000000000013e56 < y2 < 2.2000000000000001e219

   1. Initial program 17.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 49.2%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in y4 around inf 46.6%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 41.4%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)} \]

   if 2.2000000000000001e219 < y2

   1. Initial program 14.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 64.3%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in z around inf 52.4%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 52.4%

         \[\leadsto \color{blue}{\left(-1 \cdot t\right) \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

      2. neg-mul-1 52.4%

         \[\leadsto \color{blue}{\left(-t\right)} \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) \]

      3. *-commutative 52.4%

         \[\leadsto \left(-t\right) \cdot \left(z \cdot \left(a \cdot b - \color{blue}{i \cdot c}\right)\right) \]

   6. Simplified 52.4%

      \[\leadsto \color{blue}{\left(-t\right) \cdot \left(z \cdot \left(a \cdot b - i \cdot c\right)\right)} \]

   7. Taylor expanded in a around 0 65.0%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 65.0%

         \[\leadsto c \cdot \left(i \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

   9. Simplified 65.0%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(z \cdot t\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 33.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.05 \cdot 10^{+122}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -5.2 \cdot 10^{-60}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 1.45 \cdot 10^{-213}:\\ \;\;\;\;i \cdot \left(\left(z \cdot y1\right) \cdot \left(-k\right)\right)\\ \mathbf{elif}\;y2 \leq 2.4 \cdot 10^{+56}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 2.2 \cdot 10^{+219}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 40: 21.7% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{if}\;x \leq -6.6 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-196}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+158}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 5.7 \cdot 10^{+246}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* j (* x y1)))))
   (if (<= x -6.6e+65)
     t_1
     (if (<= x 1.6e-196)
       (* c (* (* z t) i))
       (if (<= x 3.3e+158)
         (* a (* t (* y2 y5)))
         (if (<= x 5.7e+246) (* b (* (* x y) a)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (j * (x * y1));
	double tmp;
	if (x <= -6.6e+65) {
		tmp = t_1;
	} else if (x <= 1.6e-196) {
		tmp = c * ((z * t) * i);
	} else if (x <= 3.3e+158) {
		tmp = a * (t * (y2 * y5));
	} else if (x <= 5.7e+246) {
		tmp = b * ((x * y) * a);
	} 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 = i * (j * (x * y1))
    if (x <= (-6.6d+65)) then
        tmp = t_1
    else if (x <= 1.6d-196) then
        tmp = c * ((z * t) * i)
    else if (x <= 3.3d+158) then
        tmp = a * (t * (y2 * y5))
    else if (x <= 5.7d+246) then
        tmp = b * ((x * y) * a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (j * (x * y1));
	double tmp;
	if (x <= -6.6e+65) {
		tmp = t_1;
	} else if (x <= 1.6e-196) {
		tmp = c * ((z * t) * i);
	} else if (x <= 3.3e+158) {
		tmp = a * (t * (y2 * y5));
	} else if (x <= 5.7e+246) {
		tmp = b * ((x * y) * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = i * (j * (x * y1))
	tmp = 0
	if x <= -6.6e+65:
		tmp = t_1
	elif x <= 1.6e-196:
		tmp = c * ((z * t) * i)
	elif x <= 3.3e+158:
		tmp = a * (t * (y2 * y5))
	elif x <= 5.7e+246:
		tmp = b * ((x * y) * a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(i * Float64(j * Float64(x * y1)))
	tmp = 0.0
	if (x <= -6.6e+65)
		tmp = t_1;
	elseif (x <= 1.6e-196)
		tmp = Float64(c * Float64(Float64(z * t) * i));
	elseif (x <= 3.3e+158)
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	elseif (x <= 5.7e+246)
		tmp = Float64(b * Float64(Float64(x * y) * a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = i * (j * (x * y1));
	tmp = 0.0;
	if (x <= -6.6e+65)
		tmp = t_1;
	elseif (x <= 1.6e-196)
		tmp = c * ((z * t) * i);
	elseif (x <= 3.3e+158)
		tmp = a * (t * (y2 * y5));
	elseif (x <= 5.7e+246)
		tmp = b * ((x * y) * a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.6e+65], t$95$1, If[LessEqual[x, 1.6e-196], N[(c * N[(N[(z * t), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.3e+158], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.7e+246], N[(b * N[(N[(x * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -6.60000000000000046e65 or 5.7e246 < x

   1. Initial program 21.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 59.2%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in i around inf 51.6%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in j around inf 44.0%

      \[\leadsto i \cdot \color{blue}{\left(j \cdot \left(x \cdot y1\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 44.0%

         \[\leadsto i \cdot \left(j \cdot \color{blue}{\left(y1 \cdot x\right)}\right) \]

   7. Simplified 44.0%

      \[\leadsto i \cdot \color{blue}{\left(j \cdot \left(y1 \cdot x\right)\right)} \]

   if -6.60000000000000046e65 < x < 1.6e-196

   1. Initial program 35.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 40.9%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in z around inf 34.5%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 34.5%

         \[\leadsto \color{blue}{\left(-1 \cdot t\right) \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

      2. neg-mul-1 34.5%

         \[\leadsto \color{blue}{\left(-t\right)} \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) \]

      3. *-commutative 34.5%

         \[\leadsto \left(-t\right) \cdot \left(z \cdot \left(a \cdot b - \color{blue}{i \cdot c}\right)\right) \]

   6. Simplified 34.5%

      \[\leadsto \color{blue}{\left(-t\right) \cdot \left(z \cdot \left(a \cdot b - i \cdot c\right)\right)} \]

   7. Taylor expanded in a around 0 22.3%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 22.3%

         \[\leadsto c \cdot \left(i \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

   9. Simplified 22.3%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(z \cdot t\right)\right)} \]

   if 1.6e-196 < x < 3.30000000000000017e158

   1. Initial program 38.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 49.2%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in y5 around inf 28.7%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot j\right) - -1 \cdot \left(a \cdot y2\right)\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 28.7%

         \[\leadsto t \cdot \left(y5 \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j - a \cdot y2\right)\right)}\right) \]

   6. Simplified 28.7%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\right)} \]

   7. Taylor expanded in i around 0 20.6%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 20.6%

         \[\leadsto a \cdot \color{blue}{\left(\left(y2 \cdot y5\right) \cdot t\right)} \]

   9. Simplified 20.6%

      \[\leadsto \color{blue}{a \cdot \left(\left(y2 \cdot y5\right) \cdot t\right)} \]

   if 3.30000000000000017e158 < x < 5.7e246

   1. Initial program 33.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 44.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 56.7%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 56.7%

         \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y - t \cdot z\right) \cdot b\right)} \]

      2. *-commutative 56.7%

         \[\leadsto a \cdot \left(\left(\color{blue}{y \cdot x} - t \cdot z\right) \cdot b\right) \]

   6. Simplified 56.7%

      \[\leadsto \color{blue}{a \cdot \left(\left(y \cdot x - t \cdot z\right) \cdot b\right)} \]

   7. Taylor expanded in y around inf 51.6%

      \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot y\right)} \cdot b\right) \]
   8. Step-by-step derivation

      1. *-commutative 51.6%

         \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot b\right) \]

   9. Simplified 51.6%

      \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot b\right) \]

   10. Taylor expanded in a around 0 51.6%

       \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative 51.6%

          \[\leadsto \color{blue}{\left(b \cdot \left(x \cdot y\right)\right) \cdot a} \]

       2. associate-*l* 61.8%

          \[\leadsto \color{blue}{b \cdot \left(\left(x \cdot y\right) \cdot a\right)} \]

   12. Simplified 61.8%

       \[\leadsto \color{blue}{b \cdot \left(\left(x \cdot y\right) \cdot a\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 29.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+65}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-196}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+158}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 5.7 \cdot 10^{+246}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 41: 19.7% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -5 \cdot 10^{+143}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 4.2 \cdot 10^{-203}:\\ \;\;\;\;j \cdot \left(i \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq 4.1 \cdot 10^{+55}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 3 \cdot 10^{+218}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -5e+143)
   (* y1 (* y4 (* k y2)))
   (if (<= y2 4.2e-203)
     (* j (* i (* x y1)))
     (if (<= y2 4.1e+55)
       (* a (* x (* y b)))
       (if (<= y2 3e+218) (* k (* y1 (* y2 y4))) (* c (* (* z t) 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 (y2 <= -5e+143) {
		tmp = y1 * (y4 * (k * y2));
	} else if (y2 <= 4.2e-203) {
		tmp = j * (i * (x * y1));
	} else if (y2 <= 4.1e+55) {
		tmp = a * (x * (y * b));
	} else if (y2 <= 3e+218) {
		tmp = k * (y1 * (y2 * y4));
	} else {
		tmp = c * ((z * t) * 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 (y2 <= (-5d+143)) then
        tmp = y1 * (y4 * (k * y2))
    else if (y2 <= 4.2d-203) then
        tmp = j * (i * (x * y1))
    else if (y2 <= 4.1d+55) then
        tmp = a * (x * (y * b))
    else if (y2 <= 3d+218) then
        tmp = k * (y1 * (y2 * y4))
    else
        tmp = c * ((z * t) * 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 (y2 <= -5e+143) {
		tmp = y1 * (y4 * (k * y2));
	} else if (y2 <= 4.2e-203) {
		tmp = j * (i * (x * y1));
	} else if (y2 <= 4.1e+55) {
		tmp = a * (x * (y * b));
	} else if (y2 <= 3e+218) {
		tmp = k * (y1 * (y2 * y4));
	} else {
		tmp = c * ((z * t) * 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 y2 <= -5e+143:
		tmp = y1 * (y4 * (k * y2))
	elif y2 <= 4.2e-203:
		tmp = j * (i * (x * y1))
	elif y2 <= 4.1e+55:
		tmp = a * (x * (y * b))
	elif y2 <= 3e+218:
		tmp = k * (y1 * (y2 * y4))
	else:
		tmp = c * ((z * t) * 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 (y2 <= -5e+143)
		tmp = Float64(y1 * Float64(y4 * Float64(k * y2)));
	elseif (y2 <= 4.2e-203)
		tmp = Float64(j * Float64(i * Float64(x * y1)));
	elseif (y2 <= 4.1e+55)
		tmp = Float64(a * Float64(x * Float64(y * b)));
	elseif (y2 <= 3e+218)
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	else
		tmp = Float64(c * Float64(Float64(z * t) * 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 (y2 <= -5e+143)
		tmp = y1 * (y4 * (k * y2));
	elseif (y2 <= 4.2e-203)
		tmp = j * (i * (x * y1));
	elseif (y2 <= 4.1e+55)
		tmp = a * (x * (y * b));
	elseif (y2 <= 3e+218)
		tmp = k * (y1 * (y2 * y4));
	else
		tmp = c * ((z * t) * 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[y2, -5e+143], N[(y1 * N[(y4 * N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 4.2e-203], N[(j * N[(i * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 4.1e+55], N[(a * N[(x * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 3e+218], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(z * t), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y2 < -5.00000000000000012e143

   1. Initial program 41.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 45.5%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in y4 around inf 46.2%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 50.8%

      \[\leadsto y1 \cdot \left(y4 \cdot \color{blue}{\left(k \cdot y2\right)}\right) \]

   if -5.00000000000000012e143 < y2 < 4.20000000000000004e-203

   1. Initial program 33.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 37.6%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in i around inf 34.7%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in j around inf 21.0%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 21.0%

         \[\leadsto \color{blue}{\left(j \cdot \left(x \cdot y1\right)\right) \cdot i} \]

      2. associate-*l* 21.7%

         \[\leadsto \color{blue}{j \cdot \left(\left(x \cdot y1\right) \cdot i\right)} \]

   7. Simplified 21.7%

      \[\leadsto \color{blue}{j \cdot \left(\left(x \cdot y1\right) \cdot i\right)} \]

   if 4.20000000000000004e-203 < y2 < 4.09999999999999981e55

   1. Initial program 43.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 44.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 26.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 26.2%

         \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y - t \cdot z\right) \cdot b\right)} \]

      2. *-commutative 26.2%

         \[\leadsto a \cdot \left(\left(\color{blue}{y \cdot x} - t \cdot z\right) \cdot b\right) \]

   6. Simplified 26.2%

      \[\leadsto \color{blue}{a \cdot \left(\left(y \cdot x - t \cdot z\right) \cdot b\right)} \]

   7. Taylor expanded in y around inf 19.4%

      \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot y\right)} \cdot b\right) \]
   8. Step-by-step derivation

      1. *-commutative 19.4%

         \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot b\right) \]

   9. Simplified 19.4%

      \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot b\right) \]

   10. Taylor expanded in y around 0 19.4%

       \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 17.7%

          \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot x\right) \cdot y\right)} \]

       2. *-commutative 17.7%

          \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot b\right)} \cdot y\right) \]

       3. associate-*l* 24.4%

          \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

   12. Simplified 24.4%

       \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

   if 4.09999999999999981e55 < y2 < 3.0000000000000001e218

   1. Initial program 17.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 49.2%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in y4 around inf 46.6%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 41.4%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)} \]

   if 3.0000000000000001e218 < y2

   1. Initial program 14.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 64.3%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in z around inf 52.4%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 52.4%

         \[\leadsto \color{blue}{\left(-1 \cdot t\right) \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

      2. neg-mul-1 52.4%

         \[\leadsto \color{blue}{\left(-t\right)} \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) \]

      3. *-commutative 52.4%

         \[\leadsto \left(-t\right) \cdot \left(z \cdot \left(a \cdot b - \color{blue}{i \cdot c}\right)\right) \]

   6. Simplified 52.4%

      \[\leadsto \color{blue}{\left(-t\right) \cdot \left(z \cdot \left(a \cdot b - i \cdot c\right)\right)} \]

   7. Taylor expanded in a around 0 65.0%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 65.0%

         \[\leadsto c \cdot \left(i \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

   9. Simplified 65.0%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(z \cdot t\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 29.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -5 \cdot 10^{+143}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 4.2 \cdot 10^{-203}:\\ \;\;\;\;j \cdot \left(i \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq 4.1 \cdot 10^{+55}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 3 \cdot 10^{+218}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 42: 21.5% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+45} \lor \neg \left(x \leq 1.02 \cdot 10^{+157}\right):\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= x -4.3e+45) (not (<= x 1.02e+157)))
   (* a (* (* x y) b))
   (* 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 ((x <= -4.3e+45) || !(x <= 1.02e+157)) {
		tmp = a * ((x * y) * b);
	} 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 ((x <= (-4.3d+45)) .or. (.not. (x <= 1.02d+157))) then
        tmp = a * ((x * y) * b)
    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 ((x <= -4.3e+45) || !(x <= 1.02e+157)) {
		tmp = a * ((x * y) * b);
	} 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 (x <= -4.3e+45) or not (x <= 1.02e+157):
		tmp = a * ((x * y) * b)
	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 ((x <= -4.3e+45) || !(x <= 1.02e+157))
		tmp = Float64(a * Float64(Float64(x * y) * b));
	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 ((x <= -4.3e+45) || ~((x <= 1.02e+157)))
		tmp = a * ((x * y) * b);
	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[Or[LessEqual[x, -4.3e+45], N[Not[LessEqual[x, 1.02e+157]], $MachinePrecision]], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.3000000000000003e45 or 1.02000000000000003e157 < x

   1. Initial program 24.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 33.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 38.1%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 38.1%

         \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y - t \cdot z\right) \cdot b\right)} \]

      2. *-commutative 38.1%

         \[\leadsto a \cdot \left(\left(\color{blue}{y \cdot x} - t \cdot z\right) \cdot b\right) \]

   6. Simplified 38.1%

      \[\leadsto \color{blue}{a \cdot \left(\left(y \cdot x - t \cdot z\right) \cdot b\right)} \]

   7. Taylor expanded in y around inf 34.3%

      \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot y\right)} \cdot b\right) \]
   8. Step-by-step derivation

      1. *-commutative 34.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot b\right) \]

   9. Simplified 34.3%

      \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot b\right) \]

   if -4.3000000000000003e45 < x < 1.02000000000000003e157

   1. Initial program 37.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 43.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in y5 around inf 28.8%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot j\right) - -1 \cdot \left(a \cdot y2\right)\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 28.8%

         \[\leadsto t \cdot \left(y5 \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j - a \cdot y2\right)\right)}\right) \]

   6. Simplified 28.8%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\right)} \]

   7. Taylor expanded in i around 0 19.7%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 19.7%

         \[\leadsto a \cdot \color{blue}{\left(\left(y2 \cdot y5\right) \cdot t\right)} \]

   9. Simplified 19.7%

      \[\leadsto \color{blue}{a \cdot \left(\left(y2 \cdot y5\right) \cdot t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 24.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+45} \lor \neg \left(x \leq 1.02 \cdot 10^{+157}\right):\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 43: 21.5% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+45} \lor \neg \left(x \leq 2.8 \cdot 10^{+159}\right):\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= x -4.2e+45) (not (<= x 2.8e+159)))
   (* b (* (* x y) a))
   (* 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 ((x <= -4.2e+45) || !(x <= 2.8e+159)) {
		tmp = b * ((x * y) * a);
	} 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 ((x <= (-4.2d+45)) .or. (.not. (x <= 2.8d+159))) then
        tmp = b * ((x * y) * a)
    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 ((x <= -4.2e+45) || !(x <= 2.8e+159)) {
		tmp = b * ((x * y) * a);
	} 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 (x <= -4.2e+45) or not (x <= 2.8e+159):
		tmp = b * ((x * y) * a)
	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 ((x <= -4.2e+45) || !(x <= 2.8e+159))
		tmp = Float64(b * Float64(Float64(x * y) * a));
	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 ((x <= -4.2e+45) || ~((x <= 2.8e+159)))
		tmp = b * ((x * y) * a);
	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[Or[LessEqual[x, -4.2e+45], N[Not[LessEqual[x, 2.8e+159]], $MachinePrecision]], N[(b * N[(N[(x * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.1999999999999999e45 or 2.8000000000000001e159 < x

   1. Initial program 24.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 33.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 38.1%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 38.1%

         \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y - t \cdot z\right) \cdot b\right)} \]

      2. *-commutative 38.1%

         \[\leadsto a \cdot \left(\left(\color{blue}{y \cdot x} - t \cdot z\right) \cdot b\right) \]

   6. Simplified 38.1%

      \[\leadsto \color{blue}{a \cdot \left(\left(y \cdot x - t \cdot z\right) \cdot b\right)} \]

   7. Taylor expanded in y around inf 34.3%

      \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot y\right)} \cdot b\right) \]
   8. Step-by-step derivation

      1. *-commutative 34.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot b\right) \]

   9. Simplified 34.3%

      \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot b\right) \]

   10. Taylor expanded in a around 0 34.3%

       \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative 34.3%

          \[\leadsto \color{blue}{\left(b \cdot \left(x \cdot y\right)\right) \cdot a} \]

       2. associate-*l* 37.9%

          \[\leadsto \color{blue}{b \cdot \left(\left(x \cdot y\right) \cdot a\right)} \]

   12. Simplified 37.9%

       \[\leadsto \color{blue}{b \cdot \left(\left(x \cdot y\right) \cdot a\right)} \]

   if -4.1999999999999999e45 < x < 2.8000000000000001e159

   1. Initial program 37.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 43.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in y5 around inf 28.8%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot j\right) - -1 \cdot \left(a \cdot y2\right)\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 28.8%

         \[\leadsto t \cdot \left(y5 \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j - a \cdot y2\right)\right)}\right) \]

   6. Simplified 28.8%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\right)} \]

   7. Taylor expanded in i around 0 19.7%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 19.7%

         \[\leadsto a \cdot \color{blue}{\left(\left(y2 \cdot y5\right) \cdot t\right)} \]

   9. Simplified 19.7%

      \[\leadsto \color{blue}{a \cdot \left(\left(y2 \cdot y5\right) \cdot t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 25.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+45} \lor \neg \left(x \leq 2.8 \cdot 10^{+159}\right):\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 44: 17.2% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(x \cdot \left(y \cdot b\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* 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(x * Float64(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[(x * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 33.3%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
2. Add Preprocessing

3. Taylor expanded in b around inf 36.6%

   \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

4. Taylor expanded in a around inf 26.2%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
5. Step-by-step derivation

   1. *-commutative 26.2%

      \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y - t \cdot z\right) \cdot b\right)} \]

   2. *-commutative 26.2%

      \[\leadsto a \cdot \left(\left(\color{blue}{y \cdot x} - t \cdot z\right) \cdot b\right) \]

6. Simplified 26.2%

   \[\leadsto \color{blue}{a \cdot \left(\left(y \cdot x - t \cdot z\right) \cdot b\right)} \]

7. Taylor expanded in y around inf 14.8%

   \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot y\right)} \cdot b\right) \]
8. Step-by-step derivation

   1. *-commutative 14.8%

      \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot b\right) \]

9. Simplified 14.8%

   \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot b\right) \]

10. Taylor expanded in y around 0 14.8%

    \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
11. Step-by-step derivation

    1. associate-*r* 14.8%

       \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot x\right) \cdot y\right)} \]

    2. *-commutative 14.8%

       \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot b\right)} \cdot y\right) \]

    3. associate-*l* 15.2%

       \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

12. Simplified 15.2%

    \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

13. Final simplification 15.2%

    \[\leadsto a \cdot \left(x \cdot \left(y \cdot b\right)\right) \]
14. Add Preprocessing

Developer target: 27.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot c - y5 \cdot a\\ t_2 := x \cdot y2 - z \cdot y3\\ t_3 := y2 \cdot t - y3 \cdot y\\ t_4 := k \cdot y2 - j \cdot y3\\ t_5 := y4 \cdot b - y5 \cdot i\\ t_6 := \left(j \cdot t - k \cdot y\right) \cdot t_5\\ t_7 := b \cdot a - i \cdot c\\ t_8 := t_7 \cdot \left(y \cdot x - t \cdot z\right)\\ t_9 := j \cdot x - k \cdot z\\ t_10 := \left(b \cdot y0 - i \cdot y1\right) \cdot t_9\\ t_11 := t_9 \cdot \left(y0 \cdot b - i \cdot y1\right)\\ t_12 := y4 \cdot y1 - y5 \cdot y0\\ t_13 := t_4 \cdot t_12\\ t_14 := \left(y2 \cdot k - y3 \cdot j\right) \cdot t_12\\ t_15 := \left(\left(\left(\left(k \cdot y\right) \cdot \left(y5 \cdot i\right) - \left(y \cdot b\right) \cdot \left(y4 \cdot k\right)\right) - \left(y5 \cdot t\right) \cdot \left(i \cdot j\right)\right) - \left(t_3 \cdot t_1 - t_14\right)\right) + \left(t_8 - \left(t_11 - \left(y2 \cdot x - y3 \cdot z\right) \cdot \left(c \cdot y0 - y1 \cdot a\right)\right)\right)\\ t_16 := \left(\left(t_6 - \left(y3 \cdot y\right) \cdot \left(y5 \cdot a - y4 \cdot c\right)\right) + \left(\left(y5 \cdot a\right) \cdot \left(t \cdot y2\right) + t_13\right)\right) + \left(t_2 \cdot \left(c \cdot y0 - a \cdot y1\right) - \left(t_10 - \left(y \cdot x - z \cdot t\right) \cdot t_7\right)\right)\\ t_17 := t \cdot y2 - y \cdot y3\\ \mathbf{if}\;y4 < -7.206256231996481 \cdot 10^{+60}:\\ \;\;\;\;\left(t_8 - \left(t_11 - t_6\right)\right) - \left(\frac{t_3}{\frac{1}{t_1}} - t_14\right)\\ \mathbf{elif}\;y4 < -3.364603505246317 \cdot 10^{-66}:\\ \;\;\;\;\left(\left(\left(\left(t \cdot c\right) \cdot \left(i \cdot z\right) - \left(a \cdot t\right) \cdot \left(b \cdot z\right)\right) - \left(y \cdot c\right) \cdot \left(i \cdot x\right)\right) - t_10\right) + \left(\left(y0 \cdot c - a \cdot y1\right) \cdot t_2 - \left(t_17 \cdot \left(y4 \cdot c - a \cdot y5\right) - \left(y1 \cdot y4 - y5 \cdot y0\right) \cdot t_4\right)\right)\\ \mathbf{elif}\;y4 < -1.2000065055686116 \cdot 10^{-105}:\\ \;\;\;\;t_16\\ \mathbf{elif}\;y4 < 6.718963124057495 \cdot 10^{-279}:\\ \;\;\;\;t_15\\ \mathbf{elif}\;y4 < 4.77962681403792 \cdot 10^{-222}:\\ \;\;\;\;t_16\\ \mathbf{elif}\;y4 < 2.2852241541266835 \cdot 10^{-175}:\\ \;\;\;\;t_15\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(k \cdot \left(i \cdot \left(z \cdot y1\right)\right) - \left(j \cdot \left(i \cdot \left(x \cdot y1\right)\right) + y0 \cdot \left(k \cdot \left(z \cdot b\right)\right)\right)\right)\right) + \left(z \cdot \left(y3 \cdot \left(a \cdot y1\right)\right) - \left(y2 \cdot \left(x \cdot \left(a \cdot y1\right)\right) + y0 \cdot \left(z \cdot \left(c \cdot y3\right)\right)\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot t_5\right) - t_17 \cdot t_1\right) + t_13\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y4 c) (* y5 a)))
        (t_2 (- (* x y2) (* z y3)))
        (t_3 (- (* y2 t) (* y3 y)))
        (t_4 (- (* k y2) (* j y3)))
        (t_5 (- (* y4 b) (* y5 i)))
        (t_6 (* (- (* j t) (* k y)) t_5))
        (t_7 (- (* b a) (* i c)))
        (t_8 (* t_7 (- (* y x) (* t z))))
        (t_9 (- (* j x) (* k z)))
        (t_10 (* (- (* b y0) (* i y1)) t_9))
        (t_11 (* t_9 (- (* y0 b) (* i y1))))
        (t_12 (- (* y4 y1) (* y5 y0)))
        (t_13 (* t_4 t_12))
        (t_14 (* (- (* y2 k) (* y3 j)) t_12))
        (t_15
         (+
          (-
           (-
            (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k)))
            (* (* y5 t) (* i j)))
           (- (* t_3 t_1) t_14))
          (- t_8 (- t_11 (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))))
        (t_16
         (+
          (+
           (- t_6 (* (* y3 y) (- (* y5 a) (* y4 c))))
           (+ (* (* y5 a) (* t y2)) t_13))
          (-
           (* t_2 (- (* c y0) (* a y1)))
           (- t_10 (* (- (* y x) (* z t)) t_7)))))
        (t_17 (- (* t y2) (* y y3))))
   (if (< y4 -7.206256231996481e+60)
     (- (- t_8 (- t_11 t_6)) (- (/ t_3 (/ 1.0 t_1)) t_14))
     (if (< y4 -3.364603505246317e-66)
       (+
        (-
         (- (- (* (* t c) (* i z)) (* (* a t) (* b z))) (* (* y c) (* i x)))
         t_10)
        (-
         (* (- (* y0 c) (* a y1)) t_2)
         (- (* t_17 (- (* y4 c) (* a y5))) (* (- (* y1 y4) (* y5 y0)) t_4))))
       (if (< y4 -1.2000065055686116e-105)
         t_16
         (if (< y4 6.718963124057495e-279)
           t_15
           (if (< y4 4.77962681403792e-222)
             t_16
             (if (< y4 2.2852241541266835e-175)
               t_15
               (+
                (-
                 (+
                  (+
                   (-
                    (* (- (* x y) (* z t)) (- (* a b) (* c i)))
                    (-
                     (* k (* i (* z y1)))
                     (+ (* j (* i (* x y1))) (* y0 (* k (* z b))))))
                   (-
                    (* z (* y3 (* a y1)))
                    (+ (* y2 (* x (* a y1))) (* y0 (* z (* c y3))))))
                  (* (- (* t j) (* y k)) t_5))
                 (* t_17 t_1))
                t_13)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y4 * c) - (y5 * a);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (y2 * t) - (y3 * y);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = (y4 * b) - (y5 * i);
	double t_6 = ((j * t) - (k * y)) * t_5;
	double t_7 = (b * a) - (i * c);
	double t_8 = t_7 * ((y * x) - (t * z));
	double t_9 = (j * x) - (k * z);
	double t_10 = ((b * y0) - (i * y1)) * t_9;
	double t_11 = t_9 * ((y0 * b) - (i * y1));
	double t_12 = (y4 * y1) - (y5 * y0);
	double t_13 = t_4 * t_12;
	double t_14 = ((y2 * k) - (y3 * j)) * t_12;
	double t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	double t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	double t_17 = (t * y2) - (y * y3);
	double tmp;
	if (y4 < -7.206256231996481e+60) {
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	} else if (y4 < -3.364603505246317e-66) {
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	} else if (y4 < -1.2000065055686116e-105) {
		tmp = t_16;
	} else if (y4 < 6.718963124057495e-279) {
		tmp = t_15;
	} else if (y4 < 4.77962681403792e-222) {
		tmp = t_16;
	} else if (y4 < 2.2852241541266835e-175) {
		tmp = t_15;
	} else {
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_10
    real(8) :: t_11
    real(8) :: t_12
    real(8) :: t_13
    real(8) :: t_14
    real(8) :: t_15
    real(8) :: t_16
    real(8) :: t_17
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = (y4 * c) - (y5 * a)
    t_2 = (x * y2) - (z * y3)
    t_3 = (y2 * t) - (y3 * y)
    t_4 = (k * y2) - (j * y3)
    t_5 = (y4 * b) - (y5 * i)
    t_6 = ((j * t) - (k * y)) * t_5
    t_7 = (b * a) - (i * c)
    t_8 = t_7 * ((y * x) - (t * z))
    t_9 = (j * x) - (k * z)
    t_10 = ((b * y0) - (i * y1)) * t_9
    t_11 = t_9 * ((y0 * b) - (i * y1))
    t_12 = (y4 * y1) - (y5 * y0)
    t_13 = t_4 * t_12
    t_14 = ((y2 * k) - (y3 * j)) * t_12
    t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))))
    t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)))
    t_17 = (t * y2) - (y * y3)
    if (y4 < (-7.206256231996481d+60)) then
        tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0d0 / t_1)) - t_14)
    else if (y4 < (-3.364603505246317d-66)) then
        tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)))
    else if (y4 < (-1.2000065055686116d-105)) then
        tmp = t_16
    else if (y4 < 6.718963124057495d-279) then
        tmp = t_15
    else if (y4 < 4.77962681403792d-222) then
        tmp = t_16
    else if (y4 < 2.2852241541266835d-175) then
        tmp = t_15
    else
        tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y4 * c) - (y5 * a);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (y2 * t) - (y3 * y);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = (y4 * b) - (y5 * i);
	double t_6 = ((j * t) - (k * y)) * t_5;
	double t_7 = (b * a) - (i * c);
	double t_8 = t_7 * ((y * x) - (t * z));
	double t_9 = (j * x) - (k * z);
	double t_10 = ((b * y0) - (i * y1)) * t_9;
	double t_11 = t_9 * ((y0 * b) - (i * y1));
	double t_12 = (y4 * y1) - (y5 * y0);
	double t_13 = t_4 * t_12;
	double t_14 = ((y2 * k) - (y3 * j)) * t_12;
	double t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	double t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	double t_17 = (t * y2) - (y * y3);
	double tmp;
	if (y4 < -7.206256231996481e+60) {
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	} else if (y4 < -3.364603505246317e-66) {
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	} else if (y4 < -1.2000065055686116e-105) {
		tmp = t_16;
	} else if (y4 < 6.718963124057495e-279) {
		tmp = t_15;
	} else if (y4 < 4.77962681403792e-222) {
		tmp = t_16;
	} else if (y4 < 2.2852241541266835e-175) {
		tmp = t_15;
	} else {
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y4 * c) - (y5 * a)
	t_2 = (x * y2) - (z * y3)
	t_3 = (y2 * t) - (y3 * y)
	t_4 = (k * y2) - (j * y3)
	t_5 = (y4 * b) - (y5 * i)
	t_6 = ((j * t) - (k * y)) * t_5
	t_7 = (b * a) - (i * c)
	t_8 = t_7 * ((y * x) - (t * z))
	t_9 = (j * x) - (k * z)
	t_10 = ((b * y0) - (i * y1)) * t_9
	t_11 = t_9 * ((y0 * b) - (i * y1))
	t_12 = (y4 * y1) - (y5 * y0)
	t_13 = t_4 * t_12
	t_14 = ((y2 * k) - (y3 * j)) * t_12
	t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))))
	t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)))
	t_17 = (t * y2) - (y * y3)
	tmp = 0
	if y4 < -7.206256231996481e+60:
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14)
	elif y4 < -3.364603505246317e-66:
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)))
	elif y4 < -1.2000065055686116e-105:
		tmp = t_16
	elif y4 < 6.718963124057495e-279:
		tmp = t_15
	elif y4 < 4.77962681403792e-222:
		tmp = t_16
	elif y4 < 2.2852241541266835e-175:
		tmp = t_15
	else:
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y4 * c) - Float64(y5 * a))
	t_2 = Float64(Float64(x * y2) - Float64(z * y3))
	t_3 = Float64(Float64(y2 * t) - Float64(y3 * y))
	t_4 = Float64(Float64(k * y2) - Float64(j * y3))
	t_5 = Float64(Float64(y4 * b) - Float64(y5 * i))
	t_6 = Float64(Float64(Float64(j * t) - Float64(k * y)) * t_5)
	t_7 = Float64(Float64(b * a) - Float64(i * c))
	t_8 = Float64(t_7 * Float64(Float64(y * x) - Float64(t * z)))
	t_9 = Float64(Float64(j * x) - Float64(k * z))
	t_10 = Float64(Float64(Float64(b * y0) - Float64(i * y1)) * t_9)
	t_11 = Float64(t_9 * Float64(Float64(y0 * b) - Float64(i * y1)))
	t_12 = Float64(Float64(y4 * y1) - Float64(y5 * y0))
	t_13 = Float64(t_4 * t_12)
	t_14 = Float64(Float64(Float64(y2 * k) - Float64(y3 * j)) * t_12)
	t_15 = Float64(Float64(Float64(Float64(Float64(Float64(k * y) * Float64(y5 * i)) - Float64(Float64(y * b) * Float64(y4 * k))) - Float64(Float64(y5 * t) * Float64(i * j))) - Float64(Float64(t_3 * t_1) - t_14)) + Float64(t_8 - Float64(t_11 - Float64(Float64(Float64(y2 * x) - Float64(y3 * z)) * Float64(Float64(c * y0) - Float64(y1 * a))))))
	t_16 = Float64(Float64(Float64(t_6 - Float64(Float64(y3 * y) * Float64(Float64(y5 * a) - Float64(y4 * c)))) + Float64(Float64(Float64(y5 * a) * Float64(t * y2)) + t_13)) + Float64(Float64(t_2 * Float64(Float64(c * y0) - Float64(a * y1))) - Float64(t_10 - Float64(Float64(Float64(y * x) - Float64(z * t)) * t_7))))
	t_17 = Float64(Float64(t * y2) - Float64(y * y3))
	tmp = 0.0
	if (y4 < -7.206256231996481e+60)
		tmp = Float64(Float64(t_8 - Float64(t_11 - t_6)) - Float64(Float64(t_3 / Float64(1.0 / t_1)) - t_14));
	elseif (y4 < -3.364603505246317e-66)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(t * c) * Float64(i * z)) - Float64(Float64(a * t) * Float64(b * z))) - Float64(Float64(y * c) * Float64(i * x))) - t_10) + Float64(Float64(Float64(Float64(y0 * c) - Float64(a * y1)) * t_2) - Float64(Float64(t_17 * Float64(Float64(y4 * c) - Float64(a * y5))) - Float64(Float64(Float64(y1 * y4) - Float64(y5 * y0)) * t_4))));
	elseif (y4 < -1.2000065055686116e-105)
		tmp = t_16;
	elseif (y4 < 6.718963124057495e-279)
		tmp = t_15;
	elseif (y4 < 4.77962681403792e-222)
		tmp = t_16;
	elseif (y4 < 2.2852241541266835e-175)
		tmp = t_15;
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) - Float64(z * t)) * Float64(Float64(a * b) - Float64(c * i))) - Float64(Float64(k * Float64(i * Float64(z * y1))) - Float64(Float64(j * Float64(i * Float64(x * y1))) + Float64(y0 * Float64(k * Float64(z * b)))))) + Float64(Float64(z * Float64(y3 * Float64(a * y1))) - Float64(Float64(y2 * Float64(x * Float64(a * y1))) + Float64(y0 * Float64(z * Float64(c * y3)))))) + Float64(Float64(Float64(t * j) - Float64(y * k)) * t_5)) - Float64(t_17 * t_1)) + t_13);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y4 * c) - (y5 * a);
	t_2 = (x * y2) - (z * y3);
	t_3 = (y2 * t) - (y3 * y);
	t_4 = (k * y2) - (j * y3);
	t_5 = (y4 * b) - (y5 * i);
	t_6 = ((j * t) - (k * y)) * t_5;
	t_7 = (b * a) - (i * c);
	t_8 = t_7 * ((y * x) - (t * z));
	t_9 = (j * x) - (k * z);
	t_10 = ((b * y0) - (i * y1)) * t_9;
	t_11 = t_9 * ((y0 * b) - (i * y1));
	t_12 = (y4 * y1) - (y5 * y0);
	t_13 = t_4 * t_12;
	t_14 = ((y2 * k) - (y3 * j)) * t_12;
	t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	t_17 = (t * y2) - (y * y3);
	tmp = 0.0;
	if (y4 < -7.206256231996481e+60)
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	elseif (y4 < -3.364603505246317e-66)
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	elseif (y4 < -1.2000065055686116e-105)
		tmp = t_16;
	elseif (y4 < 6.718963124057495e-279)
		tmp = t_15;
	elseif (y4 < 4.77962681403792e-222)
		tmp = t_16;
	elseif (y4 < 2.2852241541266835e-175)
		tmp = t_15;
	else
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y4 * c), $MachinePrecision] - N[(y5 * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y2 * t), $MachinePrecision] - N[(y3 * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(y4 * b), $MachinePrecision] - N[(y5 * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision] * t$95$5), $MachinePrecision]}, Block[{t$95$7 = N[(N[(b * a), $MachinePrecision] - N[(i * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(t$95$7 * N[(N[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$10 = N[(N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision] * t$95$9), $MachinePrecision]}, Block[{t$95$11 = N[(t$95$9 * N[(N[(y0 * b), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$12 = N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$13 = N[(t$95$4 * t$95$12), $MachinePrecision]}, Block[{t$95$14 = N[(N[(N[(y2 * k), $MachinePrecision] - N[(y3 * j), $MachinePrecision]), $MachinePrecision] * t$95$12), $MachinePrecision]}, Block[{t$95$15 = N[(N[(N[(N[(N[(N[(k * y), $MachinePrecision] * N[(y5 * i), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] * N[(y4 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y5 * t), $MachinePrecision] * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$3 * t$95$1), $MachinePrecision] - t$95$14), $MachinePrecision]), $MachinePrecision] + N[(t$95$8 - N[(t$95$11 - N[(N[(N[(y2 * x), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision] * N[(N[(c * y0), $MachinePrecision] - N[(y1 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$16 = N[(N[(N[(t$95$6 - N[(N[(y3 * y), $MachinePrecision] * N[(N[(y5 * a), $MachinePrecision] - N[(y4 * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y5 * a), $MachinePrecision] * N[(t * y2), $MachinePrecision]), $MachinePrecision] + t$95$13), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$10 - N[(N[(N[(y * x), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$17 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, If[Less[y4, -7.206256231996481e+60], N[(N[(t$95$8 - N[(t$95$11 - t$95$6), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$3 / N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision] - t$95$14), $MachinePrecision]), $MachinePrecision], If[Less[y4, -3.364603505246317e-66], N[(N[(N[(N[(N[(N[(t * c), $MachinePrecision] * N[(i * z), $MachinePrecision]), $MachinePrecision] - N[(N[(a * t), $MachinePrecision] * N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * c), $MachinePrecision] * N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$10), $MachinePrecision] + N[(N[(N[(N[(y0 * c), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision] - N[(N[(t$95$17 * N[(N[(y4 * c), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(y1 * y4), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision] * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[y4, -1.2000065055686116e-105], t$95$16, If[Less[y4, 6.718963124057495e-279], t$95$15, If[Less[y4, 4.77962681403792e-222], t$95$16, If[Less[y4, 2.2852241541266835e-175], t$95$15, N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(k * N[(i * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * N[(i * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(k * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(y3 * N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y2 * N[(x * N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(z * N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * t$95$5), $MachinePrecision]), $MachinePrecision] - N[(t$95$17 * t$95$1), $MachinePrecision]), $MachinePrecision] + t$95$13), $MachinePrecision]]]]]]]]]]]]]]]]]]]]]]]]

Reproduce

herbie shell --seed 2024021 
(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)))))