Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 30.1% → 41.9%

Time: 1.4min

Alternatives: 36

Speedup: 4.1×

• 89.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 30.1% 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: 41.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot y3 - x \cdot y2\\ t_2 := t \cdot y2 - y \cdot y3\\ t_3 := y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot t_2 + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ t_4 := x \cdot y - z \cdot t\\ t_5 := b \cdot t_4\\ t_6 := t \cdot j - y \cdot k\\ t_7 := c \cdot y0 - a \cdot y1\\ t_8 := y \cdot y3 - t \cdot y2\\ t_9 := y2 \cdot \left(\left(x \cdot t_7 + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ t_10 := y5 \cdot t_2\\ t_11 := a \cdot \left(y1 \cdot t_1 + \left(t_10 + t_5\right)\right)\\ \mathbf{if}\;y5 \leq -1.2 \cdot 10^{+109}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y5 \leq -3 \cdot 10^{-52}:\\ \;\;\;\;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(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y5 \leq -4.5 \cdot 10^{-113}:\\ \;\;\;\;t_9\\ \mathbf{elif}\;y5 \leq -6.6 \cdot 10^{-243}:\\ \;\;\;\;x \cdot \left(\left(i \cdot \left(j \cdot y1 - y \cdot c\right) + a \cdot \left(y \cdot b\right)\right) - y0 \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq 4.3 \cdot 10^{-280}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot t_6 + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot t_8\right)\\ \mathbf{elif}\;y5 \leq 1.95 \cdot 10^{-236}:\\ \;\;\;\;x \cdot \left(\left(y2 \cdot t_7 + y \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 2.7 \cdot 10^{-196}:\\ \;\;\;\;t_11\\ \mathbf{elif}\;y5 \leq 5.6 \cdot 10^{-123}:\\ \;\;\;\;c \cdot \left(y4 \cdot t_8 - \left(i \cdot t_4 + y0 \cdot t_1\right)\right)\\ \mathbf{elif}\;y5 \leq 4.9 \cdot 10^{-98}:\\ \;\;\;\;a \cdot t_5\\ \mathbf{elif}\;y5 \leq 5.8 \cdot 10^{-46}:\\ \;\;\;\;t_9\\ \mathbf{elif}\;y5 \leq 5.2 \cdot 10^{+18}:\\ \;\;\;\;t_11\\ \mathbf{elif}\;y5 \leq 1.3 \cdot 10^{+98}:\\ \;\;\;\;b \cdot \left(\left(a \cdot t_4 + y4 \cdot t_6\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq 8.2 \cdot 10^{+195}:\\ \;\;\;\;a \cdot t_10\\ \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 (- (* z y3) (* x y2)))
        (t_2 (- (* t y2) (* y y3)))
        (t_3
         (*
          y5
          (+
           (* i (- (* y k) (* t j)))
           (+ (* a t_2) (* y0 (- (* j y3) (* k y2)))))))
        (t_4 (- (* x y) (* z t)))
        (t_5 (* b t_4))
        (t_6 (- (* t j) (* y k)))
        (t_7 (- (* c y0) (* a y1)))
        (t_8 (- (* y y3) (* t y2)))
        (t_9
         (*
          y2
          (+
           (+ (* x t_7) (* k (- (* y1 y4) (* y0 y5))))
           (* t (- (* a y5) (* c y4))))))
        (t_10 (* y5 t_2))
        (t_11 (* a (+ (* y1 t_1) (+ t_10 t_5)))))
   (if (<= y5 -1.2e+109)
     t_3
     (if (<= y5 -3e-52)
       (*
        j
        (-
         (+ (* y3 (- (* y0 y5) (* y1 y4))) (* t (- (* b y4) (* i y5))))
         (* x (- (* b y0) (* i y1)))))
       (if (<= y5 -4.5e-113)
         t_9
         (if (<= y5 -6.6e-243)
           (*
            x
            (- (+ (* i (- (* j y1) (* y c))) (* a (* y b))) (* y0 (* b j))))
           (if (<= y5 4.3e-280)
             (* y4 (+ (+ (* b t_6) (* y1 (- (* k y2) (* j y3)))) (* c t_8)))
             (if (<= y5 1.95e-236)
               (*
                x
                (+
                 (+ (* y2 t_7) (* y (- (* a b) (* c i))))
                 (* j (- (* i y1) (* b y0)))))
               (if (<= y5 2.7e-196)
                 t_11
                 (if (<= y5 5.6e-123)
                   (* c (- (* y4 t_8) (+ (* i t_4) (* y0 t_1))))
                   (if (<= y5 4.9e-98)
                     (* a t_5)
                     (if (<= y5 5.8e-46)
                       t_9
                       (if (<= y5 5.2e+18)
                         t_11
                         (if (<= y5 1.3e+98)
                           (*
                            b
                            (+
                             (+ (* a t_4) (* y4 t_6))
                             (* y0 (- (* z k) (* x j)))))
                           (if (<= y5 8.2e+195) (* a t_10) 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 = (z * y3) - (x * y2);
	double t_2 = (t * y2) - (y * y3);
	double t_3 = y5 * ((i * ((y * k) - (t * j))) + ((a * t_2) + (y0 * ((j * y3) - (k * y2)))));
	double t_4 = (x * y) - (z * t);
	double t_5 = b * t_4;
	double t_6 = (t * j) - (y * k);
	double t_7 = (c * y0) - (a * y1);
	double t_8 = (y * y3) - (t * y2);
	double t_9 = y2 * (((x * t_7) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	double t_10 = y5 * t_2;
	double t_11 = a * ((y1 * t_1) + (t_10 + t_5));
	double tmp;
	if (y5 <= -1.2e+109) {
		tmp = t_3;
	} else if (y5 <= -3e-52) {
		tmp = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) - (x * ((b * y0) - (i * y1))));
	} else if (y5 <= -4.5e-113) {
		tmp = t_9;
	} else if (y5 <= -6.6e-243) {
		tmp = x * (((i * ((j * y1) - (y * c))) + (a * (y * b))) - (y0 * (b * j)));
	} else if (y5 <= 4.3e-280) {
		tmp = y4 * (((b * t_6) + (y1 * ((k * y2) - (j * y3)))) + (c * t_8));
	} else if (y5 <= 1.95e-236) {
		tmp = x * (((y2 * t_7) + (y * ((a * b) - (c * i)))) + (j * ((i * y1) - (b * y0))));
	} else if (y5 <= 2.7e-196) {
		tmp = t_11;
	} else if (y5 <= 5.6e-123) {
		tmp = c * ((y4 * t_8) - ((i * t_4) + (y0 * t_1)));
	} else if (y5 <= 4.9e-98) {
		tmp = a * t_5;
	} else if (y5 <= 5.8e-46) {
		tmp = t_9;
	} else if (y5 <= 5.2e+18) {
		tmp = t_11;
	} else if (y5 <= 1.3e+98) {
		tmp = b * (((a * t_4) + (y4 * t_6)) + (y0 * ((z * k) - (x * j))));
	} else if (y5 <= 8.2e+195) {
		tmp = a * t_10;
	} 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_10
    real(8) :: t_11
    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 = (z * y3) - (x * y2)
    t_2 = (t * y2) - (y * y3)
    t_3 = y5 * ((i * ((y * k) - (t * j))) + ((a * t_2) + (y0 * ((j * y3) - (k * y2)))))
    t_4 = (x * y) - (z * t)
    t_5 = b * t_4
    t_6 = (t * j) - (y * k)
    t_7 = (c * y0) - (a * y1)
    t_8 = (y * y3) - (t * y2)
    t_9 = y2 * (((x * t_7) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
    t_10 = y5 * t_2
    t_11 = a * ((y1 * t_1) + (t_10 + t_5))
    if (y5 <= (-1.2d+109)) then
        tmp = t_3
    else if (y5 <= (-3d-52)) then
        tmp = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) - (x * ((b * y0) - (i * y1))))
    else if (y5 <= (-4.5d-113)) then
        tmp = t_9
    else if (y5 <= (-6.6d-243)) then
        tmp = x * (((i * ((j * y1) - (y * c))) + (a * (y * b))) - (y0 * (b * j)))
    else if (y5 <= 4.3d-280) then
        tmp = y4 * (((b * t_6) + (y1 * ((k * y2) - (j * y3)))) + (c * t_8))
    else if (y5 <= 1.95d-236) then
        tmp = x * (((y2 * t_7) + (y * ((a * b) - (c * i)))) + (j * ((i * y1) - (b * y0))))
    else if (y5 <= 2.7d-196) then
        tmp = t_11
    else if (y5 <= 5.6d-123) then
        tmp = c * ((y4 * t_8) - ((i * t_4) + (y0 * t_1)))
    else if (y5 <= 4.9d-98) then
        tmp = a * t_5
    else if (y5 <= 5.8d-46) then
        tmp = t_9
    else if (y5 <= 5.2d+18) then
        tmp = t_11
    else if (y5 <= 1.3d+98) then
        tmp = b * (((a * t_4) + (y4 * t_6)) + (y0 * ((z * k) - (x * j))))
    else if (y5 <= 8.2d+195) then
        tmp = a * t_10
    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 = (z * y3) - (x * y2);
	double t_2 = (t * y2) - (y * y3);
	double t_3 = y5 * ((i * ((y * k) - (t * j))) + ((a * t_2) + (y0 * ((j * y3) - (k * y2)))));
	double t_4 = (x * y) - (z * t);
	double t_5 = b * t_4;
	double t_6 = (t * j) - (y * k);
	double t_7 = (c * y0) - (a * y1);
	double t_8 = (y * y3) - (t * y2);
	double t_9 = y2 * (((x * t_7) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	double t_10 = y5 * t_2;
	double t_11 = a * ((y1 * t_1) + (t_10 + t_5));
	double tmp;
	if (y5 <= -1.2e+109) {
		tmp = t_3;
	} else if (y5 <= -3e-52) {
		tmp = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) - (x * ((b * y0) - (i * y1))));
	} else if (y5 <= -4.5e-113) {
		tmp = t_9;
	} else if (y5 <= -6.6e-243) {
		tmp = x * (((i * ((j * y1) - (y * c))) + (a * (y * b))) - (y0 * (b * j)));
	} else if (y5 <= 4.3e-280) {
		tmp = y4 * (((b * t_6) + (y1 * ((k * y2) - (j * y3)))) + (c * t_8));
	} else if (y5 <= 1.95e-236) {
		tmp = x * (((y2 * t_7) + (y * ((a * b) - (c * i)))) + (j * ((i * y1) - (b * y0))));
	} else if (y5 <= 2.7e-196) {
		tmp = t_11;
	} else if (y5 <= 5.6e-123) {
		tmp = c * ((y4 * t_8) - ((i * t_4) + (y0 * t_1)));
	} else if (y5 <= 4.9e-98) {
		tmp = a * t_5;
	} else if (y5 <= 5.8e-46) {
		tmp = t_9;
	} else if (y5 <= 5.2e+18) {
		tmp = t_11;
	} else if (y5 <= 1.3e+98) {
		tmp = b * (((a * t_4) + (y4 * t_6)) + (y0 * ((z * k) - (x * j))));
	} else if (y5 <= 8.2e+195) {
		tmp = a * t_10;
	} 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 = (z * y3) - (x * y2)
	t_2 = (t * y2) - (y * y3)
	t_3 = y5 * ((i * ((y * k) - (t * j))) + ((a * t_2) + (y0 * ((j * y3) - (k * y2)))))
	t_4 = (x * y) - (z * t)
	t_5 = b * t_4
	t_6 = (t * j) - (y * k)
	t_7 = (c * y0) - (a * y1)
	t_8 = (y * y3) - (t * y2)
	t_9 = y2 * (((x * t_7) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
	t_10 = y5 * t_2
	t_11 = a * ((y1 * t_1) + (t_10 + t_5))
	tmp = 0
	if y5 <= -1.2e+109:
		tmp = t_3
	elif y5 <= -3e-52:
		tmp = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) - (x * ((b * y0) - (i * y1))))
	elif y5 <= -4.5e-113:
		tmp = t_9
	elif y5 <= -6.6e-243:
		tmp = x * (((i * ((j * y1) - (y * c))) + (a * (y * b))) - (y0 * (b * j)))
	elif y5 <= 4.3e-280:
		tmp = y4 * (((b * t_6) + (y1 * ((k * y2) - (j * y3)))) + (c * t_8))
	elif y5 <= 1.95e-236:
		tmp = x * (((y2 * t_7) + (y * ((a * b) - (c * i)))) + (j * ((i * y1) - (b * y0))))
	elif y5 <= 2.7e-196:
		tmp = t_11
	elif y5 <= 5.6e-123:
		tmp = c * ((y4 * t_8) - ((i * t_4) + (y0 * t_1)))
	elif y5 <= 4.9e-98:
		tmp = a * t_5
	elif y5 <= 5.8e-46:
		tmp = t_9
	elif y5 <= 5.2e+18:
		tmp = t_11
	elif y5 <= 1.3e+98:
		tmp = b * (((a * t_4) + (y4 * t_6)) + (y0 * ((z * k) - (x * j))))
	elif y5 <= 8.2e+195:
		tmp = a * t_10
	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(z * y3) - Float64(x * y2))
	t_2 = Float64(Float64(t * y2) - Float64(y * y3))
	t_3 = Float64(y5 * Float64(Float64(i * Float64(Float64(y * k) - Float64(t * j))) + Float64(Float64(a * t_2) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))))))
	t_4 = Float64(Float64(x * y) - Float64(z * t))
	t_5 = Float64(b * t_4)
	t_6 = Float64(Float64(t * j) - Float64(y * k))
	t_7 = Float64(Float64(c * y0) - Float64(a * y1))
	t_8 = Float64(Float64(y * y3) - Float64(t * y2))
	t_9 = Float64(y2 * Float64(Float64(Float64(x * t_7) + Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))))
	t_10 = Float64(y5 * t_2)
	t_11 = Float64(a * Float64(Float64(y1 * t_1) + Float64(t_10 + t_5)))
	tmp = 0.0
	if (y5 <= -1.2e+109)
		tmp = t_3;
	elseif (y5 <= -3e-52)
		tmp = 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(b * y0) - Float64(i * y1)))));
	elseif (y5 <= -4.5e-113)
		tmp = t_9;
	elseif (y5 <= -6.6e-243)
		tmp = Float64(x * Float64(Float64(Float64(i * Float64(Float64(j * y1) - Float64(y * c))) + Float64(a * Float64(y * b))) - Float64(y0 * Float64(b * j))));
	elseif (y5 <= 4.3e-280)
		tmp = Float64(y4 * Float64(Float64(Float64(b * t_6) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * t_8)));
	elseif (y5 <= 1.95e-236)
		tmp = Float64(x * Float64(Float64(Float64(y2 * t_7) + Float64(y * Float64(Float64(a * b) - Float64(c * i)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (y5 <= 2.7e-196)
		tmp = t_11;
	elseif (y5 <= 5.6e-123)
		tmp = Float64(c * Float64(Float64(y4 * t_8) - Float64(Float64(i * t_4) + Float64(y0 * t_1))));
	elseif (y5 <= 4.9e-98)
		tmp = Float64(a * t_5);
	elseif (y5 <= 5.8e-46)
		tmp = t_9;
	elseif (y5 <= 5.2e+18)
		tmp = t_11;
	elseif (y5 <= 1.3e+98)
		tmp = Float64(b * Float64(Float64(Float64(a * t_4) + Float64(y4 * t_6)) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (y5 <= 8.2e+195)
		tmp = Float64(a * t_10);
	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 = (z * y3) - (x * y2);
	t_2 = (t * y2) - (y * y3);
	t_3 = y5 * ((i * ((y * k) - (t * j))) + ((a * t_2) + (y0 * ((j * y3) - (k * y2)))));
	t_4 = (x * y) - (z * t);
	t_5 = b * t_4;
	t_6 = (t * j) - (y * k);
	t_7 = (c * y0) - (a * y1);
	t_8 = (y * y3) - (t * y2);
	t_9 = y2 * (((x * t_7) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	t_10 = y5 * t_2;
	t_11 = a * ((y1 * t_1) + (t_10 + t_5));
	tmp = 0.0;
	if (y5 <= -1.2e+109)
		tmp = t_3;
	elseif (y5 <= -3e-52)
		tmp = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) - (x * ((b * y0) - (i * y1))));
	elseif (y5 <= -4.5e-113)
		tmp = t_9;
	elseif (y5 <= -6.6e-243)
		tmp = x * (((i * ((j * y1) - (y * c))) + (a * (y * b))) - (y0 * (b * j)));
	elseif (y5 <= 4.3e-280)
		tmp = y4 * (((b * t_6) + (y1 * ((k * y2) - (j * y3)))) + (c * t_8));
	elseif (y5 <= 1.95e-236)
		tmp = x * (((y2 * t_7) + (y * ((a * b) - (c * i)))) + (j * ((i * y1) - (b * y0))));
	elseif (y5 <= 2.7e-196)
		tmp = t_11;
	elseif (y5 <= 5.6e-123)
		tmp = c * ((y4 * t_8) - ((i * t_4) + (y0 * t_1)));
	elseif (y5 <= 4.9e-98)
		tmp = a * t_5;
	elseif (y5 <= 5.8e-46)
		tmp = t_9;
	elseif (y5 <= 5.2e+18)
		tmp = t_11;
	elseif (y5 <= 1.3e+98)
		tmp = b * (((a * t_4) + (y4 * t_6)) + (y0 * ((z * k) - (x * j))));
	elseif (y5 <= 8.2e+195)
		tmp = a * t_10;
	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[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y5 * N[(N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * t$95$2), $MachinePrecision] + N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(b * t$95$4), $MachinePrecision]}, Block[{t$95$6 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(y2 * N[(N[(N[(x * t$95$7), $MachinePrecision] + N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$10 = N[(y5 * t$95$2), $MachinePrecision]}, Block[{t$95$11 = N[(a * N[(N[(y1 * t$95$1), $MachinePrecision] + N[(t$95$10 + t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -1.2e+109], t$95$3, If[LessEqual[y5, -3e-52], 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[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -4.5e-113], t$95$9, If[LessEqual[y5, -6.6e-243], N[(x * N[(N[(N[(i * N[(N[(j * y1), $MachinePrecision] - N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y0 * N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 4.3e-280], N[(y4 * N[(N[(N[(b * t$95$6), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.95e-236], N[(x * N[(N[(N[(y2 * t$95$7), $MachinePrecision] + N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 2.7e-196], t$95$11, If[LessEqual[y5, 5.6e-123], N[(c * N[(N[(y4 * t$95$8), $MachinePrecision] - N[(N[(i * t$95$4), $MachinePrecision] + N[(y0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 4.9e-98], N[(a * t$95$5), $MachinePrecision], If[LessEqual[y5, 5.8e-46], t$95$9, If[LessEqual[y5, 5.2e+18], t$95$11, If[LessEqual[y5, 1.3e+98], N[(b * N[(N[(N[(a * t$95$4), $MachinePrecision] + N[(y4 * t$95$6), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 8.2e+195], N[(a * t$95$10), $MachinePrecision], t$95$3]]]]]]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 11 regimes

2. if y5 < -1.19999999999999994e109 or 8.2000000000000001e195 < y5

   1. Initial program 16.5%

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

   3. Simplified 20.1%

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

   4. Taylor expanded in y5 around -inf 65.7%

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

   if -1.19999999999999994e109 < y5 < -3e-52

   1. Initial program 31.5%

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

   3. Simplified 45.2%

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

   4. Taylor expanded in j around inf 65.7%

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

   if -3e-52 < y5 < -4.5000000000000001e-113 or 4.90000000000000014e-98 < y5 < 5.80000000000000009e-46

   1. Initial program 42.8%

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

   3. Simplified 42.8%

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

   4. Taylor expanded in y2 around inf 68.3%

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

   if -4.5000000000000001e-113 < y5 < -6.60000000000000026e-243

   1. Initial program 49.9%

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

   3. Simplified 49.9%

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

   4. Taylor expanded in x around inf 64.3%

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

   5. Taylor expanded in i around -inf 68.9%

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

   6. Taylor expanded in y2 around 0 68.9%

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

   if -6.60000000000000026e-243 < y5 < 4.2999999999999999e-280

   1. Initial program 22.2%

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

   3. Simplified 22.2%

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

   4. Taylor expanded in y4 around inf 67.1%

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

   if 4.2999999999999999e-280 < y5 < 1.95e-236

   1. Initial program 22.2%

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

   3. Simplified 22.2%

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

   4. Taylor expanded in x around inf 88.9%

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

   if 1.95e-236 < y5 < 2.69999999999999982e-196 or 5.80000000000000009e-46 < y5 < 5.2e18

   1. Initial program 32.5%

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

   3. Simplified 37.0%

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

   4. Taylor expanded in a around inf 69.2%

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

      1. mul-1-neg 69.2%

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

      2. mul-1-neg 69.2%

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

   6. Simplified 69.2%

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

   if 2.69999999999999982e-196 < y5 < 5.5999999999999998e-123

   1. Initial program 41.9%

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

   3. Simplified 41.9%

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

   4. Taylor expanded in c around inf 68.7%

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

   if 5.5999999999999998e-123 < y5 < 4.90000000000000014e-98

   1. Initial program 0.9%

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

   3. Simplified 17.6%

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

   4. Taylor expanded in a around inf 51.1%

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

      1. mul-1-neg 51.1%

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

      2. mul-1-neg 51.1%

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

   6. Simplified 51.1%

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

   7. Taylor expanded in b around inf 68.5%

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

   if 5.2e18 < y5 < 1.3e98

   1. Initial program 31.6%

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

   3. Simplified 31.6%

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

   4. Taylor expanded in b around inf 58.2%

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

   if 1.3e98 < y5 < 8.2000000000000001e195

   1. Initial program 14.1%

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

   3. Simplified 21.0%

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

   4. Taylor expanded in a around inf 45.0%

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

      1. mul-1-neg 45.0%

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

      2. mul-1-neg 45.0%

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

   6. Simplified 45.0%

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

   7. Taylor expanded in y5 around inf 45.6%

      \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)} \]
3. Recombined 11 regimes into one program.

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -1.2 \cdot 10^{+109}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y5 \leq -3 \cdot 10^{-52}:\\ \;\;\;\;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(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y5 \leq -4.5 \cdot 10^{-113}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -6.6 \cdot 10^{-243}:\\ \;\;\;\;x \cdot \left(\left(i \cdot \left(j \cdot y1 - y \cdot c\right) + a \cdot \left(y \cdot b\right)\right) - y0 \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq 4.3 \cdot 10^{-280}:\\ \;\;\;\;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}\;y5 \leq 1.95 \cdot 10^{-236}:\\ \;\;\;\;x \cdot \left(\left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + y \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 2.7 \cdot 10^{-196}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right) + \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) + b \cdot \left(x \cdot y - z \cdot t\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 5.6 \cdot 10^{-123}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right) - \left(i \cdot \left(x \cdot y - z \cdot t\right) + y0 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 4.9 \cdot 10^{-98}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y5 \leq 5.8 \cdot 10^{-46}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 5.2 \cdot 10^{+18}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right) + \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) + b \cdot \left(x \cdot y - z \cdot t\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 1.3 \cdot 10^{+98}:\\ \;\;\;\;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}\;y5 \leq 8.2 \cdot 10^{+195}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \end{array} \]

Alternative 2: 53.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(N[(N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision] * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, Infinity], t$95$2, N[(x * N[(N[(N[(i * N[(N[(j * y1), $MachinePrecision] - N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(y2 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y0 * N[(b * j), $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 90.5%

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

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

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in x around inf 37.3%

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

   5. Taylor expanded in i around -inf 39.5%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(\left(c \cdot y - y1 \cdot j\right) \cdot i\right) + \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2 + y \cdot \left(a \cdot b\right)\right)\right) - y0 \cdot \left(b \cdot j\right)\right)} \cdot x \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.5%

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

Alternative 3: 41.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i - a \cdot b\\ t_2 := t \cdot j - y \cdot k\\ t_3 := y4 \cdot \left(\left(b \cdot t_2 + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ t_4 := x \cdot y - z \cdot t\\ t_5 := y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ t_6 := c \cdot y0 - a \cdot y1\\ t_7 := x \cdot \left(\left(y2 \cdot t_6 + y \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{if}\;y5 \leq -2.1 \cdot 10^{+175}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y5 \leq -4.2 \cdot 10^{-238}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;y5 \leq 2.3 \cdot 10^{-279}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y5 \leq 4.2 \cdot 10^{-235}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;y5 \leq 5.6 \cdot 10^{-153}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y5 \leq 6.2 \cdot 10^{-113}:\\ \;\;\;\;z \cdot \left(y3 \cdot \left(a \cdot y1 - c \cdot y0\right) + \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + t \cdot t_1\right)\right)\\ \mathbf{elif}\;y5 \leq 7.2 \cdot 10^{-32}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot t_6 + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 7 \cdot 10^{+17}:\\ \;\;\;\;t \cdot \left(z \cdot t_1\right)\\ \mathbf{elif}\;y5 \leq 1.9 \cdot 10^{+99}:\\ \;\;\;\;b \cdot \left(\left(a \cdot t_4 + y4 \cdot t_2\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq 2.75 \cdot 10^{+141} \lor \neg \left(y5 \leq 5.8 \cdot 10^{+211}\right):\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot t_4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* c i) (* a b)))
        (t_2 (- (* t j) (* y k)))
        (t_3
         (*
          y4
          (+
           (+ (* b t_2) (* y1 (- (* k y2) (* j y3))))
           (* c (- (* y y3) (* t y2))))))
        (t_4 (- (* x y) (* z t)))
        (t_5
         (*
          y5
          (+
           (* i (- (* y k) (* t j)))
           (+ (* a (- (* t y2) (* y y3))) (* y0 (- (* j y3) (* k y2)))))))
        (t_6 (- (* c y0) (* a y1)))
        (t_7
         (*
          x
          (+
           (+ (* y2 t_6) (* y (- (* a b) (* c i))))
           (* j (- (* i y1) (* b y0)))))))
   (if (<= y5 -2.1e+175)
     t_5
     (if (<= y5 -4.2e-238)
       t_7
       (if (<= y5 2.3e-279)
         t_3
         (if (<= y5 4.2e-235)
           t_7
           (if (<= y5 5.6e-153)
             t_3
             (if (<= y5 6.2e-113)
               (*
                z
                (+
                 (* y3 (- (* a y1) (* c y0)))
                 (+ (* k (- (* b y0) (* i y1))) (* t t_1))))
               (if (<= y5 7.2e-32)
                 (*
                  y2
                  (+
                   (+ (* x t_6) (* k (- (* y1 y4) (* y0 y5))))
                   (* t (- (* a y5) (* c y4)))))
                 (if (<= y5 7e+17)
                   (* t (* z t_1))
                   (if (<= y5 1.9e+99)
                     (*
                      b
                      (+ (+ (* a t_4) (* y4 t_2)) (* y0 (- (* z k) (* x j)))))
                     (if (or (<= y5 2.75e+141) (not (<= y5 5.8e+211)))
                       t_5
                       (* a (* b 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 = (c * i) - (a * b);
	double t_2 = (t * j) - (y * k);
	double t_3 = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double t_4 = (x * y) - (z * t);
	double t_5 = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))));
	double t_6 = (c * y0) - (a * y1);
	double t_7 = x * (((y2 * t_6) + (y * ((a * b) - (c * i)))) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (y5 <= -2.1e+175) {
		tmp = t_5;
	} else if (y5 <= -4.2e-238) {
		tmp = t_7;
	} else if (y5 <= 2.3e-279) {
		tmp = t_3;
	} else if (y5 <= 4.2e-235) {
		tmp = t_7;
	} else if (y5 <= 5.6e-153) {
		tmp = t_3;
	} else if (y5 <= 6.2e-113) {
		tmp = z * ((y3 * ((a * y1) - (c * y0))) + ((k * ((b * y0) - (i * y1))) + (t * t_1)));
	} else if (y5 <= 7.2e-32) {
		tmp = y2 * (((x * t_6) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y5 <= 7e+17) {
		tmp = t * (z * t_1);
	} else if (y5 <= 1.9e+99) {
		tmp = b * (((a * t_4) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))));
	} else if ((y5 <= 2.75e+141) || !(y5 <= 5.8e+211)) {
		tmp = t_5;
	} else {
		tmp = a * (b * t_4);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_1 = (c * i) - (a * b)
    t_2 = (t * j) - (y * k)
    t_3 = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    t_4 = (x * y) - (z * t)
    t_5 = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))))
    t_6 = (c * y0) - (a * y1)
    t_7 = x * (((y2 * t_6) + (y * ((a * b) - (c * i)))) + (j * ((i * y1) - (b * y0))))
    if (y5 <= (-2.1d+175)) then
        tmp = t_5
    else if (y5 <= (-4.2d-238)) then
        tmp = t_7
    else if (y5 <= 2.3d-279) then
        tmp = t_3
    else if (y5 <= 4.2d-235) then
        tmp = t_7
    else if (y5 <= 5.6d-153) then
        tmp = t_3
    else if (y5 <= 6.2d-113) then
        tmp = z * ((y3 * ((a * y1) - (c * y0))) + ((k * ((b * y0) - (i * y1))) + (t * t_1)))
    else if (y5 <= 7.2d-32) then
        tmp = y2 * (((x * t_6) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
    else if (y5 <= 7d+17) then
        tmp = t * (z * t_1)
    else if (y5 <= 1.9d+99) then
        tmp = b * (((a * t_4) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))))
    else if ((y5 <= 2.75d+141) .or. (.not. (y5 <= 5.8d+211))) then
        tmp = t_5
    else
        tmp = a * (b * 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 = (c * i) - (a * b);
	double t_2 = (t * j) - (y * k);
	double t_3 = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double t_4 = (x * y) - (z * t);
	double t_5 = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))));
	double t_6 = (c * y0) - (a * y1);
	double t_7 = x * (((y2 * t_6) + (y * ((a * b) - (c * i)))) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (y5 <= -2.1e+175) {
		tmp = t_5;
	} else if (y5 <= -4.2e-238) {
		tmp = t_7;
	} else if (y5 <= 2.3e-279) {
		tmp = t_3;
	} else if (y5 <= 4.2e-235) {
		tmp = t_7;
	} else if (y5 <= 5.6e-153) {
		tmp = t_3;
	} else if (y5 <= 6.2e-113) {
		tmp = z * ((y3 * ((a * y1) - (c * y0))) + ((k * ((b * y0) - (i * y1))) + (t * t_1)));
	} else if (y5 <= 7.2e-32) {
		tmp = y2 * (((x * t_6) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y5 <= 7e+17) {
		tmp = t * (z * t_1);
	} else if (y5 <= 1.9e+99) {
		tmp = b * (((a * t_4) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))));
	} else if ((y5 <= 2.75e+141) || !(y5 <= 5.8e+211)) {
		tmp = t_5;
	} else {
		tmp = a * (b * 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 = (c * i) - (a * b)
	t_2 = (t * j) - (y * k)
	t_3 = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	t_4 = (x * y) - (z * t)
	t_5 = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))))
	t_6 = (c * y0) - (a * y1)
	t_7 = x * (((y2 * t_6) + (y * ((a * b) - (c * i)))) + (j * ((i * y1) - (b * y0))))
	tmp = 0
	if y5 <= -2.1e+175:
		tmp = t_5
	elif y5 <= -4.2e-238:
		tmp = t_7
	elif y5 <= 2.3e-279:
		tmp = t_3
	elif y5 <= 4.2e-235:
		tmp = t_7
	elif y5 <= 5.6e-153:
		tmp = t_3
	elif y5 <= 6.2e-113:
		tmp = z * ((y3 * ((a * y1) - (c * y0))) + ((k * ((b * y0) - (i * y1))) + (t * t_1)))
	elif y5 <= 7.2e-32:
		tmp = y2 * (((x * t_6) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
	elif y5 <= 7e+17:
		tmp = t * (z * t_1)
	elif y5 <= 1.9e+99:
		tmp = b * (((a * t_4) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))))
	elif (y5 <= 2.75e+141) or not (y5 <= 5.8e+211):
		tmp = t_5
	else:
		tmp = a * (b * t_4)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(c * i) - Float64(a * b))
	t_2 = Float64(Float64(t * j) - Float64(y * k))
	t_3 = 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_4 = Float64(Float64(x * y) - Float64(z * t))
	t_5 = Float64(y5 * Float64(Float64(i * Float64(Float64(y * k) - Float64(t * j))) + Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))))))
	t_6 = Float64(Float64(c * y0) - Float64(a * y1))
	t_7 = Float64(x * Float64(Float64(Float64(y2 * t_6) + Float64(y * Float64(Float64(a * b) - Float64(c * i)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))))
	tmp = 0.0
	if (y5 <= -2.1e+175)
		tmp = t_5;
	elseif (y5 <= -4.2e-238)
		tmp = t_7;
	elseif (y5 <= 2.3e-279)
		tmp = t_3;
	elseif (y5 <= 4.2e-235)
		tmp = t_7;
	elseif (y5 <= 5.6e-153)
		tmp = t_3;
	elseif (y5 <= 6.2e-113)
		tmp = Float64(z * Float64(Float64(y3 * Float64(Float64(a * y1) - Float64(c * y0))) + Float64(Float64(k * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(t * t_1))));
	elseif (y5 <= 7.2e-32)
		tmp = Float64(y2 * Float64(Float64(Float64(x * t_6) + Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y5 <= 7e+17)
		tmp = Float64(t * Float64(z * t_1));
	elseif (y5 <= 1.9e+99)
		tmp = Float64(b * Float64(Float64(Float64(a * t_4) + Float64(y4 * t_2)) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif ((y5 <= 2.75e+141) || !(y5 <= 5.8e+211))
		tmp = t_5;
	else
		tmp = Float64(a * Float64(b * 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 = (c * i) - (a * b);
	t_2 = (t * j) - (y * k);
	t_3 = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	t_4 = (x * y) - (z * t);
	t_5 = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))));
	t_6 = (c * y0) - (a * y1);
	t_7 = x * (((y2 * t_6) + (y * ((a * b) - (c * i)))) + (j * ((i * y1) - (b * y0))));
	tmp = 0.0;
	if (y5 <= -2.1e+175)
		tmp = t_5;
	elseif (y5 <= -4.2e-238)
		tmp = t_7;
	elseif (y5 <= 2.3e-279)
		tmp = t_3;
	elseif (y5 <= 4.2e-235)
		tmp = t_7;
	elseif (y5 <= 5.6e-153)
		tmp = t_3;
	elseif (y5 <= 6.2e-113)
		tmp = z * ((y3 * ((a * y1) - (c * y0))) + ((k * ((b * y0) - (i * y1))) + (t * t_1)));
	elseif (y5 <= 7.2e-32)
		tmp = y2 * (((x * t_6) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	elseif (y5 <= 7e+17)
		tmp = t * (z * t_1);
	elseif (y5 <= 1.9e+99)
		tmp = b * (((a * t_4) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))));
	elseif ((y5 <= 2.75e+141) || ~((y5 <= 5.8e+211)))
		tmp = t_5;
	else
		tmp = a * (b * t_4);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = 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$4 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y5 * N[(N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(x * N[(N[(N[(y2 * t$95$6), $MachinePrecision] + N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -2.1e+175], t$95$5, If[LessEqual[y5, -4.2e-238], t$95$7, If[LessEqual[y5, 2.3e-279], t$95$3, If[LessEqual[y5, 4.2e-235], t$95$7, If[LessEqual[y5, 5.6e-153], t$95$3, If[LessEqual[y5, 6.2e-113], N[(z * N[(N[(y3 * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 7.2e-32], N[(y2 * N[(N[(N[(x * t$95$6), $MachinePrecision] + N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 7e+17], N[(t * N[(z * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.9e+99], N[(b * N[(N[(N[(a * t$95$4), $MachinePrecision] + N[(y4 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y5, 2.75e+141], N[Not[LessEqual[y5, 5.8e+211]], $MachinePrecision]], t$95$5, N[(a * N[(b * t$95$4), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y5 < -2.0999999999999999e175 or 1.9e99 < y5 < 2.74999999999999984e141 or 5.8000000000000001e211 < y5

   1. Initial program 17.3%

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

   3. Simplified 21.1%

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

   4. Taylor expanded in y5 around -inf 71.8%

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

   if -2.0999999999999999e175 < y5 < -4.2000000000000002e-238 or 2.29999999999999995e-279 < y5 < 4.2000000000000001e-235

   1. Initial program 38.7%

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

   3. Simplified 38.7%

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

   4. Taylor expanded in x around inf 59.3%

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

   if -4.2000000000000002e-238 < y5 < 2.29999999999999995e-279 or 4.2000000000000001e-235 < y5 < 5.6000000000000001e-153

   1. Initial program 26.4%

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

   3. Simplified 26.4%

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

   4. Taylor expanded in y4 around inf 61.0%

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

   if 5.6000000000000001e-153 < y5 < 6.20000000000000024e-113

   1. Initial program 29.8%

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

   3. Simplified 29.8%

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

   4. Taylor expanded in z around -inf 80.0%

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

      1. mul-1-neg 80.0%

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

      2. associate--l+ 80.0%

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

   6. Simplified 80.0%

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

   if 6.20000000000000024e-113 < y5 < 7.19999999999999986e-32

   1. Initial program 27.0%

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

   3. Simplified 27.0%

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

   4. Taylor expanded in y2 around inf 60.7%

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

   if 7.19999999999999986e-32 < y5 < 7e17

   1. Initial program 28.1%

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

   3. Simplified 28.1%

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

   4. Taylor expanded in t around inf 37.7%

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

      1. associate--l+ 37.7%

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

      2. mul-1-neg 37.7%

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

   6. Simplified 37.7%

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

   7. Taylor expanded in z around inf 55.5%

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

   if 7e17 < y5 < 1.9e99

   1. Initial program 31.6%

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

   3. Simplified 31.6%

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

   4. Taylor expanded in b around inf 58.2%

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

   if 2.74999999999999984e141 < y5 < 5.8000000000000001e211

   1. Initial program 13.6%

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

   3. Simplified 18.2%

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

   4. Taylor expanded in a around inf 32.4%

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

      1. mul-1-neg 32.4%

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

      2. mul-1-neg 32.4%

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

   6. Simplified 32.4%

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

   7. Taylor expanded in b around inf 46.6%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -2.1 \cdot 10^{+175}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y5 \leq -4.2 \cdot 10^{-238}:\\ \;\;\;\;x \cdot \left(\left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + y \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 2.3 \cdot 10^{-279}:\\ \;\;\;\;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}\;y5 \leq 4.2 \cdot 10^{-235}:\\ \;\;\;\;x \cdot \left(\left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + y \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 5.6 \cdot 10^{-153}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 6.2 \cdot 10^{-113}:\\ \;\;\;\;z \cdot \left(y3 \cdot \left(a \cdot y1 - c \cdot y0\right) + \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + t \cdot \left(c \cdot i - a \cdot b\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 7.2 \cdot 10^{-32}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 7 \cdot 10^{+17}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;y5 \leq 1.9 \cdot 10^{+99}:\\ \;\;\;\;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}\;y5 \leq 2.75 \cdot 10^{+141} \lor \neg \left(y5 \leq 5.8 \cdot 10^{+211}\right):\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]

Alternative 4: 42.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot y2 - y \cdot y3\\ t_2 := t \cdot j - y \cdot k\\ t_3 := y4 \cdot \left(\left(b \cdot t_2 + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ t_4 := y5 \cdot t_1\\ t_5 := x \cdot y - z \cdot t\\ t_6 := y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot t_1 + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ t_7 := c \cdot y0 - a \cdot y1\\ t_8 := x \cdot \left(\left(y2 \cdot t_7 + y \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{if}\;y5 \leq -2.3 \cdot 10^{+178}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y5 \leq -2.35 \cdot 10^{-240}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;y5 \leq 10^{-281}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y5 \leq 1.1 \cdot 10^{-235}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;y5 \leq 1.45 \cdot 10^{-154}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y5 \leq 1.52 \cdot 10^{-114}:\\ \;\;\;\;z \cdot \left(y3 \cdot \left(a \cdot y1 - c \cdot y0\right) + \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + t \cdot \left(c \cdot i - a \cdot b\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 6 \cdot 10^{-44}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot t_7 + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 7 \cdot 10^{+15}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right) + \left(t_4 + b \cdot t_5\right)\right)\\ \mathbf{elif}\;y5 \leq 6.8 \cdot 10^{+97}:\\ \;\;\;\;b \cdot \left(\left(a \cdot t_5 + y4 \cdot t_2\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq 8.6 \cdot 10^{+195}:\\ \;\;\;\;a \cdot t_4\\ \mathbf{else}:\\ \;\;\;\;t_6\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* t y2) (* y y3)))
        (t_2 (- (* t j) (* y k)))
        (t_3
         (*
          y4
          (+
           (+ (* b t_2) (* y1 (- (* k y2) (* j y3))))
           (* c (- (* y y3) (* t y2))))))
        (t_4 (* y5 t_1))
        (t_5 (- (* x y) (* z t)))
        (t_6
         (*
          y5
          (+
           (* i (- (* y k) (* t j)))
           (+ (* a t_1) (* y0 (- (* j y3) (* k y2)))))))
        (t_7 (- (* c y0) (* a y1)))
        (t_8
         (*
          x
          (+
           (+ (* y2 t_7) (* y (- (* a b) (* c i))))
           (* j (- (* i y1) (* b y0)))))))
   (if (<= y5 -2.3e+178)
     t_6
     (if (<= y5 -2.35e-240)
       t_8
       (if (<= y5 1e-281)
         t_3
         (if (<= y5 1.1e-235)
           t_8
           (if (<= y5 1.45e-154)
             t_3
             (if (<= y5 1.52e-114)
               (*
                z
                (+
                 (* y3 (- (* a y1) (* c y0)))
                 (+ (* k (- (* b y0) (* i y1))) (* t (- (* c i) (* a b))))))
               (if (<= y5 6e-44)
                 (*
                  y2
                  (+
                   (+ (* x t_7) (* k (- (* y1 y4) (* y0 y5))))
                   (* t (- (* a y5) (* c y4)))))
                 (if (<= y5 7e+15)
                   (* a (+ (* y1 (- (* z y3) (* x y2))) (+ t_4 (* b t_5))))
                   (if (<= y5 6.8e+97)
                     (*
                      b
                      (+ (+ (* a t_5) (* y4 t_2)) (* y0 (- (* z k) (* x j)))))
                     (if (<= y5 8.6e+195) (* a t_4) t_6))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (t * y2) - (y * y3);
	double t_2 = (t * j) - (y * k);
	double t_3 = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double t_4 = y5 * t_1;
	double t_5 = (x * y) - (z * t);
	double t_6 = y5 * ((i * ((y * k) - (t * j))) + ((a * t_1) + (y0 * ((j * y3) - (k * y2)))));
	double t_7 = (c * y0) - (a * y1);
	double t_8 = x * (((y2 * t_7) + (y * ((a * b) - (c * i)))) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (y5 <= -2.3e+178) {
		tmp = t_6;
	} else if (y5 <= -2.35e-240) {
		tmp = t_8;
	} else if (y5 <= 1e-281) {
		tmp = t_3;
	} else if (y5 <= 1.1e-235) {
		tmp = t_8;
	} else if (y5 <= 1.45e-154) {
		tmp = t_3;
	} else if (y5 <= 1.52e-114) {
		tmp = z * ((y3 * ((a * y1) - (c * y0))) + ((k * ((b * y0) - (i * y1))) + (t * ((c * i) - (a * b)))));
	} else if (y5 <= 6e-44) {
		tmp = y2 * (((x * t_7) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y5 <= 7e+15) {
		tmp = a * ((y1 * ((z * y3) - (x * y2))) + (t_4 + (b * t_5)));
	} else if (y5 <= 6.8e+97) {
		tmp = b * (((a * t_5) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))));
	} else if (y5 <= 8.6e+195) {
		tmp = a * t_4;
	} else {
		tmp = t_6;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: tmp
    t_1 = (t * y2) - (y * y3)
    t_2 = (t * j) - (y * k)
    t_3 = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    t_4 = y5 * t_1
    t_5 = (x * y) - (z * t)
    t_6 = y5 * ((i * ((y * k) - (t * j))) + ((a * t_1) + (y0 * ((j * y3) - (k * y2)))))
    t_7 = (c * y0) - (a * y1)
    t_8 = x * (((y2 * t_7) + (y * ((a * b) - (c * i)))) + (j * ((i * y1) - (b * y0))))
    if (y5 <= (-2.3d+178)) then
        tmp = t_6
    else if (y5 <= (-2.35d-240)) then
        tmp = t_8
    else if (y5 <= 1d-281) then
        tmp = t_3
    else if (y5 <= 1.1d-235) then
        tmp = t_8
    else if (y5 <= 1.45d-154) then
        tmp = t_3
    else if (y5 <= 1.52d-114) then
        tmp = z * ((y3 * ((a * y1) - (c * y0))) + ((k * ((b * y0) - (i * y1))) + (t * ((c * i) - (a * b)))))
    else if (y5 <= 6d-44) then
        tmp = y2 * (((x * t_7) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
    else if (y5 <= 7d+15) then
        tmp = a * ((y1 * ((z * y3) - (x * y2))) + (t_4 + (b * t_5)))
    else if (y5 <= 6.8d+97) then
        tmp = b * (((a * t_5) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))))
    else if (y5 <= 8.6d+195) then
        tmp = a * t_4
    else
        tmp = t_6
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (t * y2) - (y * y3);
	double t_2 = (t * j) - (y * k);
	double t_3 = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double t_4 = y5 * t_1;
	double t_5 = (x * y) - (z * t);
	double t_6 = y5 * ((i * ((y * k) - (t * j))) + ((a * t_1) + (y0 * ((j * y3) - (k * y2)))));
	double t_7 = (c * y0) - (a * y1);
	double t_8 = x * (((y2 * t_7) + (y * ((a * b) - (c * i)))) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (y5 <= -2.3e+178) {
		tmp = t_6;
	} else if (y5 <= -2.35e-240) {
		tmp = t_8;
	} else if (y5 <= 1e-281) {
		tmp = t_3;
	} else if (y5 <= 1.1e-235) {
		tmp = t_8;
	} else if (y5 <= 1.45e-154) {
		tmp = t_3;
	} else if (y5 <= 1.52e-114) {
		tmp = z * ((y3 * ((a * y1) - (c * y0))) + ((k * ((b * y0) - (i * y1))) + (t * ((c * i) - (a * b)))));
	} else if (y5 <= 6e-44) {
		tmp = y2 * (((x * t_7) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y5 <= 7e+15) {
		tmp = a * ((y1 * ((z * y3) - (x * y2))) + (t_4 + (b * t_5)));
	} else if (y5 <= 6.8e+97) {
		tmp = b * (((a * t_5) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))));
	} else if (y5 <= 8.6e+195) {
		tmp = a * t_4;
	} else {
		tmp = t_6;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (t * y2) - (y * y3)
	t_2 = (t * j) - (y * k)
	t_3 = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	t_4 = y5 * t_1
	t_5 = (x * y) - (z * t)
	t_6 = y5 * ((i * ((y * k) - (t * j))) + ((a * t_1) + (y0 * ((j * y3) - (k * y2)))))
	t_7 = (c * y0) - (a * y1)
	t_8 = x * (((y2 * t_7) + (y * ((a * b) - (c * i)))) + (j * ((i * y1) - (b * y0))))
	tmp = 0
	if y5 <= -2.3e+178:
		tmp = t_6
	elif y5 <= -2.35e-240:
		tmp = t_8
	elif y5 <= 1e-281:
		tmp = t_3
	elif y5 <= 1.1e-235:
		tmp = t_8
	elif y5 <= 1.45e-154:
		tmp = t_3
	elif y5 <= 1.52e-114:
		tmp = z * ((y3 * ((a * y1) - (c * y0))) + ((k * ((b * y0) - (i * y1))) + (t * ((c * i) - (a * b)))))
	elif y5 <= 6e-44:
		tmp = y2 * (((x * t_7) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
	elif y5 <= 7e+15:
		tmp = a * ((y1 * ((z * y3) - (x * y2))) + (t_4 + (b * t_5)))
	elif y5 <= 6.8e+97:
		tmp = b * (((a * t_5) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))))
	elif y5 <= 8.6e+195:
		tmp = a * t_4
	else:
		tmp = t_6
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(t * y2) - Float64(y * y3))
	t_2 = Float64(Float64(t * j) - Float64(y * k))
	t_3 = 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_4 = Float64(y5 * t_1)
	t_5 = Float64(Float64(x * y) - Float64(z * t))
	t_6 = Float64(y5 * Float64(Float64(i * Float64(Float64(y * k) - Float64(t * j))) + Float64(Float64(a * t_1) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))))))
	t_7 = Float64(Float64(c * y0) - Float64(a * y1))
	t_8 = Float64(x * Float64(Float64(Float64(y2 * t_7) + Float64(y * Float64(Float64(a * b) - Float64(c * i)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))))
	tmp = 0.0
	if (y5 <= -2.3e+178)
		tmp = t_6;
	elseif (y5 <= -2.35e-240)
		tmp = t_8;
	elseif (y5 <= 1e-281)
		tmp = t_3;
	elseif (y5 <= 1.1e-235)
		tmp = t_8;
	elseif (y5 <= 1.45e-154)
		tmp = t_3;
	elseif (y5 <= 1.52e-114)
		tmp = Float64(z * Float64(Float64(y3 * Float64(Float64(a * y1) - Float64(c * y0))) + Float64(Float64(k * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(t * Float64(Float64(c * i) - Float64(a * b))))));
	elseif (y5 <= 6e-44)
		tmp = Float64(y2 * Float64(Float64(Float64(x * t_7) + Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y5 <= 7e+15)
		tmp = Float64(a * Float64(Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))) + Float64(t_4 + Float64(b * t_5))));
	elseif (y5 <= 6.8e+97)
		tmp = Float64(b * Float64(Float64(Float64(a * t_5) + Float64(y4 * t_2)) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (y5 <= 8.6e+195)
		tmp = Float64(a * t_4);
	else
		tmp = t_6;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (t * y2) - (y * y3);
	t_2 = (t * j) - (y * k);
	t_3 = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	t_4 = y5 * t_1;
	t_5 = (x * y) - (z * t);
	t_6 = y5 * ((i * ((y * k) - (t * j))) + ((a * t_1) + (y0 * ((j * y3) - (k * y2)))));
	t_7 = (c * y0) - (a * y1);
	t_8 = x * (((y2 * t_7) + (y * ((a * b) - (c * i)))) + (j * ((i * y1) - (b * y0))));
	tmp = 0.0;
	if (y5 <= -2.3e+178)
		tmp = t_6;
	elseif (y5 <= -2.35e-240)
		tmp = t_8;
	elseif (y5 <= 1e-281)
		tmp = t_3;
	elseif (y5 <= 1.1e-235)
		tmp = t_8;
	elseif (y5 <= 1.45e-154)
		tmp = t_3;
	elseif (y5 <= 1.52e-114)
		tmp = z * ((y3 * ((a * y1) - (c * y0))) + ((k * ((b * y0) - (i * y1))) + (t * ((c * i) - (a * b)))));
	elseif (y5 <= 6e-44)
		tmp = y2 * (((x * t_7) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	elseif (y5 <= 7e+15)
		tmp = a * ((y1 * ((z * y3) - (x * y2))) + (t_4 + (b * t_5)));
	elseif (y5 <= 6.8e+97)
		tmp = b * (((a * t_5) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))));
	elseif (y5 <= 8.6e+195)
		tmp = a * t_4;
	else
		tmp = t_6;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = 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$4 = N[(y5 * t$95$1), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(y5 * N[(N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * t$95$1), $MachinePrecision] + N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(x * N[(N[(N[(y2 * t$95$7), $MachinePrecision] + N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -2.3e+178], t$95$6, If[LessEqual[y5, -2.35e-240], t$95$8, If[LessEqual[y5, 1e-281], t$95$3, If[LessEqual[y5, 1.1e-235], t$95$8, If[LessEqual[y5, 1.45e-154], t$95$3, If[LessEqual[y5, 1.52e-114], N[(z * N[(N[(y3 * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 6e-44], N[(y2 * N[(N[(N[(x * t$95$7), $MachinePrecision] + N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 7e+15], N[(a * N[(N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$4 + N[(b * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 6.8e+97], N[(b * N[(N[(N[(a * t$95$5), $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[y5, 8.6e+195], N[(a * t$95$4), $MachinePrecision], t$95$6]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y5 < -2.3000000000000001e178 or 8.59999999999999962e195 < y5

   1. Initial program 17.6%

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

   3. Simplified 21.9%

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

   4. Taylor expanded in y5 around -inf 72.0%

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

   if -2.3000000000000001e178 < y5 < -2.35000000000000006e-240 or 1e-281 < y5 < 1.09999999999999992e-235

   1. Initial program 38.7%

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

   3. Simplified 38.7%

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

   4. Taylor expanded in x around inf 59.3%

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

   if -2.35000000000000006e-240 < y5 < 1e-281 or 1.09999999999999992e-235 < y5 < 1.45e-154

   1. Initial program 26.4%

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

   3. Simplified 26.4%

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

   4. Taylor expanded in y4 around inf 61.0%

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

   if 1.45e-154 < y5 < 1.51999999999999997e-114

   1. Initial program 29.8%

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

   3. Simplified 29.8%

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

   4. Taylor expanded in z around -inf 80.0%

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

      1. mul-1-neg 80.0%

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

      2. associate--l+ 80.0%

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

   6. Simplified 80.0%

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

   if 1.51999999999999997e-114 < y5 < 6.0000000000000005e-44

   1. Initial program 21.8%

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

   3. Simplified 21.8%

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

   4. Taylor expanded in y2 around inf 64.8%

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

   if 6.0000000000000005e-44 < y5 < 7e15

   1. Initial program 34.1%

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

   3. Simplified 34.1%

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

   4. Taylor expanded in a around inf 68.0%

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

      1. mul-1-neg 68.0%

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

      2. mul-1-neg 68.0%

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

   6. Simplified 68.0%

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

   if 7e15 < y5 < 6.8000000000000002e97

   1. Initial program 31.6%

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

   3. Simplified 31.6%

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

   4. Taylor expanded in b around inf 58.2%

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

   if 6.8000000000000002e97 < y5 < 8.59999999999999962e195

   1. Initial program 14.1%

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

   3. Simplified 21.0%

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

   4. Taylor expanded in a around inf 45.0%

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

      1. mul-1-neg 45.0%

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

      2. mul-1-neg 45.0%

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

   6. Simplified 45.0%

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

   7. Taylor expanded in y5 around inf 45.6%

      \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -2.3 \cdot 10^{+178}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y5 \leq -2.35 \cdot 10^{-240}:\\ \;\;\;\;x \cdot \left(\left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + y \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 10^{-281}:\\ \;\;\;\;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}\;y5 \leq 1.1 \cdot 10^{-235}:\\ \;\;\;\;x \cdot \left(\left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + y \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 1.45 \cdot 10^{-154}:\\ \;\;\;\;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}\;y5 \leq 1.52 \cdot 10^{-114}:\\ \;\;\;\;z \cdot \left(y3 \cdot \left(a \cdot y1 - c \cdot y0\right) + \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + t \cdot \left(c \cdot i - a \cdot b\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 6 \cdot 10^{-44}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 7 \cdot 10^{+15}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right) + \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) + b \cdot \left(x \cdot y - z \cdot t\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 6.8 \cdot 10^{+97}:\\ \;\;\;\;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}\;y5 \leq 8.6 \cdot 10^{+195}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \end{array} \]

Alternative 5: 37.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ t_2 := t \cdot j - y \cdot k\\ \mathbf{if}\;y3 \leq -1.3 \cdot 10^{+80}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y3 \leq -2.5 \cdot 10^{+16}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;y3 \leq -5.5 \cdot 10^{+14}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y3 \leq 9.8 \cdot 10^{-253}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq 3.1 \cdot 10^{-240}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y3 \leq 1.36 \cdot 10^{-114}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot t_2\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y3 \leq 1.96 \cdot 10^{-78}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;y3 \leq 2800000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y3 \leq 3.6 \cdot 10^{+87}:\\ \;\;\;\;x \cdot \left(\left(i \cdot \left(j \cdot y1 - y \cdot c\right) + a \cdot \left(y \cdot b\right)\right) - y0 \cdot \left(b \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot t_2 + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* t (* c (- (* z i) (* y2 y4))))) (t_2 (- (* t j) (* y k))))
   (if (<= y3 -1.3e+80)
     (* a (* y3 (- (* z y1) (* y y5))))
     (if (<= y3 -2.5e+16)
       (* y0 (* x (- (* c y2) (* b j))))
       (if (<= y3 -5.5e+14)
         (* a (* y5 (- (* t y2) (* y y3))))
         (if (<= y3 9.8e-253)
           (* x (+ (* y (- (* a b) (* c i))) (* j (- (* i y1) (* b y0)))))
           (if (<= y3 3.1e-240)
             t_1
             (if (<= y3 1.36e-114)
               (*
                b
                (+
                 (+ (* a (- (* x y) (* z t))) (* y4 t_2))
                 (* y0 (- (* z k) (* x j)))))
               (if (<= y3 1.96e-78)
                 (* y2 (* x (- (* c y0) (* a y1))))
                 (if (<= y3 2800000000000.0)
                   t_1
                   (if (<= y3 3.6e+87)
                     (*
                      x
                      (-
                       (+ (* i (- (* j y1) (* y c))) (* a (* y b)))
                       (* y0 (* b j))))
                     (*
                      y4
                      (+
                       (+ (* b t_2) (* y1 (- (* k y2) (* j y3))))
                       (* c (- (* y y3) (* t y2))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * (c * ((z * i) - (y2 * y4)));
	double t_2 = (t * j) - (y * k);
	double tmp;
	if (y3 <= -1.3e+80) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (y3 <= -2.5e+16) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else if (y3 <= -5.5e+14) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (y3 <= 9.8e-253) {
		tmp = x * ((y * ((a * b) - (c * i))) + (j * ((i * y1) - (b * y0))));
	} else if (y3 <= 3.1e-240) {
		tmp = t_1;
	} else if (y3 <= 1.36e-114) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))));
	} else if (y3 <= 1.96e-78) {
		tmp = y2 * (x * ((c * y0) - (a * y1)));
	} else if (y3 <= 2800000000000.0) {
		tmp = t_1;
	} else if (y3 <= 3.6e+87) {
		tmp = x * (((i * ((j * y1) - (y * c))) + (a * (y * b))) - (y0 * (b * j)));
	} else {
		tmp = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (c * ((z * i) - (y2 * y4)))
    t_2 = (t * j) - (y * k)
    if (y3 <= (-1.3d+80)) then
        tmp = a * (y3 * ((z * y1) - (y * y5)))
    else if (y3 <= (-2.5d+16)) then
        tmp = y0 * (x * ((c * y2) - (b * j)))
    else if (y3 <= (-5.5d+14)) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else if (y3 <= 9.8d-253) then
        tmp = x * ((y * ((a * b) - (c * i))) + (j * ((i * y1) - (b * y0))))
    else if (y3 <= 3.1d-240) then
        tmp = t_1
    else if (y3 <= 1.36d-114) then
        tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))))
    else if (y3 <= 1.96d-78) then
        tmp = y2 * (x * ((c * y0) - (a * y1)))
    else if (y3 <= 2800000000000.0d0) then
        tmp = t_1
    else if (y3 <= 3.6d+87) then
        tmp = x * (((i * ((j * y1) - (y * c))) + (a * (y * b))) - (y0 * (b * j)))
    else
        tmp = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * (c * ((z * i) - (y2 * y4)));
	double t_2 = (t * j) - (y * k);
	double tmp;
	if (y3 <= -1.3e+80) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (y3 <= -2.5e+16) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else if (y3 <= -5.5e+14) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (y3 <= 9.8e-253) {
		tmp = x * ((y * ((a * b) - (c * i))) + (j * ((i * y1) - (b * y0))));
	} else if (y3 <= 3.1e-240) {
		tmp = t_1;
	} else if (y3 <= 1.36e-114) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))));
	} else if (y3 <= 1.96e-78) {
		tmp = y2 * (x * ((c * y0) - (a * y1)));
	} else if (y3 <= 2800000000000.0) {
		tmp = t_1;
	} else if (y3 <= 3.6e+87) {
		tmp = x * (((i * ((j * y1) - (y * c))) + (a * (y * b))) - (y0 * (b * j)));
	} else {
		tmp = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = t * (c * ((z * i) - (y2 * y4)))
	t_2 = (t * j) - (y * k)
	tmp = 0
	if y3 <= -1.3e+80:
		tmp = a * (y3 * ((z * y1) - (y * y5)))
	elif y3 <= -2.5e+16:
		tmp = y0 * (x * ((c * y2) - (b * j)))
	elif y3 <= -5.5e+14:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	elif y3 <= 9.8e-253:
		tmp = x * ((y * ((a * b) - (c * i))) + (j * ((i * y1) - (b * y0))))
	elif y3 <= 3.1e-240:
		tmp = t_1
	elif y3 <= 1.36e-114:
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))))
	elif y3 <= 1.96e-78:
		tmp = y2 * (x * ((c * y0) - (a * y1)))
	elif y3 <= 2800000000000.0:
		tmp = t_1
	elif y3 <= 3.6e+87:
		tmp = x * (((i * ((j * y1) - (y * c))) + (a * (y * b))) - (y0 * (b * j)))
	else:
		tmp = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(t * Float64(c * Float64(Float64(z * i) - Float64(y2 * y4))))
	t_2 = Float64(Float64(t * j) - Float64(y * k))
	tmp = 0.0
	if (y3 <= -1.3e+80)
		tmp = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))));
	elseif (y3 <= -2.5e+16)
		tmp = Float64(y0 * Float64(x * Float64(Float64(c * y2) - Float64(b * j))));
	elseif (y3 <= -5.5e+14)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (y3 <= 9.8e-253)
		tmp = Float64(x * Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (y3 <= 3.1e-240)
		tmp = t_1;
	elseif (y3 <= 1.36e-114)
		tmp = 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)))));
	elseif (y3 <= 1.96e-78)
		tmp = Float64(y2 * Float64(x * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (y3 <= 2800000000000.0)
		tmp = t_1;
	elseif (y3 <= 3.6e+87)
		tmp = Float64(x * Float64(Float64(Float64(i * Float64(Float64(j * y1) - Float64(y * c))) + Float64(a * Float64(y * b))) - Float64(y0 * Float64(b * j))));
	else
		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)))));
	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 * (c * ((z * i) - (y2 * y4)));
	t_2 = (t * j) - (y * k);
	tmp = 0.0;
	if (y3 <= -1.3e+80)
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	elseif (y3 <= -2.5e+16)
		tmp = y0 * (x * ((c * y2) - (b * j)));
	elseif (y3 <= -5.5e+14)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	elseif (y3 <= 9.8e-253)
		tmp = x * ((y * ((a * b) - (c * i))) + (j * ((i * y1) - (b * y0))));
	elseif (y3 <= 3.1e-240)
		tmp = t_1;
	elseif (y3 <= 1.36e-114)
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))));
	elseif (y3 <= 1.96e-78)
		tmp = y2 * (x * ((c * y0) - (a * y1)));
	elseif (y3 <= 2800000000000.0)
		tmp = t_1;
	elseif (y3 <= 3.6e+87)
		tmp = x * (((i * ((j * y1) - (y * c))) + (a * (y * b))) - (y0 * (b * j)));
	else
		tmp = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(t * N[(c * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -1.3e+80], N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -2.5e+16], N[(y0 * N[(x * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -5.5e+14], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 9.8e-253], N[(x * N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 3.1e-240], t$95$1, If[LessEqual[y3, 1.36e-114], 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[y3, 1.96e-78], N[(y2 * N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 2800000000000.0], t$95$1, If[LessEqual[y3, 3.6e+87], N[(x * N[(N[(N[(i * N[(N[(j * y1), $MachinePrecision] - N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y0 * N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y3 < -1.29999999999999991e80

   1. Initial program 22.2%

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

   3. Simplified 33.3%

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

   4. Taylor expanded in a around inf 55.8%

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

      1. mul-1-neg 55.8%

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

      2. mul-1-neg 55.8%

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

   6. Simplified 55.8%

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

   7. Taylor expanded in y3 around -inf 67.1%

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

   if -1.29999999999999991e80 < y3 < -2.5e16

   1. Initial program 23.2%

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

   3. Simplified 23.2%

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

   4. Taylor expanded in x around inf 34.7%

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

   5. Taylor expanded in y0 around inf 67.7%

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

   if -2.5e16 < y3 < -5.5e14

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in a around inf 50.0%

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

      1. mul-1-neg 50.0%

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

      2. mul-1-neg 50.0%

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

   6. Simplified 50.0%

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

   7. Taylor expanded in y5 around inf 100.0%

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

   if -5.5e14 < y3 < 9.7999999999999999e-253

   1. Initial program 37.9%

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

   3. Simplified 37.9%

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

   4. Taylor expanded in x around inf 55.4%

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

   5. Taylor expanded in y2 around 0 52.8%

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

   if 9.7999999999999999e-253 < y3 < 3.10000000000000017e-240 or 1.96e-78 < y3 < 2.8e12

   1. Initial program 13.3%

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

   3. Simplified 13.3%

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

   4. Taylor expanded in t around inf 50.5%

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

      1. associate--l+ 50.5%

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

      2. mul-1-neg 50.5%

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

   6. Simplified 50.5%

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

   7. Taylor expanded in c around -inf 54.8%

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

      1. mul-1-neg 54.8%

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

      2. unsub-neg 54.8%

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

      3. *-commutative 54.8%

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

   9. Simplified 54.8%

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

   if 3.10000000000000017e-240 < y3 < 1.3599999999999999e-114

   1. Initial program 37.2%

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

   3. Simplified 37.2%

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

   4. Taylor expanded in b around inf 52.5%

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

   if 1.3599999999999999e-114 < y3 < 1.96e-78

   1. Initial program 16.7%

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

   3. Simplified 16.7%

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

   4. Taylor expanded in y2 around inf 72.1%

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

   5. Taylor expanded in x around -inf 83.6%

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

   if 2.8e12 < y3 < 3.59999999999999994e87

   1. Initial program 17.1%

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

   3. Simplified 17.1%

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

   4. Taylor expanded in x around inf 39.6%

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

   5. Taylor expanded in i around -inf 56.2%

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

   6. Taylor expanded in y2 around 0 62.0%

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

   if 3.59999999999999994e87 < y3

   1. Initial program 25.6%

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

   3. Simplified 25.6%

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

   4. Taylor expanded in y4 around inf 43.3%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -1.3 \cdot 10^{+80}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y3 \leq -2.5 \cdot 10^{+16}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;y3 \leq -5.5 \cdot 10^{+14}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y3 \leq 9.8 \cdot 10^{-253}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq 3.1 \cdot 10^{-240}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 1.36 \cdot 10^{-114}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y3 \leq 1.96 \cdot 10^{-78}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;y3 \leq 2800000000000:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 3.6 \cdot 10^{+87}:\\ \;\;\;\;x \cdot \left(\left(i \cdot \left(j \cdot y1 - y \cdot c\right) + a \cdot \left(y \cdot b\right)\right) - y0 \cdot \left(b \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \end{array} \]

Alternative 6: 42.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot y2 - y \cdot y3\\ t_2 := y5 \cdot t_1\\ t_3 := y \cdot y3 - t \cdot y2\\ t_4 := y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot t_1 + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ t_5 := c \cdot y0 - a \cdot y1\\ t_6 := t \cdot j - y \cdot k\\ t_7 := x \cdot y - z \cdot t\\ t_8 := x \cdot \left(\left(y2 \cdot t_5 + y \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ t_9 := z \cdot y3 - x \cdot y2\\ \mathbf{if}\;y5 \leq -1.65 \cdot 10^{+174}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y5 \leq -1.6 \cdot 10^{-242}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;y5 \leq 1.8 \cdot 10^{-276}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot t_6 + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot t_3\right)\\ \mathbf{elif}\;y5 \leq 1.15 \cdot 10^{-198}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;y5 \leq 6.6 \cdot 10^{-118}:\\ \;\;\;\;c \cdot \left(y4 \cdot t_3 - \left(i \cdot t_7 + y0 \cdot t_9\right)\right)\\ \mathbf{elif}\;y5 \leq 4.3 \cdot 10^{-48}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot t_5 + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 1.3 \cdot 10^{+15}:\\ \;\;\;\;a \cdot \left(y1 \cdot t_9 + \left(t_2 + b \cdot t_7\right)\right)\\ \mathbf{elif}\;y5 \leq 7 \cdot 10^{+98}:\\ \;\;\;\;b \cdot \left(\left(a \cdot t_7 + y4 \cdot t_6\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq 7.2 \cdot 10^{+195}:\\ \;\;\;\;a \cdot t_2\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* t y2) (* y y3)))
        (t_2 (* y5 t_1))
        (t_3 (- (* y y3) (* t y2)))
        (t_4
         (*
          y5
          (+
           (* i (- (* y k) (* t j)))
           (+ (* a t_1) (* y0 (- (* j y3) (* k y2)))))))
        (t_5 (- (* c y0) (* a y1)))
        (t_6 (- (* t j) (* y k)))
        (t_7 (- (* x y) (* z t)))
        (t_8
         (*
          x
          (+
           (+ (* y2 t_5) (* y (- (* a b) (* c i))))
           (* j (- (* i y1) (* b y0))))))
        (t_9 (- (* z y3) (* x y2))))
   (if (<= y5 -1.65e+174)
     t_4
     (if (<= y5 -1.6e-242)
       t_8
       (if (<= y5 1.8e-276)
         (* y4 (+ (+ (* b t_6) (* y1 (- (* k y2) (* j y3)))) (* c t_3)))
         (if (<= y5 1.15e-198)
           t_8
           (if (<= y5 6.6e-118)
             (* c (- (* y4 t_3) (+ (* i t_7) (* y0 t_9))))
             (if (<= y5 4.3e-48)
               (*
                y2
                (+
                 (+ (* x t_5) (* k (- (* y1 y4) (* y0 y5))))
                 (* t (- (* a y5) (* c y4)))))
               (if (<= y5 1.3e+15)
                 (* a (+ (* y1 t_9) (+ t_2 (* b t_7))))
                 (if (<= y5 7e+98)
                   (*
                    b
                    (+ (+ (* a t_7) (* y4 t_6)) (* y0 (- (* z k) (* x j)))))
                   (if (<= y5 7.2e+195) (* a t_2) t_4)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (t * y2) - (y * y3);
	double t_2 = y5 * t_1;
	double t_3 = (y * y3) - (t * y2);
	double t_4 = y5 * ((i * ((y * k) - (t * j))) + ((a * t_1) + (y0 * ((j * y3) - (k * y2)))));
	double t_5 = (c * y0) - (a * y1);
	double t_6 = (t * j) - (y * k);
	double t_7 = (x * y) - (z * t);
	double t_8 = x * (((y2 * t_5) + (y * ((a * b) - (c * i)))) + (j * ((i * y1) - (b * y0))));
	double t_9 = (z * y3) - (x * y2);
	double tmp;
	if (y5 <= -1.65e+174) {
		tmp = t_4;
	} else if (y5 <= -1.6e-242) {
		tmp = t_8;
	} else if (y5 <= 1.8e-276) {
		tmp = y4 * (((b * t_6) + (y1 * ((k * y2) - (j * y3)))) + (c * t_3));
	} else if (y5 <= 1.15e-198) {
		tmp = t_8;
	} else if (y5 <= 6.6e-118) {
		tmp = c * ((y4 * t_3) - ((i * t_7) + (y0 * t_9)));
	} else if (y5 <= 4.3e-48) {
		tmp = y2 * (((x * t_5) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y5 <= 1.3e+15) {
		tmp = a * ((y1 * t_9) + (t_2 + (b * t_7)));
	} else if (y5 <= 7e+98) {
		tmp = b * (((a * t_7) + (y4 * t_6)) + (y0 * ((z * k) - (x * j))));
	} else if (y5 <= 7.2e+195) {
		tmp = a * t_2;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = (t * y2) - (y * y3)
    t_2 = y5 * t_1
    t_3 = (y * y3) - (t * y2)
    t_4 = y5 * ((i * ((y * k) - (t * j))) + ((a * t_1) + (y0 * ((j * y3) - (k * y2)))))
    t_5 = (c * y0) - (a * y1)
    t_6 = (t * j) - (y * k)
    t_7 = (x * y) - (z * t)
    t_8 = x * (((y2 * t_5) + (y * ((a * b) - (c * i)))) + (j * ((i * y1) - (b * y0))))
    t_9 = (z * y3) - (x * y2)
    if (y5 <= (-1.65d+174)) then
        tmp = t_4
    else if (y5 <= (-1.6d-242)) then
        tmp = t_8
    else if (y5 <= 1.8d-276) then
        tmp = y4 * (((b * t_6) + (y1 * ((k * y2) - (j * y3)))) + (c * t_3))
    else if (y5 <= 1.15d-198) then
        tmp = t_8
    else if (y5 <= 6.6d-118) then
        tmp = c * ((y4 * t_3) - ((i * t_7) + (y0 * t_9)))
    else if (y5 <= 4.3d-48) then
        tmp = y2 * (((x * t_5) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
    else if (y5 <= 1.3d+15) then
        tmp = a * ((y1 * t_9) + (t_2 + (b * t_7)))
    else if (y5 <= 7d+98) then
        tmp = b * (((a * t_7) + (y4 * t_6)) + (y0 * ((z * k) - (x * j))))
    else if (y5 <= 7.2d+195) then
        tmp = a * t_2
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (t * y2) - (y * y3);
	double t_2 = y5 * t_1;
	double t_3 = (y * y3) - (t * y2);
	double t_4 = y5 * ((i * ((y * k) - (t * j))) + ((a * t_1) + (y0 * ((j * y3) - (k * y2)))));
	double t_5 = (c * y0) - (a * y1);
	double t_6 = (t * j) - (y * k);
	double t_7 = (x * y) - (z * t);
	double t_8 = x * (((y2 * t_5) + (y * ((a * b) - (c * i)))) + (j * ((i * y1) - (b * y0))));
	double t_9 = (z * y3) - (x * y2);
	double tmp;
	if (y5 <= -1.65e+174) {
		tmp = t_4;
	} else if (y5 <= -1.6e-242) {
		tmp = t_8;
	} else if (y5 <= 1.8e-276) {
		tmp = y4 * (((b * t_6) + (y1 * ((k * y2) - (j * y3)))) + (c * t_3));
	} else if (y5 <= 1.15e-198) {
		tmp = t_8;
	} else if (y5 <= 6.6e-118) {
		tmp = c * ((y4 * t_3) - ((i * t_7) + (y0 * t_9)));
	} else if (y5 <= 4.3e-48) {
		tmp = y2 * (((x * t_5) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y5 <= 1.3e+15) {
		tmp = a * ((y1 * t_9) + (t_2 + (b * t_7)));
	} else if (y5 <= 7e+98) {
		tmp = b * (((a * t_7) + (y4 * t_6)) + (y0 * ((z * k) - (x * j))));
	} else if (y5 <= 7.2e+195) {
		tmp = a * t_2;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (t * y2) - (y * y3)
	t_2 = y5 * t_1
	t_3 = (y * y3) - (t * y2)
	t_4 = y5 * ((i * ((y * k) - (t * j))) + ((a * t_1) + (y0 * ((j * y3) - (k * y2)))))
	t_5 = (c * y0) - (a * y1)
	t_6 = (t * j) - (y * k)
	t_7 = (x * y) - (z * t)
	t_8 = x * (((y2 * t_5) + (y * ((a * b) - (c * i)))) + (j * ((i * y1) - (b * y0))))
	t_9 = (z * y3) - (x * y2)
	tmp = 0
	if y5 <= -1.65e+174:
		tmp = t_4
	elif y5 <= -1.6e-242:
		tmp = t_8
	elif y5 <= 1.8e-276:
		tmp = y4 * (((b * t_6) + (y1 * ((k * y2) - (j * y3)))) + (c * t_3))
	elif y5 <= 1.15e-198:
		tmp = t_8
	elif y5 <= 6.6e-118:
		tmp = c * ((y4 * t_3) - ((i * t_7) + (y0 * t_9)))
	elif y5 <= 4.3e-48:
		tmp = y2 * (((x * t_5) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
	elif y5 <= 1.3e+15:
		tmp = a * ((y1 * t_9) + (t_2 + (b * t_7)))
	elif y5 <= 7e+98:
		tmp = b * (((a * t_7) + (y4 * t_6)) + (y0 * ((z * k) - (x * j))))
	elif y5 <= 7.2e+195:
		tmp = a * t_2
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(t * y2) - Float64(y * y3))
	t_2 = Float64(y5 * t_1)
	t_3 = Float64(Float64(y * y3) - Float64(t * y2))
	t_4 = Float64(y5 * Float64(Float64(i * Float64(Float64(y * k) - Float64(t * j))) + Float64(Float64(a * t_1) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))))))
	t_5 = Float64(Float64(c * y0) - Float64(a * y1))
	t_6 = Float64(Float64(t * j) - Float64(y * k))
	t_7 = Float64(Float64(x * y) - Float64(z * t))
	t_8 = Float64(x * Float64(Float64(Float64(y2 * t_5) + Float64(y * Float64(Float64(a * b) - Float64(c * i)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))))
	t_9 = Float64(Float64(z * y3) - Float64(x * y2))
	tmp = 0.0
	if (y5 <= -1.65e+174)
		tmp = t_4;
	elseif (y5 <= -1.6e-242)
		tmp = t_8;
	elseif (y5 <= 1.8e-276)
		tmp = Float64(y4 * Float64(Float64(Float64(b * t_6) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * t_3)));
	elseif (y5 <= 1.15e-198)
		tmp = t_8;
	elseif (y5 <= 6.6e-118)
		tmp = Float64(c * Float64(Float64(y4 * t_3) - Float64(Float64(i * t_7) + Float64(y0 * t_9))));
	elseif (y5 <= 4.3e-48)
		tmp = Float64(y2 * Float64(Float64(Float64(x * t_5) + Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y5 <= 1.3e+15)
		tmp = Float64(a * Float64(Float64(y1 * t_9) + Float64(t_2 + Float64(b * t_7))));
	elseif (y5 <= 7e+98)
		tmp = Float64(b * Float64(Float64(Float64(a * t_7) + Float64(y4 * t_6)) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (y5 <= 7.2e+195)
		tmp = Float64(a * t_2);
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (t * y2) - (y * y3);
	t_2 = y5 * t_1;
	t_3 = (y * y3) - (t * y2);
	t_4 = y5 * ((i * ((y * k) - (t * j))) + ((a * t_1) + (y0 * ((j * y3) - (k * y2)))));
	t_5 = (c * y0) - (a * y1);
	t_6 = (t * j) - (y * k);
	t_7 = (x * y) - (z * t);
	t_8 = x * (((y2 * t_5) + (y * ((a * b) - (c * i)))) + (j * ((i * y1) - (b * y0))));
	t_9 = (z * y3) - (x * y2);
	tmp = 0.0;
	if (y5 <= -1.65e+174)
		tmp = t_4;
	elseif (y5 <= -1.6e-242)
		tmp = t_8;
	elseif (y5 <= 1.8e-276)
		tmp = y4 * (((b * t_6) + (y1 * ((k * y2) - (j * y3)))) + (c * t_3));
	elseif (y5 <= 1.15e-198)
		tmp = t_8;
	elseif (y5 <= 6.6e-118)
		tmp = c * ((y4 * t_3) - ((i * t_7) + (y0 * t_9)));
	elseif (y5 <= 4.3e-48)
		tmp = y2 * (((x * t_5) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	elseif (y5 <= 1.3e+15)
		tmp = a * ((y1 * t_9) + (t_2 + (b * t_7)));
	elseif (y5 <= 7e+98)
		tmp = b * (((a * t_7) + (y4 * t_6)) + (y0 * ((z * k) - (x * j))));
	elseif (y5 <= 7.2e+195)
		tmp = a * t_2;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y5 * t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y5 * N[(N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * t$95$1), $MachinePrecision] + N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(x * N[(N[(N[(y2 * t$95$5), $MachinePrecision] + N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -1.65e+174], t$95$4, If[LessEqual[y5, -1.6e-242], t$95$8, If[LessEqual[y5, 1.8e-276], N[(y4 * N[(N[(N[(b * t$95$6), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.15e-198], t$95$8, If[LessEqual[y5, 6.6e-118], N[(c * N[(N[(y4 * t$95$3), $MachinePrecision] - N[(N[(i * t$95$7), $MachinePrecision] + N[(y0 * t$95$9), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 4.3e-48], N[(y2 * N[(N[(N[(x * t$95$5), $MachinePrecision] + N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.3e+15], N[(a * N[(N[(y1 * t$95$9), $MachinePrecision] + N[(t$95$2 + N[(b * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 7e+98], N[(b * N[(N[(N[(a * t$95$7), $MachinePrecision] + N[(y4 * t$95$6), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 7.2e+195], N[(a * t$95$2), $MachinePrecision], t$95$4]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y5 < -1.65e174 or 7.1999999999999997e195 < y5

   1. Initial program 17.6%

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

   3. Simplified 21.9%

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

   4. Taylor expanded in y5 around -inf 72.0%

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

   if -1.65e174 < y5 < -1.59999999999999999e-242 or 1.79999999999999997e-276 < y5 < 1.15000000000000007e-198

   1. Initial program 37.4%

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

   3. Simplified 37.4%

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

   4. Taylor expanded in x around inf 57.6%

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

   if -1.59999999999999999e-242 < y5 < 1.79999999999999997e-276

   1. Initial program 21.1%

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

   3. Simplified 21.1%

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

   4. Taylor expanded in y4 around inf 63.6%

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

   if 1.15000000000000007e-198 < y5 < 6.5999999999999999e-118

   1. Initial program 34.6%

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

   3. Simplified 34.6%

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

   4. Taylor expanded in c around inf 69.8%

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

   if 6.5999999999999999e-118 < y5 < 4.3e-48

   1. Initial program 21.8%

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

   3. Simplified 21.8%

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

   4. Taylor expanded in y2 around inf 64.8%

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

   if 4.3e-48 < y5 < 1.3e15

   1. Initial program 34.1%

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

   3. Simplified 34.1%

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

   4. Taylor expanded in a around inf 68.0%

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

      1. mul-1-neg 68.0%

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

      2. mul-1-neg 68.0%

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

   6. Simplified 68.0%

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

   if 1.3e15 < y5 < 7e98

   1. Initial program 31.6%

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

   3. Simplified 31.6%

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

   4. Taylor expanded in b around inf 58.2%

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

   if 7e98 < y5 < 7.1999999999999997e195

   1. Initial program 14.1%

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

   3. Simplified 21.0%

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

   4. Taylor expanded in a around inf 45.0%

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

      1. mul-1-neg 45.0%

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

      2. mul-1-neg 45.0%

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

   6. Simplified 45.0%

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

   7. Taylor expanded in y5 around inf 45.6%

      \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -1.65 \cdot 10^{+174}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y5 \leq -1.6 \cdot 10^{-242}:\\ \;\;\;\;x \cdot \left(\left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + y \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 1.8 \cdot 10^{-276}:\\ \;\;\;\;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}\;y5 \leq 1.15 \cdot 10^{-198}:\\ \;\;\;\;x \cdot \left(\left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + y \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 6.6 \cdot 10^{-118}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right) - \left(i \cdot \left(x \cdot y - z \cdot t\right) + y0 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 4.3 \cdot 10^{-48}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 1.3 \cdot 10^{+15}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right) + \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) + b \cdot \left(x \cdot y - z \cdot t\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 7 \cdot 10^{+98}:\\ \;\;\;\;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}\;y5 \leq 7.2 \cdot 10^{+195}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \end{array} \]

Alternative 7: 37.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot y0 - a \cdot y1\\ t_2 := t \cdot j - y \cdot k\\ t_3 := y4 \cdot \left(\left(b \cdot t_2 + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;y2 \leq -1.16 \cdot 10^{+231}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;y2 \leq -3.6 \cdot 10^{+178}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot t_2\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq -4.8 \cdot 10^{+116}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -1 \cdot 10^{-52}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y2 \leq 8 \cdot 10^{-190}:\\ \;\;\;\;x \cdot \left(\left(i \cdot \left(j \cdot y1 - y \cdot c\right) + a \cdot \left(y \cdot b\right)\right) - y0 \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq 6.1 \cdot 10^{-152}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y2 \leq 1.3 \cdot 10^{+250}:\\ \;\;\;\;x \cdot \left(\left(y2 \cdot t_1 + y \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 2.2 \cdot 10^{+281}:\\ \;\;\;\;\left(t \cdot y5\right) \cdot \left(a \cdot y2\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(x \cdot t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* c y0) (* a y1)))
        (t_2 (- (* t j) (* y k)))
        (t_3
         (*
          y4
          (+
           (+ (* b t_2) (* y1 (- (* k y2) (* j y3))))
           (* c (- (* y y3) (* t y2)))))))
   (if (<= y2 -1.16e+231)
     (* y1 (* y2 (- (* k y4) (* x a))))
     (if (<= y2 -3.6e+178)
       (*
        b
        (+
         (+ (* a (- (* x y) (* z t))) (* y4 t_2))
         (* y0 (- (* z k) (* x j)))))
       (if (<= y2 -4.8e+116)
         (* t (* c (- (* z i) (* y2 y4))))
         (if (<= y2 -1e-52)
           t_3
           (if (<= y2 8e-190)
             (*
              x
              (- (+ (* i (- (* j y1) (* y c))) (* a (* y b))) (* y0 (* b j))))
             (if (<= y2 6.1e-152)
               t_3
               (if (<= y2 1.3e+250)
                 (*
                  x
                  (+
                   (+ (* y2 t_1) (* y (- (* a b) (* c i))))
                   (* j (- (* i y1) (* b y0)))))
                 (if (<= y2 2.2e+281)
                   (* (* t y5) (* a y2))
                   (* y2 (* x t_1))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y0) - (a * y1);
	double t_2 = (t * j) - (y * k);
	double t_3 = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double tmp;
	if (y2 <= -1.16e+231) {
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	} else if (y2 <= -3.6e+178) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))));
	} else if (y2 <= -4.8e+116) {
		tmp = t * (c * ((z * i) - (y2 * y4)));
	} else if (y2 <= -1e-52) {
		tmp = t_3;
	} else if (y2 <= 8e-190) {
		tmp = x * (((i * ((j * y1) - (y * c))) + (a * (y * b))) - (y0 * (b * j)));
	} else if (y2 <= 6.1e-152) {
		tmp = t_3;
	} else if (y2 <= 1.3e+250) {
		tmp = x * (((y2 * t_1) + (y * ((a * b) - (c * i)))) + (j * ((i * y1) - (b * y0))));
	} else if (y2 <= 2.2e+281) {
		tmp = (t * y5) * (a * y2);
	} else {
		tmp = y2 * (x * t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (c * y0) - (a * y1)
    t_2 = (t * j) - (y * k)
    t_3 = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    if (y2 <= (-1.16d+231)) then
        tmp = y1 * (y2 * ((k * y4) - (x * a)))
    else if (y2 <= (-3.6d+178)) then
        tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))))
    else if (y2 <= (-4.8d+116)) then
        tmp = t * (c * ((z * i) - (y2 * y4)))
    else if (y2 <= (-1d-52)) then
        tmp = t_3
    else if (y2 <= 8d-190) then
        tmp = x * (((i * ((j * y1) - (y * c))) + (a * (y * b))) - (y0 * (b * j)))
    else if (y2 <= 6.1d-152) then
        tmp = t_3
    else if (y2 <= 1.3d+250) then
        tmp = x * (((y2 * t_1) + (y * ((a * b) - (c * i)))) + (j * ((i * y1) - (b * y0))))
    else if (y2 <= 2.2d+281) then
        tmp = (t * y5) * (a * y2)
    else
        tmp = y2 * (x * t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y0) - (a * y1);
	double t_2 = (t * j) - (y * k);
	double t_3 = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double tmp;
	if (y2 <= -1.16e+231) {
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	} else if (y2 <= -3.6e+178) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))));
	} else if (y2 <= -4.8e+116) {
		tmp = t * (c * ((z * i) - (y2 * y4)));
	} else if (y2 <= -1e-52) {
		tmp = t_3;
	} else if (y2 <= 8e-190) {
		tmp = x * (((i * ((j * y1) - (y * c))) + (a * (y * b))) - (y0 * (b * j)));
	} else if (y2 <= 6.1e-152) {
		tmp = t_3;
	} else if (y2 <= 1.3e+250) {
		tmp = x * (((y2 * t_1) + (y * ((a * b) - (c * i)))) + (j * ((i * y1) - (b * y0))));
	} else if (y2 <= 2.2e+281) {
		tmp = (t * y5) * (a * y2);
	} else {
		tmp = y2 * (x * t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (c * y0) - (a * y1)
	t_2 = (t * j) - (y * k)
	t_3 = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	tmp = 0
	if y2 <= -1.16e+231:
		tmp = y1 * (y2 * ((k * y4) - (x * a)))
	elif y2 <= -3.6e+178:
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))))
	elif y2 <= -4.8e+116:
		tmp = t * (c * ((z * i) - (y2 * y4)))
	elif y2 <= -1e-52:
		tmp = t_3
	elif y2 <= 8e-190:
		tmp = x * (((i * ((j * y1) - (y * c))) + (a * (y * b))) - (y0 * (b * j)))
	elif y2 <= 6.1e-152:
		tmp = t_3
	elif y2 <= 1.3e+250:
		tmp = x * (((y2 * t_1) + (y * ((a * b) - (c * i)))) + (j * ((i * y1) - (b * y0))))
	elif y2 <= 2.2e+281:
		tmp = (t * y5) * (a * y2)
	else:
		tmp = y2 * (x * t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(c * y0) - Float64(a * y1))
	t_2 = Float64(Float64(t * j) - Float64(y * k))
	t_3 = 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)))))
	tmp = 0.0
	if (y2 <= -1.16e+231)
		tmp = Float64(y1 * Float64(y2 * Float64(Float64(k * y4) - Float64(x * a))));
	elseif (y2 <= -3.6e+178)
		tmp = 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)))));
	elseif (y2 <= -4.8e+116)
		tmp = Float64(t * Float64(c * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (y2 <= -1e-52)
		tmp = t_3;
	elseif (y2 <= 8e-190)
		tmp = Float64(x * Float64(Float64(Float64(i * Float64(Float64(j * y1) - Float64(y * c))) + Float64(a * Float64(y * b))) - Float64(y0 * Float64(b * j))));
	elseif (y2 <= 6.1e-152)
		tmp = t_3;
	elseif (y2 <= 1.3e+250)
		tmp = Float64(x * Float64(Float64(Float64(y2 * t_1) + Float64(y * Float64(Float64(a * b) - Float64(c * i)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (y2 <= 2.2e+281)
		tmp = Float64(Float64(t * y5) * Float64(a * y2));
	else
		tmp = Float64(y2 * Float64(x * t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (c * y0) - (a * y1);
	t_2 = (t * j) - (y * k);
	t_3 = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	tmp = 0.0;
	if (y2 <= -1.16e+231)
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	elseif (y2 <= -3.6e+178)
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))));
	elseif (y2 <= -4.8e+116)
		tmp = t * (c * ((z * i) - (y2 * y4)));
	elseif (y2 <= -1e-52)
		tmp = t_3;
	elseif (y2 <= 8e-190)
		tmp = x * (((i * ((j * y1) - (y * c))) + (a * (y * b))) - (y0 * (b * j)));
	elseif (y2 <= 6.1e-152)
		tmp = t_3;
	elseif (y2 <= 1.3e+250)
		tmp = x * (((y2 * t_1) + (y * ((a * b) - (c * i)))) + (j * ((i * y1) - (b * y0))));
	elseif (y2 <= 2.2e+281)
		tmp = (t * y5) * (a * y2);
	else
		tmp = y2 * (x * t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = 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[y2, -1.16e+231], N[(y1 * N[(y2 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -3.6e+178], 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[y2, -4.8e+116], N[(t * N[(c * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1e-52], t$95$3, If[LessEqual[y2, 8e-190], N[(x * N[(N[(N[(i * N[(N[(j * y1), $MachinePrecision] - N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y0 * N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 6.1e-152], t$95$3, If[LessEqual[y2, 1.3e+250], N[(x * N[(N[(N[(y2 * t$95$1), $MachinePrecision] + N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.2e+281], N[(N[(t * y5), $MachinePrecision] * N[(a * y2), $MachinePrecision]), $MachinePrecision], N[(y2 * N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y2 < -1.16e231

   1. Initial program 25.0%

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

   3. Simplified 25.0%

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

   4. Taylor expanded in y2 around inf 75.5%

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

   5. Taylor expanded in y1 around inf 67.1%

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

      1. *-commutative 67.1%

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

      2. +-commutative 67.1%

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

      3. mul-1-neg 67.1%

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

      4. unsub-neg 67.1%

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

      5. *-commutative 67.1%

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

   7. Simplified 67.1%

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

   if -1.16e231 < y2 < -3.5999999999999998e178

   1. Initial program 20.0%

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

   3. Simplified 20.0%

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

   4. Taylor expanded in b around inf 80.6%

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

   if -3.5999999999999998e178 < y2 < -4.8000000000000001e116

   1. Initial program 23.7%

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

   3. Simplified 23.7%

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

   4. Taylor expanded in t around inf 57.3%

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

      1. associate--l+ 57.3%

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

      2. mul-1-neg 57.3%

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

   6. Simplified 57.3%

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

   7. Taylor expanded in c around -inf 72.1%

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

      1. mul-1-neg 72.1%

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

      2. unsub-neg 72.1%

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

      3. *-commutative 72.1%

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

   9. Simplified 72.1%

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

   if -4.8000000000000001e116 < y2 < -1e-52 or 8.0000000000000002e-190 < y2 < 6.09999999999999983e-152

   1. Initial program 31.4%

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

   3. Simplified 31.4%

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

   4. Taylor expanded in y4 around inf 54.9%

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

   if -1e-52 < y2 < 8.0000000000000002e-190

   1. Initial program 29.2%

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

   3. Simplified 29.2%

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

   4. Taylor expanded in x around inf 41.8%

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

   5. Taylor expanded in i around -inf 43.1%

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

   6. Taylor expanded in y2 around 0 50.1%

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

   if 6.09999999999999983e-152 < y2 < 1.30000000000000006e250

   1. Initial program 28.5%

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

   3. Simplified 28.5%

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

   4. Taylor expanded in x around inf 49.9%

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

   if 1.30000000000000006e250 < y2 < 2.2000000000000001e281

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in t around inf 60.0%

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

      1. associate--l+ 60.0%

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

      2. mul-1-neg 60.0%

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

   6. Simplified 60.0%

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

   7. Taylor expanded in y5 around -inf 80.6%

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

      1. mul-1-neg 80.6%

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

      2. *-commutative 80.6%

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

   9. Simplified 80.6%

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

   10. Taylor expanded in i around 0 80.6%

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

       1. neg-mul-1 80.6%

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

       2. distribute-rgt-neg-in 80.6%

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

   12. Simplified 80.6%

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

   if 2.2000000000000001e281 < y2

   1. Initial program 50.0%

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

   3. Simplified 50.0%

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

   4. Taylor expanded in y2 around inf 51.1%

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

   5. Taylor expanded in x around -inf 67.7%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.16 \cdot 10^{+231}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;y2 \leq -3.6 \cdot 10^{+178}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq -4.8 \cdot 10^{+116}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -1 \cdot 10^{-52}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 8 \cdot 10^{-190}:\\ \;\;\;\;x \cdot \left(\left(i \cdot \left(j \cdot y1 - y \cdot c\right) + a \cdot \left(y \cdot b\right)\right) - y0 \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq 6.1 \cdot 10^{-152}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 1.3 \cdot 10^{+250}:\\ \;\;\;\;x \cdot \left(\left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + y \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 2.2 \cdot 10^{+281}:\\ \;\;\;\;\left(t \cdot y5\right) \cdot \left(a \cdot y2\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \end{array} \]

Alternative 8: 37.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot y5 - c \cdot y4\\ t_2 := y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ t_3 := c \cdot y0 - a \cdot y1\\ \mathbf{if}\;y2 \leq -1.55 \cdot 10^{+116}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -1.65 \cdot 10^{-54}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y2 \leq 4.6 \cdot 10^{-195}:\\ \;\;\;\;x \cdot \left(\left(i \cdot \left(j \cdot y1 - y \cdot c\right) + a \cdot \left(y \cdot b\right)\right) - y0 \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq 7 \cdot 10^{-152}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y2 \leq 10^{+74}:\\ \;\;\;\;x \cdot \left(\left(y2 \cdot t_3 + y \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 1.12 \cdot 10^{+173}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right) + \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + y2 \cdot t_1\right)\right)\\ \mathbf{elif}\;y2 \leq 1.5 \cdot 10^{+230}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot t_3 + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* a y5) (* c y4)))
        (t_2
         (*
          y4
          (+
           (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
           (* c (- (* y y3) (* t y2))))))
        (t_3 (- (* c y0) (* a y1))))
   (if (<= y2 -1.55e+116)
     (* t (* c (- (* z i) (* y2 y4))))
     (if (<= y2 -1.65e-54)
       t_2
       (if (<= y2 4.6e-195)
         (* x (- (+ (* i (- (* j y1) (* y c))) (* a (* y b))) (* y0 (* b j))))
         (if (<= y2 7e-152)
           t_2
           (if (<= y2 1e+74)
             (*
              x
              (+
               (+ (* y2 t_3) (* y (- (* a b) (* c i))))
               (* j (- (* i y1) (* b y0)))))
             (if (<= y2 1.12e+173)
               (*
                t
                (+
                 (* z (- (* c i) (* a b)))
                 (+ (* j (- (* b y4) (* i y5))) (* y2 t_1))))
               (if (<= y2 1.5e+230)
                 (* x (* c (- (* y0 y2) (* y i))))
                 (*
                  y2
                  (+
                   (+ (* x t_3) (* k (- (* y1 y4) (* y0 y5))))
                   (* 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 = (a * y5) - (c * y4);
	double t_2 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double t_3 = (c * y0) - (a * y1);
	double tmp;
	if (y2 <= -1.55e+116) {
		tmp = t * (c * ((z * i) - (y2 * y4)));
	} else if (y2 <= -1.65e-54) {
		tmp = t_2;
	} else if (y2 <= 4.6e-195) {
		tmp = x * (((i * ((j * y1) - (y * c))) + (a * (y * b))) - (y0 * (b * j)));
	} else if (y2 <= 7e-152) {
		tmp = t_2;
	} else if (y2 <= 1e+74) {
		tmp = x * (((y2 * t_3) + (y * ((a * b) - (c * i)))) + (j * ((i * y1) - (b * y0))));
	} else if (y2 <= 1.12e+173) {
		tmp = t * ((z * ((c * i) - (a * b))) + ((j * ((b * y4) - (i * y5))) + (y2 * t_1)));
	} else if (y2 <= 1.5e+230) {
		tmp = x * (c * ((y0 * y2) - (y * i)));
	} else {
		tmp = y2 * (((x * t_3) + (k * ((y1 * y4) - (y0 * y5)))) + (t * 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 = (a * y5) - (c * y4)
    t_2 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    t_3 = (c * y0) - (a * y1)
    if (y2 <= (-1.55d+116)) then
        tmp = t * (c * ((z * i) - (y2 * y4)))
    else if (y2 <= (-1.65d-54)) then
        tmp = t_2
    else if (y2 <= 4.6d-195) then
        tmp = x * (((i * ((j * y1) - (y * c))) + (a * (y * b))) - (y0 * (b * j)))
    else if (y2 <= 7d-152) then
        tmp = t_2
    else if (y2 <= 1d+74) then
        tmp = x * (((y2 * t_3) + (y * ((a * b) - (c * i)))) + (j * ((i * y1) - (b * y0))))
    else if (y2 <= 1.12d+173) then
        tmp = t * ((z * ((c * i) - (a * b))) + ((j * ((b * y4) - (i * y5))) + (y2 * t_1)))
    else if (y2 <= 1.5d+230) then
        tmp = x * (c * ((y0 * y2) - (y * i)))
    else
        tmp = y2 * (((x * t_3) + (k * ((y1 * y4) - (y0 * y5)))) + (t * 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 * y5) - (c * y4);
	double t_2 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double t_3 = (c * y0) - (a * y1);
	double tmp;
	if (y2 <= -1.55e+116) {
		tmp = t * (c * ((z * i) - (y2 * y4)));
	} else if (y2 <= -1.65e-54) {
		tmp = t_2;
	} else if (y2 <= 4.6e-195) {
		tmp = x * (((i * ((j * y1) - (y * c))) + (a * (y * b))) - (y0 * (b * j)));
	} else if (y2 <= 7e-152) {
		tmp = t_2;
	} else if (y2 <= 1e+74) {
		tmp = x * (((y2 * t_3) + (y * ((a * b) - (c * i)))) + (j * ((i * y1) - (b * y0))));
	} else if (y2 <= 1.12e+173) {
		tmp = t * ((z * ((c * i) - (a * b))) + ((j * ((b * y4) - (i * y5))) + (y2 * t_1)));
	} else if (y2 <= 1.5e+230) {
		tmp = x * (c * ((y0 * y2) - (y * i)));
	} else {
		tmp = y2 * (((x * t_3) + (k * ((y1 * y4) - (y0 * y5)))) + (t * 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 * y5) - (c * y4)
	t_2 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	t_3 = (c * y0) - (a * y1)
	tmp = 0
	if y2 <= -1.55e+116:
		tmp = t * (c * ((z * i) - (y2 * y4)))
	elif y2 <= -1.65e-54:
		tmp = t_2
	elif y2 <= 4.6e-195:
		tmp = x * (((i * ((j * y1) - (y * c))) + (a * (y * b))) - (y0 * (b * j)))
	elif y2 <= 7e-152:
		tmp = t_2
	elif y2 <= 1e+74:
		tmp = x * (((y2 * t_3) + (y * ((a * b) - (c * i)))) + (j * ((i * y1) - (b * y0))))
	elif y2 <= 1.12e+173:
		tmp = t * ((z * ((c * i) - (a * b))) + ((j * ((b * y4) - (i * y5))) + (y2 * t_1)))
	elif y2 <= 1.5e+230:
		tmp = x * (c * ((y0 * y2) - (y * i)))
	else:
		tmp = y2 * (((x * t_3) + (k * ((y1 * y4) - (y0 * y5)))) + (t * t_1))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(a * y5) - Float64(c * y4))
	t_2 = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))))
	t_3 = Float64(Float64(c * y0) - Float64(a * y1))
	tmp = 0.0
	if (y2 <= -1.55e+116)
		tmp = Float64(t * Float64(c * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (y2 <= -1.65e-54)
		tmp = t_2;
	elseif (y2 <= 4.6e-195)
		tmp = Float64(x * Float64(Float64(Float64(i * Float64(Float64(j * y1) - Float64(y * c))) + Float64(a * Float64(y * b))) - Float64(y0 * Float64(b * j))));
	elseif (y2 <= 7e-152)
		tmp = t_2;
	elseif (y2 <= 1e+74)
		tmp = Float64(x * Float64(Float64(Float64(y2 * t_3) + Float64(y * Float64(Float64(a * b) - Float64(c * i)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (y2 <= 1.12e+173)
		tmp = Float64(t * Float64(Float64(z * Float64(Float64(c * i) - Float64(a * b))) + Float64(Float64(j * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(y2 * t_1))));
	elseif (y2 <= 1.5e+230)
		tmp = Float64(x * Float64(c * Float64(Float64(y0 * y2) - Float64(y * i))));
	else
		tmp = Float64(y2 * Float64(Float64(Float64(x * t_3) + Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))) + Float64(t * 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 * y5) - (c * y4);
	t_2 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	t_3 = (c * y0) - (a * y1);
	tmp = 0.0;
	if (y2 <= -1.55e+116)
		tmp = t * (c * ((z * i) - (y2 * y4)));
	elseif (y2 <= -1.65e-54)
		tmp = t_2;
	elseif (y2 <= 4.6e-195)
		tmp = x * (((i * ((j * y1) - (y * c))) + (a * (y * b))) - (y0 * (b * j)));
	elseif (y2 <= 7e-152)
		tmp = t_2;
	elseif (y2 <= 1e+74)
		tmp = x * (((y2 * t_3) + (y * ((a * b) - (c * i)))) + (j * ((i * y1) - (b * y0))));
	elseif (y2 <= 1.12e+173)
		tmp = t * ((z * ((c * i) - (a * b))) + ((j * ((b * y4) - (i * y5))) + (y2 * t_1)));
	elseif (y2 <= 1.5e+230)
		tmp = x * (c * ((y0 * y2) - (y * i)));
	else
		tmp = y2 * (((x * t_3) + (k * ((y1 * y4) - (y0 * y5)))) + (t * t_1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -1.55e+116], N[(t * N[(c * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1.65e-54], t$95$2, If[LessEqual[y2, 4.6e-195], N[(x * N[(N[(N[(i * N[(N[(j * y1), $MachinePrecision] - N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y0 * N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 7e-152], t$95$2, If[LessEqual[y2, 1e+74], N[(x * N[(N[(N[(y2 * t$95$3), $MachinePrecision] + N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.12e+173], N[(t * N[(N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.5e+230], N[(x * N[(c * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y2 * N[(N[(N[(x * t$95$3), $MachinePrecision] + N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y2 < -1.54999999999999998e116

   1. Initial program 23.2%

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

   3. Simplified 23.2%

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

   4. Taylor expanded in t around inf 48.9%

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

      1. associate--l+ 48.9%

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

      2. mul-1-neg 48.9%

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

   6. Simplified 48.9%

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

   7. Taylor expanded in c around -inf 61.2%

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

      1. mul-1-neg 61.2%

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

      2. unsub-neg 61.2%

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

      3. *-commutative 61.2%

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

   9. Simplified 61.2%

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

   if -1.54999999999999998e116 < y2 < -1.64999999999999996e-54 or 4.6000000000000004e-195 < y2 < 7.0000000000000002e-152

   1. Initial program 31.4%

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

   3. Simplified 31.4%

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

   4. Taylor expanded in y4 around inf 54.9%

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

   if -1.64999999999999996e-54 < y2 < 4.6000000000000004e-195

   1. Initial program 29.2%

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

   3. Simplified 29.2%

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

   4. Taylor expanded in x around inf 41.8%

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

   5. Taylor expanded in i around -inf 43.1%

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

   6. Taylor expanded in y2 around 0 50.1%

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

   if 7.0000000000000002e-152 < y2 < 9.99999999999999952e73

   1. Initial program 34.9%

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

   3. Simplified 34.9%

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

   4. Taylor expanded in x around inf 50.5%

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

   if 9.99999999999999952e73 < y2 < 1.12e173

   1. Initial program 24.0%

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

   3. Simplified 24.0%

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

   4. Taylor expanded in t around inf 68.5%

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

      1. associate--l+ 68.5%

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

      2. mul-1-neg 68.5%

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

   6. Simplified 68.5%

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

   if 1.12e173 < y2 < 1.50000000000000004e230

   1. Initial program 11.1%

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

   3. Simplified 11.1%

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

   4. Taylor expanded in x around inf 56.2%

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

   5. Taylor expanded in i around -inf 56.2%

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

   6. Taylor expanded in c around inf 57.2%

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

      1. associate-*r* 67.3%

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

      2. *-commutative 67.3%

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

      3. +-commutative 67.3%

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

      4. mul-1-neg 67.3%

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

      5. unsub-neg 67.3%

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

      6. *-commutative 67.3%

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

   8. Simplified 67.3%

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

   if 1.50000000000000004e230 < y2

   1. Initial program 25.0%

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

   3. Simplified 25.0%

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

   4. Taylor expanded in y2 around inf 67.2%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.55 \cdot 10^{+116}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -1.65 \cdot 10^{-54}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 4.6 \cdot 10^{-195}:\\ \;\;\;\;x \cdot \left(\left(i \cdot \left(j \cdot y1 - y \cdot c\right) + a \cdot \left(y \cdot b\right)\right) - y0 \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq 7 \cdot 10^{-152}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 10^{+74}:\\ \;\;\;\;x \cdot \left(\left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + y \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 1.12 \cdot 10^{+173}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right) + \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 1.5 \cdot 10^{+230}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \end{array} \]

Alternative 9: 39.7% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ t_2 := c \cdot y0 - a \cdot y1\\ \mathbf{if}\;y2 \leq -4.7 \cdot 10^{+116}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -2.4 \cdot 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq 4.9 \cdot 10^{-195}:\\ \;\;\;\;x \cdot \left(\left(i \cdot \left(j \cdot y1 - y \cdot c\right) + a \cdot \left(y \cdot b\right)\right) - y0 \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq 1.08 \cdot 10^{-151}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq 1.2 \cdot 10^{+75}:\\ \;\;\;\;x \cdot \left(\left(y2 \cdot t_2 + y \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot t_2 + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          y4
          (+
           (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
           (* c (- (* y y3) (* t y2))))))
        (t_2 (- (* c y0) (* a y1))))
   (if (<= y2 -4.7e+116)
     (* t (* c (- (* z i) (* y2 y4))))
     (if (<= y2 -2.4e-53)
       t_1
       (if (<= y2 4.9e-195)
         (* x (- (+ (* i (- (* j y1) (* y c))) (* a (* y b))) (* y0 (* b j))))
         (if (<= y2 1.08e-151)
           t_1
           (if (<= y2 1.2e+75)
             (*
              x
              (+
               (+ (* y2 t_2) (* y (- (* a b) (* c i))))
               (* j (- (* i y1) (* b y0)))))
             (*
              y2
              (+
               (+ (* x t_2) (* k (- (* y1 y4) (* y0 y5))))
               (* t (- (* a y5) (* c y4))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double t_2 = (c * y0) - (a * y1);
	double tmp;
	if (y2 <= -4.7e+116) {
		tmp = t * (c * ((z * i) - (y2 * y4)));
	} else if (y2 <= -2.4e-53) {
		tmp = t_1;
	} else if (y2 <= 4.9e-195) {
		tmp = x * (((i * ((j * y1) - (y * c))) + (a * (y * b))) - (y0 * (b * j)));
	} else if (y2 <= 1.08e-151) {
		tmp = t_1;
	} else if (y2 <= 1.2e+75) {
		tmp = x * (((y2 * t_2) + (y * ((a * b) - (c * i)))) + (j * ((i * y1) - (b * y0))));
	} else {
		tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    t_2 = (c * y0) - (a * y1)
    if (y2 <= (-4.7d+116)) then
        tmp = t * (c * ((z * i) - (y2 * y4)))
    else if (y2 <= (-2.4d-53)) then
        tmp = t_1
    else if (y2 <= 4.9d-195) then
        tmp = x * (((i * ((j * y1) - (y * c))) + (a * (y * b))) - (y0 * (b * j)))
    else if (y2 <= 1.08d-151) then
        tmp = t_1
    else if (y2 <= 1.2d+75) then
        tmp = x * (((y2 * t_2) + (y * ((a * b) - (c * i)))) + (j * ((i * y1) - (b * y0))))
    else
        tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double t_2 = (c * y0) - (a * y1);
	double tmp;
	if (y2 <= -4.7e+116) {
		tmp = t * (c * ((z * i) - (y2 * y4)));
	} else if (y2 <= -2.4e-53) {
		tmp = t_1;
	} else if (y2 <= 4.9e-195) {
		tmp = x * (((i * ((j * y1) - (y * c))) + (a * (y * b))) - (y0 * (b * j)));
	} else if (y2 <= 1.08e-151) {
		tmp = t_1;
	} else if (y2 <= 1.2e+75) {
		tmp = x * (((y2 * t_2) + (y * ((a * b) - (c * i)))) + (j * ((i * y1) - (b * y0))));
	} else {
		tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	t_2 = (c * y0) - (a * y1)
	tmp = 0
	if y2 <= -4.7e+116:
		tmp = t * (c * ((z * i) - (y2 * y4)))
	elif y2 <= -2.4e-53:
		tmp = t_1
	elif y2 <= 4.9e-195:
		tmp = x * (((i * ((j * y1) - (y * c))) + (a * (y * b))) - (y0 * (b * j)))
	elif y2 <= 1.08e-151:
		tmp = t_1
	elif y2 <= 1.2e+75:
		tmp = x * (((y2 * t_2) + (y * ((a * b) - (c * i)))) + (j * ((i * y1) - (b * y0))))
	else:
		tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))))
	t_2 = Float64(Float64(c * y0) - Float64(a * y1))
	tmp = 0.0
	if (y2 <= -4.7e+116)
		tmp = Float64(t * Float64(c * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (y2 <= -2.4e-53)
		tmp = t_1;
	elseif (y2 <= 4.9e-195)
		tmp = Float64(x * Float64(Float64(Float64(i * Float64(Float64(j * y1) - Float64(y * c))) + Float64(a * Float64(y * b))) - Float64(y0 * Float64(b * j))));
	elseif (y2 <= 1.08e-151)
		tmp = t_1;
	elseif (y2 <= 1.2e+75)
		tmp = Float64(x * Float64(Float64(Float64(y2 * t_2) + Float64(y * Float64(Float64(a * b) - Float64(c * i)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	else
		tmp = Float64(y2 * Float64(Float64(Float64(x * t_2) + Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	t_2 = (c * y0) - (a * y1);
	tmp = 0.0;
	if (y2 <= -4.7e+116)
		tmp = t * (c * ((z * i) - (y2 * y4)));
	elseif (y2 <= -2.4e-53)
		tmp = t_1;
	elseif (y2 <= 4.9e-195)
		tmp = x * (((i * ((j * y1) - (y * c))) + (a * (y * b))) - (y0 * (b * j)));
	elseif (y2 <= 1.08e-151)
		tmp = t_1;
	elseif (y2 <= 1.2e+75)
		tmp = x * (((y2 * t_2) + (y * ((a * b) - (c * i)))) + (j * ((i * y1) - (b * y0))));
	else
		tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -4.7e+116], N[(t * N[(c * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -2.4e-53], t$95$1, If[LessEqual[y2, 4.9e-195], N[(x * N[(N[(N[(i * N[(N[(j * y1), $MachinePrecision] - N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y0 * N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.08e-151], t$95$1, If[LessEqual[y2, 1.2e+75], N[(x * N[(N[(N[(y2 * t$95$2), $MachinePrecision] + N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y2 * N[(N[(N[(x * t$95$2), $MachinePrecision] + N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y2 < -4.7000000000000003e116

   1. Initial program 23.2%

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

   3. Simplified 23.2%

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

   4. Taylor expanded in t around inf 48.9%

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

      1. associate--l+ 48.9%

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

      2. mul-1-neg 48.9%

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

   6. Simplified 48.9%

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

   7. Taylor expanded in c around -inf 61.2%

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

      1. mul-1-neg 61.2%

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

      2. unsub-neg 61.2%

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

      3. *-commutative 61.2%

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

   9. Simplified 61.2%

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

   if -4.7000000000000003e116 < y2 < -2.40000000000000007e-53 or 4.9000000000000003e-195 < y2 < 1.07999999999999999e-151

   1. Initial program 31.4%

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

   3. Simplified 31.4%

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

   4. Taylor expanded in y4 around inf 54.9%

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

   if -2.40000000000000007e-53 < y2 < 4.9000000000000003e-195

   1. Initial program 29.2%

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

   3. Simplified 29.2%

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

   4. Taylor expanded in x around inf 41.8%

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

   5. Taylor expanded in i around -inf 43.1%

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

   6. Taylor expanded in y2 around 0 50.1%

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

   if 1.07999999999999999e-151 < y2 < 1.2e75

   1. Initial program 34.9%

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

   3. Simplified 34.9%

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

   4. Taylor expanded in x around inf 50.5%

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

   if 1.2e75 < y2

   1. Initial program 21.7%

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

   3. Simplified 21.7%

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

   4. Taylor expanded in y2 around inf 56.8%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]
3. Recombined 5 regimes into one program.

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -4.7 \cdot 10^{+116}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -2.4 \cdot 10^{-53}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 4.9 \cdot 10^{-195}:\\ \;\;\;\;x \cdot \left(\left(i \cdot \left(j \cdot y1 - y \cdot c\right) + a \cdot \left(y \cdot b\right)\right) - y0 \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq 1.08 \cdot 10^{-151}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 1.2 \cdot 10^{+75}:\\ \;\;\;\;x \cdot \left(\left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + y \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \end{array} \]

Alternative 10: 35.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ t_2 := a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{if}\;y3 \leq -2.15 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y3 \leq -8 \cdot 10^{+17}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;y3 \leq -5.5 \cdot 10^{+14}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y3 \leq 1.4 \cdot 10^{-295}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq 1.6 \cdot 10^{-96}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y3 \leq 1.36 \cdot 10^{-39}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y3 \leq 550000000000:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 1.45 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \left(\left(i \cdot \left(j \cdot y1 - y \cdot c\right) + a \cdot \left(y \cdot b\right)\right) - y0 \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;y3 \leq 6.28 \cdot 10^{+119}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 9 \cdot 10^{+192}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y3 (- (* z y1) (* y y5)))))
        (t_2 (* a (* y5 (- (* t y2) (* y y3))))))
   (if (<= y3 -2.15e+80)
     t_1
     (if (<= y3 -8e+17)
       (* y0 (* x (- (* c y2) (* b j))))
       (if (<= y3 -5.5e+14)
         t_2
         (if (<= y3 1.4e-295)
           (* x (+ (* y (- (* a b) (* c i))) (* j (- (* i y1) (* b y0)))))
           (if (<= y3 1.6e-96)
             (* a (* b (- (* x y) (* z t))))
             (if (<= y3 1.36e-39)
               t_2
               (if (<= y3 550000000000.0)
                 (* t (* c (- (* z i) (* y2 y4))))
                 (if (<= y3 1.45e+76)
                   (*
                    x
                    (-
                     (+ (* i (- (* j y1) (* y c))) (* a (* y b)))
                     (* y0 (* b j))))
                   (if (<= y3 6.28e+119)
                     (* c (* y4 (- (* y y3) (* t y2))))
                     (if (<= y3 9e+192)
                       (* t (* z (- (* c i) (* a b))))
                       t_1))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y3 * ((z * y1) - (y * y5)));
	double t_2 = a * (y5 * ((t * y2) - (y * y3)));
	double tmp;
	if (y3 <= -2.15e+80) {
		tmp = t_1;
	} else if (y3 <= -8e+17) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else if (y3 <= -5.5e+14) {
		tmp = t_2;
	} else if (y3 <= 1.4e-295) {
		tmp = x * ((y * ((a * b) - (c * i))) + (j * ((i * y1) - (b * y0))));
	} else if (y3 <= 1.6e-96) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y3 <= 1.36e-39) {
		tmp = t_2;
	} else if (y3 <= 550000000000.0) {
		tmp = t * (c * ((z * i) - (y2 * y4)));
	} else if (y3 <= 1.45e+76) {
		tmp = x * (((i * ((j * y1) - (y * c))) + (a * (y * b))) - (y0 * (b * j)));
	} else if (y3 <= 6.28e+119) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (y3 <= 9e+192) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (y3 * ((z * y1) - (y * y5)))
    t_2 = a * (y5 * ((t * y2) - (y * y3)))
    if (y3 <= (-2.15d+80)) then
        tmp = t_1
    else if (y3 <= (-8d+17)) then
        tmp = y0 * (x * ((c * y2) - (b * j)))
    else if (y3 <= (-5.5d+14)) then
        tmp = t_2
    else if (y3 <= 1.4d-295) then
        tmp = x * ((y * ((a * b) - (c * i))) + (j * ((i * y1) - (b * y0))))
    else if (y3 <= 1.6d-96) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (y3 <= 1.36d-39) then
        tmp = t_2
    else if (y3 <= 550000000000.0d0) then
        tmp = t * (c * ((z * i) - (y2 * y4)))
    else if (y3 <= 1.45d+76) then
        tmp = x * (((i * ((j * y1) - (y * c))) + (a * (y * b))) - (y0 * (b * j)))
    else if (y3 <= 6.28d+119) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else if (y3 <= 9d+192) then
        tmp = t * (z * ((c * i) - (a * b)))
    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 * (y3 * ((z * y1) - (y * y5)));
	double t_2 = a * (y5 * ((t * y2) - (y * y3)));
	double tmp;
	if (y3 <= -2.15e+80) {
		tmp = t_1;
	} else if (y3 <= -8e+17) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else if (y3 <= -5.5e+14) {
		tmp = t_2;
	} else if (y3 <= 1.4e-295) {
		tmp = x * ((y * ((a * b) - (c * i))) + (j * ((i * y1) - (b * y0))));
	} else if (y3 <= 1.6e-96) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y3 <= 1.36e-39) {
		tmp = t_2;
	} else if (y3 <= 550000000000.0) {
		tmp = t * (c * ((z * i) - (y2 * y4)));
	} else if (y3 <= 1.45e+76) {
		tmp = x * (((i * ((j * y1) - (y * c))) + (a * (y * b))) - (y0 * (b * j)));
	} else if (y3 <= 6.28e+119) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (y3 <= 9e+192) {
		tmp = t * (z * ((c * i) - (a * b)));
	} 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 * (y3 * ((z * y1) - (y * y5)))
	t_2 = a * (y5 * ((t * y2) - (y * y3)))
	tmp = 0
	if y3 <= -2.15e+80:
		tmp = t_1
	elif y3 <= -8e+17:
		tmp = y0 * (x * ((c * y2) - (b * j)))
	elif y3 <= -5.5e+14:
		tmp = t_2
	elif y3 <= 1.4e-295:
		tmp = x * ((y * ((a * b) - (c * i))) + (j * ((i * y1) - (b * y0))))
	elif y3 <= 1.6e-96:
		tmp = a * (b * ((x * y) - (z * t)))
	elif y3 <= 1.36e-39:
		tmp = t_2
	elif y3 <= 550000000000.0:
		tmp = t * (c * ((z * i) - (y2 * y4)))
	elif y3 <= 1.45e+76:
		tmp = x * (((i * ((j * y1) - (y * c))) + (a * (y * b))) - (y0 * (b * j)))
	elif y3 <= 6.28e+119:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	elif y3 <= 9e+192:
		tmp = t * (z * ((c * i) - (a * b)))
	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(y3 * Float64(Float64(z * y1) - Float64(y * y5))))
	t_2 = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))
	tmp = 0.0
	if (y3 <= -2.15e+80)
		tmp = t_1;
	elseif (y3 <= -8e+17)
		tmp = Float64(y0 * Float64(x * Float64(Float64(c * y2) - Float64(b * j))));
	elseif (y3 <= -5.5e+14)
		tmp = t_2;
	elseif (y3 <= 1.4e-295)
		tmp = Float64(x * Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (y3 <= 1.6e-96)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y3 <= 1.36e-39)
		tmp = t_2;
	elseif (y3 <= 550000000000.0)
		tmp = Float64(t * Float64(c * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (y3 <= 1.45e+76)
		tmp = Float64(x * Float64(Float64(Float64(i * Float64(Float64(j * y1) - Float64(y * c))) + Float64(a * Float64(y * b))) - Float64(y0 * Float64(b * j))));
	elseif (y3 <= 6.28e+119)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (y3 <= 9e+192)
		tmp = Float64(t * Float64(z * Float64(Float64(c * i) - Float64(a * b))));
	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 * (y3 * ((z * y1) - (y * y5)));
	t_2 = a * (y5 * ((t * y2) - (y * y3)));
	tmp = 0.0;
	if (y3 <= -2.15e+80)
		tmp = t_1;
	elseif (y3 <= -8e+17)
		tmp = y0 * (x * ((c * y2) - (b * j)));
	elseif (y3 <= -5.5e+14)
		tmp = t_2;
	elseif (y3 <= 1.4e-295)
		tmp = x * ((y * ((a * b) - (c * i))) + (j * ((i * y1) - (b * y0))));
	elseif (y3 <= 1.6e-96)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (y3 <= 1.36e-39)
		tmp = t_2;
	elseif (y3 <= 550000000000.0)
		tmp = t * (c * ((z * i) - (y2 * y4)));
	elseif (y3 <= 1.45e+76)
		tmp = x * (((i * ((j * y1) - (y * c))) + (a * (y * b))) - (y0 * (b * j)));
	elseif (y3 <= 6.28e+119)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	elseif (y3 <= 9e+192)
		tmp = t * (z * ((c * i) - (a * b)));
	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[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -2.15e+80], t$95$1, If[LessEqual[y3, -8e+17], N[(y0 * N[(x * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -5.5e+14], t$95$2, If[LessEqual[y3, 1.4e-295], N[(x * N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.6e-96], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.36e-39], t$95$2, If[LessEqual[y3, 550000000000.0], N[(t * N[(c * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.45e+76], N[(x * N[(N[(N[(i * N[(N[(j * y1), $MachinePrecision] - N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y0 * N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 6.28e+119], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 9e+192], N[(t * N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y3 < -2.15000000000000002e80 or 9e192 < y3

   1. Initial program 24.6%

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

   3. Simplified 34.4%

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

   4. Taylor expanded in a around inf 50.9%

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

      1. mul-1-neg 50.9%

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

      2. mul-1-neg 50.9%

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

   6. Simplified 50.9%

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

   7. Taylor expanded in y3 around -inf 62.7%

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

   if -2.15000000000000002e80 < y3 < -8e17

   1. Initial program 23.2%

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

   3. Simplified 23.2%

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

   4. Taylor expanded in x around inf 34.7%

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

   5. Taylor expanded in y0 around inf 67.7%

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

   if -8e17 < y3 < -5.5e14 or 1.60000000000000006e-96 < y3 < 1.35999999999999994e-39

   1. Initial program 7.6%

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

   3. Simplified 14.7%

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

   4. Taylor expanded in a around inf 50.1%

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

      1. mul-1-neg 50.1%

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

      2. mul-1-neg 50.1%

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

   6. Simplified 50.1%

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

   7. Taylor expanded in y5 around inf 65.2%

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

   if -5.5e14 < y3 < 1.4e-295

   1. Initial program 34.1%

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

   3. Simplified 34.1%

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

   4. Taylor expanded in x around inf 53.4%

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

   5. Taylor expanded in y2 around 0 51.8%

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

   if 1.4e-295 < y3 < 1.60000000000000006e-96

   1. Initial program 39.7%

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

   3. Simplified 42.0%

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

   4. Taylor expanded in a around inf 42.2%

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

      1. mul-1-neg 42.2%

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

      2. mul-1-neg 42.2%

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

   6. Simplified 42.2%

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

   7. Taylor expanded in b around inf 47.4%

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

   if 1.35999999999999994e-39 < y3 < 5.5e11

   1. Initial program 21.4%

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

   3. Simplified 21.4%

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

   4. Taylor expanded in t around inf 31.2%

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

      1. associate--l+ 31.2%

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

      2. mul-1-neg 31.2%

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

   6. Simplified 31.2%

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

   7. Taylor expanded in c around -inf 60.4%

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

      1. mul-1-neg 60.4%

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

      2. unsub-neg 60.4%

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

      3. *-commutative 60.4%

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

   9. Simplified 60.4%

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

   if 5.5e11 < y3 < 1.4500000000000001e76

   1. Initial program 20.5%

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

   3. Simplified 20.5%

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

   4. Taylor expanded in x around inf 47.1%

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

   5. Taylor expanded in i around -inf 60.3%

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

   6. Taylor expanded in y2 around 0 67.6%

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

   if 1.4500000000000001e76 < y3 < 6.28000000000000014e119

   1. Initial program 12.5%

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

   3. Simplified 12.5%

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

   4. Taylor expanded in y4 around inf 50.0%

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

   5. Taylor expanded in c around inf 52.1%

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

   if 6.28000000000000014e119 < y3 < 9e192

   1. Initial program 23.8%

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

   3. Simplified 23.8%

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

   4. Taylor expanded in t around inf 42.9%

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

      1. associate--l+ 42.9%

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

      2. mul-1-neg 42.9%

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

   6. Simplified 42.9%

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

   7. Taylor expanded in z around inf 47.9%

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

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -2.15 \cdot 10^{+80}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y3 \leq -8 \cdot 10^{+17}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;y3 \leq -5.5 \cdot 10^{+14}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y3 \leq 1.4 \cdot 10^{-295}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq 1.6 \cdot 10^{-96}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y3 \leq 1.36 \cdot 10^{-39}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y3 \leq 550000000000:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 1.45 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \left(\left(i \cdot \left(j \cdot y1 - y \cdot c\right) + a \cdot \left(y \cdot b\right)\right) - y0 \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;y3 \leq 6.28 \cdot 10^{+119}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 9 \cdot 10^{+192}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \end{array} \]

Alternative 11: 32.0% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot y4 - x \cdot a\\ t_2 := y \cdot \left(a \cdot b - c \cdot i\right)\\ \mathbf{if}\;y \leq -1.16 \cdot 10^{+154}:\\ \;\;\;\;x \cdot t_2\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-11}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot t_1\right)\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-300}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-23}:\\ \;\;\;\;y2 \cdot \left(y1 \cdot t_1\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+131}:\\ \;\;\;\;x \cdot \left(t_2 + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+201}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* k y4) (* x a))) (t_2 (* y (- (* a b) (* c i)))))
   (if (<= y -1.16e+154)
     (* x t_2)
     (if (<= y -7.2e-11)
       (* y1 (* y2 t_1))
       (if (<= y 3.5e-300)
         (* a (* z (- (* y1 y3) (* t b))))
         (if (<= y 2.3e-23)
           (* y2 (* y1 t_1))
           (if (<= y 1.3e+131)
             (* x (+ t_2 (* j (- (* i y1) (* b y0)))))
             (if (<= y 2.8e+201)
               (* t (* z (- (* c i) (* a b))))
               (* c (* y4 (- (* y y3) (* t y2))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (k * y4) - (x * a);
	double t_2 = y * ((a * b) - (c * i));
	double tmp;
	if (y <= -1.16e+154) {
		tmp = x * t_2;
	} else if (y <= -7.2e-11) {
		tmp = y1 * (y2 * t_1);
	} else if (y <= 3.5e-300) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (y <= 2.3e-23) {
		tmp = y2 * (y1 * t_1);
	} else if (y <= 1.3e+131) {
		tmp = x * (t_2 + (j * ((i * y1) - (b * y0))));
	} else if (y <= 2.8e+201) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (k * y4) - (x * a)
    t_2 = y * ((a * b) - (c * i))
    if (y <= (-1.16d+154)) then
        tmp = x * t_2
    else if (y <= (-7.2d-11)) then
        tmp = y1 * (y2 * t_1)
    else if (y <= 3.5d-300) then
        tmp = a * (z * ((y1 * y3) - (t * b)))
    else if (y <= 2.3d-23) then
        tmp = y2 * (y1 * t_1)
    else if (y <= 1.3d+131) then
        tmp = x * (t_2 + (j * ((i * y1) - (b * y0))))
    else if (y <= 2.8d+201) then
        tmp = t * (z * ((c * i) - (a * b)))
    else
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (k * y4) - (x * a);
	double t_2 = y * ((a * b) - (c * i));
	double tmp;
	if (y <= -1.16e+154) {
		tmp = x * t_2;
	} else if (y <= -7.2e-11) {
		tmp = y1 * (y2 * t_1);
	} else if (y <= 3.5e-300) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (y <= 2.3e-23) {
		tmp = y2 * (y1 * t_1);
	} else if (y <= 1.3e+131) {
		tmp = x * (t_2 + (j * ((i * y1) - (b * y0))));
	} else if (y <= 2.8e+201) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (k * y4) - (x * a)
	t_2 = y * ((a * b) - (c * i))
	tmp = 0
	if y <= -1.16e+154:
		tmp = x * t_2
	elif y <= -7.2e-11:
		tmp = y1 * (y2 * t_1)
	elif y <= 3.5e-300:
		tmp = a * (z * ((y1 * y3) - (t * b)))
	elif y <= 2.3e-23:
		tmp = y2 * (y1 * t_1)
	elif y <= 1.3e+131:
		tmp = x * (t_2 + (j * ((i * y1) - (b * y0))))
	elif y <= 2.8e+201:
		tmp = t * (z * ((c * i) - (a * b)))
	else:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(k * y4) - Float64(x * a))
	t_2 = Float64(y * Float64(Float64(a * b) - Float64(c * i)))
	tmp = 0.0
	if (y <= -1.16e+154)
		tmp = Float64(x * t_2);
	elseif (y <= -7.2e-11)
		tmp = Float64(y1 * Float64(y2 * t_1));
	elseif (y <= 3.5e-300)
		tmp = Float64(a * Float64(z * Float64(Float64(y1 * y3) - Float64(t * b))));
	elseif (y <= 2.3e-23)
		tmp = Float64(y2 * Float64(y1 * t_1));
	elseif (y <= 1.3e+131)
		tmp = Float64(x * Float64(t_2 + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (y <= 2.8e+201)
		tmp = Float64(t * Float64(z * Float64(Float64(c * i) - Float64(a * b))));
	else
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (k * y4) - (x * a);
	t_2 = y * ((a * b) - (c * i));
	tmp = 0.0;
	if (y <= -1.16e+154)
		tmp = x * t_2;
	elseif (y <= -7.2e-11)
		tmp = y1 * (y2 * t_1);
	elseif (y <= 3.5e-300)
		tmp = a * (z * ((y1 * y3) - (t * b)));
	elseif (y <= 2.3e-23)
		tmp = y2 * (y1 * t_1);
	elseif (y <= 1.3e+131)
		tmp = x * (t_2 + (j * ((i * y1) - (b * y0))));
	elseif (y <= 2.8e+201)
		tmp = t * (z * ((c * i) - (a * b)));
	else
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.16e+154], N[(x * t$95$2), $MachinePrecision], If[LessEqual[y, -7.2e-11], N[(y1 * N[(y2 * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e-300], N[(a * N[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e-23], N[(y2 * N[(y1 * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e+131], N[(x * N[(t$95$2 + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e+201], N[(t * N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -1.16000000000000001e154

   1. Initial program 26.5%

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

   3. Simplified 26.5%

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

   4. Taylor expanded in x around inf 47.3%

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

   5. Taylor expanded in y around inf 62.5%

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

   if -1.16000000000000001e154 < y < -7.19999999999999969e-11

   1. Initial program 16.1%

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

   3. Simplified 16.1%

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

   4. Taylor expanded in y2 around inf 42.5%

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

   5. Taylor expanded in y1 around inf 45.9%

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

      1. *-commutative 45.9%

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

      2. +-commutative 45.9%

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

      3. mul-1-neg 45.9%

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

      4. unsub-neg 45.9%

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

      5. *-commutative 45.9%

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

   7. Simplified 45.9%

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

   if -7.19999999999999969e-11 < y < 3.5000000000000002e-300

   1. Initial program 20.6%

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

   3. Simplified 23.5%

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

   4. Taylor expanded in a around inf 42.5%

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

      1. mul-1-neg 42.5%

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

      2. mul-1-neg 42.5%

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

   6. Simplified 42.5%

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

   7. Taylor expanded in z around inf 43.2%

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

      1. cancel-sign-sub-inv 43.2%

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

      2. metadata-eval 43.2%

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

      3. *-lft-identity 43.2%

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

      4. +-commutative 43.2%

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

      5. mul-1-neg 43.2%

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

      6. unsub-neg 43.2%

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

      7. *-commutative 43.2%

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

   9. Simplified 43.2%

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

   if 3.5000000000000002e-300 < y < 2.3000000000000001e-23

   1. Initial program 45.6%

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

   3. Simplified 45.6%

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

   4. Taylor expanded in y2 around inf 42.0%

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

   5. Taylor expanded in y1 around inf 44.1%

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

      1. +-commutative 44.1%

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

      2. mul-1-neg 44.1%

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

      3. unsub-neg 44.1%

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

      4. *-commutative 44.1%

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

   7. Simplified 44.1%

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

   if 2.3000000000000001e-23 < y < 1.3e131

   1. Initial program 44.4%

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

   3. Simplified 44.4%

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

   4. Taylor expanded in x around inf 45.8%

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

   5. Taylor expanded in y2 around 0 49.0%

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

   if 1.3e131 < y < 2.80000000000000005e201

   1. Initial program 5.9%

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

   3. Simplified 5.9%

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

   4. Taylor expanded in t around inf 53.1%

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

      1. associate--l+ 53.1%

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

      2. mul-1-neg 53.1%

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

   6. Simplified 53.1%

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

   7. Taylor expanded in z around inf 65.2%

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

   if 2.80000000000000005e201 < y

   1. Initial program 29.6%

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

   3. Simplified 29.6%

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

   4. Taylor expanded in y4 around inf 37.6%

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

   5. Taylor expanded in c around inf 49.0%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.16 \cdot 10^{+154}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-11}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-300}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-23}:\\ \;\;\;\;y2 \cdot \left(y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+131}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+201}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \end{array} \]

Alternative 12: 31.9% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ t_2 := a \cdot b - c \cdot i\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{+154}:\\ \;\;\;\;x \cdot \left(y \cdot t_2\right)\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8.1 \cdot 10^{-305}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+143} \lor \neg \left(y \leq 2.8 \cdot 10^{+260}\right):\\ \;\;\;\;y \cdot \left(x \cdot t_2\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y1 (* y2 (- (* k y4) (* x a))))) (t_2 (- (* a b) (* c i))))
   (if (<= y -1.3e+154)
     (* x (* y t_2))
     (if (<= y -4.6e-13)
       t_1
       (if (<= y 8.1e-305)
         (* a (* z (- (* y1 y3) (* t b))))
         (if (<= y 1.6e-23)
           t_1
           (if (or (<= y 4.2e+143) (not (<= y 2.8e+260)))
             (* y (* x t_2))
             (* c (* y4 (- (* y y3) (* t y2)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * (y2 * ((k * y4) - (x * a)));
	double t_2 = (a * b) - (c * i);
	double tmp;
	if (y <= -1.3e+154) {
		tmp = x * (y * t_2);
	} else if (y <= -4.6e-13) {
		tmp = t_1;
	} else if (y <= 8.1e-305) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (y <= 1.6e-23) {
		tmp = t_1;
	} else if ((y <= 4.2e+143) || !(y <= 2.8e+260)) {
		tmp = y * (x * t_2);
	} else {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y1 * (y2 * ((k * y4) - (x * a)))
    t_2 = (a * b) - (c * i)
    if (y <= (-1.3d+154)) then
        tmp = x * (y * t_2)
    else if (y <= (-4.6d-13)) then
        tmp = t_1
    else if (y <= 8.1d-305) then
        tmp = a * (z * ((y1 * y3) - (t * b)))
    else if (y <= 1.6d-23) then
        tmp = t_1
    else if ((y <= 4.2d+143) .or. (.not. (y <= 2.8d+260))) then
        tmp = y * (x * t_2)
    else
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * (y2 * ((k * y4) - (x * a)));
	double t_2 = (a * b) - (c * i);
	double tmp;
	if (y <= -1.3e+154) {
		tmp = x * (y * t_2);
	} else if (y <= -4.6e-13) {
		tmp = t_1;
	} else if (y <= 8.1e-305) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (y <= 1.6e-23) {
		tmp = t_1;
	} else if ((y <= 4.2e+143) || !(y <= 2.8e+260)) {
		tmp = y * (x * t_2);
	} else {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y1 * (y2 * ((k * y4) - (x * a)))
	t_2 = (a * b) - (c * i)
	tmp = 0
	if y <= -1.3e+154:
		tmp = x * (y * t_2)
	elif y <= -4.6e-13:
		tmp = t_1
	elif y <= 8.1e-305:
		tmp = a * (z * ((y1 * y3) - (t * b)))
	elif y <= 1.6e-23:
		tmp = t_1
	elif (y <= 4.2e+143) or not (y <= 2.8e+260):
		tmp = y * (x * t_2)
	else:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y1 * Float64(y2 * Float64(Float64(k * y4) - Float64(x * a))))
	t_2 = Float64(Float64(a * b) - Float64(c * i))
	tmp = 0.0
	if (y <= -1.3e+154)
		tmp = Float64(x * Float64(y * t_2));
	elseif (y <= -4.6e-13)
		tmp = t_1;
	elseif (y <= 8.1e-305)
		tmp = Float64(a * Float64(z * Float64(Float64(y1 * y3) - Float64(t * b))));
	elseif (y <= 1.6e-23)
		tmp = t_1;
	elseif ((y <= 4.2e+143) || !(y <= 2.8e+260))
		tmp = Float64(y * Float64(x * t_2));
	else
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y1 * (y2 * ((k * y4) - (x * a)));
	t_2 = (a * b) - (c * i);
	tmp = 0.0;
	if (y <= -1.3e+154)
		tmp = x * (y * t_2);
	elseif (y <= -4.6e-13)
		tmp = t_1;
	elseif (y <= 8.1e-305)
		tmp = a * (z * ((y1 * y3) - (t * b)));
	elseif (y <= 1.6e-23)
		tmp = t_1;
	elseif ((y <= 4.2e+143) || ~((y <= 2.8e+260)))
		tmp = y * (x * t_2);
	else
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y1 * N[(y2 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.3e+154], N[(x * N[(y * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.6e-13], t$95$1, If[LessEqual[y, 8.1e-305], N[(a * N[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e-23], t$95$1, If[Or[LessEqual[y, 4.2e+143], N[Not[LessEqual[y, 2.8e+260]], $MachinePrecision]], N[(y * N[(x * t$95$2), $MachinePrecision]), $MachinePrecision], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.29999999999999994e154

   1. Initial program 26.5%

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

   3. Simplified 26.5%

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

   4. Taylor expanded in x around inf 47.3%

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

   5. Taylor expanded in y around inf 62.5%

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

   if -1.29999999999999994e154 < y < -4.59999999999999958e-13 or 8.0999999999999997e-305 < y < 1.59999999999999988e-23

   1. Initial program 34.4%

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

   3. Simplified 34.4%

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

   4. Taylor expanded in y2 around inf 42.2%

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

   5. Taylor expanded in y1 around inf 43.6%

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

      1. *-commutative 43.6%

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

      2. +-commutative 43.6%

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

      3. mul-1-neg 43.6%

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

      4. unsub-neg 43.6%

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

      5. *-commutative 43.6%

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

   7. Simplified 43.6%

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

   if -4.59999999999999958e-13 < y < 8.0999999999999997e-305

   1. Initial program 20.6%

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

   3. Simplified 23.5%

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

   4. Taylor expanded in a around inf 42.5%

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

      1. mul-1-neg 42.5%

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

      2. mul-1-neg 42.5%

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

   6. Simplified 42.5%

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

   7. Taylor expanded in z around inf 43.2%

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

      1. cancel-sign-sub-inv 43.2%

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

      2. metadata-eval 43.2%

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

      3. *-lft-identity 43.2%

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

      4. +-commutative 43.2%

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

      5. mul-1-neg 43.2%

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

      6. unsub-neg 43.2%

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

      7. *-commutative 43.2%

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

   9. Simplified 43.2%

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

   if 1.59999999999999988e-23 < y < 4.19999999999999975e143 or 2.7999999999999998e260 < y

   1. Initial program 34.1%

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

   3. Simplified 34.1%

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

   4. Taylor expanded in x around inf 50.8%

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

   5. Taylor expanded in y around inf 53.0%

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

   if 4.19999999999999975e143 < y < 2.7999999999999998e260

   1. Initial program 22.2%

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

   3. Simplified 22.2%

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

   4. Taylor expanded in y4 around inf 52.2%

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

   5. Taylor expanded in c around inf 41.4%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+154}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-13}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;y \leq 8.1 \cdot 10^{-305}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-23}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+143} \lor \neg \left(y \leq 2.8 \cdot 10^{+260}\right):\\ \;\;\;\;y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \end{array} \]

Alternative 13: 31.8% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot y4 - x \cdot a\\ t_2 := a \cdot b - c \cdot i\\ \mathbf{if}\;y \leq -1.16 \cdot 10^{+154}:\\ \;\;\;\;x \cdot \left(y \cdot t_2\right)\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-15}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot t_1\right)\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-308}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-24}:\\ \;\;\;\;y2 \cdot \left(y1 \cdot t_1\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+144} \lor \neg \left(y \leq 1.16 \cdot 10^{+260}\right):\\ \;\;\;\;y \cdot \left(x \cdot t_2\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* k y4) (* x a))) (t_2 (- (* a b) (* c i))))
   (if (<= y -1.16e+154)
     (* x (* y t_2))
     (if (<= y -1.1e-15)
       (* y1 (* y2 t_1))
       (if (<= y 3e-308)
         (* a (* z (- (* y1 y3) (* t b))))
         (if (<= y 1.7e-24)
           (* y2 (* y1 t_1))
           (if (or (<= y 2.2e+144) (not (<= y 1.16e+260)))
             (* y (* x t_2))
             (* c (* y4 (- (* y y3) (* t y2)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (k * y4) - (x * a);
	double t_2 = (a * b) - (c * i);
	double tmp;
	if (y <= -1.16e+154) {
		tmp = x * (y * t_2);
	} else if (y <= -1.1e-15) {
		tmp = y1 * (y2 * t_1);
	} else if (y <= 3e-308) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (y <= 1.7e-24) {
		tmp = y2 * (y1 * t_1);
	} else if ((y <= 2.2e+144) || !(y <= 1.16e+260)) {
		tmp = y * (x * t_2);
	} else {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (k * y4) - (x * a)
    t_2 = (a * b) - (c * i)
    if (y <= (-1.16d+154)) then
        tmp = x * (y * t_2)
    else if (y <= (-1.1d-15)) then
        tmp = y1 * (y2 * t_1)
    else if (y <= 3d-308) then
        tmp = a * (z * ((y1 * y3) - (t * b)))
    else if (y <= 1.7d-24) then
        tmp = y2 * (y1 * t_1)
    else if ((y <= 2.2d+144) .or. (.not. (y <= 1.16d+260))) then
        tmp = y * (x * t_2)
    else
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (k * y4) - (x * a);
	double t_2 = (a * b) - (c * i);
	double tmp;
	if (y <= -1.16e+154) {
		tmp = x * (y * t_2);
	} else if (y <= -1.1e-15) {
		tmp = y1 * (y2 * t_1);
	} else if (y <= 3e-308) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (y <= 1.7e-24) {
		tmp = y2 * (y1 * t_1);
	} else if ((y <= 2.2e+144) || !(y <= 1.16e+260)) {
		tmp = y * (x * t_2);
	} else {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (k * y4) - (x * a)
	t_2 = (a * b) - (c * i)
	tmp = 0
	if y <= -1.16e+154:
		tmp = x * (y * t_2)
	elif y <= -1.1e-15:
		tmp = y1 * (y2 * t_1)
	elif y <= 3e-308:
		tmp = a * (z * ((y1 * y3) - (t * b)))
	elif y <= 1.7e-24:
		tmp = y2 * (y1 * t_1)
	elif (y <= 2.2e+144) or not (y <= 1.16e+260):
		tmp = y * (x * t_2)
	else:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(k * y4) - Float64(x * a))
	t_2 = Float64(Float64(a * b) - Float64(c * i))
	tmp = 0.0
	if (y <= -1.16e+154)
		tmp = Float64(x * Float64(y * t_2));
	elseif (y <= -1.1e-15)
		tmp = Float64(y1 * Float64(y2 * t_1));
	elseif (y <= 3e-308)
		tmp = Float64(a * Float64(z * Float64(Float64(y1 * y3) - Float64(t * b))));
	elseif (y <= 1.7e-24)
		tmp = Float64(y2 * Float64(y1 * t_1));
	elseif ((y <= 2.2e+144) || !(y <= 1.16e+260))
		tmp = Float64(y * Float64(x * t_2));
	else
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (k * y4) - (x * a);
	t_2 = (a * b) - (c * i);
	tmp = 0.0;
	if (y <= -1.16e+154)
		tmp = x * (y * t_2);
	elseif (y <= -1.1e-15)
		tmp = y1 * (y2 * t_1);
	elseif (y <= 3e-308)
		tmp = a * (z * ((y1 * y3) - (t * b)));
	elseif (y <= 1.7e-24)
		tmp = y2 * (y1 * t_1);
	elseif ((y <= 2.2e+144) || ~((y <= 1.16e+260)))
		tmp = y * (x * t_2);
	else
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.16e+154], N[(x * N[(y * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.1e-15], N[(y1 * N[(y2 * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3e-308], N[(a * N[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e-24], N[(y2 * N[(y1 * t$95$1), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 2.2e+144], N[Not[LessEqual[y, 1.16e+260]], $MachinePrecision]], N[(y * N[(x * t$95$2), $MachinePrecision]), $MachinePrecision], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1.16000000000000001e154

   1. Initial program 26.5%

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

   3. Simplified 26.5%

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

   4. Taylor expanded in x around inf 47.3%

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

   5. Taylor expanded in y around inf 62.5%

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

   if -1.16000000000000001e154 < y < -1.09999999999999993e-15

   1. Initial program 16.1%

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

   3. Simplified 16.1%

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

   4. Taylor expanded in y2 around inf 42.5%

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

   5. Taylor expanded in y1 around inf 45.9%

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

      1. *-commutative 45.9%

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

      2. +-commutative 45.9%

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

      3. mul-1-neg 45.9%

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

      4. unsub-neg 45.9%

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

      5. *-commutative 45.9%

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

   7. Simplified 45.9%

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

   if -1.09999999999999993e-15 < y < 3.00000000000000022e-308

   1. Initial program 20.6%

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

   3. Simplified 23.5%

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

   4. Taylor expanded in a around inf 42.5%

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

      1. mul-1-neg 42.5%

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

      2. mul-1-neg 42.5%

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

   6. Simplified 42.5%

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

   7. Taylor expanded in z around inf 43.2%

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

      1. cancel-sign-sub-inv 43.2%

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

      2. metadata-eval 43.2%

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

      3. *-lft-identity 43.2%

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

      4. +-commutative 43.2%

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

      5. mul-1-neg 43.2%

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

      6. unsub-neg 43.2%

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

      7. *-commutative 43.2%

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

   9. Simplified 43.2%

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

   if 3.00000000000000022e-308 < y < 1.69999999999999996e-24

   1. Initial program 45.6%

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

   3. Simplified 45.6%

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

   4. Taylor expanded in y2 around inf 42.0%

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

   5. Taylor expanded in y1 around inf 44.1%

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

      1. +-commutative 44.1%

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

      2. mul-1-neg 44.1%

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

      3. unsub-neg 44.1%

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

      4. *-commutative 44.1%

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

   7. Simplified 44.1%

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

   if 1.69999999999999996e-24 < y < 2.19999999999999988e144 or 1.16e260 < y

   1. Initial program 34.1%

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

   3. Simplified 34.1%

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

   4. Taylor expanded in x around inf 50.8%

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

   5. Taylor expanded in y around inf 53.0%

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

   if 2.19999999999999988e144 < y < 1.16e260

   1. Initial program 22.2%

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

   3. Simplified 22.2%

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

   4. Taylor expanded in y4 around inf 52.2%

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

   5. Taylor expanded in c around inf 41.4%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.16 \cdot 10^{+154}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-15}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-308}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-24}:\\ \;\;\;\;y2 \cdot \left(y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+144} \lor \neg \left(y \leq 1.16 \cdot 10^{+260}\right):\\ \;\;\;\;y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \end{array} \]

Alternative 14: 28.1% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ t_2 := a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{if}\;b \leq -6.8 \cdot 10^{+93}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{-172}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-243}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+57}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(x \cdot i\right)\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+192}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y4 (- (* y y3) (* t y2)))))
        (t_2 (* a (* b (- (* x y) (* z t))))))
   (if (<= b -6.8e+93)
     (* y4 (* t (* b j)))
     (if (<= b -2.2e-172)
       t_2
       (if (<= b 1.2e-243)
         (* k (* y2 (- (* y1 y4) (* y0 y5))))
         (if (<= b 7e+34)
           t_1
           (if (<= b 6e+57)
             (* y1 (* j (* x i)))
             (if (<= b 2.8e+192) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y4 * ((y * y3) - (t * y2)));
	double t_2 = a * (b * ((x * y) - (z * t)));
	double tmp;
	if (b <= -6.8e+93) {
		tmp = y4 * (t * (b * j));
	} else if (b <= -2.2e-172) {
		tmp = t_2;
	} else if (b <= 1.2e-243) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (b <= 7e+34) {
		tmp = t_1;
	} else if (b <= 6e+57) {
		tmp = y1 * (j * (x * i));
	} else if (b <= 2.8e+192) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * (y4 * ((y * y3) - (t * y2)))
    t_2 = a * (b * ((x * y) - (z * t)))
    if (b <= (-6.8d+93)) then
        tmp = y4 * (t * (b * j))
    else if (b <= (-2.2d-172)) then
        tmp = t_2
    else if (b <= 1.2d-243) then
        tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
    else if (b <= 7d+34) then
        tmp = t_1
    else if (b <= 6d+57) then
        tmp = y1 * (j * (x * i))
    else if (b <= 2.8d+192) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y4 * ((y * y3) - (t * y2)));
	double t_2 = a * (b * ((x * y) - (z * t)));
	double tmp;
	if (b <= -6.8e+93) {
		tmp = y4 * (t * (b * j));
	} else if (b <= -2.2e-172) {
		tmp = t_2;
	} else if (b <= 1.2e-243) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (b <= 7e+34) {
		tmp = t_1;
	} else if (b <= 6e+57) {
		tmp = y1 * (j * (x * i));
	} else if (b <= 2.8e+192) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (y4 * ((y * y3) - (t * y2)))
	t_2 = a * (b * ((x * y) - (z * t)))
	tmp = 0
	if b <= -6.8e+93:
		tmp = y4 * (t * (b * j))
	elif b <= -2.2e-172:
		tmp = t_2
	elif b <= 1.2e-243:
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
	elif b <= 7e+34:
		tmp = t_1
	elif b <= 6e+57:
		tmp = y1 * (j * (x * i))
	elif b <= 2.8e+192:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))))
	t_2 = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))))
	tmp = 0.0
	if (b <= -6.8e+93)
		tmp = Float64(y4 * Float64(t * Float64(b * j)));
	elseif (b <= -2.2e-172)
		tmp = t_2;
	elseif (b <= 1.2e-243)
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	elseif (b <= 7e+34)
		tmp = t_1;
	elseif (b <= 6e+57)
		tmp = Float64(y1 * Float64(j * Float64(x * i)));
	elseif (b <= 2.8e+192)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (y4 * ((y * y3) - (t * y2)));
	t_2 = a * (b * ((x * y) - (z * t)));
	tmp = 0.0;
	if (b <= -6.8e+93)
		tmp = y4 * (t * (b * j));
	elseif (b <= -2.2e-172)
		tmp = t_2;
	elseif (b <= 1.2e-243)
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	elseif (b <= 7e+34)
		tmp = t_1;
	elseif (b <= 6e+57)
		tmp = y1 * (j * (x * i));
	elseif (b <= 2.8e+192)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $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[b, -6.8e+93], N[(y4 * N[(t * N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.2e-172], t$95$2, If[LessEqual[b, 1.2e-243], N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7e+34], t$95$1, If[LessEqual[b, 6e+57], N[(y1 * N[(j * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.8e+192], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -6.8000000000000001e93

   1. Initial program 14.6%

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

   3. Simplified 14.6%

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

   4. Taylor expanded in t around inf 27.2%

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

      1. associate--l+ 27.2%

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

      2. mul-1-neg 27.2%

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

   6. Simplified 27.2%

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

   7. Taylor expanded in j around inf 42.4%

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

   8. Taylor expanded in b around inf 46.9%

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

   if -6.8000000000000001e93 < b < -2.20000000000000009e-172 or 2.79999999999999976e192 < b

   1. Initial program 23.2%

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

   3. Simplified 30.4%

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

   4. Taylor expanded in a around inf 41.7%

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

      1. mul-1-neg 41.7%

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

      2. mul-1-neg 41.7%

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

   6. Simplified 41.7%

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

   7. Taylor expanded in b around inf 46.7%

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

   if -2.20000000000000009e-172 < b < 1.2e-243

   1. Initial program 33.5%

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

   3. Simplified 33.5%

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

   4. Taylor expanded in y2 around inf 48.5%

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

   5. Taylor expanded in k around inf 46.3%

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

   if 1.2e-243 < b < 6.99999999999999996e34 or 5.9999999999999999e57 < b < 2.79999999999999976e192

   1. Initial program 38.8%

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

   3. Simplified 38.8%

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

   4. Taylor expanded in y4 around inf 46.7%

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

   5. Taylor expanded in c around inf 39.9%

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

   if 6.99999999999999996e34 < b < 5.9999999999999999e57

   1. Initial program 16.7%

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

   3. Simplified 16.7%

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

   4. Taylor expanded in x around inf 66.7%

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

   5. Taylor expanded in j around inf 50.6%

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

   6. Taylor expanded in y1 around inf 67.3%

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

      1. *-commutative 67.3%

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

      2. associate-*r* 67.3%

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

      3. associate-*l* 83.3%

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

      4. *-commutative 83.3%

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

   8. Simplified 83.3%

      \[\leadsto \color{blue}{y1 \cdot \left(j \cdot \left(i \cdot x\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{+93}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{-172}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-243}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+34}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+57}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(x \cdot i\right)\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+192}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]

Alternative 15: 29.7% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{if}\;b \leq -4.2 \cdot 10^{+93}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-172}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 10^{-249}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 5.9 \cdot 10^{+57}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(x \cdot i\right)\right)\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+171}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* t (* c (- (* z i) (* y2 y4))))))
   (if (<= b -4.2e+93)
     (* y4 (* t (* b j)))
     (if (<= b -2.4e-172)
       t_1
       (if (<= b 1e-249)
         (* k (* y2 (- (* y1 y4) (* y0 y5))))
         (if (<= b 9.5e+19)
           t_1
           (if (<= b 5.9e+57)
             (* y1 (* j (* x i)))
             (if (<= b 5.2e+171)
               (* c (* y4 (- (* y y3) (* t y2))))
               (* a (* b (- (* x y) (* z t))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * (c * ((z * i) - (y2 * y4)));
	double tmp;
	if (b <= -4.2e+93) {
		tmp = y4 * (t * (b * j));
	} else if (b <= -2.4e-172) {
		tmp = t_1;
	} else if (b <= 1e-249) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (b <= 9.5e+19) {
		tmp = t_1;
	} else if (b <= 5.9e+57) {
		tmp = y1 * (j * (x * i));
	} else if (b <= 5.2e+171) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else {
		tmp = a * (b * ((x * y) - (z * t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (c * ((z * i) - (y2 * y4)))
    if (b <= (-4.2d+93)) then
        tmp = y4 * (t * (b * j))
    else if (b <= (-2.4d-172)) then
        tmp = t_1
    else if (b <= 1d-249) then
        tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
    else if (b <= 9.5d+19) then
        tmp = t_1
    else if (b <= 5.9d+57) then
        tmp = y1 * (j * (x * i))
    else if (b <= 5.2d+171) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else
        tmp = a * (b * ((x * y) - (z * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * (c * ((z * i) - (y2 * y4)));
	double tmp;
	if (b <= -4.2e+93) {
		tmp = y4 * (t * (b * j));
	} else if (b <= -2.4e-172) {
		tmp = t_1;
	} else if (b <= 1e-249) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (b <= 9.5e+19) {
		tmp = t_1;
	} else if (b <= 5.9e+57) {
		tmp = y1 * (j * (x * i));
	} else if (b <= 5.2e+171) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else {
		tmp = a * (b * ((x * y) - (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = t * (c * ((z * i) - (y2 * y4)))
	tmp = 0
	if b <= -4.2e+93:
		tmp = y4 * (t * (b * j))
	elif b <= -2.4e-172:
		tmp = t_1
	elif b <= 1e-249:
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
	elif b <= 9.5e+19:
		tmp = t_1
	elif b <= 5.9e+57:
		tmp = y1 * (j * (x * i))
	elif b <= 5.2e+171:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	else:
		tmp = a * (b * ((x * y) - (z * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(t * Float64(c * Float64(Float64(z * i) - Float64(y2 * y4))))
	tmp = 0.0
	if (b <= -4.2e+93)
		tmp = Float64(y4 * Float64(t * Float64(b * j)));
	elseif (b <= -2.4e-172)
		tmp = t_1;
	elseif (b <= 1e-249)
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	elseif (b <= 9.5e+19)
		tmp = t_1;
	elseif (b <= 5.9e+57)
		tmp = Float64(y1 * Float64(j * Float64(x * i)));
	elseif (b <= 5.2e+171)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	else
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = t * (c * ((z * i) - (y2 * y4)));
	tmp = 0.0;
	if (b <= -4.2e+93)
		tmp = y4 * (t * (b * j));
	elseif (b <= -2.4e-172)
		tmp = t_1;
	elseif (b <= 1e-249)
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	elseif (b <= 9.5e+19)
		tmp = t_1;
	elseif (b <= 5.9e+57)
		tmp = y1 * (j * (x * i));
	elseif (b <= 5.2e+171)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	else
		tmp = a * (b * ((x * y) - (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(t * N[(c * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.2e+93], N[(y4 * N[(t * N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.4e-172], t$95$1, If[LessEqual[b, 1e-249], N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.5e+19], t$95$1, If[LessEqual[b, 5.9e+57], N[(y1 * N[(j * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.2e+171], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -4.1999999999999996e93

   1. Initial program 14.6%

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

   3. Simplified 14.6%

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

   4. Taylor expanded in t around inf 27.2%

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

      1. associate--l+ 27.2%

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

      2. mul-1-neg 27.2%

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

   6. Simplified 27.2%

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

   7. Taylor expanded in j around inf 42.4%

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

   8. Taylor expanded in b around inf 46.9%

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

   if -4.1999999999999996e93 < b < -2.4000000000000001e-172 or 1.00000000000000005e-249 < b < 9.5e19

   1. Initial program 30.8%

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

   3. Simplified 30.8%

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

   4. Taylor expanded in t around inf 42.3%

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

      1. associate--l+ 42.3%

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

      2. mul-1-neg 42.3%

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

   6. Simplified 42.3%

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

   7. Taylor expanded in c around -inf 42.7%

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

      1. mul-1-neg 42.7%

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

      2. unsub-neg 42.7%

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

      3. *-commutative 42.7%

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

   9. Simplified 42.7%

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

   if -2.4000000000000001e-172 < b < 1.00000000000000005e-249

   1. Initial program 34.2%

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

   3. Simplified 34.2%

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

   4. Taylor expanded in y2 around inf 46.2%

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

   5. Taylor expanded in k around inf 47.9%

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

   if 9.5e19 < b < 5.90000000000000013e57

   1. Initial program 33.2%

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

   3. Simplified 33.2%

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

   4. Taylor expanded in x around inf 55.6%

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

   5. Taylor expanded in j around inf 45.6%

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

   6. Taylor expanded in y1 around inf 45.9%

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

      1. *-commutative 45.9%

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

      2. associate-*r* 45.9%

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

      3. associate-*l* 56.6%

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

      4. *-commutative 56.6%

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

   8. Simplified 56.6%

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

   if 5.90000000000000013e57 < b < 5.2e171

   1. Initial program 29.4%

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

   3. Simplified 29.4%

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

   4. Taylor expanded in y4 around inf 42.3%

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

   5. Taylor expanded in c around inf 48.8%

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

   if 5.2e171 < b

   1. Initial program 24.9%

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

   3. Simplified 29.1%

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

   4. Taylor expanded in a around inf 50.9%

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

      1. mul-1-neg 50.9%

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

      2. mul-1-neg 50.9%

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

   6. Simplified 50.9%

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

   7. Taylor expanded in b around inf 54.7%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{+93}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-172}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 10^{-249}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+19}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 5.9 \cdot 10^{+57}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(x \cdot i\right)\right)\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+171}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]

Alternative 16: 32.1% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{if}\;c \leq -5.4 \cdot 10^{+149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -8.4 \cdot 10^{+77}:\\ \;\;\;\;y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -9 \cdot 10^{+34}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;c \leq -1.85 \cdot 10^{-256}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;c \leq 3.6 \cdot 10^{-15}:\\ \;\;\;\;t \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{+41}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* t (* c (- (* z i) (* y2 y4))))))
   (if (<= c -5.4e+149)
     t_1
     (if (<= c -8.4e+77)
       (* y (* x (- (* a b) (* c i))))
       (if (<= c -9e+34)
         (* y0 (* x (- (* c y2) (* b j))))
         (if (<= c -1.85e-256)
           (* y1 (* y2 (- (* k y4) (* x a))))
           (if (<= c 3.6e-15)
             (* t (* j (- (* b y4) (* i y5))))
             (if (<= c 4.5e+41) (* 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 = t * (c * ((z * i) - (y2 * y4)));
	double tmp;
	if (c <= -5.4e+149) {
		tmp = t_1;
	} else if (c <= -8.4e+77) {
		tmp = y * (x * ((a * b) - (c * i)));
	} else if (c <= -9e+34) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else if (c <= -1.85e-256) {
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	} else if (c <= 3.6e-15) {
		tmp = t * (j * ((b * y4) - (i * y5)));
	} else if (c <= 4.5e+41) {
		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 = t * (c * ((z * i) - (y2 * y4)))
    if (c <= (-5.4d+149)) then
        tmp = t_1
    else if (c <= (-8.4d+77)) then
        tmp = y * (x * ((a * b) - (c * i)))
    else if (c <= (-9d+34)) then
        tmp = y0 * (x * ((c * y2) - (b * j)))
    else if (c <= (-1.85d-256)) then
        tmp = y1 * (y2 * ((k * y4) - (x * a)))
    else if (c <= 3.6d-15) then
        tmp = t * (j * ((b * y4) - (i * y5)))
    else if (c <= 4.5d+41) 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 = t * (c * ((z * i) - (y2 * y4)));
	double tmp;
	if (c <= -5.4e+149) {
		tmp = t_1;
	} else if (c <= -8.4e+77) {
		tmp = y * (x * ((a * b) - (c * i)));
	} else if (c <= -9e+34) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else if (c <= -1.85e-256) {
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	} else if (c <= 3.6e-15) {
		tmp = t * (j * ((b * y4) - (i * y5)));
	} else if (c <= 4.5e+41) {
		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 = t * (c * ((z * i) - (y2 * y4)))
	tmp = 0
	if c <= -5.4e+149:
		tmp = t_1
	elif c <= -8.4e+77:
		tmp = y * (x * ((a * b) - (c * i)))
	elif c <= -9e+34:
		tmp = y0 * (x * ((c * y2) - (b * j)))
	elif c <= -1.85e-256:
		tmp = y1 * (y2 * ((k * y4) - (x * a)))
	elif c <= 3.6e-15:
		tmp = t * (j * ((b * y4) - (i * y5)))
	elif c <= 4.5e+41:
		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(t * Float64(c * Float64(Float64(z * i) - Float64(y2 * y4))))
	tmp = 0.0
	if (c <= -5.4e+149)
		tmp = t_1;
	elseif (c <= -8.4e+77)
		tmp = Float64(y * Float64(x * Float64(Float64(a * b) - Float64(c * i))));
	elseif (c <= -9e+34)
		tmp = Float64(y0 * Float64(x * Float64(Float64(c * y2) - Float64(b * j))));
	elseif (c <= -1.85e-256)
		tmp = Float64(y1 * Float64(y2 * Float64(Float64(k * y4) - Float64(x * a))));
	elseif (c <= 3.6e-15)
		tmp = Float64(t * Float64(j * Float64(Float64(b * y4) - Float64(i * y5))));
	elseif (c <= 4.5e+41)
		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 = t * (c * ((z * i) - (y2 * y4)));
	tmp = 0.0;
	if (c <= -5.4e+149)
		tmp = t_1;
	elseif (c <= -8.4e+77)
		tmp = y * (x * ((a * b) - (c * i)));
	elseif (c <= -9e+34)
		tmp = y0 * (x * ((c * y2) - (b * j)));
	elseif (c <= -1.85e-256)
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	elseif (c <= 3.6e-15)
		tmp = t * (j * ((b * y4) - (i * y5)));
	elseif (c <= 4.5e+41)
		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[(t * N[(c * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -5.4e+149], t$95$1, If[LessEqual[c, -8.4e+77], N[(y * N[(x * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -9e+34], N[(y0 * N[(x * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.85e-256], N[(y1 * N[(y2 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.6e-15], N[(t * N[(j * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.5e+41], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -5.4000000000000002e149 or 4.5000000000000001e41 < c

   1. Initial program 22.2%

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

   3. Simplified 22.2%

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

   4. Taylor expanded in t around inf 37.7%

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

      1. associate--l+ 37.7%

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

      2. mul-1-neg 37.7%

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

   6. Simplified 37.7%

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

   7. Taylor expanded in c around -inf 48.6%

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

      1. mul-1-neg 48.6%

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

      2. unsub-neg 48.6%

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

      3. *-commutative 48.6%

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

   9. Simplified 48.6%

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

   if -5.4000000000000002e149 < c < -8.3999999999999995e77

   1. Initial program 19.2%

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

   3. Simplified 19.2%

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

   4. Taylor expanded in x around inf 50.3%

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

   5. Taylor expanded in y around inf 57.8%

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

   if -8.3999999999999995e77 < c < -9.0000000000000001e34

   1. Initial program 25.7%

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

   3. Simplified 25.7%

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

   4. Taylor expanded in x around inf 66.8%

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

   5. Taylor expanded in y0 around inf 59.2%

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

   if -9.0000000000000001e34 < c < -1.85000000000000014e-256

   1. Initial program 31.8%

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

   3. Simplified 31.8%

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

   4. Taylor expanded in y2 around inf 41.1%

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

   5. Taylor expanded in y1 around inf 46.6%

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

      1. *-commutative 46.6%

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

      2. +-commutative 46.6%

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

      3. mul-1-neg 46.6%

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

      4. unsub-neg 46.6%

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

      5. *-commutative 46.6%

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

   7. Simplified 46.6%

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

   if -1.85000000000000014e-256 < c < 3.6000000000000001e-15

   1. Initial program 36.4%

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

   3. Simplified 36.4%

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

   4. Taylor expanded in t around inf 46.3%

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

      1. associate--l+ 46.3%

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

      2. mul-1-neg 46.3%

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

   6. Simplified 46.3%

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

   7. Taylor expanded in j around inf 36.0%

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

   if 3.6000000000000001e-15 < c < 4.5000000000000001e41

   1. Initial program 30.0%

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

   3. Simplified 30.0%

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

   4. Taylor expanded in a around inf 70.1%

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

      1. mul-1-neg 70.1%

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

      2. mul-1-neg 70.1%

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

   6. Simplified 70.1%

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

   7. Taylor expanded in b around inf 80.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.4 \cdot 10^{+149}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq -8.4 \cdot 10^{+77}:\\ \;\;\;\;y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -9 \cdot 10^{+34}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;c \leq -1.85 \cdot 10^{-256}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;c \leq 3.6 \cdot 10^{-15}:\\ \;\;\;\;t \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{+41}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \end{array} \]

Alternative 17: 31.8% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot y4 - x \cdot a\\ t_2 := a \cdot b - c \cdot i\\ \mathbf{if}\;y \leq -2.45 \cdot 10^{+154}:\\ \;\;\;\;x \cdot \left(y \cdot t_2\right)\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-15}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot t_1\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-308}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-23}:\\ \;\;\;\;y2 \cdot \left(y1 \cdot t_1\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+145}:\\ \;\;\;\;t_2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{+260}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot t_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* k y4) (* x a))) (t_2 (- (* a b) (* c i))))
   (if (<= y -2.45e+154)
     (* x (* y t_2))
     (if (<= y -1.9e-15)
       (* y1 (* y2 t_1))
       (if (<= y -2e-308)
         (* a (* z (- (* y1 y3) (* t b))))
         (if (<= y 3.4e-23)
           (* y2 (* y1 t_1))
           (if (<= y 1.6e+145)
             (* t_2 (* x y))
             (if (<= y 1.16e+260)
               (* c (* y4 (- (* y y3) (* t y2))))
               (* y (* x 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 * y4) - (x * a);
	double t_2 = (a * b) - (c * i);
	double tmp;
	if (y <= -2.45e+154) {
		tmp = x * (y * t_2);
	} else if (y <= -1.9e-15) {
		tmp = y1 * (y2 * t_1);
	} else if (y <= -2e-308) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (y <= 3.4e-23) {
		tmp = y2 * (y1 * t_1);
	} else if (y <= 1.6e+145) {
		tmp = t_2 * (x * y);
	} else if (y <= 1.16e+260) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else {
		tmp = y * (x * 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 * y4) - (x * a)
    t_2 = (a * b) - (c * i)
    if (y <= (-2.45d+154)) then
        tmp = x * (y * t_2)
    else if (y <= (-1.9d-15)) then
        tmp = y1 * (y2 * t_1)
    else if (y <= (-2d-308)) then
        tmp = a * (z * ((y1 * y3) - (t * b)))
    else if (y <= 3.4d-23) then
        tmp = y2 * (y1 * t_1)
    else if (y <= 1.6d+145) then
        tmp = t_2 * (x * y)
    else if (y <= 1.16d+260) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else
        tmp = y * (x * 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 * y4) - (x * a);
	double t_2 = (a * b) - (c * i);
	double tmp;
	if (y <= -2.45e+154) {
		tmp = x * (y * t_2);
	} else if (y <= -1.9e-15) {
		tmp = y1 * (y2 * t_1);
	} else if (y <= -2e-308) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (y <= 3.4e-23) {
		tmp = y2 * (y1 * t_1);
	} else if (y <= 1.6e+145) {
		tmp = t_2 * (x * y);
	} else if (y <= 1.16e+260) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else {
		tmp = y * (x * 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 * y4) - (x * a)
	t_2 = (a * b) - (c * i)
	tmp = 0
	if y <= -2.45e+154:
		tmp = x * (y * t_2)
	elif y <= -1.9e-15:
		tmp = y1 * (y2 * t_1)
	elif y <= -2e-308:
		tmp = a * (z * ((y1 * y3) - (t * b)))
	elif y <= 3.4e-23:
		tmp = y2 * (y1 * t_1)
	elif y <= 1.6e+145:
		tmp = t_2 * (x * y)
	elif y <= 1.16e+260:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	else:
		tmp = y * (x * 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(k * y4) - Float64(x * a))
	t_2 = Float64(Float64(a * b) - Float64(c * i))
	tmp = 0.0
	if (y <= -2.45e+154)
		tmp = Float64(x * Float64(y * t_2));
	elseif (y <= -1.9e-15)
		tmp = Float64(y1 * Float64(y2 * t_1));
	elseif (y <= -2e-308)
		tmp = Float64(a * Float64(z * Float64(Float64(y1 * y3) - Float64(t * b))));
	elseif (y <= 3.4e-23)
		tmp = Float64(y2 * Float64(y1 * t_1));
	elseif (y <= 1.6e+145)
		tmp = Float64(t_2 * Float64(x * y));
	elseif (y <= 1.16e+260)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	else
		tmp = Float64(y * Float64(x * 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 * y4) - (x * a);
	t_2 = (a * b) - (c * i);
	tmp = 0.0;
	if (y <= -2.45e+154)
		tmp = x * (y * t_2);
	elseif (y <= -1.9e-15)
		tmp = y1 * (y2 * t_1);
	elseif (y <= -2e-308)
		tmp = a * (z * ((y1 * y3) - (t * b)));
	elseif (y <= 3.4e-23)
		tmp = y2 * (y1 * t_1);
	elseif (y <= 1.6e+145)
		tmp = t_2 * (x * y);
	elseif (y <= 1.16e+260)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	else
		tmp = y * (x * 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[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.45e+154], N[(x * N[(y * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.9e-15], N[(y1 * N[(y2 * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2e-308], N[(a * N[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e-23], N[(y2 * N[(y1 * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e+145], N[(t$95$2 * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.16e+260], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * t$95$2), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -2.4500000000000001e154

   1. Initial program 26.5%

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

   3. Simplified 26.5%

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

   4. Taylor expanded in x around inf 47.3%

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

   5. Taylor expanded in y around inf 62.5%

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

   if -2.4500000000000001e154 < y < -1.9000000000000001e-15

   1. Initial program 16.1%

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

   3. Simplified 16.1%

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

   4. Taylor expanded in y2 around inf 42.5%

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

   5. Taylor expanded in y1 around inf 45.9%

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

      1. *-commutative 45.9%

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

      2. +-commutative 45.9%

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

      3. mul-1-neg 45.9%

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

      4. unsub-neg 45.9%

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

      5. *-commutative 45.9%

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

   7. Simplified 45.9%

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

   if -1.9000000000000001e-15 < y < -1.9999999999999998e-308

   1. Initial program 20.6%

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

   3. Simplified 23.5%

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

   4. Taylor expanded in a around inf 42.5%

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

      1. mul-1-neg 42.5%

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

      2. mul-1-neg 42.5%

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

   6. Simplified 42.5%

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

   7. Taylor expanded in z around inf 43.2%

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

      1. cancel-sign-sub-inv 43.2%

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

      2. metadata-eval 43.2%

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

      3. *-lft-identity 43.2%

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

      4. +-commutative 43.2%

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

      5. mul-1-neg 43.2%

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

      6. unsub-neg 43.2%

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

      7. *-commutative 43.2%

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

   9. Simplified 43.2%

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

   if -1.9999999999999998e-308 < y < 3.4000000000000001e-23

   1. Initial program 45.6%

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

   3. Simplified 45.6%

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

   4. Taylor expanded in y2 around inf 42.0%

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

   5. Taylor expanded in y1 around inf 44.1%

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

      1. +-commutative 44.1%

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

      2. mul-1-neg 44.1%

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

      3. unsub-neg 44.1%

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

      4. *-commutative 44.1%

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

   7. Simplified 44.1%

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

   if 3.4000000000000001e-23 < y < 1.60000000000000004e145

   1. Initial program 40.0%

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

   3. Simplified 40.0%

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

   4. Taylor expanded in x around inf 47.9%

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

   5. Taylor expanded in i around -inf 47.7%

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

   6. Taylor expanded in y around inf 47.5%

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

      1. mul-1-neg 47.5%

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

      2. unsub-neg 47.5%

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

      3. *-commutative 47.5%

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

      4. *-commutative 47.5%

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

   8. Simplified 47.5%

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

   if 1.60000000000000004e145 < y < 1.16e260

   1. Initial program 22.2%

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

   3. Simplified 22.2%

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

   4. Taylor expanded in y4 around inf 52.2%

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

   5. Taylor expanded in c around inf 41.4%

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

   if 1.16e260 < y

   1. Initial program 21.4%

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

   3. Simplified 21.4%

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

   4. Taylor expanded in x around inf 57.2%

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

   5. Taylor expanded in y around inf 64.8%

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

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{+154}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-15}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-308}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-23}:\\ \;\;\;\;y2 \cdot \left(y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+145}:\\ \;\;\;\;\left(a \cdot b - c \cdot i\right) \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{+260}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \end{array} \]

Alternative 18: 28.3% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{if}\;y3 \leq -2000000:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;y3 \leq -6.8 \cdot 10^{-100}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;y3 \leq 8.8 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y3 \leq 3900000:\\ \;\;\;\;\left(b \cdot j\right) \cdot \left(t \cdot y4\right)\\ \mathbf{elif}\;y3 \leq 2.02 \cdot 10^{+179}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(y3 \cdot \left(-y1\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* b (- (* x y) (* z t))))))
   (if (<= y3 -2000000.0)
     (* a (* z (- (* y1 y3) (* t b))))
     (if (<= y3 -6.8e-100)
       (* i (* y1 (* x j)))
       (if (<= y3 8.8e-86)
         t_1
         (if (<= y3 3900000.0)
           (* (* b j) (* t y4))
           (if (<= y3 2.02e+179) t_1 (* y4 (* j (* y3 (- 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 * (b * ((x * y) - (z * t)));
	double tmp;
	if (y3 <= -2000000.0) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (y3 <= -6.8e-100) {
		tmp = i * (y1 * (x * j));
	} else if (y3 <= 8.8e-86) {
		tmp = t_1;
	} else if (y3 <= 3900000.0) {
		tmp = (b * j) * (t * y4);
	} else if (y3 <= 2.02e+179) {
		tmp = t_1;
	} else {
		tmp = y4 * (j * (y3 * -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 * (b * ((x * y) - (z * t)))
    if (y3 <= (-2000000.0d0)) then
        tmp = a * (z * ((y1 * y3) - (t * b)))
    else if (y3 <= (-6.8d-100)) then
        tmp = i * (y1 * (x * j))
    else if (y3 <= 8.8d-86) then
        tmp = t_1
    else if (y3 <= 3900000.0d0) then
        tmp = (b * j) * (t * y4)
    else if (y3 <= 2.02d+179) then
        tmp = t_1
    else
        tmp = y4 * (j * (y3 * -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 * (b * ((x * y) - (z * t)));
	double tmp;
	if (y3 <= -2000000.0) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (y3 <= -6.8e-100) {
		tmp = i * (y1 * (x * j));
	} else if (y3 <= 8.8e-86) {
		tmp = t_1;
	} else if (y3 <= 3900000.0) {
		tmp = (b * j) * (t * y4);
	} else if (y3 <= 2.02e+179) {
		tmp = t_1;
	} else {
		tmp = y4 * (j * (y3 * -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 * (b * ((x * y) - (z * t)))
	tmp = 0
	if y3 <= -2000000.0:
		tmp = a * (z * ((y1 * y3) - (t * b)))
	elif y3 <= -6.8e-100:
		tmp = i * (y1 * (x * j))
	elif y3 <= 8.8e-86:
		tmp = t_1
	elif y3 <= 3900000.0:
		tmp = (b * j) * (t * y4)
	elif y3 <= 2.02e+179:
		tmp = t_1
	else:
		tmp = y4 * (j * (y3 * -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(b * Float64(Float64(x * y) - Float64(z * t))))
	tmp = 0.0
	if (y3 <= -2000000.0)
		tmp = Float64(a * Float64(z * Float64(Float64(y1 * y3) - Float64(t * b))));
	elseif (y3 <= -6.8e-100)
		tmp = Float64(i * Float64(y1 * Float64(x * j)));
	elseif (y3 <= 8.8e-86)
		tmp = t_1;
	elseif (y3 <= 3900000.0)
		tmp = Float64(Float64(b * j) * Float64(t * y4));
	elseif (y3 <= 2.02e+179)
		tmp = t_1;
	else
		tmp = Float64(y4 * Float64(j * Float64(y3 * Float64(-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 * (b * ((x * y) - (z * t)));
	tmp = 0.0;
	if (y3 <= -2000000.0)
		tmp = a * (z * ((y1 * y3) - (t * b)));
	elseif (y3 <= -6.8e-100)
		tmp = i * (y1 * (x * j));
	elseif (y3 <= 8.8e-86)
		tmp = t_1;
	elseif (y3 <= 3900000.0)
		tmp = (b * j) * (t * y4);
	elseif (y3 <= 2.02e+179)
		tmp = t_1;
	else
		tmp = y4 * (j * (y3 * -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[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -2000000.0], N[(a * N[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -6.8e-100], N[(i * N[(y1 * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 8.8e-86], t$95$1, If[LessEqual[y3, 3900000.0], N[(N[(b * j), $MachinePrecision] * N[(t * y4), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 2.02e+179], t$95$1, N[(y4 * N[(j * N[(y3 * (-y1)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y3 < -2e6

   1. Initial program 21.7%

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

   3. Simplified 29.6%

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

   4. Taylor expanded in a around inf 47.5%

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

      1. mul-1-neg 47.5%

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

      2. mul-1-neg 47.5%

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

   6. Simplified 47.5%

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

   7. Taylor expanded in z around inf 44.0%

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

      1. cancel-sign-sub-inv 44.0%

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

      2. metadata-eval 44.0%

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

      3. *-lft-identity 44.0%

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

      4. +-commutative 44.0%

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

      5. mul-1-neg 44.0%

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

      6. unsub-neg 44.0%

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

      7. *-commutative 44.0%

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

   9. Simplified 44.0%

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

   if -2e6 < y3 < -6.79999999999999953e-100

   1. Initial program 35.7%

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

   3. Simplified 35.7%

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

   4. Taylor expanded in x around inf 44.0%

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

   5. Taylor expanded in j around inf 30.7%

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

   6. Taylor expanded in y1 around inf 34.1%

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

   if -6.79999999999999953e-100 < y3 < 8.8000000000000006e-86 or 3.9e6 < y3 < 2.0200000000000001e179

   1. Initial program 32.0%

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

   3. Simplified 34.3%

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

   4. Taylor expanded in a around inf 38.7%

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

      1. mul-1-neg 38.7%

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

      2. mul-1-neg 38.7%

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

   6. Simplified 38.7%

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

   7. Taylor expanded in b around inf 40.7%

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

   if 8.8000000000000006e-86 < y3 < 3.9e6

   1. Initial program 16.5%

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

   3. Simplified 16.5%

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

   4. Taylor expanded in t around inf 42.8%

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

      1. associate--l+ 42.8%

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

      2. mul-1-neg 42.8%

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

   6. Simplified 42.8%

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

   7. Taylor expanded in j around inf 38.2%

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

   8. Taylor expanded in y4 around inf 33.2%

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

      1. *-commutative 33.2%

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

      2. *-commutative 33.2%

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

      3. associate-*l* 43.2%

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

      4. *-commutative 43.2%

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

   10. Simplified 43.2%

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

   if 2.0200000000000001e179 < y3

   1. Initial program 24.1%

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

   3. Simplified 24.1%

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

   4. Taylor expanded in y4 around inf 41.8%

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

   5. Taylor expanded in j around inf 52.4%

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

      1. associate-*r* 45.5%

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

      2. *-commutative 45.5%

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

      3. mul-1-neg 45.5%

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

      4. sub-neg 45.5%

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

      5. *-commutative 45.5%

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

   7. Simplified 45.5%

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

   8. Taylor expanded in b around 0 32.3%

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

      1. mul-1-neg 32.3%

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

      2. distribute-rgt-neg-in 32.3%

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

      3. associate-*r* 42.1%

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

      4. *-commutative 42.1%

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

   10. Simplified 42.1%

       \[\leadsto \color{blue}{y4 \cdot \left(-j \cdot \left(y1 \cdot y3\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -2000000:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;y3 \leq -6.8 \cdot 10^{-100}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;y3 \leq 8.8 \cdot 10^{-86}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y3 \leq 3900000:\\ \;\;\;\;\left(b \cdot j\right) \cdot \left(t \cdot y4\right)\\ \mathbf{elif}\;y3 \leq 2.02 \cdot 10^{+179}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(y3 \cdot \left(-y1\right)\right)\right)\\ \end{array} \]

Alternative 19: 28.6% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{if}\;y3 \leq -4600000:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;y3 \leq -2 \cdot 10^{-109}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;y3 \leq 8 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y3 \leq 3900000:\\ \;\;\;\;\left(b \cdot j\right) \cdot \left(t \cdot y4\right)\\ \mathbf{elif}\;y3 \leq 7 \cdot 10^{+194}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* b (- (* x y) (* z t))))))
   (if (<= y3 -4600000.0)
     (* a (* z (- (* y1 y3) (* t b))))
     (if (<= y3 -2e-109)
       (* i (* y1 (* x j)))
       (if (<= y3 8e-86)
         t_1
         (if (<= y3 3900000.0)
           (* (* b j) (* t y4))
           (if (<= y3 7e+194) t_1 (* 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 = a * (b * ((x * y) - (z * t)));
	double tmp;
	if (y3 <= -4600000.0) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (y3 <= -2e-109) {
		tmp = i * (y1 * (x * j));
	} else if (y3 <= 8e-86) {
		tmp = t_1;
	} else if (y3 <= 3900000.0) {
		tmp = (b * j) * (t * y4);
	} else if (y3 <= 7e+194) {
		tmp = t_1;
	} 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 = a * (b * ((x * y) - (z * t)))
    if (y3 <= (-4600000.0d0)) then
        tmp = a * (z * ((y1 * y3) - (t * b)))
    else if (y3 <= (-2d-109)) then
        tmp = i * (y1 * (x * j))
    else if (y3 <= 8d-86) then
        tmp = t_1
    else if (y3 <= 3900000.0d0) then
        tmp = (b * j) * (t * y4)
    else if (y3 <= 7d+194) then
        tmp = t_1
    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 = a * (b * ((x * y) - (z * t)));
	double tmp;
	if (y3 <= -4600000.0) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (y3 <= -2e-109) {
		tmp = i * (y1 * (x * j));
	} else if (y3 <= 8e-86) {
		tmp = t_1;
	} else if (y3 <= 3900000.0) {
		tmp = (b * j) * (t * y4);
	} else if (y3 <= 7e+194) {
		tmp = t_1;
	} 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 = a * (b * ((x * y) - (z * t)))
	tmp = 0
	if y3 <= -4600000.0:
		tmp = a * (z * ((y1 * y3) - (t * b)))
	elif y3 <= -2e-109:
		tmp = i * (y1 * (x * j))
	elif y3 <= 8e-86:
		tmp = t_1
	elif y3 <= 3900000.0:
		tmp = (b * j) * (t * y4)
	elif y3 <= 7e+194:
		tmp = t_1
	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(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))))
	tmp = 0.0
	if (y3 <= -4600000.0)
		tmp = Float64(a * Float64(z * Float64(Float64(y1 * y3) - Float64(t * b))));
	elseif (y3 <= -2e-109)
		tmp = Float64(i * Float64(y1 * Float64(x * j)));
	elseif (y3 <= 8e-86)
		tmp = t_1;
	elseif (y3 <= 3900000.0)
		tmp = Float64(Float64(b * j) * Float64(t * y4));
	elseif (y3 <= 7e+194)
		tmp = t_1;
	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 = a * (b * ((x * y) - (z * t)));
	tmp = 0.0;
	if (y3 <= -4600000.0)
		tmp = a * (z * ((y1 * y3) - (t * b)));
	elseif (y3 <= -2e-109)
		tmp = i * (y1 * (x * j));
	elseif (y3 <= 8e-86)
		tmp = t_1;
	elseif (y3 <= 3900000.0)
		tmp = (b * j) * (t * y4);
	elseif (y3 <= 7e+194)
		tmp = t_1;
	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[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -4600000.0], N[(a * N[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -2e-109], N[(i * N[(y1 * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 8e-86], t$95$1, If[LessEqual[y3, 3900000.0], N[(N[(b * j), $MachinePrecision] * N[(t * y4), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 7e+194], t$95$1, N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y3 < -4.6e6

   1. Initial program 21.7%

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

   3. Simplified 29.6%

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

   4. Taylor expanded in a around inf 47.5%

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

      1. mul-1-neg 47.5%

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

      2. mul-1-neg 47.5%

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

   6. Simplified 47.5%

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

   7. Taylor expanded in z around inf 44.0%

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

      1. cancel-sign-sub-inv 44.0%

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

      2. metadata-eval 44.0%

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

      3. *-lft-identity 44.0%

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

      4. +-commutative 44.0%

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

      5. mul-1-neg 44.0%

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

      6. unsub-neg 44.0%

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

      7. *-commutative 44.0%

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

   9. Simplified 44.0%

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

   if -4.6e6 < y3 < -2e-109

   1. Initial program 35.7%

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

   3. Simplified 35.7%

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

   4. Taylor expanded in x around inf 44.0%

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

   5. Taylor expanded in j around inf 30.7%

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

   6. Taylor expanded in y1 around inf 34.1%

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

   if -2e-109 < y3 < 8.00000000000000068e-86 or 3.9e6 < y3 < 6.9999999999999995e194

   1. Initial program 30.8%

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

   3. Simplified 33.0%

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

   4. Taylor expanded in a around inf 38.1%

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

      1. mul-1-neg 38.1%

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

      2. mul-1-neg 38.1%

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

   6. Simplified 38.1%

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

   7. Taylor expanded in b around inf 40.7%

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

   if 8.00000000000000068e-86 < y3 < 3.9e6

   1. Initial program 16.5%

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

   3. Simplified 16.5%

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

   4. Taylor expanded in t around inf 42.8%

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

      1. associate--l+ 42.8%

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

      2. mul-1-neg 42.8%

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

   6. Simplified 42.8%

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

   7. Taylor expanded in j around inf 38.2%

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

   8. Taylor expanded in y4 around inf 33.2%

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

      1. *-commutative 33.2%

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

      2. *-commutative 33.2%

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

      3. associate-*l* 43.2%

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

      4. *-commutative 43.2%

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

   10. Simplified 43.2%

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

   if 6.9999999999999995e194 < y3

   1. Initial program 29.1%

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

   3. Simplified 37.4%

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

   4. Taylor expanded in a around inf 41.6%

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

      1. mul-1-neg 41.6%

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

      2. mul-1-neg 41.6%

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

   6. Simplified 41.6%

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

   7. Taylor expanded in y5 around inf 46.1%

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

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -4600000:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;y3 \leq -2 \cdot 10^{-109}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;y3 \leq 8 \cdot 10^{-86}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y3 \leq 3900000:\\ \;\;\;\;\left(b \cdot j\right) \cdot \left(t \cdot y4\right)\\ \mathbf{elif}\;y3 \leq 7 \cdot 10^{+194}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \end{array} \]

Alternative 20: 30.1% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;a \leq -3.7 \cdot 10^{+223}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-166}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-265}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{-114}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+181}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y4 (- (* y y3) (* t y2))))))
   (if (<= a -3.7e+223)
     (* a (* y5 (- (* t y2) (* y y3))))
     (if (<= a -2.1e-166)
       (* a (* b (- (* x y) (* z t))))
       (if (<= a 8.5e-265)
         t_1
         (if (<= a 2.45e-114)
           (* b (* y0 (- (* z k) (* x j))))
           (if (<= a 1.8e+181) t_1 (* a (* z (- (* y1 y3) (* t b)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y4 * ((y * y3) - (t * y2)));
	double tmp;
	if (a <= -3.7e+223) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (a <= -2.1e-166) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (a <= 8.5e-265) {
		tmp = t_1;
	} else if (a <= 2.45e-114) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (a <= 1.8e+181) {
		tmp = t_1;
	} else {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (y4 * ((y * y3) - (t * y2)))
    if (a <= (-3.7d+223)) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else if (a <= (-2.1d-166)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (a <= 8.5d-265) then
        tmp = t_1
    else if (a <= 2.45d-114) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (a <= 1.8d+181) then
        tmp = t_1
    else
        tmp = a * (z * ((y1 * y3) - (t * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y4 * ((y * y3) - (t * y2)));
	double tmp;
	if (a <= -3.7e+223) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (a <= -2.1e-166) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (a <= 8.5e-265) {
		tmp = t_1;
	} else if (a <= 2.45e-114) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (a <= 1.8e+181) {
		tmp = t_1;
	} else {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (y4 * ((y * y3) - (t * y2)))
	tmp = 0
	if a <= -3.7e+223:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	elif a <= -2.1e-166:
		tmp = a * (b * ((x * y) - (z * t)))
	elif a <= 8.5e-265:
		tmp = t_1
	elif a <= 2.45e-114:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif a <= 1.8e+181:
		tmp = t_1
	else:
		tmp = a * (z * ((y1 * y3) - (t * b)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))))
	tmp = 0.0
	if (a <= -3.7e+223)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (a <= -2.1e-166)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (a <= 8.5e-265)
		tmp = t_1;
	elseif (a <= 2.45e-114)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (a <= 1.8e+181)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(z * Float64(Float64(y1 * y3) - Float64(t * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (y4 * ((y * y3) - (t * y2)));
	tmp = 0.0;
	if (a <= -3.7e+223)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	elseif (a <= -2.1e-166)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (a <= 8.5e-265)
		tmp = t_1;
	elseif (a <= 2.45e-114)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (a <= 1.8e+181)
		tmp = t_1;
	else
		tmp = a * (z * ((y1 * y3) - (t * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.7e+223], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.1e-166], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.5e-265], t$95$1, If[LessEqual[a, 2.45e-114], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.8e+181], t$95$1, N[(a * N[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.7000000000000002e223

   1. Initial program 17.6%

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

   3. Simplified 26.3%

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

   4. Taylor expanded in a around inf 78.3%

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

      1. mul-1-neg 78.3%

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

      2. mul-1-neg 78.3%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 78.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in y5 around inf 61.5%

      \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)} \]

   if -3.7000000000000002e223 < a < -2.0999999999999999e-166

   1. Initial program 30.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 36.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 39.4%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 39.4%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 39.4%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 39.4%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 46.1%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   if -2.0999999999999999e-166 < a < 8.4999999999999997e-265 or 2.4499999999999999e-114 < a < 1.79999999999999992e181

   1. Initial program 29.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 29.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 40.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 36.5%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   if 8.4999999999999997e-265 < a < 2.4499999999999999e-114

   1. Initial program 29.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 29.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 37.8%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot b} \]

   5. Taylor expanded in y0 around inf 45.2%

      \[\leadsto \color{blue}{\left(k \cdot z - j \cdot x\right) \cdot \left(y0 \cdot b\right)} \]
   6. Step-by-step derivation

      1. *-commutative 45.2%

         \[\leadsto \color{blue}{\left(y0 \cdot b\right) \cdot \left(k \cdot z - j \cdot x\right)} \]

      2. *-commutative 45.2%

         \[\leadsto \color{blue}{\left(b \cdot y0\right)} \cdot \left(k \cdot z - j \cdot x\right) \]

      3. associate-*l* 45.3%

         \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   7. Simplified 45.3%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   if 1.79999999999999992e181 < a

   1. Initial program 27.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 53.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 53.9%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 53.9%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 53.9%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in z around inf 47.3%

      \[\leadsto \color{blue}{a \cdot \left(z \cdot \left(-1 \cdot \left(t \cdot b\right) - -1 \cdot \left(y1 \cdot y3\right)\right)\right)} \]
   8. Step-by-step derivation

      1. cancel-sign-sub-inv 47.3%

         \[\leadsto a \cdot \left(z \cdot \color{blue}{\left(-1 \cdot \left(t \cdot b\right) + \left(--1\right) \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      2. metadata-eval 47.3%

         \[\leadsto a \cdot \left(z \cdot \left(-1 \cdot \left(t \cdot b\right) + \color{blue}{1} \cdot \left(y1 \cdot y3\right)\right)\right) \]

      3. *-lft-identity 47.3%

         \[\leadsto a \cdot \left(z \cdot \left(-1 \cdot \left(t \cdot b\right) + \color{blue}{y1 \cdot y3}\right)\right) \]

      4. +-commutative 47.3%

         \[\leadsto a \cdot \left(z \cdot \color{blue}{\left(y1 \cdot y3 + -1 \cdot \left(t \cdot b\right)\right)}\right) \]

      5. mul-1-neg 47.3%

         \[\leadsto a \cdot \left(z \cdot \left(y1 \cdot y3 + \color{blue}{\left(-t \cdot b\right)}\right)\right) \]

      6. unsub-neg 47.3%

         \[\leadsto a \cdot \left(z \cdot \color{blue}{\left(y1 \cdot y3 - t \cdot b\right)}\right) \]

      7. *-commutative 47.3%

         \[\leadsto a \cdot \left(z \cdot \left(y1 \cdot y3 - \color{blue}{b \cdot t}\right)\right) \]

   9. Simplified 47.3%

      \[\leadsto \color{blue}{a \cdot \left(z \cdot \left(y1 \cdot y3 - b \cdot t\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{+223}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-166}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-265}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{-114}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+181}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \end{array} \]

Alternative 21: 29.4% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{if}\;b \leq -1.25 \cdot 10^{+94}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-173}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-250}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+208}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* t (* c (- (* z i) (* y2 y4))))))
   (if (<= b -1.25e+94)
     (* y4 (* t (* b j)))
     (if (<= b -2.1e-173)
       t_1
       (if (<= b 5e-250)
         (* k (* y2 (- (* y1 y4) (* y0 y5))))
         (if (<= b 2.4e+18)
           t_1
           (if (<= b 3.6e+208)
             (* x (* c (- (* y0 y2) (* y i))))
             (* a (* b (- (* x y) (* z t)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * (c * ((z * i) - (y2 * y4)));
	double tmp;
	if (b <= -1.25e+94) {
		tmp = y4 * (t * (b * j));
	} else if (b <= -2.1e-173) {
		tmp = t_1;
	} else if (b <= 5e-250) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (b <= 2.4e+18) {
		tmp = t_1;
	} else if (b <= 3.6e+208) {
		tmp = x * (c * ((y0 * y2) - (y * i)));
	} else {
		tmp = a * (b * ((x * y) - (z * t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (c * ((z * i) - (y2 * y4)))
    if (b <= (-1.25d+94)) then
        tmp = y4 * (t * (b * j))
    else if (b <= (-2.1d-173)) then
        tmp = t_1
    else if (b <= 5d-250) then
        tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
    else if (b <= 2.4d+18) then
        tmp = t_1
    else if (b <= 3.6d+208) then
        tmp = x * (c * ((y0 * y2) - (y * i)))
    else
        tmp = a * (b * ((x * y) - (z * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * (c * ((z * i) - (y2 * y4)));
	double tmp;
	if (b <= -1.25e+94) {
		tmp = y4 * (t * (b * j));
	} else if (b <= -2.1e-173) {
		tmp = t_1;
	} else if (b <= 5e-250) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (b <= 2.4e+18) {
		tmp = t_1;
	} else if (b <= 3.6e+208) {
		tmp = x * (c * ((y0 * y2) - (y * i)));
	} else {
		tmp = a * (b * ((x * y) - (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = t * (c * ((z * i) - (y2 * y4)))
	tmp = 0
	if b <= -1.25e+94:
		tmp = y4 * (t * (b * j))
	elif b <= -2.1e-173:
		tmp = t_1
	elif b <= 5e-250:
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
	elif b <= 2.4e+18:
		tmp = t_1
	elif b <= 3.6e+208:
		tmp = x * (c * ((y0 * y2) - (y * i)))
	else:
		tmp = a * (b * ((x * y) - (z * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(t * Float64(c * Float64(Float64(z * i) - Float64(y2 * y4))))
	tmp = 0.0
	if (b <= -1.25e+94)
		tmp = Float64(y4 * Float64(t * Float64(b * j)));
	elseif (b <= -2.1e-173)
		tmp = t_1;
	elseif (b <= 5e-250)
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	elseif (b <= 2.4e+18)
		tmp = t_1;
	elseif (b <= 3.6e+208)
		tmp = Float64(x * Float64(c * Float64(Float64(y0 * y2) - Float64(y * i))));
	else
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = t * (c * ((z * i) - (y2 * y4)));
	tmp = 0.0;
	if (b <= -1.25e+94)
		tmp = y4 * (t * (b * j));
	elseif (b <= -2.1e-173)
		tmp = t_1;
	elseif (b <= 5e-250)
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	elseif (b <= 2.4e+18)
		tmp = t_1;
	elseif (b <= 3.6e+208)
		tmp = x * (c * ((y0 * y2) - (y * i)));
	else
		tmp = a * (b * ((x * y) - (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(t * N[(c * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.25e+94], N[(y4 * N[(t * N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.1e-173], t$95$1, If[LessEqual[b, 5e-250], N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.4e+18], t$95$1, If[LessEqual[b, 3.6e+208], N[(x * N[(c * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.25000000000000003e94

   1. Initial program 14.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 14.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 27.2%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 27.2%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

      2. mul-1-neg 27.2%

         \[\leadsto t \cdot \left(\color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)} + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right) \]

   6. Simplified 27.2%

      \[\leadsto \color{blue}{t \cdot \left(\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

   7. Taylor expanded in j around inf 42.4%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} \]

   8. Taylor expanded in b around inf 46.9%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b\right)\right)} \]

   if -1.25000000000000003e94 < b < -2.10000000000000001e-173 or 5.00000000000000027e-250 < b < 2.4e18

   1. Initial program 29.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 29.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 42.2%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 42.2%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

      2. mul-1-neg 42.2%

         \[\leadsto t \cdot \left(\color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)} + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right) \]

   6. Simplified 42.2%

      \[\leadsto \color{blue}{t \cdot \left(\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

   7. Taylor expanded in c around -inf 42.5%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 42.5%

         \[\leadsto t \cdot \left(c \cdot \left(i \cdot z + \color{blue}{\left(-y4 \cdot y2\right)}\right)\right) \]

      2. unsub-neg 42.5%

         \[\leadsto t \cdot \left(c \cdot \color{blue}{\left(i \cdot z - y4 \cdot y2\right)}\right) \]

      3. *-commutative 42.5%

         \[\leadsto t \cdot \left(c \cdot \left(i \cdot z - \color{blue}{y2 \cdot y4}\right)\right) \]

   9. Simplified 42.5%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(i \cdot z - y2 \cdot y4\right)\right)} \]

   if -2.10000000000000001e-173 < b < 5.00000000000000027e-250

   1. Initial program 34.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 34.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 46.2%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in k around inf 47.9%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right)} \]

   if 2.4e18 < b < 3.60000000000000003e208

   1. Initial program 33.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 33.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 42.6%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in i around -inf 39.8%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(\left(c \cdot y - y1 \cdot j\right) \cdot i\right) + \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2 + y \cdot \left(a \cdot b\right)\right)\right) - y0 \cdot \left(b \cdot j\right)\right)} \cdot x \]

   6. Taylor expanded in c around inf 37.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right) \cdot x\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 48.9%

         \[\leadsto \color{blue}{\left(c \cdot \left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right)\right) \cdot x} \]

      2. *-commutative 48.9%

         \[\leadsto \color{blue}{x \cdot \left(c \cdot \left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right)\right)} \]

      3. +-commutative 48.9%

         \[\leadsto x \cdot \left(c \cdot \color{blue}{\left(y0 \cdot y2 + -1 \cdot \left(i \cdot y\right)\right)}\right) \]

      4. mul-1-neg 48.9%

         \[\leadsto x \cdot \left(c \cdot \left(y0 \cdot y2 + \color{blue}{\left(-i \cdot y\right)}\right)\right) \]

      5. unsub-neg 48.9%

         \[\leadsto x \cdot \left(c \cdot \color{blue}{\left(y0 \cdot y2 - i \cdot y\right)}\right) \]

      6. *-commutative 48.9%

         \[\leadsto x \cdot \left(c \cdot \left(y0 \cdot y2 - \color{blue}{y \cdot i}\right)\right) \]

   8. Simplified 48.9%

      \[\leadsto \color{blue}{x \cdot \left(c \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)} \]

   if 3.60000000000000003e208 < b

   1. Initial program 26.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 58.7%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 58.7%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 58.7%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 58.7%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 63.6%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 46.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+94}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-173}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-250}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+18}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+208}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]

Alternative 22: 22.3% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+107}:\\ \;\;\;\;b \cdot \left(j \cdot \left(x \cdot \left(-y0\right)\right)\right)\\ \mathbf{elif}\;x \leq -8.4 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-237}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-200}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(y3 \cdot \left(-y1\right)\right)\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-124}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+50}:\\ \;\;\;\;\left(t \cdot i\right) \cdot \left(j \cdot \left(-y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -1.2e+107)
   (* b (* j (* x (- y0))))
   (if (<= x -8.4e+15)
     (* x (* j (* i y1)))
     (if (<= x -3.5e-237)
       (* y4 (* t (* b j)))
       (if (<= x 1.35e-200)
         (* y4 (* j (* y3 (- y1))))
         (if (<= x 3.2e-124)
           (* y4 (* b (* t j)))
           (if (<= x 1.5e+50)
             (* (* t i) (* j (- y5)))
             (* y (* b (* x a))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -1.2e+107) {
		tmp = b * (j * (x * -y0));
	} else if (x <= -8.4e+15) {
		tmp = x * (j * (i * y1));
	} else if (x <= -3.5e-237) {
		tmp = y4 * (t * (b * j));
	} else if (x <= 1.35e-200) {
		tmp = y4 * (j * (y3 * -y1));
	} else if (x <= 3.2e-124) {
		tmp = y4 * (b * (t * j));
	} else if (x <= 1.5e+50) {
		tmp = (t * i) * (j * -y5);
	} else {
		tmp = y * (b * (x * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (x <= (-1.2d+107)) then
        tmp = b * (j * (x * -y0))
    else if (x <= (-8.4d+15)) then
        tmp = x * (j * (i * y1))
    else if (x <= (-3.5d-237)) then
        tmp = y4 * (t * (b * j))
    else if (x <= 1.35d-200) then
        tmp = y4 * (j * (y3 * -y1))
    else if (x <= 3.2d-124) then
        tmp = y4 * (b * (t * j))
    else if (x <= 1.5d+50) then
        tmp = (t * i) * (j * -y5)
    else
        tmp = y * (b * (x * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -1.2e+107) {
		tmp = b * (j * (x * -y0));
	} else if (x <= -8.4e+15) {
		tmp = x * (j * (i * y1));
	} else if (x <= -3.5e-237) {
		tmp = y4 * (t * (b * j));
	} else if (x <= 1.35e-200) {
		tmp = y4 * (j * (y3 * -y1));
	} else if (x <= 3.2e-124) {
		tmp = y4 * (b * (t * j));
	} else if (x <= 1.5e+50) {
		tmp = (t * i) * (j * -y5);
	} else {
		tmp = y * (b * (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if x <= -1.2e+107:
		tmp = b * (j * (x * -y0))
	elif x <= -8.4e+15:
		tmp = x * (j * (i * y1))
	elif x <= -3.5e-237:
		tmp = y4 * (t * (b * j))
	elif x <= 1.35e-200:
		tmp = y4 * (j * (y3 * -y1))
	elif x <= 3.2e-124:
		tmp = y4 * (b * (t * j))
	elif x <= 1.5e+50:
		tmp = (t * i) * (j * -y5)
	else:
		tmp = y * (b * (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (x <= -1.2e+107)
		tmp = Float64(b * Float64(j * Float64(x * Float64(-y0))));
	elseif (x <= -8.4e+15)
		tmp = Float64(x * Float64(j * Float64(i * y1)));
	elseif (x <= -3.5e-237)
		tmp = Float64(y4 * Float64(t * Float64(b * j)));
	elseif (x <= 1.35e-200)
		tmp = Float64(y4 * Float64(j * Float64(y3 * Float64(-y1))));
	elseif (x <= 3.2e-124)
		tmp = Float64(y4 * Float64(b * Float64(t * j)));
	elseif (x <= 1.5e+50)
		tmp = Float64(Float64(t * i) * Float64(j * Float64(-y5)));
	else
		tmp = Float64(y * Float64(b * Float64(x * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (x <= -1.2e+107)
		tmp = b * (j * (x * -y0));
	elseif (x <= -8.4e+15)
		tmp = x * (j * (i * y1));
	elseif (x <= -3.5e-237)
		tmp = y4 * (t * (b * j));
	elseif (x <= 1.35e-200)
		tmp = y4 * (j * (y3 * -y1));
	elseif (x <= 3.2e-124)
		tmp = y4 * (b * (t * j));
	elseif (x <= 1.5e+50)
		tmp = (t * i) * (j * -y5);
	else
		tmp = y * (b * (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[x, -1.2e+107], N[(b * N[(j * N[(x * (-y0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -8.4e+15], N[(x * N[(j * N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.5e-237], N[(y4 * N[(t * N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.35e-200], N[(y4 * N[(j * N[(y3 * (-y1)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.2e-124], N[(y4 * N[(b * N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.5e+50], N[(N[(t * i), $MachinePrecision] * N[(j * (-y5)), $MachinePrecision]), $MachinePrecision], N[(y * N[(b * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if x < -1.2e107

   1. Initial program 31.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 64.2%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in j around inf 37.2%

      \[\leadsto \color{blue}{\left(j \cdot \left(y1 \cdot i - y0 \cdot b\right)\right)} \cdot x \]

   6. Taylor expanded in y1 around 0 42.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y0 \cdot \left(j \cdot b\right)\right)\right)} \cdot x \]
   7. Step-by-step derivation

      1. mul-1-neg 42.0%

         \[\leadsto \color{blue}{\left(-y0 \cdot \left(j \cdot b\right)\right)} \cdot x \]

      2. *-commutative 42.0%

         \[\leadsto \left(-y0 \cdot \color{blue}{\left(b \cdot j\right)}\right) \cdot x \]

      3. distribute-rgt-neg-in 42.0%

         \[\leadsto \color{blue}{\left(y0 \cdot \left(-b \cdot j\right)\right)} \cdot x \]

      4. *-commutative 42.0%

         \[\leadsto \left(y0 \cdot \left(-\color{blue}{j \cdot b}\right)\right) \cdot x \]

      5. distribute-rgt-neg-in 42.0%

         \[\leadsto \left(y0 \cdot \color{blue}{\left(j \cdot \left(-b\right)\right)}\right) \cdot x \]

   8. Simplified 42.0%

      \[\leadsto \color{blue}{\left(y0 \cdot \left(j \cdot \left(-b\right)\right)\right)} \cdot x \]

   9. Taylor expanded in y0 around 0 44.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(j \cdot \left(b \cdot x\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 44.6%

          \[\leadsto \color{blue}{-y0 \cdot \left(j \cdot \left(b \cdot x\right)\right)} \]

       2. associate-*r* 44.5%

          \[\leadsto -y0 \cdot \color{blue}{\left(\left(j \cdot b\right) \cdot x\right)} \]

       3. *-commutative 44.5%

          \[\leadsto -y0 \cdot \left(\color{blue}{\left(b \cdot j\right)} \cdot x\right) \]

       4. associate-*r* 49.4%

          \[\leadsto -y0 \cdot \color{blue}{\left(b \cdot \left(j \cdot x\right)\right)} \]

       5. associate-*r* 44.6%

          \[\leadsto -\color{blue}{\left(y0 \cdot b\right) \cdot \left(j \cdot x\right)} \]

       6. *-commutative 44.6%

          \[\leadsto -\color{blue}{\left(b \cdot y0\right)} \cdot \left(j \cdot x\right) \]

       7. associate-*l* 44.5%

          \[\leadsto -\color{blue}{b \cdot \left(y0 \cdot \left(j \cdot x\right)\right)} \]

       8. distribute-rgt-neg-in 44.5%

          \[\leadsto \color{blue}{b \cdot \left(-y0 \cdot \left(j \cdot x\right)\right)} \]

       9. *-commutative 44.5%

          \[\leadsto b \cdot \left(-\color{blue}{\left(j \cdot x\right) \cdot y0}\right) \]

       10. associate-*l* 47.0%

           \[\leadsto b \cdot \left(-\color{blue}{j \cdot \left(x \cdot y0\right)}\right) \]

       11. *-commutative 47.0%

           \[\leadsto b \cdot \left(-j \cdot \color{blue}{\left(y0 \cdot x\right)}\right) \]

       12. distribute-rgt-neg-in 47.0%

           \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(-y0 \cdot x\right)\right)} \]

   11. Simplified 47.0%

       \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(-y0 \cdot x\right)\right)} \]

   if -1.2e107 < x < -8.4e15

   1. Initial program 29.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 29.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 41.8%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in j around inf 48.2%

      \[\leadsto \color{blue}{\left(j \cdot \left(y1 \cdot i - y0 \cdot b\right)\right)} \cdot x \]

   6. Taylor expanded in y1 around inf 37.3%

      \[\leadsto \color{blue}{\left(i \cdot \left(y1 \cdot j\right)\right)} \cdot x \]
   7. Step-by-step derivation

      1. *-commutative 37.3%

         \[\leadsto \color{blue}{\left(\left(y1 \cdot j\right) \cdot i\right)} \cdot x \]

      2. *-commutative 37.3%

         \[\leadsto \left(\color{blue}{\left(j \cdot y1\right)} \cdot i\right) \cdot x \]

      3. associate-*l* 48.3%

         \[\leadsto \color{blue}{\left(j \cdot \left(y1 \cdot i\right)\right)} \cdot x \]

   8. Simplified 48.3%

      \[\leadsto \color{blue}{\left(j \cdot \left(y1 \cdot i\right)\right)} \cdot x \]

   if -8.4e15 < x < -3.49999999999999983e-237

   1. Initial program 32.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 32.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 42.7%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 42.7%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

      2. mul-1-neg 42.7%

         \[\leadsto t \cdot \left(\color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)} + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right) \]

   6. Simplified 42.7%

      \[\leadsto \color{blue}{t \cdot \left(\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

   7. Taylor expanded in j around inf 34.9%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} \]

   8. Taylor expanded in b around inf 35.3%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b\right)\right)} \]

   if -3.49999999999999983e-237 < x < 1.3500000000000001e-200

   1. Initial program 31.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 37.8%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in j around inf 41.2%

      \[\leadsto \color{blue}{y4 \cdot \left(j \cdot \left(t \cdot b + -1 \cdot \left(y1 \cdot y3\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 35.6%

         \[\leadsto \color{blue}{\left(y4 \cdot j\right) \cdot \left(t \cdot b + -1 \cdot \left(y1 \cdot y3\right)\right)} \]

      2. *-commutative 35.6%

         \[\leadsto \color{blue}{\left(j \cdot y4\right)} \cdot \left(t \cdot b + -1 \cdot \left(y1 \cdot y3\right)\right) \]

      3. mul-1-neg 35.6%

         \[\leadsto \left(j \cdot y4\right) \cdot \left(t \cdot b + \color{blue}{\left(-y1 \cdot y3\right)}\right) \]

      4. sub-neg 35.6%

         \[\leadsto \left(j \cdot y4\right) \cdot \color{blue}{\left(t \cdot b - y1 \cdot y3\right)} \]

      5. *-commutative 35.6%

         \[\leadsto \left(j \cdot y4\right) \cdot \left(\color{blue}{b \cdot t} - y1 \cdot y3\right) \]

   7. Simplified 35.6%

      \[\leadsto \color{blue}{\left(j \cdot y4\right) \cdot \left(b \cdot t - y1 \cdot y3\right)} \]

   8. Taylor expanded in b around 0 27.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y4 \cdot \left(y1 \cdot \left(y3 \cdot j\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 27.4%

         \[\leadsto \color{blue}{-y4 \cdot \left(y1 \cdot \left(y3 \cdot j\right)\right)} \]

      2. distribute-rgt-neg-in 27.4%

         \[\leadsto \color{blue}{y4 \cdot \left(-y1 \cdot \left(y3 \cdot j\right)\right)} \]

      3. associate-*r* 30.1%

         \[\leadsto y4 \cdot \left(-\color{blue}{\left(y1 \cdot y3\right) \cdot j}\right) \]

      4. *-commutative 30.1%

         \[\leadsto y4 \cdot \left(-\color{blue}{j \cdot \left(y1 \cdot y3\right)}\right) \]

   10. Simplified 30.1%

       \[\leadsto \color{blue}{y4 \cdot \left(-j \cdot \left(y1 \cdot y3\right)\right)} \]

   if 1.3500000000000001e-200 < x < 3.20000000000000004e-124

   1. Initial program 27.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 27.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 37.3%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 37.3%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

      2. mul-1-neg 37.3%

         \[\leadsto t \cdot \left(\color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)} + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right) \]

   6. Simplified 37.3%

      \[\leadsto \color{blue}{t \cdot \left(\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

   7. Taylor expanded in j around inf 28.0%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} \]

   8. Taylor expanded in y4 around inf 28.2%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 28.2%

         \[\leadsto \color{blue}{\left(t \cdot \left(b \cdot j\right)\right) \cdot y4} \]

      2. *-commutative 28.2%

         \[\leadsto \color{blue}{\left(\left(b \cdot j\right) \cdot t\right)} \cdot y4 \]

      3. associate-*l* 28.2%

         \[\leadsto \color{blue}{\left(b \cdot j\right) \cdot \left(t \cdot y4\right)} \]

      4. *-commutative 28.2%

         \[\leadsto \color{blue}{\left(j \cdot b\right)} \cdot \left(t \cdot y4\right) \]

   10. Simplified 28.2%

       \[\leadsto \color{blue}{\left(j \cdot b\right) \cdot \left(t \cdot y4\right)} \]

   11. Taylor expanded in j around 0 28.2%

       \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)} \]
   12. Step-by-step derivation

       1. *-commutative 28.2%

          \[\leadsto y4 \cdot \left(t \cdot \color{blue}{\left(j \cdot b\right)}\right) \]

       2. associate-*r* 37.1%

          \[\leadsto y4 \cdot \color{blue}{\left(\left(t \cdot j\right) \cdot b\right)} \]

   13. Simplified 37.1%

       \[\leadsto \color{blue}{y4 \cdot \left(\left(t \cdot j\right) \cdot b\right)} \]

   if 3.20000000000000004e-124 < x < 1.4999999999999999e50

   1. Initial program 22.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 22.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 33.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 33.4%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

      2. mul-1-neg 33.4%

         \[\leadsto t \cdot \left(\color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)} + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right) \]

   6. Simplified 33.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

   7. Taylor expanded in y5 around -inf 23.9%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(i \cdot j - a \cdot y2\right) \cdot \left(t \cdot y5\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 23.9%

         \[\leadsto \color{blue}{-\left(i \cdot j - a \cdot y2\right) \cdot \left(t \cdot y5\right)} \]

      2. *-commutative 23.9%

         \[\leadsto -\color{blue}{\left(t \cdot y5\right) \cdot \left(i \cdot j - a \cdot y2\right)} \]

   9. Simplified 23.9%

      \[\leadsto \color{blue}{-\left(t \cdot y5\right) \cdot \left(i \cdot j - a \cdot y2\right)} \]

   10. Taylor expanded in i around inf 26.9%

       \[\leadsto -\color{blue}{i \cdot \left(t \cdot \left(j \cdot y5\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 31.5%

          \[\leadsto -\color{blue}{\left(i \cdot t\right) \cdot \left(j \cdot y5\right)} \]

       2. *-commutative 31.5%

          \[\leadsto -\color{blue}{\left(j \cdot y5\right) \cdot \left(i \cdot t\right)} \]

   12. Simplified 31.5%

       \[\leadsto -\color{blue}{\left(j \cdot y5\right) \cdot \left(i \cdot t\right)} \]

   if 1.4999999999999999e50 < x

   1. Initial program 25.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 34.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 42.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 42.8%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 42.8%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 42.8%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 35.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   8. Taylor expanded in y around inf 34.1%

      \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

   9. Taylor expanded in a around 0 34.1%

      \[\leadsto \color{blue}{y \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 34.1%

          \[\leadsto y \cdot \color{blue}{\left(\left(b \cdot x\right) \cdot a\right)} \]

       2. associate-*l* 37.3%

          \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(x \cdot a\right)\right)} \]

   11. Simplified 37.3%

       \[\leadsto \color{blue}{y \cdot \left(b \cdot \left(x \cdot a\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 37.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+107}:\\ \;\;\;\;b \cdot \left(j \cdot \left(x \cdot \left(-y0\right)\right)\right)\\ \mathbf{elif}\;x \leq -8.4 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-237}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-200}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(y3 \cdot \left(-y1\right)\right)\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-124}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+50}:\\ \;\;\;\;\left(t \cdot i\right) \cdot \left(j \cdot \left(-y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a\right)\right)\\ \end{array} \]

Alternative 23: 22.3% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+104}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(x \cdot \left(-j\right)\right)\right)\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-237}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-202}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(y3 \cdot \left(-y1\right)\right)\right)\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-128}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+52}:\\ \;\;\;\;\left(t \cdot i\right) \cdot \left(j \cdot \left(-y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -2.6e+104)
   (* y0 (* b (* x (- j))))
   (if (<= x -1.6e+20)
     (* x (* j (* i y1)))
     (if (<= x -2.1e-237)
       (* y4 (* t (* b j)))
       (if (<= x 6.2e-202)
         (* y4 (* j (* y3 (- y1))))
         (if (<= x 6.8e-128)
           (* y4 (* b (* t j)))
           (if (<= x 3.6e+52)
             (* (* t i) (* j (- y5)))
             (* y (* b (* x a))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -2.6e+104) {
		tmp = y0 * (b * (x * -j));
	} else if (x <= -1.6e+20) {
		tmp = x * (j * (i * y1));
	} else if (x <= -2.1e-237) {
		tmp = y4 * (t * (b * j));
	} else if (x <= 6.2e-202) {
		tmp = y4 * (j * (y3 * -y1));
	} else if (x <= 6.8e-128) {
		tmp = y4 * (b * (t * j));
	} else if (x <= 3.6e+52) {
		tmp = (t * i) * (j * -y5);
	} else {
		tmp = y * (b * (x * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (x <= (-2.6d+104)) then
        tmp = y0 * (b * (x * -j))
    else if (x <= (-1.6d+20)) then
        tmp = x * (j * (i * y1))
    else if (x <= (-2.1d-237)) then
        tmp = y4 * (t * (b * j))
    else if (x <= 6.2d-202) then
        tmp = y4 * (j * (y3 * -y1))
    else if (x <= 6.8d-128) then
        tmp = y4 * (b * (t * j))
    else if (x <= 3.6d+52) then
        tmp = (t * i) * (j * -y5)
    else
        tmp = y * (b * (x * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -2.6e+104) {
		tmp = y0 * (b * (x * -j));
	} else if (x <= -1.6e+20) {
		tmp = x * (j * (i * y1));
	} else if (x <= -2.1e-237) {
		tmp = y4 * (t * (b * j));
	} else if (x <= 6.2e-202) {
		tmp = y4 * (j * (y3 * -y1));
	} else if (x <= 6.8e-128) {
		tmp = y4 * (b * (t * j));
	} else if (x <= 3.6e+52) {
		tmp = (t * i) * (j * -y5);
	} else {
		tmp = y * (b * (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if x <= -2.6e+104:
		tmp = y0 * (b * (x * -j))
	elif x <= -1.6e+20:
		tmp = x * (j * (i * y1))
	elif x <= -2.1e-237:
		tmp = y4 * (t * (b * j))
	elif x <= 6.2e-202:
		tmp = y4 * (j * (y3 * -y1))
	elif x <= 6.8e-128:
		tmp = y4 * (b * (t * j))
	elif x <= 3.6e+52:
		tmp = (t * i) * (j * -y5)
	else:
		tmp = y * (b * (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (x <= -2.6e+104)
		tmp = Float64(y0 * Float64(b * Float64(x * Float64(-j))));
	elseif (x <= -1.6e+20)
		tmp = Float64(x * Float64(j * Float64(i * y1)));
	elseif (x <= -2.1e-237)
		tmp = Float64(y4 * Float64(t * Float64(b * j)));
	elseif (x <= 6.2e-202)
		tmp = Float64(y4 * Float64(j * Float64(y3 * Float64(-y1))));
	elseif (x <= 6.8e-128)
		tmp = Float64(y4 * Float64(b * Float64(t * j)));
	elseif (x <= 3.6e+52)
		tmp = Float64(Float64(t * i) * Float64(j * Float64(-y5)));
	else
		tmp = Float64(y * Float64(b * Float64(x * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (x <= -2.6e+104)
		tmp = y0 * (b * (x * -j));
	elseif (x <= -1.6e+20)
		tmp = x * (j * (i * y1));
	elseif (x <= -2.1e-237)
		tmp = y4 * (t * (b * j));
	elseif (x <= 6.2e-202)
		tmp = y4 * (j * (y3 * -y1));
	elseif (x <= 6.8e-128)
		tmp = y4 * (b * (t * j));
	elseif (x <= 3.6e+52)
		tmp = (t * i) * (j * -y5);
	else
		tmp = y * (b * (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[x, -2.6e+104], N[(y0 * N[(b * N[(x * (-j)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.6e+20], N[(x * N[(j * N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.1e-237], N[(y4 * N[(t * N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.2e-202], N[(y4 * N[(j * N[(y3 * (-y1)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.8e-128], N[(y4 * N[(b * N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.6e+52], N[(N[(t * i), $MachinePrecision] * N[(j * (-y5)), $MachinePrecision]), $MachinePrecision], N[(y * N[(b * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if x < -2.6e104

   1. Initial program 31.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 64.2%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in j around inf 37.2%

      \[\leadsto \color{blue}{\left(j \cdot \left(y1 \cdot i - y0 \cdot b\right)\right)} \cdot x \]

   6. Taylor expanded in y0 around inf 49.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(b \cdot \left(j \cdot x\right)\right)\right)} \]

   if -2.6e104 < x < -1.6e20

   1. Initial program 29.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 29.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 41.8%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in j around inf 48.2%

      \[\leadsto \color{blue}{\left(j \cdot \left(y1 \cdot i - y0 \cdot b\right)\right)} \cdot x \]

   6. Taylor expanded in y1 around inf 37.3%

      \[\leadsto \color{blue}{\left(i \cdot \left(y1 \cdot j\right)\right)} \cdot x \]
   7. Step-by-step derivation

      1. *-commutative 37.3%

         \[\leadsto \color{blue}{\left(\left(y1 \cdot j\right) \cdot i\right)} \cdot x \]

      2. *-commutative 37.3%

         \[\leadsto \left(\color{blue}{\left(j \cdot y1\right)} \cdot i\right) \cdot x \]

      3. associate-*l* 48.3%

         \[\leadsto \color{blue}{\left(j \cdot \left(y1 \cdot i\right)\right)} \cdot x \]

   8. Simplified 48.3%

      \[\leadsto \color{blue}{\left(j \cdot \left(y1 \cdot i\right)\right)} \cdot x \]

   if -1.6e20 < x < -2.1000000000000001e-237

   1. Initial program 32.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 32.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 42.7%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 42.7%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

      2. mul-1-neg 42.7%

         \[\leadsto t \cdot \left(\color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)} + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right) \]

   6. Simplified 42.7%

      \[\leadsto \color{blue}{t \cdot \left(\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

   7. Taylor expanded in j around inf 34.9%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} \]

   8. Taylor expanded in b around inf 35.3%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b\right)\right)} \]

   if -2.1000000000000001e-237 < x < 6.2e-202

   1. Initial program 31.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 37.8%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in j around inf 41.2%

      \[\leadsto \color{blue}{y4 \cdot \left(j \cdot \left(t \cdot b + -1 \cdot \left(y1 \cdot y3\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 35.6%

         \[\leadsto \color{blue}{\left(y4 \cdot j\right) \cdot \left(t \cdot b + -1 \cdot \left(y1 \cdot y3\right)\right)} \]

      2. *-commutative 35.6%

         \[\leadsto \color{blue}{\left(j \cdot y4\right)} \cdot \left(t \cdot b + -1 \cdot \left(y1 \cdot y3\right)\right) \]

      3. mul-1-neg 35.6%

         \[\leadsto \left(j \cdot y4\right) \cdot \left(t \cdot b + \color{blue}{\left(-y1 \cdot y3\right)}\right) \]

      4. sub-neg 35.6%

         \[\leadsto \left(j \cdot y4\right) \cdot \color{blue}{\left(t \cdot b - y1 \cdot y3\right)} \]

      5. *-commutative 35.6%

         \[\leadsto \left(j \cdot y4\right) \cdot \left(\color{blue}{b \cdot t} - y1 \cdot y3\right) \]

   7. Simplified 35.6%

      \[\leadsto \color{blue}{\left(j \cdot y4\right) \cdot \left(b \cdot t - y1 \cdot y3\right)} \]

   8. Taylor expanded in b around 0 27.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y4 \cdot \left(y1 \cdot \left(y3 \cdot j\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 27.4%

         \[\leadsto \color{blue}{-y4 \cdot \left(y1 \cdot \left(y3 \cdot j\right)\right)} \]

      2. distribute-rgt-neg-in 27.4%

         \[\leadsto \color{blue}{y4 \cdot \left(-y1 \cdot \left(y3 \cdot j\right)\right)} \]

      3. associate-*r* 30.1%

         \[\leadsto y4 \cdot \left(-\color{blue}{\left(y1 \cdot y3\right) \cdot j}\right) \]

      4. *-commutative 30.1%

         \[\leadsto y4 \cdot \left(-\color{blue}{j \cdot \left(y1 \cdot y3\right)}\right) \]

   10. Simplified 30.1%

       \[\leadsto \color{blue}{y4 \cdot \left(-j \cdot \left(y1 \cdot y3\right)\right)} \]

   if 6.2e-202 < x < 6.7999999999999995e-128

   1. Initial program 27.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 27.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 37.3%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 37.3%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

      2. mul-1-neg 37.3%

         \[\leadsto t \cdot \left(\color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)} + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right) \]

   6. Simplified 37.3%

      \[\leadsto \color{blue}{t \cdot \left(\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

   7. Taylor expanded in j around inf 28.0%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} \]

   8. Taylor expanded in y4 around inf 28.2%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 28.2%

         \[\leadsto \color{blue}{\left(t \cdot \left(b \cdot j\right)\right) \cdot y4} \]

      2. *-commutative 28.2%

         \[\leadsto \color{blue}{\left(\left(b \cdot j\right) \cdot t\right)} \cdot y4 \]

      3. associate-*l* 28.2%

         \[\leadsto \color{blue}{\left(b \cdot j\right) \cdot \left(t \cdot y4\right)} \]

      4. *-commutative 28.2%

         \[\leadsto \color{blue}{\left(j \cdot b\right)} \cdot \left(t \cdot y4\right) \]

   10. Simplified 28.2%

       \[\leadsto \color{blue}{\left(j \cdot b\right) \cdot \left(t \cdot y4\right)} \]

   11. Taylor expanded in j around 0 28.2%

       \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)} \]
   12. Step-by-step derivation

       1. *-commutative 28.2%

          \[\leadsto y4 \cdot \left(t \cdot \color{blue}{\left(j \cdot b\right)}\right) \]

       2. associate-*r* 37.1%

          \[\leadsto y4 \cdot \color{blue}{\left(\left(t \cdot j\right) \cdot b\right)} \]

   13. Simplified 37.1%

       \[\leadsto \color{blue}{y4 \cdot \left(\left(t \cdot j\right) \cdot b\right)} \]

   if 6.7999999999999995e-128 < x < 3.6e52

   1. Initial program 22.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 22.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 33.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 33.4%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

      2. mul-1-neg 33.4%

         \[\leadsto t \cdot \left(\color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)} + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right) \]

   6. Simplified 33.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

   7. Taylor expanded in y5 around -inf 23.9%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(i \cdot j - a \cdot y2\right) \cdot \left(t \cdot y5\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 23.9%

         \[\leadsto \color{blue}{-\left(i \cdot j - a \cdot y2\right) \cdot \left(t \cdot y5\right)} \]

      2. *-commutative 23.9%

         \[\leadsto -\color{blue}{\left(t \cdot y5\right) \cdot \left(i \cdot j - a \cdot y2\right)} \]

   9. Simplified 23.9%

      \[\leadsto \color{blue}{-\left(t \cdot y5\right) \cdot \left(i \cdot j - a \cdot y2\right)} \]

   10. Taylor expanded in i around inf 26.9%

       \[\leadsto -\color{blue}{i \cdot \left(t \cdot \left(j \cdot y5\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 31.5%

          \[\leadsto -\color{blue}{\left(i \cdot t\right) \cdot \left(j \cdot y5\right)} \]

       2. *-commutative 31.5%

          \[\leadsto -\color{blue}{\left(j \cdot y5\right) \cdot \left(i \cdot t\right)} \]

   12. Simplified 31.5%

       \[\leadsto -\color{blue}{\left(j \cdot y5\right) \cdot \left(i \cdot t\right)} \]

   if 3.6e52 < x

   1. Initial program 25.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 34.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 42.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 42.8%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 42.8%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 42.8%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 35.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   8. Taylor expanded in y around inf 34.1%

      \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

   9. Taylor expanded in a around 0 34.1%

      \[\leadsto \color{blue}{y \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 34.1%

          \[\leadsto y \cdot \color{blue}{\left(\left(b \cdot x\right) \cdot a\right)} \]

       2. associate-*l* 37.3%

          \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(x \cdot a\right)\right)} \]

   11. Simplified 37.3%

       \[\leadsto \color{blue}{y \cdot \left(b \cdot \left(x \cdot a\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 37.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+104}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(x \cdot \left(-j\right)\right)\right)\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-237}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-202}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(y3 \cdot \left(-y1\right)\right)\right)\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-128}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+52}:\\ \;\;\;\;\left(t \cdot i\right) \cdot \left(j \cdot \left(-y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a\right)\right)\\ \end{array} \]

Alternative 24: 22.2% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot \left(x \cdot y\right)\right)\\ \mathbf{if}\;x \leq -2.3 \cdot 10^{+127}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.12 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+47}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+121}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+152}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* b (* x y)))))
   (if (<= x -2.3e+127)
     t_1
     (if (<= x -1.12e+24)
       (* x (* j (* i y1)))
       (if (<= x -6e-62)
         t_1
         (if (<= x 2.4e+47)
           (* y4 (* t (* b j)))
           (if (<= x 5.2e+121)
             t_1
             (if (<= x 5.5e+152)
               (* i (* y1 (* x j)))
               (* y (* b (* x a)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (b * (x * y));
	double tmp;
	if (x <= -2.3e+127) {
		tmp = t_1;
	} else if (x <= -1.12e+24) {
		tmp = x * (j * (i * y1));
	} else if (x <= -6e-62) {
		tmp = t_1;
	} else if (x <= 2.4e+47) {
		tmp = y4 * (t * (b * j));
	} else if (x <= 5.2e+121) {
		tmp = t_1;
	} else if (x <= 5.5e+152) {
		tmp = i * (y1 * (x * j));
	} else {
		tmp = y * (b * (x * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (b * (x * y))
    if (x <= (-2.3d+127)) then
        tmp = t_1
    else if (x <= (-1.12d+24)) then
        tmp = x * (j * (i * y1))
    else if (x <= (-6d-62)) then
        tmp = t_1
    else if (x <= 2.4d+47) then
        tmp = y4 * (t * (b * j))
    else if (x <= 5.2d+121) then
        tmp = t_1
    else if (x <= 5.5d+152) then
        tmp = i * (y1 * (x * j))
    else
        tmp = y * (b * (x * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (b * (x * y));
	double tmp;
	if (x <= -2.3e+127) {
		tmp = t_1;
	} else if (x <= -1.12e+24) {
		tmp = x * (j * (i * y1));
	} else if (x <= -6e-62) {
		tmp = t_1;
	} else if (x <= 2.4e+47) {
		tmp = y4 * (t * (b * j));
	} else if (x <= 5.2e+121) {
		tmp = t_1;
	} else if (x <= 5.5e+152) {
		tmp = i * (y1 * (x * j));
	} else {
		tmp = y * (b * (x * a));
	}
	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))
	tmp = 0
	if x <= -2.3e+127:
		tmp = t_1
	elif x <= -1.12e+24:
		tmp = x * (j * (i * y1))
	elif x <= -6e-62:
		tmp = t_1
	elif x <= 2.4e+47:
		tmp = y4 * (t * (b * j))
	elif x <= 5.2e+121:
		tmp = t_1
	elif x <= 5.5e+152:
		tmp = i * (y1 * (x * j))
	else:
		tmp = y * (b * (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(b * Float64(x * y)))
	tmp = 0.0
	if (x <= -2.3e+127)
		tmp = t_1;
	elseif (x <= -1.12e+24)
		tmp = Float64(x * Float64(j * Float64(i * y1)));
	elseif (x <= -6e-62)
		tmp = t_1;
	elseif (x <= 2.4e+47)
		tmp = Float64(y4 * Float64(t * Float64(b * j)));
	elseif (x <= 5.2e+121)
		tmp = t_1;
	elseif (x <= 5.5e+152)
		tmp = Float64(i * Float64(y1 * Float64(x * j)));
	else
		tmp = Float64(y * Float64(b * Float64(x * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (b * (x * y));
	tmp = 0.0;
	if (x <= -2.3e+127)
		tmp = t_1;
	elseif (x <= -1.12e+24)
		tmp = x * (j * (i * y1));
	elseif (x <= -6e-62)
		tmp = t_1;
	elseif (x <= 2.4e+47)
		tmp = y4 * (t * (b * j));
	elseif (x <= 5.2e+121)
		tmp = t_1;
	elseif (x <= 5.5e+152)
		tmp = i * (y1 * (x * j));
	else
		tmp = y * (b * (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(b * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.3e+127], t$95$1, If[LessEqual[x, -1.12e+24], N[(x * N[(j * N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6e-62], t$95$1, If[LessEqual[x, 2.4e+47], N[(y4 * N[(t * N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.2e+121], t$95$1, If[LessEqual[x, 5.5e+152], N[(i * N[(y1 * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(b * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2.3000000000000002e127 or -1.12e24 < x < -6.0000000000000002e-62 or 2.40000000000000019e47 < x < 5.1999999999999998e121

   1. Initial program 30.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 38.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 48.3%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 48.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 48.3%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 48.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 47.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   8. Taylor expanded in y around inf 38.4%

      \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

   if -2.3000000000000002e127 < x < -1.12e24

   1. Initial program 27.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 27.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 45.9%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in j around inf 42.0%

      \[\leadsto \color{blue}{\left(j \cdot \left(y1 \cdot i - y0 \cdot b\right)\right)} \cdot x \]

   6. Taylor expanded in y1 around inf 33.4%

      \[\leadsto \color{blue}{\left(i \cdot \left(y1 \cdot j\right)\right)} \cdot x \]
   7. Step-by-step derivation

      1. *-commutative 33.4%

         \[\leadsto \color{blue}{\left(\left(y1 \cdot j\right) \cdot i\right)} \cdot x \]

      2. *-commutative 33.4%

         \[\leadsto \left(\color{blue}{\left(j \cdot y1\right)} \cdot i\right) \cdot x \]

      3. associate-*l* 41.9%

         \[\leadsto \color{blue}{\left(j \cdot \left(y1 \cdot i\right)\right)} \cdot x \]

   8. Simplified 41.9%

      \[\leadsto \color{blue}{\left(j \cdot \left(y1 \cdot i\right)\right)} \cdot x \]

   if -6.0000000000000002e-62 < x < 2.40000000000000019e47

   1. Initial program 28.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 38.2%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 38.2%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

      2. mul-1-neg 38.2%

         \[\leadsto t \cdot \left(\color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)} + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right) \]

   6. Simplified 38.2%

      \[\leadsto \color{blue}{t \cdot \left(\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

   7. Taylor expanded in j around inf 28.6%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} \]

   8. Taylor expanded in b around inf 26.7%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b\right)\right)} \]

   if 5.1999999999999998e121 < x < 5.4999999999999999e152

   1. Initial program 42.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 42.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 44.5%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in j around inf 44.4%

      \[\leadsto \color{blue}{\left(j \cdot \left(y1 \cdot i - y0 \cdot b\right)\right)} \cdot x \]

   6. Taylor expanded in y1 around inf 58.3%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x\right)\right)} \]

   if 5.4999999999999999e152 < x

   1. Initial program 20.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 33.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 33.9%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 33.9%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 33.9%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 34.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   8. Taylor expanded in y around inf 37.2%

      \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

   9. Taylor expanded in a around 0 42.1%

      \[\leadsto \color{blue}{y \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 42.1%

          \[\leadsto y \cdot \color{blue}{\left(\left(b \cdot x\right) \cdot a\right)} \]

       2. associate-*l* 49.8%

          \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(x \cdot a\right)\right)} \]

   11. Simplified 49.8%

       \[\leadsto \color{blue}{y \cdot \left(b \cdot \left(x \cdot a\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 35.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+127}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;x \leq -1.12 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-62}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+47}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+121}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+152}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a\right)\right)\\ \end{array} \]

Alternative 25: 22.3% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot \left(x \cdot y\right)\right)\\ \mathbf{if}\;x \leq -2 \cdot 10^{+127}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.55 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-62}:\\ \;\;\;\;\left(x \cdot b\right) \cdot \left(y \cdot a\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+47}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+127}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+153}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* b (* x y)))))
   (if (<= x -2e+127)
     t_1
     (if (<= x -2.55e+20)
       (* x (* j (* i y1)))
       (if (<= x -4.5e-62)
         (* (* x b) (* y a))
         (if (<= x 2.2e+47)
           (* y4 (* t (* b j)))
           (if (<= x 7.8e+127)
             t_1
             (if (<= x 4.2e+153)
               (* i (* y1 (* x j)))
               (* y (* b (* x a)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (b * (x * y));
	double tmp;
	if (x <= -2e+127) {
		tmp = t_1;
	} else if (x <= -2.55e+20) {
		tmp = x * (j * (i * y1));
	} else if (x <= -4.5e-62) {
		tmp = (x * b) * (y * a);
	} else if (x <= 2.2e+47) {
		tmp = y4 * (t * (b * j));
	} else if (x <= 7.8e+127) {
		tmp = t_1;
	} else if (x <= 4.2e+153) {
		tmp = i * (y1 * (x * j));
	} else {
		tmp = y * (b * (x * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (b * (x * y))
    if (x <= (-2d+127)) then
        tmp = t_1
    else if (x <= (-2.55d+20)) then
        tmp = x * (j * (i * y1))
    else if (x <= (-4.5d-62)) then
        tmp = (x * b) * (y * a)
    else if (x <= 2.2d+47) then
        tmp = y4 * (t * (b * j))
    else if (x <= 7.8d+127) then
        tmp = t_1
    else if (x <= 4.2d+153) then
        tmp = i * (y1 * (x * j))
    else
        tmp = y * (b * (x * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (b * (x * y));
	double tmp;
	if (x <= -2e+127) {
		tmp = t_1;
	} else if (x <= -2.55e+20) {
		tmp = x * (j * (i * y1));
	} else if (x <= -4.5e-62) {
		tmp = (x * b) * (y * a);
	} else if (x <= 2.2e+47) {
		tmp = y4 * (t * (b * j));
	} else if (x <= 7.8e+127) {
		tmp = t_1;
	} else if (x <= 4.2e+153) {
		tmp = i * (y1 * (x * j));
	} else {
		tmp = y * (b * (x * a));
	}
	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))
	tmp = 0
	if x <= -2e+127:
		tmp = t_1
	elif x <= -2.55e+20:
		tmp = x * (j * (i * y1))
	elif x <= -4.5e-62:
		tmp = (x * b) * (y * a)
	elif x <= 2.2e+47:
		tmp = y4 * (t * (b * j))
	elif x <= 7.8e+127:
		tmp = t_1
	elif x <= 4.2e+153:
		tmp = i * (y1 * (x * j))
	else:
		tmp = y * (b * (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(b * Float64(x * y)))
	tmp = 0.0
	if (x <= -2e+127)
		tmp = t_1;
	elseif (x <= -2.55e+20)
		tmp = Float64(x * Float64(j * Float64(i * y1)));
	elseif (x <= -4.5e-62)
		tmp = Float64(Float64(x * b) * Float64(y * a));
	elseif (x <= 2.2e+47)
		tmp = Float64(y4 * Float64(t * Float64(b * j)));
	elseif (x <= 7.8e+127)
		tmp = t_1;
	elseif (x <= 4.2e+153)
		tmp = Float64(i * Float64(y1 * Float64(x * j)));
	else
		tmp = Float64(y * Float64(b * Float64(x * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (b * (x * y));
	tmp = 0.0;
	if (x <= -2e+127)
		tmp = t_1;
	elseif (x <= -2.55e+20)
		tmp = x * (j * (i * y1));
	elseif (x <= -4.5e-62)
		tmp = (x * b) * (y * a);
	elseif (x <= 2.2e+47)
		tmp = y4 * (t * (b * j));
	elseif (x <= 7.8e+127)
		tmp = t_1;
	elseif (x <= 4.2e+153)
		tmp = i * (y1 * (x * j));
	else
		tmp = y * (b * (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(b * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2e+127], t$95$1, If[LessEqual[x, -2.55e+20], N[(x * N[(j * N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.5e-62], N[(N[(x * b), $MachinePrecision] * N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.2e+47], N[(y4 * N[(t * N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.8e+127], t$95$1, If[LessEqual[x, 4.2e+153], N[(i * N[(y1 * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(b * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -1.99999999999999991e127 or 2.1999999999999999e47 < x < 7.79999999999999962e127

   1. Initial program 30.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 39.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 49.4%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 49.4%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 49.4%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 49.4%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 46.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   8. Taylor expanded in y around inf 37.0%

      \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

   if -1.99999999999999991e127 < x < -2.55e20

   1. Initial program 27.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 27.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 45.9%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in j around inf 42.0%

      \[\leadsto \color{blue}{\left(j \cdot \left(y1 \cdot i - y0 \cdot b\right)\right)} \cdot x \]

   6. Taylor expanded in y1 around inf 33.4%

      \[\leadsto \color{blue}{\left(i \cdot \left(y1 \cdot j\right)\right)} \cdot x \]
   7. Step-by-step derivation

      1. *-commutative 33.4%

         \[\leadsto \color{blue}{\left(\left(y1 \cdot j\right) \cdot i\right)} \cdot x \]

      2. *-commutative 33.4%

         \[\leadsto \left(\color{blue}{\left(j \cdot y1\right)} \cdot i\right) \cdot x \]

      3. associate-*l* 41.9%

         \[\leadsto \color{blue}{\left(j \cdot \left(y1 \cdot i\right)\right)} \cdot x \]

   8. Simplified 41.9%

      \[\leadsto \color{blue}{\left(j \cdot \left(y1 \cdot i\right)\right)} \cdot x \]

   if -2.55e20 < x < -4.50000000000000018e-62

   1. Initial program 31.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 36.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 45.6%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 45.6%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 45.6%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 45.6%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 50.6%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   8. Taylor expanded in y around inf 41.7%

      \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

   9. Taylor expanded in a around 0 37.4%

      \[\leadsto \color{blue}{y \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 41.7%

          \[\leadsto \color{blue}{\left(y \cdot a\right) \cdot \left(b \cdot x\right)} \]

   11. Simplified 41.7%

       \[\leadsto \color{blue}{\left(y \cdot a\right) \cdot \left(b \cdot x\right)} \]

   if -4.50000000000000018e-62 < x < 2.1999999999999999e47

   1. Initial program 28.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 38.2%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 38.2%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

      2. mul-1-neg 38.2%

         \[\leadsto t \cdot \left(\color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)} + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right) \]

   6. Simplified 38.2%

      \[\leadsto \color{blue}{t \cdot \left(\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

   7. Taylor expanded in j around inf 28.6%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} \]

   8. Taylor expanded in b around inf 26.7%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b\right)\right)} \]

   if 7.79999999999999962e127 < x < 4.20000000000000033e153

   1. Initial program 42.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 42.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 44.5%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in j around inf 44.4%

      \[\leadsto \color{blue}{\left(j \cdot \left(y1 \cdot i - y0 \cdot b\right)\right)} \cdot x \]

   6. Taylor expanded in y1 around inf 58.3%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x\right)\right)} \]

   if 4.20000000000000033e153 < x

   1. Initial program 20.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 33.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 33.9%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 33.9%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 33.9%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 34.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   8. Taylor expanded in y around inf 37.2%

      \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

   9. Taylor expanded in a around 0 42.1%

      \[\leadsto \color{blue}{y \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 42.1%

          \[\leadsto y \cdot \color{blue}{\left(\left(b \cdot x\right) \cdot a\right)} \]

       2. associate-*l* 49.8%

          \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(x \cdot a\right)\right)} \]

   11. Simplified 49.8%

       \[\leadsto \color{blue}{y \cdot \left(b \cdot \left(x \cdot a\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 35.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+127}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;x \leq -2.55 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-62}:\\ \;\;\;\;\left(x \cdot b\right) \cdot \left(y \cdot a\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+47}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+127}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+153}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a\right)\right)\\ \end{array} \]

Alternative 26: 22.8% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+104}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(x \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+47}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+125}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 3.15 \cdot 10^{+155}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -2.6e+104)
   (* y0 (* j (* x (- b))))
   (if (<= x -3.6e+15)
     (* x (* j (* i y1)))
     (if (<= x 1.7e+47)
       (* y4 (* t (* b j)))
       (if (<= x 6.2e+125)
         (* a (* b (* x y)))
         (if (<= x 3.15e+155) (* i (* y1 (* x j))) (* y (* b (* x a)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -2.6e+104) {
		tmp = y0 * (j * (x * -b));
	} else if (x <= -3.6e+15) {
		tmp = x * (j * (i * y1));
	} else if (x <= 1.7e+47) {
		tmp = y4 * (t * (b * j));
	} else if (x <= 6.2e+125) {
		tmp = a * (b * (x * y));
	} else if (x <= 3.15e+155) {
		tmp = i * (y1 * (x * j));
	} else {
		tmp = y * (b * (x * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (x <= (-2.6d+104)) then
        tmp = y0 * (j * (x * -b))
    else if (x <= (-3.6d+15)) then
        tmp = x * (j * (i * y1))
    else if (x <= 1.7d+47) then
        tmp = y4 * (t * (b * j))
    else if (x <= 6.2d+125) then
        tmp = a * (b * (x * y))
    else if (x <= 3.15d+155) then
        tmp = i * (y1 * (x * j))
    else
        tmp = y * (b * (x * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -2.6e+104) {
		tmp = y0 * (j * (x * -b));
	} else if (x <= -3.6e+15) {
		tmp = x * (j * (i * y1));
	} else if (x <= 1.7e+47) {
		tmp = y4 * (t * (b * j));
	} else if (x <= 6.2e+125) {
		tmp = a * (b * (x * y));
	} else if (x <= 3.15e+155) {
		tmp = i * (y1 * (x * j));
	} else {
		tmp = y * (b * (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if x <= -2.6e+104:
		tmp = y0 * (j * (x * -b))
	elif x <= -3.6e+15:
		tmp = x * (j * (i * y1))
	elif x <= 1.7e+47:
		tmp = y4 * (t * (b * j))
	elif x <= 6.2e+125:
		tmp = a * (b * (x * y))
	elif x <= 3.15e+155:
		tmp = i * (y1 * (x * j))
	else:
		tmp = y * (b * (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (x <= -2.6e+104)
		tmp = Float64(y0 * Float64(j * Float64(x * Float64(-b))));
	elseif (x <= -3.6e+15)
		tmp = Float64(x * Float64(j * Float64(i * y1)));
	elseif (x <= 1.7e+47)
		tmp = Float64(y4 * Float64(t * Float64(b * j)));
	elseif (x <= 6.2e+125)
		tmp = Float64(a * Float64(b * Float64(x * y)));
	elseif (x <= 3.15e+155)
		tmp = Float64(i * Float64(y1 * Float64(x * j)));
	else
		tmp = Float64(y * Float64(b * Float64(x * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (x <= -2.6e+104)
		tmp = y0 * (j * (x * -b));
	elseif (x <= -3.6e+15)
		tmp = x * (j * (i * y1));
	elseif (x <= 1.7e+47)
		tmp = y4 * (t * (b * j));
	elseif (x <= 6.2e+125)
		tmp = a * (b * (x * y));
	elseif (x <= 3.15e+155)
		tmp = i * (y1 * (x * j));
	else
		tmp = y * (b * (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[x, -2.6e+104], N[(y0 * N[(j * N[(x * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.6e+15], N[(x * N[(j * N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.7e+47], N[(y4 * N[(t * N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.2e+125], N[(a * N[(b * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.15e+155], N[(i * N[(y1 * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(b * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -2.6e104

   1. Initial program 31.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 64.2%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in j around inf 37.2%

      \[\leadsto \color{blue}{\left(j \cdot \left(y1 \cdot i - y0 \cdot b\right)\right)} \cdot x \]

   6. Taylor expanded in y1 around 0 44.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(j \cdot \left(b \cdot x\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 44.6%

         \[\leadsto \color{blue}{-y0 \cdot \left(j \cdot \left(b \cdot x\right)\right)} \]

   8. Simplified 44.6%

      \[\leadsto \color{blue}{-y0 \cdot \left(j \cdot \left(b \cdot x\right)\right)} \]

   if -2.6e104 < x < -3.6e15

   1. Initial program 29.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 29.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 41.8%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in j around inf 48.2%

      \[\leadsto \color{blue}{\left(j \cdot \left(y1 \cdot i - y0 \cdot b\right)\right)} \cdot x \]

   6. Taylor expanded in y1 around inf 37.3%

      \[\leadsto \color{blue}{\left(i \cdot \left(y1 \cdot j\right)\right)} \cdot x \]
   7. Step-by-step derivation

      1. *-commutative 37.3%

         \[\leadsto \color{blue}{\left(\left(y1 \cdot j\right) \cdot i\right)} \cdot x \]

      2. *-commutative 37.3%

         \[\leadsto \left(\color{blue}{\left(j \cdot y1\right)} \cdot i\right) \cdot x \]

      3. associate-*l* 48.3%

         \[\leadsto \color{blue}{\left(j \cdot \left(y1 \cdot i\right)\right)} \cdot x \]

   8. Simplified 48.3%

      \[\leadsto \color{blue}{\left(j \cdot \left(y1 \cdot i\right)\right)} \cdot x \]

   if -3.6e15 < x < 1.6999999999999999e47

   1. Initial program 29.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 29.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 38.7%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 38.7%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

      2. mul-1-neg 38.7%

         \[\leadsto t \cdot \left(\color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)} + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right) \]

   6. Simplified 38.7%

      \[\leadsto \color{blue}{t \cdot \left(\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

   7. Taylor expanded in j around inf 28.6%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} \]

   8. Taylor expanded in b around inf 26.3%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b\right)\right)} \]

   if 1.6999999999999999e47 < x < 6.2e125

   1. Initial program 26.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 42.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 63.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 63.2%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 63.2%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 63.2%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 42.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   8. Taylor expanded in y around inf 32.7%

      \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

   if 6.2e125 < x < 3.15e155

   1. Initial program 42.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 42.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 44.5%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in j around inf 44.4%

      \[\leadsto \color{blue}{\left(j \cdot \left(y1 \cdot i - y0 \cdot b\right)\right)} \cdot x \]

   6. Taylor expanded in y1 around inf 58.3%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x\right)\right)} \]

   if 3.15e155 < x

   1. Initial program 20.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 33.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 33.9%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 33.9%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 33.9%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 34.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   8. Taylor expanded in y around inf 37.2%

      \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

   9. Taylor expanded in a around 0 42.1%

      \[\leadsto \color{blue}{y \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 42.1%

          \[\leadsto y \cdot \color{blue}{\left(\left(b \cdot x\right) \cdot a\right)} \]

       2. associate-*l* 49.8%

          \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(x \cdot a\right)\right)} \]

   11. Simplified 49.8%

       \[\leadsto \color{blue}{y \cdot \left(b \cdot \left(x \cdot a\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 35.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+104}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(x \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+47}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+125}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 3.15 \cdot 10^{+155}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a\right)\right)\\ \end{array} \]

Alternative 27: 27.7% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -8 \cdot 10^{+128}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(y3 \cdot \left(-y1\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -1.85 \cdot 10^{-22}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(t \cdot b\right)\right)\\ \mathbf{elif}\;y1 \leq 2.6 \cdot 10^{+189}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y1 -8e+128)
   (* y4 (* j (* y3 (- y1))))
   (if (<= y1 -1.85e-22)
     (* y4 (* j (* t b)))
     (if (<= y1 2.6e+189)
       (* a (* b (- (* x y) (* z t))))
       (* x (* j (* i 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 tmp;
	if (y1 <= -8e+128) {
		tmp = y4 * (j * (y3 * -y1));
	} else if (y1 <= -1.85e-22) {
		tmp = y4 * (j * (t * b));
	} else if (y1 <= 2.6e+189) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = x * (j * (i * 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) :: tmp
    if (y1 <= (-8d+128)) then
        tmp = y4 * (j * (y3 * -y1))
    else if (y1 <= (-1.85d-22)) then
        tmp = y4 * (j * (t * b))
    else if (y1 <= 2.6d+189) then
        tmp = a * (b * ((x * y) - (z * t)))
    else
        tmp = x * (j * (i * 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 tmp;
	if (y1 <= -8e+128) {
		tmp = y4 * (j * (y3 * -y1));
	} else if (y1 <= -1.85e-22) {
		tmp = y4 * (j * (t * b));
	} else if (y1 <= 2.6e+189) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = x * (j * (i * y1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y1 <= -8e+128:
		tmp = y4 * (j * (y3 * -y1))
	elif y1 <= -1.85e-22:
		tmp = y4 * (j * (t * b))
	elif y1 <= 2.6e+189:
		tmp = a * (b * ((x * y) - (z * t)))
	else:
		tmp = x * (j * (i * y1))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y1 <= -8e+128)
		tmp = Float64(y4 * Float64(j * Float64(y3 * Float64(-y1))));
	elseif (y1 <= -1.85e-22)
		tmp = Float64(y4 * Float64(j * Float64(t * b)));
	elseif (y1 <= 2.6e+189)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	else
		tmp = Float64(x * Float64(j * Float64(i * 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)
	tmp = 0.0;
	if (y1 <= -8e+128)
		tmp = y4 * (j * (y3 * -y1));
	elseif (y1 <= -1.85e-22)
		tmp = y4 * (j * (t * b));
	elseif (y1 <= 2.6e+189)
		tmp = a * (b * ((x * y) - (z * t)));
	else
		tmp = x * (j * (i * y1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y1, -8e+128], N[(y4 * N[(j * N[(y3 * (-y1)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -1.85e-22], N[(y4 * N[(j * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 2.6e+189], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(j * N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y1 < -8.0000000000000006e128

   1. Initial program 21.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 21.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 46.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in j around inf 39.8%

      \[\leadsto \color{blue}{y4 \cdot \left(j \cdot \left(t \cdot b + -1 \cdot \left(y1 \cdot y3\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 30.5%

         \[\leadsto \color{blue}{\left(y4 \cdot j\right) \cdot \left(t \cdot b + -1 \cdot \left(y1 \cdot y3\right)\right)} \]

      2. *-commutative 30.5%

         \[\leadsto \color{blue}{\left(j \cdot y4\right)} \cdot \left(t \cdot b + -1 \cdot \left(y1 \cdot y3\right)\right) \]

      3. mul-1-neg 30.5%

         \[\leadsto \left(j \cdot y4\right) \cdot \left(t \cdot b + \color{blue}{\left(-y1 \cdot y3\right)}\right) \]

      4. sub-neg 30.5%

         \[\leadsto \left(j \cdot y4\right) \cdot \color{blue}{\left(t \cdot b - y1 \cdot y3\right)} \]

      5. *-commutative 30.5%

         \[\leadsto \left(j \cdot y4\right) \cdot \left(\color{blue}{b \cdot t} - y1 \cdot y3\right) \]

   7. Simplified 30.5%

      \[\leadsto \color{blue}{\left(j \cdot y4\right) \cdot \left(b \cdot t - y1 \cdot y3\right)} \]

   8. Taylor expanded in b around 0 40.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y4 \cdot \left(y1 \cdot \left(y3 \cdot j\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 40.0%

         \[\leadsto \color{blue}{-y4 \cdot \left(y1 \cdot \left(y3 \cdot j\right)\right)} \]

      2. distribute-rgt-neg-in 40.0%

         \[\leadsto \color{blue}{y4 \cdot \left(-y1 \cdot \left(y3 \cdot j\right)\right)} \]

      3. associate-*r* 40.0%

         \[\leadsto y4 \cdot \left(-\color{blue}{\left(y1 \cdot y3\right) \cdot j}\right) \]

      4. *-commutative 40.0%

         \[\leadsto y4 \cdot \left(-\color{blue}{j \cdot \left(y1 \cdot y3\right)}\right) \]

   10. Simplified 40.0%

       \[\leadsto \color{blue}{y4 \cdot \left(-j \cdot \left(y1 \cdot y3\right)\right)} \]

   if -8.0000000000000006e128 < y1 < -1.85e-22

   1. Initial program 21.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 21.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 34.1%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 34.1%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

      2. mul-1-neg 34.1%

         \[\leadsto t \cdot \left(\color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)} + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right) \]

   6. Simplified 34.1%

      \[\leadsto \color{blue}{t \cdot \left(\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

   7. Taylor expanded in j around inf 40.8%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} \]

   8. Taylor expanded in y4 around inf 37.5%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 40.4%

         \[\leadsto y4 \cdot \color{blue}{\left(\left(t \cdot b\right) \cdot j\right)} \]

   10. Simplified 40.4%

       \[\leadsto \color{blue}{y4 \cdot \left(\left(t \cdot b\right) \cdot j\right)} \]

   if -1.85e-22 < y1 < 2.59999999999999981e189

   1. Initial program 32.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 37.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 41.4%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 41.4%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 41.4%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 41.4%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 37.4%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   if 2.59999999999999981e189 < y1

   1. Initial program 18.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 18.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 50.5%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in j around inf 55.3%

      \[\leadsto \color{blue}{\left(j \cdot \left(y1 \cdot i - y0 \cdot b\right)\right)} \cdot x \]

   6. Taylor expanded in y1 around inf 47.3%

      \[\leadsto \color{blue}{\left(i \cdot \left(y1 \cdot j\right)\right)} \cdot x \]
   7. Step-by-step derivation

      1. *-commutative 47.3%

         \[\leadsto \color{blue}{\left(\left(y1 \cdot j\right) \cdot i\right)} \cdot x \]

      2. *-commutative 47.3%

         \[\leadsto \left(\color{blue}{\left(j \cdot y1\right)} \cdot i\right) \cdot x \]

      3. associate-*l* 55.7%

         \[\leadsto \color{blue}{\left(j \cdot \left(y1 \cdot i\right)\right)} \cdot x \]

   8. Simplified 55.7%

      \[\leadsto \color{blue}{\left(j \cdot \left(y1 \cdot i\right)\right)} \cdot x \]
3. Recombined 4 regimes into one program.

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -8 \cdot 10^{+128}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(y3 \cdot \left(-y1\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -1.85 \cdot 10^{-22}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(t \cdot b\right)\right)\\ \mathbf{elif}\;y1 \leq 2.6 \cdot 10^{+189}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1\right)\right)\\ \end{array} \]

Alternative 28: 28.9% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -1.08 \cdot 10^{+273}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(y3 \cdot \left(-y1\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -4.7 \cdot 10^{-76}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 1.45 \cdot 10^{+193}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y1 -1.08e+273)
   (* y4 (* j (* y3 (- y1))))
   (if (<= y1 -4.7e-76)
     (* b (* y0 (- (* z k) (* x j))))
     (if (<= y1 1.45e+193)
       (* a (* b (- (* x y) (* z t))))
       (* x (* j (* i 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 tmp;
	if (y1 <= -1.08e+273) {
		tmp = y4 * (j * (y3 * -y1));
	} else if (y1 <= -4.7e-76) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y1 <= 1.45e+193) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = x * (j * (i * 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) :: tmp
    if (y1 <= (-1.08d+273)) then
        tmp = y4 * (j * (y3 * -y1))
    else if (y1 <= (-4.7d-76)) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (y1 <= 1.45d+193) then
        tmp = a * (b * ((x * y) - (z * t)))
    else
        tmp = x * (j * (i * 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 tmp;
	if (y1 <= -1.08e+273) {
		tmp = y4 * (j * (y3 * -y1));
	} else if (y1 <= -4.7e-76) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y1 <= 1.45e+193) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = x * (j * (i * y1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y1 <= -1.08e+273:
		tmp = y4 * (j * (y3 * -y1))
	elif y1 <= -4.7e-76:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif y1 <= 1.45e+193:
		tmp = a * (b * ((x * y) - (z * t)))
	else:
		tmp = x * (j * (i * y1))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y1 <= -1.08e+273)
		tmp = Float64(y4 * Float64(j * Float64(y3 * Float64(-y1))));
	elseif (y1 <= -4.7e-76)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (y1 <= 1.45e+193)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	else
		tmp = Float64(x * Float64(j * Float64(i * 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)
	tmp = 0.0;
	if (y1 <= -1.08e+273)
		tmp = y4 * (j * (y3 * -y1));
	elseif (y1 <= -4.7e-76)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (y1 <= 1.45e+193)
		tmp = a * (b * ((x * y) - (z * t)));
	else
		tmp = x * (j * (i * y1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y1, -1.08e+273], N[(y4 * N[(j * N[(y3 * (-y1)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -4.7e-76], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.45e+193], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(j * N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y1 < -1.08000000000000005e273

   1. Initial program 16.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 16.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 50.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in j around inf 67.1%

      \[\leadsto \color{blue}{y4 \cdot \left(j \cdot \left(t \cdot b + -1 \cdot \left(y1 \cdot y3\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 43.0%

         \[\leadsto \color{blue}{\left(y4 \cdot j\right) \cdot \left(t \cdot b + -1 \cdot \left(y1 \cdot y3\right)\right)} \]

      2. *-commutative 43.0%

         \[\leadsto \color{blue}{\left(j \cdot y4\right)} \cdot \left(t \cdot b + -1 \cdot \left(y1 \cdot y3\right)\right) \]

      3. mul-1-neg 43.0%

         \[\leadsto \left(j \cdot y4\right) \cdot \left(t \cdot b + \color{blue}{\left(-y1 \cdot y3\right)}\right) \]

      4. sub-neg 43.0%

         \[\leadsto \left(j \cdot y4\right) \cdot \color{blue}{\left(t \cdot b - y1 \cdot y3\right)} \]

      5. *-commutative 43.0%

         \[\leadsto \left(j \cdot y4\right) \cdot \left(\color{blue}{b \cdot t} - y1 \cdot y3\right) \]

   7. Simplified 43.0%

      \[\leadsto \color{blue}{\left(j \cdot y4\right) \cdot \left(b \cdot t - y1 \cdot y3\right)} \]

   8. Taylor expanded in b around 0 67.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y4 \cdot \left(y1 \cdot \left(y3 \cdot j\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 67.0%

         \[\leadsto \color{blue}{-y4 \cdot \left(y1 \cdot \left(y3 \cdot j\right)\right)} \]

      2. distribute-rgt-neg-in 67.0%

         \[\leadsto \color{blue}{y4 \cdot \left(-y1 \cdot \left(y3 \cdot j\right)\right)} \]

      3. associate-*r* 67.0%

         \[\leadsto y4 \cdot \left(-\color{blue}{\left(y1 \cdot y3\right) \cdot j}\right) \]

      4. *-commutative 67.0%

         \[\leadsto y4 \cdot \left(-\color{blue}{j \cdot \left(y1 \cdot y3\right)}\right) \]

   10. Simplified 67.0%

       \[\leadsto \color{blue}{y4 \cdot \left(-j \cdot \left(y1 \cdot y3\right)\right)} \]

   if -1.08000000000000005e273 < y1 < -4.7000000000000002e-76

   1. Initial program 20.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 20.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 39.7%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot b} \]

   5. Taylor expanded in y0 around inf 31.1%

      \[\leadsto \color{blue}{\left(k \cdot z - j \cdot x\right) \cdot \left(y0 \cdot b\right)} \]
   6. Step-by-step derivation

      1. *-commutative 31.1%

         \[\leadsto \color{blue}{\left(y0 \cdot b\right) \cdot \left(k \cdot z - j \cdot x\right)} \]

      2. *-commutative 31.1%

         \[\leadsto \color{blue}{\left(b \cdot y0\right)} \cdot \left(k \cdot z - j \cdot x\right) \]

      3. associate-*l* 37.6%

         \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   7. Simplified 37.6%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   if -4.7000000000000002e-76 < y1 < 1.45000000000000007e193

   1. Initial program 34.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 39.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 41.3%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 41.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 41.3%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 41.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 38.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   if 1.45000000000000007e193 < y1

   1. Initial program 18.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 18.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 50.5%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in j around inf 55.3%

      \[\leadsto \color{blue}{\left(j \cdot \left(y1 \cdot i - y0 \cdot b\right)\right)} \cdot x \]

   6. Taylor expanded in y1 around inf 47.3%

      \[\leadsto \color{blue}{\left(i \cdot \left(y1 \cdot j\right)\right)} \cdot x \]
   7. Step-by-step derivation

      1. *-commutative 47.3%

         \[\leadsto \color{blue}{\left(\left(y1 \cdot j\right) \cdot i\right)} \cdot x \]

      2. *-commutative 47.3%

         \[\leadsto \left(\color{blue}{\left(j \cdot y1\right)} \cdot i\right) \cdot x \]

      3. associate-*l* 55.7%

         \[\leadsto \color{blue}{\left(j \cdot \left(y1 \cdot i\right)\right)} \cdot x \]

   8. Simplified 55.7%

      \[\leadsto \color{blue}{\left(j \cdot \left(y1 \cdot i\right)\right)} \cdot x \]
3. Recombined 4 regimes into one program.

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -1.08 \cdot 10^{+273}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(y3 \cdot \left(-y1\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -4.7 \cdot 10^{-76}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 1.45 \cdot 10^{+193}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1\right)\right)\\ \end{array} \]

Alternative 29: 22.8% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+104}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(x \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;x \leq -9.8 \cdot 10^{+25}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-126}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+47}:\\ \;\;\;\;\left(t \cdot i\right) \cdot \left(j \cdot \left(-y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -2.8e+104)
   (* y0 (* j (* x (- b))))
   (if (<= x -9.8e+25)
     (* x (* j (* i y1)))
     (if (<= x 1.5e-126)
       (* y4 (* t (* b j)))
       (if (<= x 3e+47) (* (* t i) (* j (- y5))) (* y (* b (* x a))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -2.8e+104) {
		tmp = y0 * (j * (x * -b));
	} else if (x <= -9.8e+25) {
		tmp = x * (j * (i * y1));
	} else if (x <= 1.5e-126) {
		tmp = y4 * (t * (b * j));
	} else if (x <= 3e+47) {
		tmp = (t * i) * (j * -y5);
	} else {
		tmp = y * (b * (x * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (x <= (-2.8d+104)) then
        tmp = y0 * (j * (x * -b))
    else if (x <= (-9.8d+25)) then
        tmp = x * (j * (i * y1))
    else if (x <= 1.5d-126) then
        tmp = y4 * (t * (b * j))
    else if (x <= 3d+47) then
        tmp = (t * i) * (j * -y5)
    else
        tmp = y * (b * (x * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -2.8e+104) {
		tmp = y0 * (j * (x * -b));
	} else if (x <= -9.8e+25) {
		tmp = x * (j * (i * y1));
	} else if (x <= 1.5e-126) {
		tmp = y4 * (t * (b * j));
	} else if (x <= 3e+47) {
		tmp = (t * i) * (j * -y5);
	} else {
		tmp = y * (b * (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if x <= -2.8e+104:
		tmp = y0 * (j * (x * -b))
	elif x <= -9.8e+25:
		tmp = x * (j * (i * y1))
	elif x <= 1.5e-126:
		tmp = y4 * (t * (b * j))
	elif x <= 3e+47:
		tmp = (t * i) * (j * -y5)
	else:
		tmp = y * (b * (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (x <= -2.8e+104)
		tmp = Float64(y0 * Float64(j * Float64(x * Float64(-b))));
	elseif (x <= -9.8e+25)
		tmp = Float64(x * Float64(j * Float64(i * y1)));
	elseif (x <= 1.5e-126)
		tmp = Float64(y4 * Float64(t * Float64(b * j)));
	elseif (x <= 3e+47)
		tmp = Float64(Float64(t * i) * Float64(j * Float64(-y5)));
	else
		tmp = Float64(y * Float64(b * Float64(x * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (x <= -2.8e+104)
		tmp = y0 * (j * (x * -b));
	elseif (x <= -9.8e+25)
		tmp = x * (j * (i * y1));
	elseif (x <= 1.5e-126)
		tmp = y4 * (t * (b * j));
	elseif (x <= 3e+47)
		tmp = (t * i) * (j * -y5);
	else
		tmp = y * (b * (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[x, -2.8e+104], N[(y0 * N[(j * N[(x * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -9.8e+25], N[(x * N[(j * N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.5e-126], N[(y4 * N[(t * N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3e+47], N[(N[(t * i), $MachinePrecision] * N[(j * (-y5)), $MachinePrecision]), $MachinePrecision], N[(y * N[(b * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2.8e104

   1. Initial program 31.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 64.2%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in j around inf 37.2%

      \[\leadsto \color{blue}{\left(j \cdot \left(y1 \cdot i - y0 \cdot b\right)\right)} \cdot x \]

   6. Taylor expanded in y1 around 0 44.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(j \cdot \left(b \cdot x\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 44.6%

         \[\leadsto \color{blue}{-y0 \cdot \left(j \cdot \left(b \cdot x\right)\right)} \]

   8. Simplified 44.6%

      \[\leadsto \color{blue}{-y0 \cdot \left(j \cdot \left(b \cdot x\right)\right)} \]

   if -2.8e104 < x < -9.8000000000000002e25

   1. Initial program 29.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 29.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 41.8%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in j around inf 48.2%

      \[\leadsto \color{blue}{\left(j \cdot \left(y1 \cdot i - y0 \cdot b\right)\right)} \cdot x \]

   6. Taylor expanded in y1 around inf 37.3%

      \[\leadsto \color{blue}{\left(i \cdot \left(y1 \cdot j\right)\right)} \cdot x \]
   7. Step-by-step derivation

      1. *-commutative 37.3%

         \[\leadsto \color{blue}{\left(\left(y1 \cdot j\right) \cdot i\right)} \cdot x \]

      2. *-commutative 37.3%

         \[\leadsto \left(\color{blue}{\left(j \cdot y1\right)} \cdot i\right) \cdot x \]

      3. associate-*l* 48.3%

         \[\leadsto \color{blue}{\left(j \cdot \left(y1 \cdot i\right)\right)} \cdot x \]

   8. Simplified 48.3%

      \[\leadsto \color{blue}{\left(j \cdot \left(y1 \cdot i\right)\right)} \cdot x \]

   if -9.8000000000000002e25 < x < 1.5000000000000001e-126

   1. Initial program 31.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 41.6%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 41.6%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

      2. mul-1-neg 41.6%

         \[\leadsto t \cdot \left(\color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)} + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right) \]

   6. Simplified 41.6%

      \[\leadsto \color{blue}{t \cdot \left(\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

   7. Taylor expanded in j around inf 28.1%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} \]

   8. Taylor expanded in b around inf 28.3%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b\right)\right)} \]

   if 1.5000000000000001e-126 < x < 3.0000000000000001e47

   1. Initial program 22.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 22.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 33.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 33.4%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

      2. mul-1-neg 33.4%

         \[\leadsto t \cdot \left(\color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)} + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right) \]

   6. Simplified 33.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

   7. Taylor expanded in y5 around -inf 23.9%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(i \cdot j - a \cdot y2\right) \cdot \left(t \cdot y5\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 23.9%

         \[\leadsto \color{blue}{-\left(i \cdot j - a \cdot y2\right) \cdot \left(t \cdot y5\right)} \]

      2. *-commutative 23.9%

         \[\leadsto -\color{blue}{\left(t \cdot y5\right) \cdot \left(i \cdot j - a \cdot y2\right)} \]

   9. Simplified 23.9%

      \[\leadsto \color{blue}{-\left(t \cdot y5\right) \cdot \left(i \cdot j - a \cdot y2\right)} \]

   10. Taylor expanded in i around inf 26.9%

       \[\leadsto -\color{blue}{i \cdot \left(t \cdot \left(j \cdot y5\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 31.5%

          \[\leadsto -\color{blue}{\left(i \cdot t\right) \cdot \left(j \cdot y5\right)} \]

       2. *-commutative 31.5%

          \[\leadsto -\color{blue}{\left(j \cdot y5\right) \cdot \left(i \cdot t\right)} \]

   12. Simplified 31.5%

       \[\leadsto -\color{blue}{\left(j \cdot y5\right) \cdot \left(i \cdot t\right)} \]

   if 3.0000000000000001e47 < x

   1. Initial program 25.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 34.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 42.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 42.8%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 42.8%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 42.8%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 35.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   8. Taylor expanded in y around inf 34.1%

      \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

   9. Taylor expanded in a around 0 34.1%

      \[\leadsto \color{blue}{y \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 34.1%

          \[\leadsto y \cdot \color{blue}{\left(\left(b \cdot x\right) \cdot a\right)} \]

       2. associate-*l* 37.3%

          \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(x \cdot a\right)\right)} \]

   11. Simplified 37.3%

       \[\leadsto \color{blue}{y \cdot \left(b \cdot \left(x \cdot a\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 34.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+104}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(x \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;x \leq -9.8 \cdot 10^{+25}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-126}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+47}:\\ \;\;\;\;\left(t \cdot i\right) \cdot \left(j \cdot \left(-y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a\right)\right)\\ \end{array} \]

Alternative 30: 22.7% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+106}:\\ \;\;\;\;b \cdot \left(j \cdot \left(x \cdot \left(-y0\right)\right)\right)\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-124}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+48}:\\ \;\;\;\;\left(t \cdot i\right) \cdot \left(j \cdot \left(-y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -1.1e+106)
   (* b (* j (* x (- y0))))
   (if (<= x -5.2e+23)
     (* x (* j (* i y1)))
     (if (<= x 1.75e-124)
       (* y4 (* t (* b j)))
       (if (<= x 8.2e+48) (* (* t i) (* j (- y5))) (* y (* b (* x a))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -1.1e+106) {
		tmp = b * (j * (x * -y0));
	} else if (x <= -5.2e+23) {
		tmp = x * (j * (i * y1));
	} else if (x <= 1.75e-124) {
		tmp = y4 * (t * (b * j));
	} else if (x <= 8.2e+48) {
		tmp = (t * i) * (j * -y5);
	} else {
		tmp = y * (b * (x * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (x <= (-1.1d+106)) then
        tmp = b * (j * (x * -y0))
    else if (x <= (-5.2d+23)) then
        tmp = x * (j * (i * y1))
    else if (x <= 1.75d-124) then
        tmp = y4 * (t * (b * j))
    else if (x <= 8.2d+48) then
        tmp = (t * i) * (j * -y5)
    else
        tmp = y * (b * (x * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -1.1e+106) {
		tmp = b * (j * (x * -y0));
	} else if (x <= -5.2e+23) {
		tmp = x * (j * (i * y1));
	} else if (x <= 1.75e-124) {
		tmp = y4 * (t * (b * j));
	} else if (x <= 8.2e+48) {
		tmp = (t * i) * (j * -y5);
	} else {
		tmp = y * (b * (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if x <= -1.1e+106:
		tmp = b * (j * (x * -y0))
	elif x <= -5.2e+23:
		tmp = x * (j * (i * y1))
	elif x <= 1.75e-124:
		tmp = y4 * (t * (b * j))
	elif x <= 8.2e+48:
		tmp = (t * i) * (j * -y5)
	else:
		tmp = y * (b * (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (x <= -1.1e+106)
		tmp = Float64(b * Float64(j * Float64(x * Float64(-y0))));
	elseif (x <= -5.2e+23)
		tmp = Float64(x * Float64(j * Float64(i * y1)));
	elseif (x <= 1.75e-124)
		tmp = Float64(y4 * Float64(t * Float64(b * j)));
	elseif (x <= 8.2e+48)
		tmp = Float64(Float64(t * i) * Float64(j * Float64(-y5)));
	else
		tmp = Float64(y * Float64(b * Float64(x * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (x <= -1.1e+106)
		tmp = b * (j * (x * -y0));
	elseif (x <= -5.2e+23)
		tmp = x * (j * (i * y1));
	elseif (x <= 1.75e-124)
		tmp = y4 * (t * (b * j));
	elseif (x <= 8.2e+48)
		tmp = (t * i) * (j * -y5);
	else
		tmp = y * (b * (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[x, -1.1e+106], N[(b * N[(j * N[(x * (-y0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.2e+23], N[(x * N[(j * N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.75e-124], N[(y4 * N[(t * N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.2e+48], N[(N[(t * i), $MachinePrecision] * N[(j * (-y5)), $MachinePrecision]), $MachinePrecision], N[(y * N[(b * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.09999999999999996e106

   1. Initial program 31.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 64.2%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in j around inf 37.2%

      \[\leadsto \color{blue}{\left(j \cdot \left(y1 \cdot i - y0 \cdot b\right)\right)} \cdot x \]

   6. Taylor expanded in y1 around 0 42.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y0 \cdot \left(j \cdot b\right)\right)\right)} \cdot x \]
   7. Step-by-step derivation

      1. mul-1-neg 42.0%

         \[\leadsto \color{blue}{\left(-y0 \cdot \left(j \cdot b\right)\right)} \cdot x \]

      2. *-commutative 42.0%

         \[\leadsto \left(-y0 \cdot \color{blue}{\left(b \cdot j\right)}\right) \cdot x \]

      3. distribute-rgt-neg-in 42.0%

         \[\leadsto \color{blue}{\left(y0 \cdot \left(-b \cdot j\right)\right)} \cdot x \]

      4. *-commutative 42.0%

         \[\leadsto \left(y0 \cdot \left(-\color{blue}{j \cdot b}\right)\right) \cdot x \]

      5. distribute-rgt-neg-in 42.0%

         \[\leadsto \left(y0 \cdot \color{blue}{\left(j \cdot \left(-b\right)\right)}\right) \cdot x \]

   8. Simplified 42.0%

      \[\leadsto \color{blue}{\left(y0 \cdot \left(j \cdot \left(-b\right)\right)\right)} \cdot x \]

   9. Taylor expanded in y0 around 0 44.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(j \cdot \left(b \cdot x\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 44.6%

          \[\leadsto \color{blue}{-y0 \cdot \left(j \cdot \left(b \cdot x\right)\right)} \]

       2. associate-*r* 44.5%

          \[\leadsto -y0 \cdot \color{blue}{\left(\left(j \cdot b\right) \cdot x\right)} \]

       3. *-commutative 44.5%

          \[\leadsto -y0 \cdot \left(\color{blue}{\left(b \cdot j\right)} \cdot x\right) \]

       4. associate-*r* 49.4%

          \[\leadsto -y0 \cdot \color{blue}{\left(b \cdot \left(j \cdot x\right)\right)} \]

       5. associate-*r* 44.6%

          \[\leadsto -\color{blue}{\left(y0 \cdot b\right) \cdot \left(j \cdot x\right)} \]

       6. *-commutative 44.6%

          \[\leadsto -\color{blue}{\left(b \cdot y0\right)} \cdot \left(j \cdot x\right) \]

       7. associate-*l* 44.5%

          \[\leadsto -\color{blue}{b \cdot \left(y0 \cdot \left(j \cdot x\right)\right)} \]

       8. distribute-rgt-neg-in 44.5%

          \[\leadsto \color{blue}{b \cdot \left(-y0 \cdot \left(j \cdot x\right)\right)} \]

       9. *-commutative 44.5%

          \[\leadsto b \cdot \left(-\color{blue}{\left(j \cdot x\right) \cdot y0}\right) \]

       10. associate-*l* 47.0%

           \[\leadsto b \cdot \left(-\color{blue}{j \cdot \left(x \cdot y0\right)}\right) \]

       11. *-commutative 47.0%

           \[\leadsto b \cdot \left(-j \cdot \color{blue}{\left(y0 \cdot x\right)}\right) \]

       12. distribute-rgt-neg-in 47.0%

           \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(-y0 \cdot x\right)\right)} \]

   11. Simplified 47.0%

       \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(-y0 \cdot x\right)\right)} \]

   if -1.09999999999999996e106 < x < -5.19999999999999983e23

   1. Initial program 29.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 29.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 41.8%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in j around inf 48.2%

      \[\leadsto \color{blue}{\left(j \cdot \left(y1 \cdot i - y0 \cdot b\right)\right)} \cdot x \]

   6. Taylor expanded in y1 around inf 37.3%

      \[\leadsto \color{blue}{\left(i \cdot \left(y1 \cdot j\right)\right)} \cdot x \]
   7. Step-by-step derivation

      1. *-commutative 37.3%

         \[\leadsto \color{blue}{\left(\left(y1 \cdot j\right) \cdot i\right)} \cdot x \]

      2. *-commutative 37.3%

         \[\leadsto \left(\color{blue}{\left(j \cdot y1\right)} \cdot i\right) \cdot x \]

      3. associate-*l* 48.3%

         \[\leadsto \color{blue}{\left(j \cdot \left(y1 \cdot i\right)\right)} \cdot x \]

   8. Simplified 48.3%

      \[\leadsto \color{blue}{\left(j \cdot \left(y1 \cdot i\right)\right)} \cdot x \]

   if -5.19999999999999983e23 < x < 1.7499999999999999e-124

   1. Initial program 31.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 41.6%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 41.6%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

      2. mul-1-neg 41.6%

         \[\leadsto t \cdot \left(\color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)} + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right) \]

   6. Simplified 41.6%

      \[\leadsto \color{blue}{t \cdot \left(\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

   7. Taylor expanded in j around inf 28.1%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} \]

   8. Taylor expanded in b around inf 28.3%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b\right)\right)} \]

   if 1.7499999999999999e-124 < x < 8.2000000000000005e48

   1. Initial program 22.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 22.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 33.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 33.4%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

      2. mul-1-neg 33.4%

         \[\leadsto t \cdot \left(\color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)} + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right) \]

   6. Simplified 33.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

   7. Taylor expanded in y5 around -inf 23.9%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(i \cdot j - a \cdot y2\right) \cdot \left(t \cdot y5\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 23.9%

         \[\leadsto \color{blue}{-\left(i \cdot j - a \cdot y2\right) \cdot \left(t \cdot y5\right)} \]

      2. *-commutative 23.9%

         \[\leadsto -\color{blue}{\left(t \cdot y5\right) \cdot \left(i \cdot j - a \cdot y2\right)} \]

   9. Simplified 23.9%

      \[\leadsto \color{blue}{-\left(t \cdot y5\right) \cdot \left(i \cdot j - a \cdot y2\right)} \]

   10. Taylor expanded in i around inf 26.9%

       \[\leadsto -\color{blue}{i \cdot \left(t \cdot \left(j \cdot y5\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 31.5%

          \[\leadsto -\color{blue}{\left(i \cdot t\right) \cdot \left(j \cdot y5\right)} \]

       2. *-commutative 31.5%

          \[\leadsto -\color{blue}{\left(j \cdot y5\right) \cdot \left(i \cdot t\right)} \]

   12. Simplified 31.5%

       \[\leadsto -\color{blue}{\left(j \cdot y5\right) \cdot \left(i \cdot t\right)} \]

   if 8.2000000000000005e48 < x

   1. Initial program 25.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 34.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 42.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 42.8%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 42.8%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 42.8%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 35.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   8. Taylor expanded in y around inf 34.1%

      \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

   9. Taylor expanded in a around 0 34.1%

      \[\leadsto \color{blue}{y \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 34.1%

          \[\leadsto y \cdot \color{blue}{\left(\left(b \cdot x\right) \cdot a\right)} \]

       2. associate-*l* 37.3%

          \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(x \cdot a\right)\right)} \]

   11. Simplified 37.3%

       \[\leadsto \color{blue}{y \cdot \left(b \cdot \left(x \cdot a\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 35.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+106}:\\ \;\;\;\;b \cdot \left(j \cdot \left(x \cdot \left(-y0\right)\right)\right)\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-124}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+48}:\\ \;\;\;\;\left(t \cdot i\right) \cdot \left(j \cdot \left(-y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a\right)\right)\\ \end{array} \]

Alternative 31: 22.6% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-62}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+47}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+125}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{+151}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -3.2e-62)
   (* a (* y (* x b)))
   (if (<= x 2.3e+47)
     (* y4 (* t (* b j)))
     (if (<= x 3e+125)
       (* a (* b (* x y)))
       (if (<= x 2.25e+151) (* i (* y1 (* x j))) (* y (* b (* x a))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -3.2e-62) {
		tmp = a * (y * (x * b));
	} else if (x <= 2.3e+47) {
		tmp = y4 * (t * (b * j));
	} else if (x <= 3e+125) {
		tmp = a * (b * (x * y));
	} else if (x <= 2.25e+151) {
		tmp = i * (y1 * (x * j));
	} else {
		tmp = y * (b * (x * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (x <= (-3.2d-62)) then
        tmp = a * (y * (x * b))
    else if (x <= 2.3d+47) then
        tmp = y4 * (t * (b * j))
    else if (x <= 3d+125) then
        tmp = a * (b * (x * y))
    else if (x <= 2.25d+151) then
        tmp = i * (y1 * (x * j))
    else
        tmp = y * (b * (x * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -3.2e-62) {
		tmp = a * (y * (x * b));
	} else if (x <= 2.3e+47) {
		tmp = y4 * (t * (b * j));
	} else if (x <= 3e+125) {
		tmp = a * (b * (x * y));
	} else if (x <= 2.25e+151) {
		tmp = i * (y1 * (x * j));
	} else {
		tmp = y * (b * (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if x <= -3.2e-62:
		tmp = a * (y * (x * b))
	elif x <= 2.3e+47:
		tmp = y4 * (t * (b * j))
	elif x <= 3e+125:
		tmp = a * (b * (x * y))
	elif x <= 2.25e+151:
		tmp = i * (y1 * (x * j))
	else:
		tmp = y * (b * (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (x <= -3.2e-62)
		tmp = Float64(a * Float64(y * Float64(x * b)));
	elseif (x <= 2.3e+47)
		tmp = Float64(y4 * Float64(t * Float64(b * j)));
	elseif (x <= 3e+125)
		tmp = Float64(a * Float64(b * Float64(x * y)));
	elseif (x <= 2.25e+151)
		tmp = Float64(i * Float64(y1 * Float64(x * j)));
	else
		tmp = Float64(y * Float64(b * Float64(x * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (x <= -3.2e-62)
		tmp = a * (y * (x * b));
	elseif (x <= 2.3e+47)
		tmp = y4 * (t * (b * j));
	elseif (x <= 3e+125)
		tmp = a * (b * (x * y));
	elseif (x <= 2.25e+151)
		tmp = i * (y1 * (x * j));
	else
		tmp = y * (b * (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[x, -3.2e-62], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.3e+47], N[(y4 * N[(t * N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3e+125], N[(a * N[(b * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.25e+151], N[(i * N[(y1 * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(b * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -3.20000000000000021e-62

   1. Initial program 31.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 37.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 40.1%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 40.1%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 40.1%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 40.1%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 42.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   8. Taylor expanded in y around inf 32.0%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(b \cdot x\right)\right)} \]

   if -3.20000000000000021e-62 < x < 2.2999999999999999e47

   1. Initial program 28.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 38.2%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 38.2%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

      2. mul-1-neg 38.2%

         \[\leadsto t \cdot \left(\color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)} + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right) \]

   6. Simplified 38.2%

      \[\leadsto \color{blue}{t \cdot \left(\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

   7. Taylor expanded in j around inf 28.6%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} \]

   8. Taylor expanded in b around inf 26.7%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b\right)\right)} \]

   if 2.2999999999999999e47 < x < 3.00000000000000015e125

   1. Initial program 26.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 42.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 63.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 63.2%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 63.2%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 63.2%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 42.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   8. Taylor expanded in y around inf 32.7%

      \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

   if 3.00000000000000015e125 < x < 2.2499999999999999e151

   1. Initial program 42.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 42.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 44.5%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in j around inf 44.4%

      \[\leadsto \color{blue}{\left(j \cdot \left(y1 \cdot i - y0 \cdot b\right)\right)} \cdot x \]

   6. Taylor expanded in y1 around inf 58.3%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x\right)\right)} \]

   if 2.2499999999999999e151 < x

   1. Initial program 20.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 33.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 33.9%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 33.9%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 33.9%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 34.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   8. Taylor expanded in y around inf 37.2%

      \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

   9. Taylor expanded in a around 0 42.1%

      \[\leadsto \color{blue}{y \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 42.1%

          \[\leadsto y \cdot \color{blue}{\left(\left(b \cdot x\right) \cdot a\right)} \]

       2. associate-*l* 49.8%

          \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(x \cdot a\right)\right)} \]

   11. Simplified 49.8%

       \[\leadsto \color{blue}{y \cdot \left(b \cdot \left(x \cdot a\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 33.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-62}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+47}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+125}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{+151}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a\right)\right)\\ \end{array} \]

Alternative 32: 21.9% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-62}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-90}:\\ \;\;\;\;t \cdot \left(j \cdot \left(b \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+156}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -6e-62)
   (* a (* y (* x b)))
   (if (<= x 3.3e-90)
     (* t (* j (* b y4)))
     (if (<= x 2.9e+156) (* i (* y1 (* x j))) (* y (* b (* x a)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -6e-62) {
		tmp = a * (y * (x * b));
	} else if (x <= 3.3e-90) {
		tmp = t * (j * (b * y4));
	} else if (x <= 2.9e+156) {
		tmp = i * (y1 * (x * j));
	} else {
		tmp = y * (b * (x * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (x <= (-6d-62)) then
        tmp = a * (y * (x * b))
    else if (x <= 3.3d-90) then
        tmp = t * (j * (b * y4))
    else if (x <= 2.9d+156) then
        tmp = i * (y1 * (x * j))
    else
        tmp = y * (b * (x * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -6e-62) {
		tmp = a * (y * (x * b));
	} else if (x <= 3.3e-90) {
		tmp = t * (j * (b * y4));
	} else if (x <= 2.9e+156) {
		tmp = i * (y1 * (x * j));
	} else {
		tmp = y * (b * (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if x <= -6e-62:
		tmp = a * (y * (x * b))
	elif x <= 3.3e-90:
		tmp = t * (j * (b * y4))
	elif x <= 2.9e+156:
		tmp = i * (y1 * (x * j))
	else:
		tmp = y * (b * (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (x <= -6e-62)
		tmp = Float64(a * Float64(y * Float64(x * b)));
	elseif (x <= 3.3e-90)
		tmp = Float64(t * Float64(j * Float64(b * y4)));
	elseif (x <= 2.9e+156)
		tmp = Float64(i * Float64(y1 * Float64(x * j)));
	else
		tmp = Float64(y * Float64(b * Float64(x * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (x <= -6e-62)
		tmp = a * (y * (x * b));
	elseif (x <= 3.3e-90)
		tmp = t * (j * (b * y4));
	elseif (x <= 2.9e+156)
		tmp = i * (y1 * (x * j));
	else
		tmp = y * (b * (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[x, -6e-62], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.3e-90], N[(t * N[(j * N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.9e+156], N[(i * N[(y1 * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(b * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -6.0000000000000002e-62

   1. Initial program 31.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 37.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 40.1%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 40.1%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 40.1%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 40.1%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 42.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   8. Taylor expanded in y around inf 32.0%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(b \cdot x\right)\right)} \]

   if -6.0000000000000002e-62 < x < 3.3e-90

   1. Initial program 29.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 29.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 39.6%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 39.6%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

      2. mul-1-neg 39.6%

         \[\leadsto t \cdot \left(\color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)} + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right) \]

   6. Simplified 39.6%

      \[\leadsto \color{blue}{t \cdot \left(\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

   7. Taylor expanded in j around inf 28.8%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} \]

   8. Taylor expanded in y4 around inf 25.4%

      \[\leadsto t \cdot \left(j \cdot \color{blue}{\left(y4 \cdot b\right)}\right) \]

   if 3.3e-90 < x < 2.9000000000000001e156

   1. Initial program 28.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 41.2%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in j around inf 24.3%

      \[\leadsto \color{blue}{\left(j \cdot \left(y1 \cdot i - y0 \cdot b\right)\right)} \cdot x \]

   6. Taylor expanded in y1 around inf 24.3%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x\right)\right)} \]

   if 2.9000000000000001e156 < x

   1. Initial program 21.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 26.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 32.1%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 32.1%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 32.1%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 32.1%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 35.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   8. Taylor expanded in y around inf 38.2%

      \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

   9. Taylor expanded in a around 0 43.2%

      \[\leadsto \color{blue}{y \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 43.2%

          \[\leadsto y \cdot \color{blue}{\left(\left(b \cdot x\right) \cdot a\right)} \]

       2. associate-*l* 51.1%

          \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(x \cdot a\right)\right)} \]

   11. Simplified 51.1%

       \[\leadsto \color{blue}{y \cdot \left(b \cdot \left(x \cdot a\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 31.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-62}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-90}:\\ \;\;\;\;t \cdot \left(j \cdot \left(b \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+156}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a\right)\right)\\ \end{array} \]

Alternative 33: 20.3% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -3 \cdot 10^{+228} \lor \neg \left(y1 \leq 2.4 \cdot 10^{+150}\right):\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= y1 -3e+228) (not (<= y1 2.4e+150)))
   (* i (* y1 (* x j)))
   (* a (* x (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y1 <= -3e+228) || !(y1 <= 2.4e+150)) {
		tmp = i * (y1 * (x * j));
	} else {
		tmp = a * (x * (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((y1 <= (-3d+228)) .or. (.not. (y1 <= 2.4d+150))) then
        tmp = i * (y1 * (x * j))
    else
        tmp = a * (x * (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y1 <= -3e+228) || !(y1 <= 2.4e+150)) {
		tmp = i * (y1 * (x * j));
	} else {
		tmp = a * (x * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (y1 <= -3e+228) or not (y1 <= 2.4e+150):
		tmp = i * (y1 * (x * j))
	else:
		tmp = a * (x * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((y1 <= -3e+228) || !(y1 <= 2.4e+150))
		tmp = Float64(i * Float64(y1 * Float64(x * j)));
	else
		tmp = Float64(a * Float64(x * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((y1 <= -3e+228) || ~((y1 <= 2.4e+150)))
		tmp = i * (y1 * (x * j));
	else
		tmp = a * (x * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[y1, -3e+228], N[Not[LessEqual[y1, 2.4e+150]], $MachinePrecision]], N[(i * N[(y1 * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y1 < -3.0000000000000001e228 or 2.40000000000000003e150 < y1

   1. Initial program 18.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 18.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 43.0%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in j around inf 44.3%

      \[\leadsto \color{blue}{\left(j \cdot \left(y1 \cdot i - y0 \cdot b\right)\right)} \cdot x \]

   6. Taylor expanded in y1 around inf 41.5%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x\right)\right)} \]

   if -3.0000000000000001e228 < y1 < 2.40000000000000003e150

   1. Initial program 31.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 35.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 39.4%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 39.4%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 39.4%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 39.4%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 34.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   8. Taylor expanded in y around inf 22.3%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(b \cdot x\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 23.8%

         \[\leadsto a \cdot \color{blue}{\left(\left(y \cdot b\right) \cdot x\right)} \]

      2. *-commutative 23.8%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot y\right)} \cdot x\right) \]

   10. Simplified 23.8%

       \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot y\right) \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 28.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -3 \cdot 10^{+228} \lor \neg \left(y1 \leq 2.4 \cdot 10^{+150}\right):\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \end{array} \]

Alternative 34: 22.5% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-62}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+47}:\\ \;\;\;\;t \cdot \left(j \cdot \left(b \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -3.8e-62)
   (* a (* y (* x b)))
   (if (<= x 2.4e+47) (* t (* j (* b y4))) (* a (* b (* 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 tmp;
	if (x <= -3.8e-62) {
		tmp = a * (y * (x * b));
	} else if (x <= 2.4e+47) {
		tmp = t * (j * (b * y4));
	} else {
		tmp = a * (b * (x * y));
	}
	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 <= (-3.8d-62)) then
        tmp = a * (y * (x * b))
    else if (x <= 2.4d+47) then
        tmp = t * (j * (b * y4))
    else
        tmp = a * (b * (x * y))
    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 <= -3.8e-62) {
		tmp = a * (y * (x * b));
	} else if (x <= 2.4e+47) {
		tmp = t * (j * (b * y4));
	} else {
		tmp = a * (b * (x * y));
	}
	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 <= -3.8e-62:
		tmp = a * (y * (x * b))
	elif x <= 2.4e+47:
		tmp = t * (j * (b * y4))
	else:
		tmp = a * (b * (x * y))
	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 <= -3.8e-62)
		tmp = Float64(a * Float64(y * Float64(x * b)));
	elseif (x <= 2.4e+47)
		tmp = Float64(t * Float64(j * Float64(b * y4)));
	else
		tmp = Float64(a * Float64(b * 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)
	tmp = 0.0;
	if (x <= -3.8e-62)
		tmp = a * (y * (x * b));
	elseif (x <= 2.4e+47)
		tmp = t * (j * (b * y4));
	else
		tmp = a * (b * (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_] := If[LessEqual[x, -3.8e-62], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.4e+47], N[(t * N[(j * N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.80000000000000006e-62

   1. Initial program 31.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 37.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 40.1%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 40.1%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 40.1%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 40.1%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 42.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   8. Taylor expanded in y around inf 32.0%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(b \cdot x\right)\right)} \]

   if -3.80000000000000006e-62 < x < 2.40000000000000019e47

   1. Initial program 28.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 38.2%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 38.2%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

      2. mul-1-neg 38.2%

         \[\leadsto t \cdot \left(\color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)} + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right) \]

   6. Simplified 38.2%

      \[\leadsto \color{blue}{t \cdot \left(\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

   7. Taylor expanded in j around inf 28.6%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} \]

   8. Taylor expanded in y4 around inf 22.5%

      \[\leadsto t \cdot \left(j \cdot \color{blue}{\left(y4 \cdot b\right)}\right) \]

   if 2.40000000000000019e47 < x

   1. Initial program 24.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 33.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 42.1%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 42.1%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 42.1%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 42.1%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 34.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   8. Taylor expanded in y around inf 33.6%

      \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 28.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-62}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+47}:\\ \;\;\;\;t \cdot \left(j \cdot \left(b \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y\right)\right)\\ \end{array} \]

Alternative 35: 17.3% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(b \cdot \left(x \cdot y\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* b (* 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) {
	return a * (b * (x * y));
}

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 * (b * (x * y))
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 * (b * (x * y));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * (b * (x * y))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(b * Float64(x * y)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * (b * (x * y));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(b * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 28.3%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

3. Simplified 33.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

4. Taylor expanded in a around inf 37.0%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
5. Step-by-step derivation

   1. mul-1-neg 37.0%

      \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

   2. mul-1-neg 37.0%

      \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

6. Simplified 37.0%

   \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

7. Taylor expanded in b around inf 31.2%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

8. Taylor expanded in y around inf 21.0%

   \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

9. Final simplification 21.0%

   \[\leadsto a \cdot \left(b \cdot \left(x \cdot y\right)\right) \]

Alternative 36: 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 28.3%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

3. Simplified 33.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

4. Taylor expanded in a around inf 37.0%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
5. Step-by-step derivation

   1. mul-1-neg 37.0%

      \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

   2. mul-1-neg 37.0%

      \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

6. Simplified 37.0%

   \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

7. Taylor expanded in b around inf 31.2%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

8. Taylor expanded in y around inf 20.6%

   \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(b \cdot x\right)\right)} \]
9. Step-by-step derivation

   1. associate-*r* 21.3%

      \[\leadsto a \cdot \color{blue}{\left(\left(y \cdot b\right) \cdot x\right)} \]

   2. *-commutative 21.3%

      \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot y\right)} \cdot x\right) \]

10. Simplified 21.3%

    \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot y\right) \cdot x\right)} \]

11. Final simplification 21.3%

    \[\leadsto a \cdot \left(x \cdot \left(y \cdot b\right)\right) \]

Developer target: 27.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot c - y5 \cdot a\\ t_2 := x \cdot y2 - z \cdot y3\\ t_3 := y2 \cdot t - y3 \cdot y\\ t_4 := k \cdot y2 - j \cdot y3\\ t_5 := y4 \cdot b - y5 \cdot i\\ t_6 := \left(j \cdot t - k \cdot y\right) \cdot t_5\\ t_7 := b \cdot a - i \cdot c\\ t_8 := t_7 \cdot \left(y \cdot x - t \cdot z\right)\\ t_9 := j \cdot x - k \cdot z\\ t_10 := \left(b \cdot y0 - i \cdot y1\right) \cdot t_9\\ t_11 := t_9 \cdot \left(y0 \cdot b - i \cdot y1\right)\\ t_12 := y4 \cdot y1 - y5 \cdot y0\\ t_13 := t_4 \cdot t_12\\ t_14 := \left(y2 \cdot k - y3 \cdot j\right) \cdot t_12\\ t_15 := \left(\left(\left(\left(k \cdot y\right) \cdot \left(y5 \cdot i\right) - \left(y \cdot b\right) \cdot \left(y4 \cdot k\right)\right) - \left(y5 \cdot t\right) \cdot \left(i \cdot j\right)\right) - \left(t_3 \cdot t_1 - t_14\right)\right) + \left(t_8 - \left(t_11 - \left(y2 \cdot x - y3 \cdot z\right) \cdot \left(c \cdot y0 - y1 \cdot a\right)\right)\right)\\ t_16 := \left(\left(t_6 - \left(y3 \cdot y\right) \cdot \left(y5 \cdot a - y4 \cdot c\right)\right) + \left(\left(y5 \cdot a\right) \cdot \left(t \cdot y2\right) + t_13\right)\right) + \left(t_2 \cdot \left(c \cdot y0 - a \cdot y1\right) - \left(t_10 - \left(y \cdot x - z \cdot t\right) \cdot t_7\right)\right)\\ t_17 := t \cdot y2 - y \cdot y3\\ \mathbf{if}\;y4 < -7.206256231996481 \cdot 10^{+60}:\\ \;\;\;\;\left(t_8 - \left(t_11 - t_6\right)\right) - \left(\frac{t_3}{\frac{1}{t_1}} - t_14\right)\\ \mathbf{elif}\;y4 < -3.364603505246317 \cdot 10^{-66}:\\ \;\;\;\;\left(\left(\left(\left(t \cdot c\right) \cdot \left(i \cdot z\right) - \left(a \cdot t\right) \cdot \left(b \cdot z\right)\right) - \left(y \cdot c\right) \cdot \left(i \cdot x\right)\right) - t_10\right) + \left(\left(y0 \cdot c - a \cdot y1\right) \cdot t_2 - \left(t_17 \cdot \left(y4 \cdot c - a \cdot y5\right) - \left(y1 \cdot y4 - y5 \cdot y0\right) \cdot t_4\right)\right)\\ \mathbf{elif}\;y4 < -1.2000065055686116 \cdot 10^{-105}:\\ \;\;\;\;t_16\\ \mathbf{elif}\;y4 < 6.718963124057495 \cdot 10^{-279}:\\ \;\;\;\;t_15\\ \mathbf{elif}\;y4 < 4.77962681403792 \cdot 10^{-222}:\\ \;\;\;\;t_16\\ \mathbf{elif}\;y4 < 2.2852241541266835 \cdot 10^{-175}:\\ \;\;\;\;t_15\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(k \cdot \left(i \cdot \left(z \cdot y1\right)\right) - \left(j \cdot \left(i \cdot \left(x \cdot y1\right)\right) + y0 \cdot \left(k \cdot \left(z \cdot b\right)\right)\right)\right)\right) + \left(z \cdot \left(y3 \cdot \left(a \cdot y1\right)\right) - \left(y2 \cdot \left(x \cdot \left(a \cdot y1\right)\right) + y0 \cdot \left(z \cdot \left(c \cdot y3\right)\right)\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot t_5\right) - t_17 \cdot t_1\right) + t_13\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y4 c) (* y5 a)))
        (t_2 (- (* x y2) (* z y3)))
        (t_3 (- (* y2 t) (* y3 y)))
        (t_4 (- (* k y2) (* j y3)))
        (t_5 (- (* y4 b) (* y5 i)))
        (t_6 (* (- (* j t) (* k y)) t_5))
        (t_7 (- (* b a) (* i c)))
        (t_8 (* t_7 (- (* y x) (* t z))))
        (t_9 (- (* j x) (* k z)))
        (t_10 (* (- (* b y0) (* i y1)) t_9))
        (t_11 (* t_9 (- (* y0 b) (* i y1))))
        (t_12 (- (* y4 y1) (* y5 y0)))
        (t_13 (* t_4 t_12))
        (t_14 (* (- (* y2 k) (* y3 j)) t_12))
        (t_15
         (+
          (-
           (-
            (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k)))
            (* (* y5 t) (* i j)))
           (- (* t_3 t_1) t_14))
          (- t_8 (- t_11 (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))))
        (t_16
         (+
          (+
           (- t_6 (* (* y3 y) (- (* y5 a) (* y4 c))))
           (+ (* (* y5 a) (* t y2)) t_13))
          (-
           (* t_2 (- (* c y0) (* a y1)))
           (- t_10 (* (- (* y x) (* z t)) t_7)))))
        (t_17 (- (* t y2) (* y y3))))
   (if (< y4 -7.206256231996481e+60)
     (- (- t_8 (- t_11 t_6)) (- (/ t_3 (/ 1.0 t_1)) t_14))
     (if (< y4 -3.364603505246317e-66)
       (+
        (-
         (- (- (* (* t c) (* i z)) (* (* a t) (* b z))) (* (* y c) (* i x)))
         t_10)
        (-
         (* (- (* y0 c) (* a y1)) t_2)
         (- (* t_17 (- (* y4 c) (* a y5))) (* (- (* y1 y4) (* y5 y0)) t_4))))
       (if (< y4 -1.2000065055686116e-105)
         t_16
         (if (< y4 6.718963124057495e-279)
           t_15
           (if (< y4 4.77962681403792e-222)
             t_16
             (if (< y4 2.2852241541266835e-175)
               t_15
               (+
                (-
                 (+
                  (+
                   (-
                    (* (- (* x y) (* z t)) (- (* a b) (* c i)))
                    (-
                     (* k (* i (* z y1)))
                     (+ (* j (* i (* x y1))) (* y0 (* k (* z b))))))
                   (-
                    (* z (* y3 (* a y1)))
                    (+ (* y2 (* x (* a y1))) (* y0 (* z (* c y3))))))
                  (* (- (* t j) (* y k)) t_5))
                 (* t_17 t_1))
                t_13)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y4 * c) - (y5 * a);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (y2 * t) - (y3 * y);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = (y4 * b) - (y5 * i);
	double t_6 = ((j * t) - (k * y)) * t_5;
	double t_7 = (b * a) - (i * c);
	double t_8 = t_7 * ((y * x) - (t * z));
	double t_9 = (j * x) - (k * z);
	double t_10 = ((b * y0) - (i * y1)) * t_9;
	double t_11 = t_9 * ((y0 * b) - (i * y1));
	double t_12 = (y4 * y1) - (y5 * y0);
	double t_13 = t_4 * t_12;
	double t_14 = ((y2 * k) - (y3 * j)) * t_12;
	double t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	double t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	double t_17 = (t * y2) - (y * y3);
	double tmp;
	if (y4 < -7.206256231996481e+60) {
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	} else if (y4 < -3.364603505246317e-66) {
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	} else if (y4 < -1.2000065055686116e-105) {
		tmp = t_16;
	} else if (y4 < 6.718963124057495e-279) {
		tmp = t_15;
	} else if (y4 < 4.77962681403792e-222) {
		tmp = t_16;
	} else if (y4 < 2.2852241541266835e-175) {
		tmp = t_15;
	} else {
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_10
    real(8) :: t_11
    real(8) :: t_12
    real(8) :: t_13
    real(8) :: t_14
    real(8) :: t_15
    real(8) :: t_16
    real(8) :: t_17
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = (y4 * c) - (y5 * a)
    t_2 = (x * y2) - (z * y3)
    t_3 = (y2 * t) - (y3 * y)
    t_4 = (k * y2) - (j * y3)
    t_5 = (y4 * b) - (y5 * i)
    t_6 = ((j * t) - (k * y)) * t_5
    t_7 = (b * a) - (i * c)
    t_8 = t_7 * ((y * x) - (t * z))
    t_9 = (j * x) - (k * z)
    t_10 = ((b * y0) - (i * y1)) * t_9
    t_11 = t_9 * ((y0 * b) - (i * y1))
    t_12 = (y4 * y1) - (y5 * y0)
    t_13 = t_4 * t_12
    t_14 = ((y2 * k) - (y3 * j)) * t_12
    t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))))
    t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)))
    t_17 = (t * y2) - (y * y3)
    if (y4 < (-7.206256231996481d+60)) then
        tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0d0 / t_1)) - t_14)
    else if (y4 < (-3.364603505246317d-66)) then
        tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)))
    else if (y4 < (-1.2000065055686116d-105)) then
        tmp = t_16
    else if (y4 < 6.718963124057495d-279) then
        tmp = t_15
    else if (y4 < 4.77962681403792d-222) then
        tmp = t_16
    else if (y4 < 2.2852241541266835d-175) then
        tmp = t_15
    else
        tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y4 * c) - (y5 * a);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (y2 * t) - (y3 * y);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = (y4 * b) - (y5 * i);
	double t_6 = ((j * t) - (k * y)) * t_5;
	double t_7 = (b * a) - (i * c);
	double t_8 = t_7 * ((y * x) - (t * z));
	double t_9 = (j * x) - (k * z);
	double t_10 = ((b * y0) - (i * y1)) * t_9;
	double t_11 = t_9 * ((y0 * b) - (i * y1));
	double t_12 = (y4 * y1) - (y5 * y0);
	double t_13 = t_4 * t_12;
	double t_14 = ((y2 * k) - (y3 * j)) * t_12;
	double t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	double t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	double t_17 = (t * y2) - (y * y3);
	double tmp;
	if (y4 < -7.206256231996481e+60) {
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	} else if (y4 < -3.364603505246317e-66) {
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	} else if (y4 < -1.2000065055686116e-105) {
		tmp = t_16;
	} else if (y4 < 6.718963124057495e-279) {
		tmp = t_15;
	} else if (y4 < 4.77962681403792e-222) {
		tmp = t_16;
	} else if (y4 < 2.2852241541266835e-175) {
		tmp = t_15;
	} else {
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y4 * c) - (y5 * a)
	t_2 = (x * y2) - (z * y3)
	t_3 = (y2 * t) - (y3 * y)
	t_4 = (k * y2) - (j * y3)
	t_5 = (y4 * b) - (y5 * i)
	t_6 = ((j * t) - (k * y)) * t_5
	t_7 = (b * a) - (i * c)
	t_8 = t_7 * ((y * x) - (t * z))
	t_9 = (j * x) - (k * z)
	t_10 = ((b * y0) - (i * y1)) * t_9
	t_11 = t_9 * ((y0 * b) - (i * y1))
	t_12 = (y4 * y1) - (y5 * y0)
	t_13 = t_4 * t_12
	t_14 = ((y2 * k) - (y3 * j)) * t_12
	t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))))
	t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)))
	t_17 = (t * y2) - (y * y3)
	tmp = 0
	if y4 < -7.206256231996481e+60:
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14)
	elif y4 < -3.364603505246317e-66:
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)))
	elif y4 < -1.2000065055686116e-105:
		tmp = t_16
	elif y4 < 6.718963124057495e-279:
		tmp = t_15
	elif y4 < 4.77962681403792e-222:
		tmp = t_16
	elif y4 < 2.2852241541266835e-175:
		tmp = t_15
	else:
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y4 * c) - Float64(y5 * a))
	t_2 = Float64(Float64(x * y2) - Float64(z * y3))
	t_3 = Float64(Float64(y2 * t) - Float64(y3 * y))
	t_4 = Float64(Float64(k * y2) - Float64(j * y3))
	t_5 = Float64(Float64(y4 * b) - Float64(y5 * i))
	t_6 = Float64(Float64(Float64(j * t) - Float64(k * y)) * t_5)
	t_7 = Float64(Float64(b * a) - Float64(i * c))
	t_8 = Float64(t_7 * Float64(Float64(y * x) - Float64(t * z)))
	t_9 = Float64(Float64(j * x) - Float64(k * z))
	t_10 = Float64(Float64(Float64(b * y0) - Float64(i * y1)) * t_9)
	t_11 = Float64(t_9 * Float64(Float64(y0 * b) - Float64(i * y1)))
	t_12 = Float64(Float64(y4 * y1) - Float64(y5 * y0))
	t_13 = Float64(t_4 * t_12)
	t_14 = Float64(Float64(Float64(y2 * k) - Float64(y3 * j)) * t_12)
	t_15 = Float64(Float64(Float64(Float64(Float64(Float64(k * y) * Float64(y5 * i)) - Float64(Float64(y * b) * Float64(y4 * k))) - Float64(Float64(y5 * t) * Float64(i * j))) - Float64(Float64(t_3 * t_1) - t_14)) + Float64(t_8 - Float64(t_11 - Float64(Float64(Float64(y2 * x) - Float64(y3 * z)) * Float64(Float64(c * y0) - Float64(y1 * a))))))
	t_16 = Float64(Float64(Float64(t_6 - Float64(Float64(y3 * y) * Float64(Float64(y5 * a) - Float64(y4 * c)))) + Float64(Float64(Float64(y5 * a) * Float64(t * y2)) + t_13)) + Float64(Float64(t_2 * Float64(Float64(c * y0) - Float64(a * y1))) - Float64(t_10 - Float64(Float64(Float64(y * x) - Float64(z * t)) * t_7))))
	t_17 = Float64(Float64(t * y2) - Float64(y * y3))
	tmp = 0.0
	if (y4 < -7.206256231996481e+60)
		tmp = Float64(Float64(t_8 - Float64(t_11 - t_6)) - Float64(Float64(t_3 / Float64(1.0 / t_1)) - t_14));
	elseif (y4 < -3.364603505246317e-66)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(t * c) * Float64(i * z)) - Float64(Float64(a * t) * Float64(b * z))) - Float64(Float64(y * c) * Float64(i * x))) - t_10) + Float64(Float64(Float64(Float64(y0 * c) - Float64(a * y1)) * t_2) - Float64(Float64(t_17 * Float64(Float64(y4 * c) - Float64(a * y5))) - Float64(Float64(Float64(y1 * y4) - Float64(y5 * y0)) * t_4))));
	elseif (y4 < -1.2000065055686116e-105)
		tmp = t_16;
	elseif (y4 < 6.718963124057495e-279)
		tmp = t_15;
	elseif (y4 < 4.77962681403792e-222)
		tmp = t_16;
	elseif (y4 < 2.2852241541266835e-175)
		tmp = t_15;
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) - Float64(z * t)) * Float64(Float64(a * b) - Float64(c * i))) - Float64(Float64(k * Float64(i * Float64(z * y1))) - Float64(Float64(j * Float64(i * Float64(x * y1))) + Float64(y0 * Float64(k * Float64(z * b)))))) + Float64(Float64(z * Float64(y3 * Float64(a * y1))) - Float64(Float64(y2 * Float64(x * Float64(a * y1))) + Float64(y0 * Float64(z * Float64(c * y3)))))) + Float64(Float64(Float64(t * j) - Float64(y * k)) * t_5)) - Float64(t_17 * t_1)) + t_13);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y4 * c) - (y5 * a);
	t_2 = (x * y2) - (z * y3);
	t_3 = (y2 * t) - (y3 * y);
	t_4 = (k * y2) - (j * y3);
	t_5 = (y4 * b) - (y5 * i);
	t_6 = ((j * t) - (k * y)) * t_5;
	t_7 = (b * a) - (i * c);
	t_8 = t_7 * ((y * x) - (t * z));
	t_9 = (j * x) - (k * z);
	t_10 = ((b * y0) - (i * y1)) * t_9;
	t_11 = t_9 * ((y0 * b) - (i * y1));
	t_12 = (y4 * y1) - (y5 * y0);
	t_13 = t_4 * t_12;
	t_14 = ((y2 * k) - (y3 * j)) * t_12;
	t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	t_17 = (t * y2) - (y * y3);
	tmp = 0.0;
	if (y4 < -7.206256231996481e+60)
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	elseif (y4 < -3.364603505246317e-66)
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	elseif (y4 < -1.2000065055686116e-105)
		tmp = t_16;
	elseif (y4 < 6.718963124057495e-279)
		tmp = t_15;
	elseif (y4 < 4.77962681403792e-222)
		tmp = t_16;
	elseif (y4 < 2.2852241541266835e-175)
		tmp = t_15;
	else
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y4 * c), $MachinePrecision] - N[(y5 * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y2 * t), $MachinePrecision] - N[(y3 * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(y4 * b), $MachinePrecision] - N[(y5 * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision] * t$95$5), $MachinePrecision]}, Block[{t$95$7 = N[(N[(b * a), $MachinePrecision] - N[(i * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(t$95$7 * N[(N[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$10 = N[(N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision] * t$95$9), $MachinePrecision]}, Block[{t$95$11 = N[(t$95$9 * N[(N[(y0 * b), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$12 = N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$13 = N[(t$95$4 * t$95$12), $MachinePrecision]}, Block[{t$95$14 = N[(N[(N[(y2 * k), $MachinePrecision] - N[(y3 * j), $MachinePrecision]), $MachinePrecision] * t$95$12), $MachinePrecision]}, Block[{t$95$15 = N[(N[(N[(N[(N[(N[(k * y), $MachinePrecision] * N[(y5 * i), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] * N[(y4 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y5 * t), $MachinePrecision] * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$3 * t$95$1), $MachinePrecision] - t$95$14), $MachinePrecision]), $MachinePrecision] + N[(t$95$8 - N[(t$95$11 - N[(N[(N[(y2 * x), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision] * N[(N[(c * y0), $MachinePrecision] - N[(y1 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$16 = N[(N[(N[(t$95$6 - N[(N[(y3 * y), $MachinePrecision] * N[(N[(y5 * a), $MachinePrecision] - N[(y4 * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y5 * a), $MachinePrecision] * N[(t * y2), $MachinePrecision]), $MachinePrecision] + t$95$13), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$10 - N[(N[(N[(y * x), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$17 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, If[Less[y4, -7.206256231996481e+60], N[(N[(t$95$8 - N[(t$95$11 - t$95$6), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$3 / N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision] - t$95$14), $MachinePrecision]), $MachinePrecision], If[Less[y4, -3.364603505246317e-66], N[(N[(N[(N[(N[(N[(t * c), $MachinePrecision] * N[(i * z), $MachinePrecision]), $MachinePrecision] - N[(N[(a * t), $MachinePrecision] * N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * c), $MachinePrecision] * N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$10), $MachinePrecision] + N[(N[(N[(N[(y0 * c), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision] - N[(N[(t$95$17 * N[(N[(y4 * c), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(y1 * y4), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision] * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[y4, -1.2000065055686116e-105], t$95$16, If[Less[y4, 6.718963124057495e-279], t$95$15, If[Less[y4, 4.77962681403792e-222], t$95$16, If[Less[y4, 2.2852241541266835e-175], t$95$15, N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(k * N[(i * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * N[(i * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(k * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(y3 * N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y2 * N[(x * N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(z * N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * t$95$5), $MachinePrecision]), $MachinePrecision] - N[(t$95$17 * t$95$1), $MachinePrecision]), $MachinePrecision] + t$95$13), $MachinePrecision]]]]]]]]]]]]]]]]]]]]]]]]

Reproduce

herbie shell --seed 2023199 
(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)))))