Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 29.6% → 39.3%

Time: 1.2min

Alternatives: 42

Speedup: 2.6×

• 88.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 29.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 39.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot y0 - a \cdot y1\\ t_2 := i \cdot y1 - b \cdot y0\\ t_3 := x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot t\_1\right) + j \cdot t\_2\right)\\ t_4 := y1 \cdot y4 - y0 \cdot y5\\ t_5 := 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 t\_2\right)\\ t_6 := b \cdot y0 - i \cdot y1\\ t_7 := z \cdot t\_6\\ t_8 := k \cdot \left(\left(y \cdot \left(i \cdot y5 - b \cdot y4\right) + y2 \cdot t\_4\right) + t\_7\right)\\ t_9 := y \cdot k - t \cdot j\\ \mathbf{if}\;i \leq -7.5 \cdot 10^{+147}:\\ \;\;\;\;k \cdot t\_7\\ \mathbf{elif}\;i \leq -2.65 \cdot 10^{+106}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(t \cdot i - y0 \cdot y3\right)\\ \mathbf{elif}\;i \leq -1.1 \cdot 10^{+101}:\\ \;\;\;\;y1 \cdot \left(\left(k \cdot \left(y2 \cdot y4\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right) - i \cdot \left(z \cdot k\right)\right)\\ \mathbf{elif}\;i \leq -3.6 \cdot 10^{-46}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;i \leq -4.1 \cdot 10^{-88}:\\ \;\;\;\;y4 \cdot \left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - b \cdot t\_9\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq -8.5 \cdot 10^{-168}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;i \leq -3.6 \cdot 10^{-213}:\\ \;\;\;\;\left(z \cdot a\right) \cdot \left(y1 \cdot y3 - t \cdot b\right)\\ \mathbf{elif}\;i \leq -1.52 \cdot 10^{-263}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{-267}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot t\_4 + x \cdot t\_1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq 3.8 \cdot 10^{-218}:\\ \;\;\;\;z \cdot \left(k \cdot t\_6 + \left(t \cdot \left(c \cdot i - a \cdot b\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;i \leq 6 \cdot 10^{-200}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;i \leq 2.15 \cdot 10^{-128}:\\ \;\;\;\;t\_8\\ \mathbf{elif}\;i \leq 1.16 \cdot 10^{-52}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;i \leq 1.02 \cdot 10^{+109}:\\ \;\;\;\;t\_8\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(c \cdot \left(z \cdot t - x \cdot y\right) + y5 \cdot t\_9\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* c y0) (* a y1)))
        (t_2 (- (* i y1) (* b y0)))
        (t_3 (* x (+ (+ (* y (- (* a b) (* c i))) (* y2 t_1)) (* j t_2))))
        (t_4 (- (* y1 y4) (* y0 y5)))
        (t_5
         (*
          j
          (+
           (+ (* y3 (- (* y0 y5) (* y1 y4))) (* t (- (* b y4) (* i y5))))
           (* x t_2))))
        (t_6 (- (* b y0) (* i y1)))
        (t_7 (* z t_6))
        (t_8 (* k (+ (+ (* y (- (* i y5) (* b y4))) (* y2 t_4)) t_7)))
        (t_9 (- (* y k) (* t j))))
   (if (<= i -7.5e+147)
     (* k t_7)
     (if (<= i -2.65e+106)
       (* (* z c) (- (* t i) (* y0 y3)))
       (if (<= i -1.1e+101)
         (*
          y1
          (- (+ (* k (* y2 y4)) (* a (- (* z y3) (* x y2)))) (* i (* z k))))
         (if (<= i -3.6e-46)
           t_5
           (if (<= i -4.1e-88)
             (*
              y4
              (+
               (- (* y1 (- (* k y2) (* j y3))) (* b t_9))
               (* c (- (* y y3) (* t y2)))))
             (if (<= i -8.5e-168)
               t_3
               (if (<= i -3.6e-213)
                 (* (* z a) (- (* y1 y3) (* t b)))
                 (if (<= i -1.52e-263)
                   (*
                    b
                    (+
                     (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
                     (* y0 (- (* z k) (* x j)))))
                   (if (<= i 4.8e-267)
                     (*
                      y2
                      (+ (+ (* k t_4) (* x t_1)) (* t (- (* a y5) (* c y4)))))
                     (if (<= i 3.8e-218)
                       (*
                        z
                        (+
                         (* k t_6)
                         (+
                          (* t (- (* c i) (* a b)))
                          (* y3 (- (* a y1) (* c y0))))))
                       (if (<= i 6e-200)
                         t_3
                         (if (<= i 2.15e-128)
                           t_8
                           (if (<= i 1.16e-52)
                             t_5
                             (if (<= i 1.02e+109)
                               t_8
                               (*
                                i
                                (+
                                 (* y1 (- (* x j) (* z k)))
                                 (+
                                  (* c (- (* z t) (* x y)))
                                  (* y5 t_9))))))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y0) - (a * y1);
	double t_2 = (i * y1) - (b * y0);
	double t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * t_2));
	double t_4 = (y1 * y4) - (y0 * y5);
	double t_5 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * t_2));
	double t_6 = (b * y0) - (i * y1);
	double t_7 = z * t_6;
	double t_8 = k * (((y * ((i * y5) - (b * y4))) + (y2 * t_4)) + t_7);
	double t_9 = (y * k) - (t * j);
	double tmp;
	if (i <= -7.5e+147) {
		tmp = k * t_7;
	} else if (i <= -2.65e+106) {
		tmp = (z * c) * ((t * i) - (y0 * y3));
	} else if (i <= -1.1e+101) {
		tmp = y1 * (((k * (y2 * y4)) + (a * ((z * y3) - (x * y2)))) - (i * (z * k)));
	} else if (i <= -3.6e-46) {
		tmp = t_5;
	} else if (i <= -4.1e-88) {
		tmp = y4 * (((y1 * ((k * y2) - (j * y3))) - (b * t_9)) + (c * ((y * y3) - (t * y2))));
	} else if (i <= -8.5e-168) {
		tmp = t_3;
	} else if (i <= -3.6e-213) {
		tmp = (z * a) * ((y1 * y3) - (t * b));
	} else if (i <= -1.52e-263) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (i <= 4.8e-267) {
		tmp = y2 * (((k * t_4) + (x * t_1)) + (t * ((a * y5) - (c * y4))));
	} else if (i <= 3.8e-218) {
		tmp = z * ((k * t_6) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	} else if (i <= 6e-200) {
		tmp = t_3;
	} else if (i <= 2.15e-128) {
		tmp = t_8;
	} else if (i <= 1.16e-52) {
		tmp = t_5;
	} else if (i <= 1.02e+109) {
		tmp = t_8;
	} else {
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((c * ((z * t) - (x * y))) + (y5 * t_9)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = (c * y0) - (a * y1)
    t_2 = (i * y1) - (b * y0)
    t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * t_2))
    t_4 = (y1 * y4) - (y0 * y5)
    t_5 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * t_2))
    t_6 = (b * y0) - (i * y1)
    t_7 = z * t_6
    t_8 = k * (((y * ((i * y5) - (b * y4))) + (y2 * t_4)) + t_7)
    t_9 = (y * k) - (t * j)
    if (i <= (-7.5d+147)) then
        tmp = k * t_7
    else if (i <= (-2.65d+106)) then
        tmp = (z * c) * ((t * i) - (y0 * y3))
    else if (i <= (-1.1d+101)) then
        tmp = y1 * (((k * (y2 * y4)) + (a * ((z * y3) - (x * y2)))) - (i * (z * k)))
    else if (i <= (-3.6d-46)) then
        tmp = t_5
    else if (i <= (-4.1d-88)) then
        tmp = y4 * (((y1 * ((k * y2) - (j * y3))) - (b * t_9)) + (c * ((y * y3) - (t * y2))))
    else if (i <= (-8.5d-168)) then
        tmp = t_3
    else if (i <= (-3.6d-213)) then
        tmp = (z * a) * ((y1 * y3) - (t * b))
    else if (i <= (-1.52d-263)) then
        tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    else if (i <= 4.8d-267) then
        tmp = y2 * (((k * t_4) + (x * t_1)) + (t * ((a * y5) - (c * y4))))
    else if (i <= 3.8d-218) then
        tmp = z * ((k * t_6) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))))
    else if (i <= 6d-200) then
        tmp = t_3
    else if (i <= 2.15d-128) then
        tmp = t_8
    else if (i <= 1.16d-52) then
        tmp = t_5
    else if (i <= 1.02d+109) then
        tmp = t_8
    else
        tmp = i * ((y1 * ((x * j) - (z * k))) + ((c * ((z * t) - (x * y))) + (y5 * t_9)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y0) - (a * y1);
	double t_2 = (i * y1) - (b * y0);
	double t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * t_2));
	double t_4 = (y1 * y4) - (y0 * y5);
	double t_5 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * t_2));
	double t_6 = (b * y0) - (i * y1);
	double t_7 = z * t_6;
	double t_8 = k * (((y * ((i * y5) - (b * y4))) + (y2 * t_4)) + t_7);
	double t_9 = (y * k) - (t * j);
	double tmp;
	if (i <= -7.5e+147) {
		tmp = k * t_7;
	} else if (i <= -2.65e+106) {
		tmp = (z * c) * ((t * i) - (y0 * y3));
	} else if (i <= -1.1e+101) {
		tmp = y1 * (((k * (y2 * y4)) + (a * ((z * y3) - (x * y2)))) - (i * (z * k)));
	} else if (i <= -3.6e-46) {
		tmp = t_5;
	} else if (i <= -4.1e-88) {
		tmp = y4 * (((y1 * ((k * y2) - (j * y3))) - (b * t_9)) + (c * ((y * y3) - (t * y2))));
	} else if (i <= -8.5e-168) {
		tmp = t_3;
	} else if (i <= -3.6e-213) {
		tmp = (z * a) * ((y1 * y3) - (t * b));
	} else if (i <= -1.52e-263) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (i <= 4.8e-267) {
		tmp = y2 * (((k * t_4) + (x * t_1)) + (t * ((a * y5) - (c * y4))));
	} else if (i <= 3.8e-218) {
		tmp = z * ((k * t_6) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	} else if (i <= 6e-200) {
		tmp = t_3;
	} else if (i <= 2.15e-128) {
		tmp = t_8;
	} else if (i <= 1.16e-52) {
		tmp = t_5;
	} else if (i <= 1.02e+109) {
		tmp = t_8;
	} else {
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((c * ((z * t) - (x * y))) + (y5 * t_9)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (c * y0) - (a * y1)
	t_2 = (i * y1) - (b * y0)
	t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * t_2))
	t_4 = (y1 * y4) - (y0 * y5)
	t_5 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * t_2))
	t_6 = (b * y0) - (i * y1)
	t_7 = z * t_6
	t_8 = k * (((y * ((i * y5) - (b * y4))) + (y2 * t_4)) + t_7)
	t_9 = (y * k) - (t * j)
	tmp = 0
	if i <= -7.5e+147:
		tmp = k * t_7
	elif i <= -2.65e+106:
		tmp = (z * c) * ((t * i) - (y0 * y3))
	elif i <= -1.1e+101:
		tmp = y1 * (((k * (y2 * y4)) + (a * ((z * y3) - (x * y2)))) - (i * (z * k)))
	elif i <= -3.6e-46:
		tmp = t_5
	elif i <= -4.1e-88:
		tmp = y4 * (((y1 * ((k * y2) - (j * y3))) - (b * t_9)) + (c * ((y * y3) - (t * y2))))
	elif i <= -8.5e-168:
		tmp = t_3
	elif i <= -3.6e-213:
		tmp = (z * a) * ((y1 * y3) - (t * b))
	elif i <= -1.52e-263:
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	elif i <= 4.8e-267:
		tmp = y2 * (((k * t_4) + (x * t_1)) + (t * ((a * y5) - (c * y4))))
	elif i <= 3.8e-218:
		tmp = z * ((k * t_6) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))))
	elif i <= 6e-200:
		tmp = t_3
	elif i <= 2.15e-128:
		tmp = t_8
	elif i <= 1.16e-52:
		tmp = t_5
	elif i <= 1.02e+109:
		tmp = t_8
	else:
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((c * ((z * t) - (x * y))) + (y5 * t_9)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(c * y0) - Float64(a * y1))
	t_2 = Float64(Float64(i * y1) - Float64(b * y0))
	t_3 = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * t_1)) + Float64(j * t_2)))
	t_4 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_5 = Float64(j * Float64(Float64(Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(t * Float64(Float64(b * y4) - Float64(i * y5)))) + Float64(x * t_2)))
	t_6 = Float64(Float64(b * y0) - Float64(i * y1))
	t_7 = Float64(z * t_6)
	t_8 = Float64(k * Float64(Float64(Float64(y * Float64(Float64(i * y5) - Float64(b * y4))) + Float64(y2 * t_4)) + t_7))
	t_9 = Float64(Float64(y * k) - Float64(t * j))
	tmp = 0.0
	if (i <= -7.5e+147)
		tmp = Float64(k * t_7);
	elseif (i <= -2.65e+106)
		tmp = Float64(Float64(z * c) * Float64(Float64(t * i) - Float64(y0 * y3)));
	elseif (i <= -1.1e+101)
		tmp = Float64(y1 * Float64(Float64(Float64(k * Float64(y2 * y4)) + Float64(a * Float64(Float64(z * y3) - Float64(x * y2)))) - Float64(i * Float64(z * k))));
	elseif (i <= -3.6e-46)
		tmp = t_5;
	elseif (i <= -4.1e-88)
		tmp = Float64(y4 * Float64(Float64(Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))) - Float64(b * t_9)) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (i <= -8.5e-168)
		tmp = t_3;
	elseif (i <= -3.6e-213)
		tmp = Float64(Float64(z * a) * Float64(Float64(y1 * y3) - Float64(t * b)));
	elseif (i <= -1.52e-263)
		tmp = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (i <= 4.8e-267)
		tmp = Float64(y2 * Float64(Float64(Float64(k * t_4) + Float64(x * t_1)) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (i <= 3.8e-218)
		tmp = Float64(z * Float64(Float64(k * t_6) + Float64(Float64(t * Float64(Float64(c * i) - Float64(a * b))) + Float64(y3 * Float64(Float64(a * y1) - Float64(c * y0))))));
	elseif (i <= 6e-200)
		tmp = t_3;
	elseif (i <= 2.15e-128)
		tmp = t_8;
	elseif (i <= 1.16e-52)
		tmp = t_5;
	elseif (i <= 1.02e+109)
		tmp = t_8;
	else
		tmp = Float64(i * Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) + Float64(Float64(c * Float64(Float64(z * t) - Float64(x * y))) + Float64(y5 * t_9))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (c * y0) - (a * y1);
	t_2 = (i * y1) - (b * y0);
	t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * t_2));
	t_4 = (y1 * y4) - (y0 * y5);
	t_5 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * t_2));
	t_6 = (b * y0) - (i * y1);
	t_7 = z * t_6;
	t_8 = k * (((y * ((i * y5) - (b * y4))) + (y2 * t_4)) + t_7);
	t_9 = (y * k) - (t * j);
	tmp = 0.0;
	if (i <= -7.5e+147)
		tmp = k * t_7;
	elseif (i <= -2.65e+106)
		tmp = (z * c) * ((t * i) - (y0 * y3));
	elseif (i <= -1.1e+101)
		tmp = y1 * (((k * (y2 * y4)) + (a * ((z * y3) - (x * y2)))) - (i * (z * k)));
	elseif (i <= -3.6e-46)
		tmp = t_5;
	elseif (i <= -4.1e-88)
		tmp = y4 * (((y1 * ((k * y2) - (j * y3))) - (b * t_9)) + (c * ((y * y3) - (t * y2))));
	elseif (i <= -8.5e-168)
		tmp = t_3;
	elseif (i <= -3.6e-213)
		tmp = (z * a) * ((y1 * y3) - (t * b));
	elseif (i <= -1.52e-263)
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	elseif (i <= 4.8e-267)
		tmp = y2 * (((k * t_4) + (x * t_1)) + (t * ((a * y5) - (c * y4))));
	elseif (i <= 3.8e-218)
		tmp = z * ((k * t_6) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	elseif (i <= 6e-200)
		tmp = t_3;
	elseif (i <= 2.15e-128)
		tmp = t_8;
	elseif (i <= 1.16e-52)
		tmp = t_5;
	elseif (i <= 1.02e+109)
		tmp = t_8;
	else
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((c * ((z * t) - (x * y))) + (y5 * t_9)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = 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 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(z * t$95$6), $MachinePrecision]}, Block[{t$95$8 = N[(k * N[(N[(N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$4), $MachinePrecision]), $MachinePrecision] + t$95$7), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -7.5e+147], N[(k * t$95$7), $MachinePrecision], If[LessEqual[i, -2.65e+106], N[(N[(z * c), $MachinePrecision] * N[(N[(t * i), $MachinePrecision] - N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.1e+101], N[(y1 * N[(N[(N[(k * N[(y2 * y4), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -3.6e-46], t$95$5, If[LessEqual[i, -4.1e-88], N[(y4 * N[(N[(N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * t$95$9), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -8.5e-168], t$95$3, If[LessEqual[i, -3.6e-213], N[(N[(z * a), $MachinePrecision] * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.52e-263], N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.8e-267], N[(y2 * N[(N[(N[(k * t$95$4), $MachinePrecision] + N[(x * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.8e-218], N[(z * N[(N[(k * t$95$6), $MachinePrecision] + N[(N[(t * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 6e-200], t$95$3, If[LessEqual[i, 2.15e-128], t$95$8, If[LessEqual[i, 1.16e-52], t$95$5, If[LessEqual[i, 1.02e+109], t$95$8, N[(i * N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(c * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * t$95$9), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 12 regimes

2. if i < -7.50000000000000037e147

   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 28.7%

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

   5. Taylor expanded in z around -inf 32.6%

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

   6. Taylor expanded in k around inf 53.9%

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

   if -7.50000000000000037e147 < i < -2.65e106

   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%

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

   5. Taylor expanded in c around inf 50.3%

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

   6. Taylor expanded in z around inf 70.4%

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

      1. associate-*r* 70.4%

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

      2. +-commutative 70.4%

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

      3. mul-1-neg 70.4%

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

      4. unsub-neg 70.4%

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

      5. *-commutative 70.4%

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

   8. Simplified 70.4%

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

   if -2.65e106 < i < -1.1e101

   1. Initial program 25.0%

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

   3. Taylor expanded in y1 around inf 75.0%

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

   4. Taylor expanded in j around 0 100.0%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + k \cdot \left(y2 \cdot y4\right)\right) - i \cdot \left(k \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. *-commutative 100.0%

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

      5. *-commutative 100.0%

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

   6. Simplified 100.0%

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

   if -1.1e101 < i < -3.6e-46 or 2.14999999999999997e-128 < i < 1.1599999999999999e-52

   1. Initial program 37.4%

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

   3. Taylor expanded in j around inf 63.5%

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

   if -3.6e-46 < i < -4.1000000000000001e-88

   1. Initial program 25.0%

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

   3. Taylor expanded in y4 around inf 92.0%

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

   if -4.1000000000000001e-88 < i < -8.4999999999999994e-168 or 3.7999999999999999e-218 < i < 5.99999999999999989e-200

   1. Initial program 47.2%

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

   3. Simplified 47.1%

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

   5. Taylor expanded in x around inf 83.8%

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

   if -8.4999999999999994e-168 < i < -3.6000000000000001e-213

   1. Initial program 38.4%

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

   3. Simplified 38.4%

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

   5. Taylor expanded in a around inf 74.0%

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

   6. Taylor expanded in z around inf 63.8%

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

      1. associate-*r* 63.8%

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

      2. *-commutative 63.8%

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

      3. +-commutative 63.8%

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

      4. mul-1-neg 63.8%

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

      5. unsub-neg 63.8%

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

   8. Simplified 63.8%

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

   if -3.6000000000000001e-213 < i < -1.52000000000000005e-263

   1. Initial program 28.6%

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

   3. Simplified 28.6%

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

   5. Taylor expanded in b around inf 72.0%

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

   if -1.52000000000000005e-263 < i < 4.7999999999999996e-267

   1. Initial program 10.5%

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

   3. Taylor expanded in y2 around inf 60.9%

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

   if 4.7999999999999996e-267 < i < 3.7999999999999999e-218

   1. Initial program 14.3%

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

   3. Simplified 14.3%

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

   5. Taylor expanded in z around -inf 85.7%

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

   if 5.99999999999999989e-200 < i < 2.14999999999999997e-128 or 1.1599999999999999e-52 < i < 1.01999999999999994e109

   1. Initial program 28.5%

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

   3. Taylor expanded in k around inf 60.8%

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

   if 1.01999999999999994e109 < i

   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%

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

   5. Taylor expanded in i around -inf 71.7%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
3. Recombined 12 regimes into one program.

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -7.5 \cdot 10^{+147}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;i \leq -2.65 \cdot 10^{+106}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(t \cdot i - y0 \cdot y3\right)\\ \mathbf{elif}\;i \leq -1.1 \cdot 10^{+101}:\\ \;\;\;\;y1 \cdot \left(\left(k \cdot \left(y2 \cdot y4\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right) - i \cdot \left(z \cdot k\right)\right)\\ \mathbf{elif}\;i \leq -3.6 \cdot 10^{-46}:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq -4.1 \cdot 10^{-88}:\\ \;\;\;\;y4 \cdot \left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - b \cdot \left(y \cdot k - t \cdot j\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq -8.5 \cdot 10^{-168}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq -3.6 \cdot 10^{-213}:\\ \;\;\;\;\left(z \cdot a\right) \cdot \left(y1 \cdot y3 - t \cdot b\right)\\ \mathbf{elif}\;i \leq -1.52 \cdot 10^{-263}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{-267}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq 3.8 \cdot 10^{-218}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot \left(c \cdot i - a \cdot b\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;i \leq 6 \cdot 10^{-200}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq 2.15 \cdot 10^{-128}:\\ \;\;\;\;k \cdot \left(\left(y \cdot \left(i \cdot y5 - b \cdot y4\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;i \leq 1.16 \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(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq 1.02 \cdot 10^{+109}:\\ \;\;\;\;k \cdot \left(\left(y \cdot \left(i \cdot y5 - b \cdot y4\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(c \cdot \left(z \cdot t - x \cdot y\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 52.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot j - y \cdot k\\ t_2 := x \cdot y - z \cdot t\\ t_3 := \left(\left(\left(\left(\left(a \cdot b - c \cdot i\right) \cdot t\_2 + \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t\_1 \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + \left(t \cdot y2 - y \cdot y3\right) \cdot \left(a \cdot y5 - c \cdot y4\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ \mathbf{if}\;t\_3 \leq \infty:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(a \cdot t\_2 + y4 \cdot t\_1\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

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

C

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

Python

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

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(t * j) - Float64(y * k))
	t_2 = Float64(Float64(x * y) - Float64(z * t))
	t_3 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(a * b) - Float64(c * i)) * t_2) + Float64(Float64(Float64(x * j) - Float64(z * k)) * Float64(Float64(i * y1) - Float64(b * y0)))) + Float64(Float64(Float64(x * y2) - Float64(z * y3)) * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(t_1 * 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_3 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(b * Float64(Float64(Float64(a * t_2) + Float64(y4 * t_1)) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (t * j) - (y * k);
	t_2 = (x * y) - (z * t);
	t_3 = (((((((a * b) - (c * i)) * t_2) + (((x * j) - (z * k)) * ((i * y1) - (b * y0)))) + (((x * y2) - (z * y3)) * ((c * y0) - (a * y1)))) + (t_1 * ((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_3 <= Inf)
		tmp = t_3;
	else
		tmp = b * (((a * t_2) + (y4 * t_1)) + (y0 * ((z * k) - (x * j))));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 90.2%

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

   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 0.6%

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

   5. Taylor expanded in b around inf 40.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 57.1%

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

Alternative 3: 40.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot y3 - x \cdot y2\\ t_2 := x \cdot y - z \cdot t\\ t_3 := i \cdot y1 - b \cdot y0\\ t_4 := x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot t\_3\right)\\ t_5 := 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 t\_3\right)\\ t_6 := b \cdot y0 - i \cdot y1\\ t_7 := z \cdot t\_6\\ t_8 := k \cdot \left(\left(y \cdot \left(i \cdot y5 - b \cdot y4\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t\_7\right)\\ t_9 := y \cdot k - t \cdot j\\ \mathbf{if}\;i \leq -8.6 \cdot 10^{+151}:\\ \;\;\;\;k \cdot t\_7\\ \mathbf{elif}\;i \leq -7.2 \cdot 10^{+106}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(t \cdot i - y0 \cdot y3\right)\\ \mathbf{elif}\;i \leq -1.65 \cdot 10^{+101}:\\ \;\;\;\;y1 \cdot \left(\left(k \cdot \left(y2 \cdot y4\right) + a \cdot t\_1\right) - i \cdot \left(z \cdot k\right)\right)\\ \mathbf{elif}\;i \leq -1.62 \cdot 10^{-31}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;i \leq -1.7 \cdot 10^{-95}:\\ \;\;\;\;y4 \cdot \left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - b \cdot t\_9\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq -3.7 \cdot 10^{-165}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;i \leq -2.4 \cdot 10^{-218}:\\ \;\;\;\;a \cdot \left(\left(y1 \cdot t\_1 + b \cdot t\_2\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;i \leq -5.3 \cdot 10^{-267}:\\ \;\;\;\;b \cdot \left(\left(a \cdot t\_2 + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;i \leq 4.05 \cdot 10^{-218}:\\ \;\;\;\;z \cdot \left(k \cdot t\_6 + \left(t \cdot \left(c \cdot i - a \cdot b\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;i \leq 1.65 \cdot 10^{-202}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;i \leq 2.4 \cdot 10^{-128}:\\ \;\;\;\;t\_8\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{-53}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{+109}:\\ \;\;\;\;t\_8\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(c \cdot \left(z \cdot t - x \cdot y\right) + y5 \cdot t\_9\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 (- (* z y3) (* x y2)))
        (t_2 (- (* x y) (* z t)))
        (t_3 (- (* i y1) (* b y0)))
        (t_4
         (*
          x
          (+
           (+ (* y (- (* a b) (* c i))) (* y2 (- (* c y0) (* a y1))))
           (* j t_3))))
        (t_5
         (*
          j
          (+
           (+ (* y3 (- (* y0 y5) (* y1 y4))) (* t (- (* b y4) (* i y5))))
           (* x t_3))))
        (t_6 (- (* b y0) (* i y1)))
        (t_7 (* z t_6))
        (t_8
         (*
          k
          (+
           (+ (* y (- (* i y5) (* b y4))) (* y2 (- (* y1 y4) (* y0 y5))))
           t_7)))
        (t_9 (- (* y k) (* t j))))
   (if (<= i -8.6e+151)
     (* k t_7)
     (if (<= i -7.2e+106)
       (* (* z c) (- (* t i) (* y0 y3)))
       (if (<= i -1.65e+101)
         (* y1 (- (+ (* k (* y2 y4)) (* a t_1)) (* i (* z k))))
         (if (<= i -1.62e-31)
           t_5
           (if (<= i -1.7e-95)
             (*
              y4
              (+
               (- (* y1 (- (* k y2) (* j y3))) (* b t_9))
               (* c (- (* y y3) (* t y2)))))
             (if (<= i -3.7e-165)
               t_4
               (if (<= i -2.4e-218)
                 (*
                  a
                  (+ (+ (* y1 t_1) (* b t_2)) (* y5 (- (* t y2) (* y y3)))))
                 (if (<= i -5.3e-267)
                   (*
                    b
                    (+
                     (+ (* a t_2) (* y4 (- (* t j) (* y k))))
                     (* y0 (- (* z k) (* x j)))))
                   (if (<= i 4.05e-218)
                     (*
                      z
                      (+
                       (* k t_6)
                       (+
                        (* t (- (* c i) (* a b)))
                        (* y3 (- (* a y1) (* c y0))))))
                     (if (<= i 1.65e-202)
                       t_4
                       (if (<= i 2.4e-128)
                         t_8
                         (if (<= i 1.1e-53)
                           t_5
                           (if (<= i 1.1e+109)
                             t_8
                             (*
                              i
                              (+
                               (* y1 (- (* x j) (* z k)))
                               (+
                                (* c (- (* z t) (* x y)))
                                (* y5 t_9)))))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (z * y3) - (x * y2);
	double t_2 = (x * y) - (z * t);
	double t_3 = (i * y1) - (b * y0);
	double t_4 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_3));
	double t_5 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * t_3));
	double t_6 = (b * y0) - (i * y1);
	double t_7 = z * t_6;
	double t_8 = k * (((y * ((i * y5) - (b * y4))) + (y2 * ((y1 * y4) - (y0 * y5)))) + t_7);
	double t_9 = (y * k) - (t * j);
	double tmp;
	if (i <= -8.6e+151) {
		tmp = k * t_7;
	} else if (i <= -7.2e+106) {
		tmp = (z * c) * ((t * i) - (y0 * y3));
	} else if (i <= -1.65e+101) {
		tmp = y1 * (((k * (y2 * y4)) + (a * t_1)) - (i * (z * k)));
	} else if (i <= -1.62e-31) {
		tmp = t_5;
	} else if (i <= -1.7e-95) {
		tmp = y4 * (((y1 * ((k * y2) - (j * y3))) - (b * t_9)) + (c * ((y * y3) - (t * y2))));
	} else if (i <= -3.7e-165) {
		tmp = t_4;
	} else if (i <= -2.4e-218) {
		tmp = a * (((y1 * t_1) + (b * t_2)) + (y5 * ((t * y2) - (y * y3))));
	} else if (i <= -5.3e-267) {
		tmp = b * (((a * t_2) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (i <= 4.05e-218) {
		tmp = z * ((k * t_6) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	} else if (i <= 1.65e-202) {
		tmp = t_4;
	} else if (i <= 2.4e-128) {
		tmp = t_8;
	} else if (i <= 1.1e-53) {
		tmp = t_5;
	} else if (i <= 1.1e+109) {
		tmp = t_8;
	} else {
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((c * ((z * t) - (x * y))) + (y5 * t_9)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = (z * y3) - (x * y2)
    t_2 = (x * y) - (z * t)
    t_3 = (i * y1) - (b * y0)
    t_4 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_3))
    t_5 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * t_3))
    t_6 = (b * y0) - (i * y1)
    t_7 = z * t_6
    t_8 = k * (((y * ((i * y5) - (b * y4))) + (y2 * ((y1 * y4) - (y0 * y5)))) + t_7)
    t_9 = (y * k) - (t * j)
    if (i <= (-8.6d+151)) then
        tmp = k * t_7
    else if (i <= (-7.2d+106)) then
        tmp = (z * c) * ((t * i) - (y0 * y3))
    else if (i <= (-1.65d+101)) then
        tmp = y1 * (((k * (y2 * y4)) + (a * t_1)) - (i * (z * k)))
    else if (i <= (-1.62d-31)) then
        tmp = t_5
    else if (i <= (-1.7d-95)) then
        tmp = y4 * (((y1 * ((k * y2) - (j * y3))) - (b * t_9)) + (c * ((y * y3) - (t * y2))))
    else if (i <= (-3.7d-165)) then
        tmp = t_4
    else if (i <= (-2.4d-218)) then
        tmp = a * (((y1 * t_1) + (b * t_2)) + (y5 * ((t * y2) - (y * y3))))
    else if (i <= (-5.3d-267)) then
        tmp = b * (((a * t_2) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    else if (i <= 4.05d-218) then
        tmp = z * ((k * t_6) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))))
    else if (i <= 1.65d-202) then
        tmp = t_4
    else if (i <= 2.4d-128) then
        tmp = t_8
    else if (i <= 1.1d-53) then
        tmp = t_5
    else if (i <= 1.1d+109) then
        tmp = t_8
    else
        tmp = i * ((y1 * ((x * j) - (z * k))) + ((c * ((z * t) - (x * y))) + (y5 * t_9)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (z * y3) - (x * y2);
	double t_2 = (x * y) - (z * t);
	double t_3 = (i * y1) - (b * y0);
	double t_4 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_3));
	double t_5 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * t_3));
	double t_6 = (b * y0) - (i * y1);
	double t_7 = z * t_6;
	double t_8 = k * (((y * ((i * y5) - (b * y4))) + (y2 * ((y1 * y4) - (y0 * y5)))) + t_7);
	double t_9 = (y * k) - (t * j);
	double tmp;
	if (i <= -8.6e+151) {
		tmp = k * t_7;
	} else if (i <= -7.2e+106) {
		tmp = (z * c) * ((t * i) - (y0 * y3));
	} else if (i <= -1.65e+101) {
		tmp = y1 * (((k * (y2 * y4)) + (a * t_1)) - (i * (z * k)));
	} else if (i <= -1.62e-31) {
		tmp = t_5;
	} else if (i <= -1.7e-95) {
		tmp = y4 * (((y1 * ((k * y2) - (j * y3))) - (b * t_9)) + (c * ((y * y3) - (t * y2))));
	} else if (i <= -3.7e-165) {
		tmp = t_4;
	} else if (i <= -2.4e-218) {
		tmp = a * (((y1 * t_1) + (b * t_2)) + (y5 * ((t * y2) - (y * y3))));
	} else if (i <= -5.3e-267) {
		tmp = b * (((a * t_2) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (i <= 4.05e-218) {
		tmp = z * ((k * t_6) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	} else if (i <= 1.65e-202) {
		tmp = t_4;
	} else if (i <= 2.4e-128) {
		tmp = t_8;
	} else if (i <= 1.1e-53) {
		tmp = t_5;
	} else if (i <= 1.1e+109) {
		tmp = t_8;
	} else {
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((c * ((z * t) - (x * y))) + (y5 * t_9)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (z * y3) - (x * y2)
	t_2 = (x * y) - (z * t)
	t_3 = (i * y1) - (b * y0)
	t_4 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_3))
	t_5 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * t_3))
	t_6 = (b * y0) - (i * y1)
	t_7 = z * t_6
	t_8 = k * (((y * ((i * y5) - (b * y4))) + (y2 * ((y1 * y4) - (y0 * y5)))) + t_7)
	t_9 = (y * k) - (t * j)
	tmp = 0
	if i <= -8.6e+151:
		tmp = k * t_7
	elif i <= -7.2e+106:
		tmp = (z * c) * ((t * i) - (y0 * y3))
	elif i <= -1.65e+101:
		tmp = y1 * (((k * (y2 * y4)) + (a * t_1)) - (i * (z * k)))
	elif i <= -1.62e-31:
		tmp = t_5
	elif i <= -1.7e-95:
		tmp = y4 * (((y1 * ((k * y2) - (j * y3))) - (b * t_9)) + (c * ((y * y3) - (t * y2))))
	elif i <= -3.7e-165:
		tmp = t_4
	elif i <= -2.4e-218:
		tmp = a * (((y1 * t_1) + (b * t_2)) + (y5 * ((t * y2) - (y * y3))))
	elif i <= -5.3e-267:
		tmp = b * (((a * t_2) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	elif i <= 4.05e-218:
		tmp = z * ((k * t_6) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))))
	elif i <= 1.65e-202:
		tmp = t_4
	elif i <= 2.4e-128:
		tmp = t_8
	elif i <= 1.1e-53:
		tmp = t_5
	elif i <= 1.1e+109:
		tmp = t_8
	else:
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((c * ((z * t) - (x * y))) + (y5 * t_9)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(z * y3) - Float64(x * y2))
	t_2 = Float64(Float64(x * y) - Float64(z * t))
	t_3 = Float64(Float64(i * y1) - Float64(b * y0))
	t_4 = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * t_3)))
	t_5 = Float64(j * Float64(Float64(Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(t * Float64(Float64(b * y4) - Float64(i * y5)))) + Float64(x * t_3)))
	t_6 = Float64(Float64(b * y0) - Float64(i * y1))
	t_7 = Float64(z * t_6)
	t_8 = Float64(k * Float64(Float64(Float64(y * Float64(Float64(i * y5) - Float64(b * y4))) + Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5)))) + t_7))
	t_9 = Float64(Float64(y * k) - Float64(t * j))
	tmp = 0.0
	if (i <= -8.6e+151)
		tmp = Float64(k * t_7);
	elseif (i <= -7.2e+106)
		tmp = Float64(Float64(z * c) * Float64(Float64(t * i) - Float64(y0 * y3)));
	elseif (i <= -1.65e+101)
		tmp = Float64(y1 * Float64(Float64(Float64(k * Float64(y2 * y4)) + Float64(a * t_1)) - Float64(i * Float64(z * k))));
	elseif (i <= -1.62e-31)
		tmp = t_5;
	elseif (i <= -1.7e-95)
		tmp = Float64(y4 * Float64(Float64(Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))) - Float64(b * t_9)) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (i <= -3.7e-165)
		tmp = t_4;
	elseif (i <= -2.4e-218)
		tmp = Float64(a * Float64(Float64(Float64(y1 * t_1) + Float64(b * t_2)) + Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3)))));
	elseif (i <= -5.3e-267)
		tmp = Float64(b * Float64(Float64(Float64(a * t_2) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (i <= 4.05e-218)
		tmp = Float64(z * Float64(Float64(k * t_6) + Float64(Float64(t * Float64(Float64(c * i) - Float64(a * b))) + Float64(y3 * Float64(Float64(a * y1) - Float64(c * y0))))));
	elseif (i <= 1.65e-202)
		tmp = t_4;
	elseif (i <= 2.4e-128)
		tmp = t_8;
	elseif (i <= 1.1e-53)
		tmp = t_5;
	elseif (i <= 1.1e+109)
		tmp = t_8;
	else
		tmp = Float64(i * Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) + Float64(Float64(c * Float64(Float64(z * t) - Float64(x * y))) + Float64(y5 * t_9))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (z * y3) - (x * y2);
	t_2 = (x * y) - (z * t);
	t_3 = (i * y1) - (b * y0);
	t_4 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_3));
	t_5 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * t_3));
	t_6 = (b * y0) - (i * y1);
	t_7 = z * t_6;
	t_8 = k * (((y * ((i * y5) - (b * y4))) + (y2 * ((y1 * y4) - (y0 * y5)))) + t_7);
	t_9 = (y * k) - (t * j);
	tmp = 0.0;
	if (i <= -8.6e+151)
		tmp = k * t_7;
	elseif (i <= -7.2e+106)
		tmp = (z * c) * ((t * i) - (y0 * y3));
	elseif (i <= -1.65e+101)
		tmp = y1 * (((k * (y2 * y4)) + (a * t_1)) - (i * (z * k)));
	elseif (i <= -1.62e-31)
		tmp = t_5;
	elseif (i <= -1.7e-95)
		tmp = y4 * (((y1 * ((k * y2) - (j * y3))) - (b * t_9)) + (c * ((y * y3) - (t * y2))));
	elseif (i <= -3.7e-165)
		tmp = t_4;
	elseif (i <= -2.4e-218)
		tmp = a * (((y1 * t_1) + (b * t_2)) + (y5 * ((t * y2) - (y * y3))));
	elseif (i <= -5.3e-267)
		tmp = b * (((a * t_2) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	elseif (i <= 4.05e-218)
		tmp = z * ((k * t_6) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	elseif (i <= 1.65e-202)
		tmp = t_4;
	elseif (i <= 2.4e-128)
		tmp = t_8;
	elseif (i <= 1.1e-53)
		tmp = t_5;
	elseif (i <= 1.1e+109)
		tmp = t_8;
	else
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((c * ((z * t) - (x * y))) + (y5 * t_9)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = 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 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(z * t$95$6), $MachinePrecision]}, Block[{t$95$8 = N[(k * N[(N[(N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$7), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -8.6e+151], N[(k * t$95$7), $MachinePrecision], If[LessEqual[i, -7.2e+106], N[(N[(z * c), $MachinePrecision] * N[(N[(t * i), $MachinePrecision] - N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.65e+101], N[(y1 * N[(N[(N[(k * N[(y2 * y4), $MachinePrecision]), $MachinePrecision] + N[(a * t$95$1), $MachinePrecision]), $MachinePrecision] - N[(i * N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.62e-31], t$95$5, If[LessEqual[i, -1.7e-95], N[(y4 * N[(N[(N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * t$95$9), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -3.7e-165], t$95$4, If[LessEqual[i, -2.4e-218], N[(a * N[(N[(N[(y1 * t$95$1), $MachinePrecision] + N[(b * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -5.3e-267], N[(b * N[(N[(N[(a * t$95$2), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.05e-218], N[(z * N[(N[(k * t$95$6), $MachinePrecision] + N[(N[(t * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.65e-202], t$95$4, If[LessEqual[i, 2.4e-128], t$95$8, If[LessEqual[i, 1.1e-53], t$95$5, If[LessEqual[i, 1.1e+109], t$95$8, N[(i * N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(c * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * t$95$9), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 11 regimes

2. if i < -8.59999999999999965e151

   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 28.7%

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

   5. Taylor expanded in z around -inf 32.6%

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

   6. Taylor expanded in k around inf 53.9%

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

   if -8.59999999999999965e151 < i < -7.2000000000000002e106

   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%

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

   5. Taylor expanded in c around inf 50.3%

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

   6. Taylor expanded in z around inf 70.4%

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

      1. associate-*r* 70.4%

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

      2. +-commutative 70.4%

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

      3. mul-1-neg 70.4%

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

      4. unsub-neg 70.4%

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

      5. *-commutative 70.4%

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

   8. Simplified 70.4%

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

   if -7.2000000000000002e106 < i < -1.65000000000000006e101

   1. Initial program 25.0%

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

   3. Taylor expanded in y1 around inf 75.0%

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

   4. Taylor expanded in j around 0 100.0%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + k \cdot \left(y2 \cdot y4\right)\right) - i \cdot \left(k \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. *-commutative 100.0%

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

      5. *-commutative 100.0%

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

   6. Simplified 100.0%

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

   if -1.65000000000000006e101 < i < -1.62e-31 or 2.3999999999999998e-128 < i < 1.10000000000000009e-53

   1. Initial program 37.4%

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

   3. Taylor expanded in j around inf 63.5%

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

   if -1.62e-31 < i < -1.69999999999999997e-95

   1. Initial program 25.0%

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

   3. Taylor expanded in y4 around inf 92.0%

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

   if -1.69999999999999997e-95 < i < -3.70000000000000001e-165 or 4.04999999999999994e-218 < i < 1.64999999999999995e-202

   1. Initial program 47.2%

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

   3. Simplified 47.1%

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

   5. Taylor expanded in x around inf 83.8%

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

   if -3.70000000000000001e-165 < i < -2.4000000000000001e-218

   1. Initial program 38.4%

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

   3. Simplified 38.4%

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

   5. Taylor expanded in a around inf 74.0%

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

   if -2.4000000000000001e-218 < i < -5.2999999999999996e-267

   1. Initial program 28.6%

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

   3. Simplified 28.6%

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

   5. Taylor expanded in b around inf 72.0%

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

   if -5.2999999999999996e-267 < i < 4.04999999999999994e-218

   1. Initial program 12.1%

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

   3. Simplified 12.1%

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

   5. Taylor expanded in z around -inf 58.9%

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

   if 1.64999999999999995e-202 < i < 2.3999999999999998e-128 or 1.10000000000000009e-53 < i < 1.1e109

   1. Initial program 28.5%

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

   3. Taylor expanded in k around inf 60.8%

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

   if 1.1e109 < i

   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%

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

   5. Taylor expanded in i around -inf 71.7%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
3. Recombined 11 regimes into one program.

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -8.6 \cdot 10^{+151}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;i \leq -7.2 \cdot 10^{+106}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(t \cdot i - y0 \cdot y3\right)\\ \mathbf{elif}\;i \leq -1.65 \cdot 10^{+101}:\\ \;\;\;\;y1 \cdot \left(\left(k \cdot \left(y2 \cdot y4\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right) - i \cdot \left(z \cdot k\right)\right)\\ \mathbf{elif}\;i \leq -1.62 \cdot 10^{-31}:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq -1.7 \cdot 10^{-95}:\\ \;\;\;\;y4 \cdot \left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - b \cdot \left(y \cdot k - t \cdot j\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq -3.7 \cdot 10^{-165}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq -2.4 \cdot 10^{-218}:\\ \;\;\;\;a \cdot \left(\left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right) + b \cdot \left(x \cdot y - z \cdot t\right)\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;i \leq -5.3 \cdot 10^{-267}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;i \leq 4.05 \cdot 10^{-218}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot \left(c \cdot i - a \cdot b\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;i \leq 1.65 \cdot 10^{-202}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq 2.4 \cdot 10^{-128}:\\ \;\;\;\;k \cdot \left(\left(y \cdot \left(i \cdot y5 - b \cdot y4\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{-53}:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{+109}:\\ \;\;\;\;k \cdot \left(\left(y \cdot \left(i \cdot y5 - b \cdot y4\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(c \cdot \left(z \cdot t - x \cdot y\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 39.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot y2 - j \cdot y3\\ t_2 := y1 \cdot y4 - y0 \cdot y5\\ t_3 := z \cdot \left(b \cdot y0 - i \cdot y1\right)\\ t_4 := b \cdot y4 - i \cdot y5\\ t_5 := y4 \cdot \left(\left(y1 \cdot t\_1 - b \cdot \left(y \cdot k - t \cdot j\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ t_6 := j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot t\_4\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{if}\;k \leq -1.4 \cdot 10^{+185}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq -2.15 \cdot 10^{+108}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0 - t \cdot a\right)\right)\\ \mathbf{elif}\;k \leq -8 \cdot 10^{+39}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;k \leq -3.6 \cdot 10^{-31}:\\ \;\;\;\;k \cdot t\_3\\ \mathbf{elif}\;k \leq -1.22 \cdot 10^{-71}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;k \leq -7.5 \cdot 10^{-219}:\\ \;\;\;\;y0 \cdot \left(\left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;k \leq 9 \cdot 10^{-302}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;k \leq 2.6 \cdot 10^{-253}:\\ \;\;\;\;t\_1 \cdot t\_2 + t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot t\_4\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 1.06 \cdot 10^{-22}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;k \leq 5.2 \cdot 10^{+34}:\\ \;\;\;\;y1 \cdot \left(\left(k \cdot \left(y2 \cdot y4\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right) - i \cdot \left(z \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(\left(y \cdot \left(i \cdot y5 - b \cdot y4\right) + y2 \cdot t\_2\right) + t\_3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* k y2) (* j y3)))
        (t_2 (- (* y1 y4) (* y0 y5)))
        (t_3 (* z (- (* b y0) (* i y1))))
        (t_4 (- (* b y4) (* i y5)))
        (t_5
         (*
          y4
          (+
           (- (* y1 t_1) (* b (- (* y k) (* t j))))
           (* c (- (* y y3) (* t y2))))))
        (t_6
         (*
          j
          (+
           (+ (* y3 (- (* y0 y5) (* y1 y4))) (* t t_4))
           (* x (- (* i y1) (* b y0)))))))
   (if (<= k -1.4e+185)
     (* b (* k (- (* z y0) (* y y4))))
     (if (<= k -2.15e+108)
       (* b (* z (- (* k y0) (* t a))))
       (if (<= k -8e+39)
         t_5
         (if (<= k -3.6e-31)
           (* k t_3)
           (if (<= k -1.22e-71)
             t_6
             (if (<= k -7.5e-219)
               (*
                y0
                (+
                 (+ (* y5 (- (* j y3) (* k y2))) (* c (- (* x y2) (* z y3))))
                 (* b (- (* z k) (* x j)))))
               (if (<= k 9e-302)
                 t_5
                 (if (<= k 2.6e-253)
                   (+
                    (* t_1 t_2)
                    (*
                     t
                     (+
                      (+ (* z (- (* c i) (* a b))) (* j t_4))
                      (* y2 (- (* a y5) (* c y4))))))
                   (if (<= k 1.06e-22)
                     t_6
                     (if (<= k 5.2e+34)
                       (*
                        y1
                        (-
                         (+ (* k (* y2 y4)) (* a (- (* z y3) (* x y2))))
                         (* i (* z k))))
                       (*
                        k
                        (+
                         (+ (* y (- (* i y5) (* b y4))) (* y2 t_2))
                         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 = (k * y2) - (j * y3);
	double t_2 = (y1 * y4) - (y0 * y5);
	double t_3 = z * ((b * y0) - (i * y1));
	double t_4 = (b * y4) - (i * y5);
	double t_5 = y4 * (((y1 * t_1) - (b * ((y * k) - (t * j)))) + (c * ((y * y3) - (t * y2))));
	double t_6 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * t_4)) + (x * ((i * y1) - (b * y0))));
	double tmp;
	if (k <= -1.4e+185) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (k <= -2.15e+108) {
		tmp = b * (z * ((k * y0) - (t * a)));
	} else if (k <= -8e+39) {
		tmp = t_5;
	} else if (k <= -3.6e-31) {
		tmp = k * t_3;
	} else if (k <= -1.22e-71) {
		tmp = t_6;
	} else if (k <= -7.5e-219) {
		tmp = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * ((x * y2) - (z * y3)))) + (b * ((z * k) - (x * j))));
	} else if (k <= 9e-302) {
		tmp = t_5;
	} else if (k <= 2.6e-253) {
		tmp = (t_1 * t_2) + (t * (((z * ((c * i) - (a * b))) + (j * t_4)) + (y2 * ((a * y5) - (c * y4)))));
	} else if (k <= 1.06e-22) {
		tmp = t_6;
	} else if (k <= 5.2e+34) {
		tmp = y1 * (((k * (y2 * y4)) + (a * ((z * y3) - (x * y2)))) - (i * (z * k)));
	} else {
		tmp = k * (((y * ((i * y5) - (b * y4))) + (y2 * t_2)) + t_3);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = (k * y2) - (j * y3)
    t_2 = (y1 * y4) - (y0 * y5)
    t_3 = z * ((b * y0) - (i * y1))
    t_4 = (b * y4) - (i * y5)
    t_5 = y4 * (((y1 * t_1) - (b * ((y * k) - (t * j)))) + (c * ((y * y3) - (t * y2))))
    t_6 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * t_4)) + (x * ((i * y1) - (b * y0))))
    if (k <= (-1.4d+185)) then
        tmp = b * (k * ((z * y0) - (y * y4)))
    else if (k <= (-2.15d+108)) then
        tmp = b * (z * ((k * y0) - (t * a)))
    else if (k <= (-8d+39)) then
        tmp = t_5
    else if (k <= (-3.6d-31)) then
        tmp = k * t_3
    else if (k <= (-1.22d-71)) then
        tmp = t_6
    else if (k <= (-7.5d-219)) then
        tmp = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * ((x * y2) - (z * y3)))) + (b * ((z * k) - (x * j))))
    else if (k <= 9d-302) then
        tmp = t_5
    else if (k <= 2.6d-253) then
        tmp = (t_1 * t_2) + (t * (((z * ((c * i) - (a * b))) + (j * t_4)) + (y2 * ((a * y5) - (c * y4)))))
    else if (k <= 1.06d-22) then
        tmp = t_6
    else if (k <= 5.2d+34) then
        tmp = y1 * (((k * (y2 * y4)) + (a * ((z * y3) - (x * y2)))) - (i * (z * k)))
    else
        tmp = k * (((y * ((i * y5) - (b * y4))) + (y2 * t_2)) + 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 = (k * y2) - (j * y3);
	double t_2 = (y1 * y4) - (y0 * y5);
	double t_3 = z * ((b * y0) - (i * y1));
	double t_4 = (b * y4) - (i * y5);
	double t_5 = y4 * (((y1 * t_1) - (b * ((y * k) - (t * j)))) + (c * ((y * y3) - (t * y2))));
	double t_6 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * t_4)) + (x * ((i * y1) - (b * y0))));
	double tmp;
	if (k <= -1.4e+185) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (k <= -2.15e+108) {
		tmp = b * (z * ((k * y0) - (t * a)));
	} else if (k <= -8e+39) {
		tmp = t_5;
	} else if (k <= -3.6e-31) {
		tmp = k * t_3;
	} else if (k <= -1.22e-71) {
		tmp = t_6;
	} else if (k <= -7.5e-219) {
		tmp = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * ((x * y2) - (z * y3)))) + (b * ((z * k) - (x * j))));
	} else if (k <= 9e-302) {
		tmp = t_5;
	} else if (k <= 2.6e-253) {
		tmp = (t_1 * t_2) + (t * (((z * ((c * i) - (a * b))) + (j * t_4)) + (y2 * ((a * y5) - (c * y4)))));
	} else if (k <= 1.06e-22) {
		tmp = t_6;
	} else if (k <= 5.2e+34) {
		tmp = y1 * (((k * (y2 * y4)) + (a * ((z * y3) - (x * y2)))) - (i * (z * k)));
	} else {
		tmp = k * (((y * ((i * y5) - (b * y4))) + (y2 * t_2)) + 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 = (k * y2) - (j * y3)
	t_2 = (y1 * y4) - (y0 * y5)
	t_3 = z * ((b * y0) - (i * y1))
	t_4 = (b * y4) - (i * y5)
	t_5 = y4 * (((y1 * t_1) - (b * ((y * k) - (t * j)))) + (c * ((y * y3) - (t * y2))))
	t_6 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * t_4)) + (x * ((i * y1) - (b * y0))))
	tmp = 0
	if k <= -1.4e+185:
		tmp = b * (k * ((z * y0) - (y * y4)))
	elif k <= -2.15e+108:
		tmp = b * (z * ((k * y0) - (t * a)))
	elif k <= -8e+39:
		tmp = t_5
	elif k <= -3.6e-31:
		tmp = k * t_3
	elif k <= -1.22e-71:
		tmp = t_6
	elif k <= -7.5e-219:
		tmp = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * ((x * y2) - (z * y3)))) + (b * ((z * k) - (x * j))))
	elif k <= 9e-302:
		tmp = t_5
	elif k <= 2.6e-253:
		tmp = (t_1 * t_2) + (t * (((z * ((c * i) - (a * b))) + (j * t_4)) + (y2 * ((a * y5) - (c * y4)))))
	elif k <= 1.06e-22:
		tmp = t_6
	elif k <= 5.2e+34:
		tmp = y1 * (((k * (y2 * y4)) + (a * ((z * y3) - (x * y2)))) - (i * (z * k)))
	else:
		tmp = k * (((y * ((i * y5) - (b * y4))) + (y2 * t_2)) + 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(k * y2) - Float64(j * y3))
	t_2 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_3 = Float64(z * Float64(Float64(b * y0) - Float64(i * y1)))
	t_4 = Float64(Float64(b * y4) - Float64(i * y5))
	t_5 = Float64(y4 * Float64(Float64(Float64(y1 * t_1) - Float64(b * Float64(Float64(y * k) - Float64(t * j)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))))
	t_6 = Float64(j * Float64(Float64(Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(t * t_4)) + Float64(x * Float64(Float64(i * y1) - Float64(b * y0)))))
	tmp = 0.0
	if (k <= -1.4e+185)
		tmp = Float64(b * Float64(k * Float64(Float64(z * y0) - Float64(y * y4))));
	elseif (k <= -2.15e+108)
		tmp = Float64(b * Float64(z * Float64(Float64(k * y0) - Float64(t * a))));
	elseif (k <= -8e+39)
		tmp = t_5;
	elseif (k <= -3.6e-31)
		tmp = Float64(k * t_3);
	elseif (k <= -1.22e-71)
		tmp = t_6;
	elseif (k <= -7.5e-219)
		tmp = Float64(y0 * Float64(Float64(Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))) + Float64(c * Float64(Float64(x * y2) - Float64(z * y3)))) + Float64(b * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (k <= 9e-302)
		tmp = t_5;
	elseif (k <= 2.6e-253)
		tmp = Float64(Float64(t_1 * t_2) + Float64(t * Float64(Float64(Float64(z * Float64(Float64(c * i) - Float64(a * b))) + Float64(j * t_4)) + Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))))));
	elseif (k <= 1.06e-22)
		tmp = t_6;
	elseif (k <= 5.2e+34)
		tmp = Float64(y1 * Float64(Float64(Float64(k * Float64(y2 * y4)) + Float64(a * Float64(Float64(z * y3) - Float64(x * y2)))) - Float64(i * Float64(z * k))));
	else
		tmp = Float64(k * Float64(Float64(Float64(y * Float64(Float64(i * y5) - Float64(b * y4))) + Float64(y2 * t_2)) + 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 = (k * y2) - (j * y3);
	t_2 = (y1 * y4) - (y0 * y5);
	t_3 = z * ((b * y0) - (i * y1));
	t_4 = (b * y4) - (i * y5);
	t_5 = y4 * (((y1 * t_1) - (b * ((y * k) - (t * j)))) + (c * ((y * y3) - (t * y2))));
	t_6 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * t_4)) + (x * ((i * y1) - (b * y0))));
	tmp = 0.0;
	if (k <= -1.4e+185)
		tmp = b * (k * ((z * y0) - (y * y4)));
	elseif (k <= -2.15e+108)
		tmp = b * (z * ((k * y0) - (t * a)));
	elseif (k <= -8e+39)
		tmp = t_5;
	elseif (k <= -3.6e-31)
		tmp = k * t_3;
	elseif (k <= -1.22e-71)
		tmp = t_6;
	elseif (k <= -7.5e-219)
		tmp = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * ((x * y2) - (z * y3)))) + (b * ((z * k) - (x * j))));
	elseif (k <= 9e-302)
		tmp = t_5;
	elseif (k <= 2.6e-253)
		tmp = (t_1 * t_2) + (t * (((z * ((c * i) - (a * b))) + (j * t_4)) + (y2 * ((a * y5) - (c * y4)))));
	elseif (k <= 1.06e-22)
		tmp = t_6;
	elseif (k <= 5.2e+34)
		tmp = y1 * (((k * (y2 * y4)) + (a * ((z * y3) - (x * y2)))) - (i * (z * k)));
	else
		tmp = k * (((y * ((i * y5) - (b * y4))) + (y2 * t_2)) + 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[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y4 * N[(N[(N[(y1 * t$95$1), $MachinePrecision] - N[(b * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(j * N[(N[(N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * t$95$4), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -1.4e+185], N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -2.15e+108], N[(b * N[(z * N[(N[(k * y0), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -8e+39], t$95$5, If[LessEqual[k, -3.6e-31], N[(k * t$95$3), $MachinePrecision], If[LessEqual[k, -1.22e-71], t$95$6, If[LessEqual[k, -7.5e-219], N[(y0 * N[(N[(N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 9e-302], t$95$5, If[LessEqual[k, 2.6e-253], N[(N[(t$95$1 * t$95$2), $MachinePrecision] + N[(t * N[(N[(N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$4), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.06e-22], t$95$6, If[LessEqual[k, 5.2e+34], N[(y1 * N[(N[(N[(k * N[(y2 * y4), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(N[(N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$2), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if k < -1.39999999999999991e185

   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%

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

   5. Taylor expanded in b around inf 46.7%

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

   6. Taylor expanded in k around -inf 73.8%

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

      1. associate-*r* 73.8%

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

      2. neg-mul-1 73.8%

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

      3. *-commutative 73.8%

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

   8. Simplified 73.8%

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

   if -1.39999999999999991e185 < k < -2.14999999999999998e108

   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%

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

   5. Taylor expanded in b around inf 29.1%

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

   6. Taylor expanded in z around -inf 64.5%

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

      1. associate-*r* 64.5%

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

      2. neg-mul-1 64.5%

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

      3. *-commutative 64.5%

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

   8. Simplified 64.5%

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

   if -2.14999999999999998e108 < k < -7.99999999999999952e39 or -7.4999999999999996e-219 < k < 9.00000000000000018e-302

   1. Initial program 38.2%

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

   3. Taylor expanded in y4 around inf 68.0%

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

   if -7.99999999999999952e39 < k < -3.60000000000000004e-31

   1. Initial program 21.0%

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

   3. Simplified 21.0%

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

   5. Taylor expanded in z around -inf 47.9%

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

   6. Taylor expanded in k around inf 67.1%

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

   if -3.60000000000000004e-31 < k < -1.21999999999999999e-71 or 2.6e-253 < k < 1.06000000000000008e-22

   1. Initial program 24.8%

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

   3. Taylor expanded in j around inf 54.5%

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

   if -1.21999999999999999e-71 < k < -7.4999999999999996e-219

   1. Initial program 49.8%

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

   3. Taylor expanded in y0 around inf 57.0%

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

   if 9.00000000000000018e-302 < k < 2.6e-253

   1. Initial program 46.9%

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

   3. Taylor expanded in t around inf 73.4%

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

   if 1.06000000000000008e-22 < k < 5.19999999999999995e34

   1. Initial program 16.7%

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

   3. Taylor expanded in y1 around inf 59.0%

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

   4. Taylor expanded in j around 0 75.7%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + k \cdot \left(y2 \cdot y4\right)\right) - i \cdot \left(k \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 75.7%

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

      2. mul-1-neg 75.7%

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

      3. unsub-neg 75.7%

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

      4. *-commutative 75.7%

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

      5. *-commutative 75.7%

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

   6. Simplified 75.7%

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

   if 5.19999999999999995e34 < k

   1. Initial program 31.6%

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

   3. Taylor expanded in k around inf 61.5%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.4 \cdot 10^{+185}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq -2.15 \cdot 10^{+108}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0 - t \cdot a\right)\right)\\ \mathbf{elif}\;k \leq -8 \cdot 10^{+39}:\\ \;\;\;\;y4 \cdot \left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - b \cdot \left(y \cdot k - t \cdot j\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq -3.6 \cdot 10^{-31}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;k \leq -1.22 \cdot 10^{-71}:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq -7.5 \cdot 10^{-219}:\\ \;\;\;\;y0 \cdot \left(\left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;k \leq 9 \cdot 10^{-302}:\\ \;\;\;\;y4 \cdot \left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - b \cdot \left(y \cdot k - t \cdot j\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 2.6 \cdot 10^{-253}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 1.06 \cdot 10^{-22}:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 5.2 \cdot 10^{+34}:\\ \;\;\;\;y1 \cdot \left(\left(k \cdot \left(y2 \cdot y4\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right) - i \cdot \left(z \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(\left(y \cdot \left(i \cdot y5 - b \cdot y4\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 35.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot y1 - b \cdot y0\\ t_2 := k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ t_3 := j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot t\_1\right)\\ t_4 := y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\\ \mathbf{if}\;k \leq -5.2 \cdot 10^{+185}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq -6.6 \cdot 10^{+107}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0 - t \cdot a\right)\right)\\ \mathbf{elif}\;k \leq -8.5 \cdot 10^{+39}:\\ \;\;\;\;y4 \cdot \left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - b \cdot \left(y \cdot k - t \cdot j\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq -9.5 \cdot 10^{-8}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;k \leq -5 \cdot 10^{-26}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;k \leq -5.8 \cdot 10^{-96}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;k \leq -1.06 \cdot 10^{-159}:\\ \;\;\;\;x \cdot t\_4\\ \mathbf{elif}\;k \leq -1.18 \cdot 10^{-222}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;k \leq 2.5 \cdot 10^{-286}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + t\_4\right) + j \cdot t\_1\right)\\ \mathbf{elif}\;k \leq 1.9 \cdot 10^{+44}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* i y1) (* b y0)))
        (t_2 (* k (* z (- (* b y0) (* i y1)))))
        (t_3
         (*
          j
          (+
           (+ (* y3 (- (* y0 y5) (* y1 y4))) (* t (- (* b y4) (* i y5))))
           (* x t_1))))
        (t_4 (* y2 (- (* c y0) (* a y1)))))
   (if (<= k -5.2e+185)
     (* b (* k (- (* z y0) (* y y4))))
     (if (<= k -6.6e+107)
       (* b (* z (- (* k y0) (* t a))))
       (if (<= k -8.5e+39)
         (*
          y4
          (+
           (- (* y1 (- (* k y2) (* j y3))) (* b (- (* y k) (* t j))))
           (* c (- (* y y3) (* t y2)))))
         (if (<= k -9.5e-8)
           t_2
           (if (<= k -5e-26)
             (* i (* y1 (- (* x j) (* z k))))
             (if (<= k -5.8e-96)
               t_3
               (if (<= k -1.06e-159)
                 (* x t_4)
                 (if (<= k -1.18e-222)
                   t_3
                   (if (<= k 2.5e-286)
                     (* x (+ (+ (* y (- (* a b) (* c i))) t_4) (* j t_1)))
                     (if (<= k 1.9e+44) t_3 t_2))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (i * y1) - (b * y0);
	double t_2 = k * (z * ((b * y0) - (i * y1)));
	double t_3 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * t_1));
	double t_4 = y2 * ((c * y0) - (a * y1));
	double tmp;
	if (k <= -5.2e+185) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (k <= -6.6e+107) {
		tmp = b * (z * ((k * y0) - (t * a)));
	} else if (k <= -8.5e+39) {
		tmp = y4 * (((y1 * ((k * y2) - (j * y3))) - (b * ((y * k) - (t * j)))) + (c * ((y * y3) - (t * y2))));
	} else if (k <= -9.5e-8) {
		tmp = t_2;
	} else if (k <= -5e-26) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (k <= -5.8e-96) {
		tmp = t_3;
	} else if (k <= -1.06e-159) {
		tmp = x * t_4;
	} else if (k <= -1.18e-222) {
		tmp = t_3;
	} else if (k <= 2.5e-286) {
		tmp = x * (((y * ((a * b) - (c * i))) + t_4) + (j * t_1));
	} else if (k <= 1.9e+44) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (i * y1) - (b * y0)
    t_2 = k * (z * ((b * y0) - (i * y1)))
    t_3 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * t_1))
    t_4 = y2 * ((c * y0) - (a * y1))
    if (k <= (-5.2d+185)) then
        tmp = b * (k * ((z * y0) - (y * y4)))
    else if (k <= (-6.6d+107)) then
        tmp = b * (z * ((k * y0) - (t * a)))
    else if (k <= (-8.5d+39)) then
        tmp = y4 * (((y1 * ((k * y2) - (j * y3))) - (b * ((y * k) - (t * j)))) + (c * ((y * y3) - (t * y2))))
    else if (k <= (-9.5d-8)) then
        tmp = t_2
    else if (k <= (-5d-26)) then
        tmp = i * (y1 * ((x * j) - (z * k)))
    else if (k <= (-5.8d-96)) then
        tmp = t_3
    else if (k <= (-1.06d-159)) then
        tmp = x * t_4
    else if (k <= (-1.18d-222)) then
        tmp = t_3
    else if (k <= 2.5d-286) then
        tmp = x * (((y * ((a * b) - (c * i))) + t_4) + (j * t_1))
    else if (k <= 1.9d+44) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (i * y1) - (b * y0);
	double t_2 = k * (z * ((b * y0) - (i * y1)));
	double t_3 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * t_1));
	double t_4 = y2 * ((c * y0) - (a * y1));
	double tmp;
	if (k <= -5.2e+185) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (k <= -6.6e+107) {
		tmp = b * (z * ((k * y0) - (t * a)));
	} else if (k <= -8.5e+39) {
		tmp = y4 * (((y1 * ((k * y2) - (j * y3))) - (b * ((y * k) - (t * j)))) + (c * ((y * y3) - (t * y2))));
	} else if (k <= -9.5e-8) {
		tmp = t_2;
	} else if (k <= -5e-26) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (k <= -5.8e-96) {
		tmp = t_3;
	} else if (k <= -1.06e-159) {
		tmp = x * t_4;
	} else if (k <= -1.18e-222) {
		tmp = t_3;
	} else if (k <= 2.5e-286) {
		tmp = x * (((y * ((a * b) - (c * i))) + t_4) + (j * t_1));
	} else if (k <= 1.9e+44) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (i * y1) - (b * y0)
	t_2 = k * (z * ((b * y0) - (i * y1)))
	t_3 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * t_1))
	t_4 = y2 * ((c * y0) - (a * y1))
	tmp = 0
	if k <= -5.2e+185:
		tmp = b * (k * ((z * y0) - (y * y4)))
	elif k <= -6.6e+107:
		tmp = b * (z * ((k * y0) - (t * a)))
	elif k <= -8.5e+39:
		tmp = y4 * (((y1 * ((k * y2) - (j * y3))) - (b * ((y * k) - (t * j)))) + (c * ((y * y3) - (t * y2))))
	elif k <= -9.5e-8:
		tmp = t_2
	elif k <= -5e-26:
		tmp = i * (y1 * ((x * j) - (z * k)))
	elif k <= -5.8e-96:
		tmp = t_3
	elif k <= -1.06e-159:
		tmp = x * t_4
	elif k <= -1.18e-222:
		tmp = t_3
	elif k <= 2.5e-286:
		tmp = x * (((y * ((a * b) - (c * i))) + t_4) + (j * t_1))
	elif k <= 1.9e+44:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(i * y1) - Float64(b * y0))
	t_2 = Float64(k * Float64(z * Float64(Float64(b * y0) - Float64(i * y1))))
	t_3 = Float64(j * Float64(Float64(Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(t * Float64(Float64(b * y4) - Float64(i * y5)))) + Float64(x * t_1)))
	t_4 = Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))
	tmp = 0.0
	if (k <= -5.2e+185)
		tmp = Float64(b * Float64(k * Float64(Float64(z * y0) - Float64(y * y4))));
	elseif (k <= -6.6e+107)
		tmp = Float64(b * Float64(z * Float64(Float64(k * y0) - Float64(t * a))));
	elseif (k <= -8.5e+39)
		tmp = Float64(y4 * Float64(Float64(Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))) - Float64(b * Float64(Float64(y * k) - Float64(t * j)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (k <= -9.5e-8)
		tmp = t_2;
	elseif (k <= -5e-26)
		tmp = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))));
	elseif (k <= -5.8e-96)
		tmp = t_3;
	elseif (k <= -1.06e-159)
		tmp = Float64(x * t_4);
	elseif (k <= -1.18e-222)
		tmp = t_3;
	elseif (k <= 2.5e-286)
		tmp = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + t_4) + Float64(j * t_1)));
	elseif (k <= 1.9e+44)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (i * y1) - (b * y0);
	t_2 = k * (z * ((b * y0) - (i * y1)));
	t_3 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * t_1));
	t_4 = y2 * ((c * y0) - (a * y1));
	tmp = 0.0;
	if (k <= -5.2e+185)
		tmp = b * (k * ((z * y0) - (y * y4)));
	elseif (k <= -6.6e+107)
		tmp = b * (z * ((k * y0) - (t * a)));
	elseif (k <= -8.5e+39)
		tmp = y4 * (((y1 * ((k * y2) - (j * y3))) - (b * ((y * k) - (t * j)))) + (c * ((y * y3) - (t * y2))));
	elseif (k <= -9.5e-8)
		tmp = t_2;
	elseif (k <= -5e-26)
		tmp = i * (y1 * ((x * j) - (z * k)));
	elseif (k <= -5.8e-96)
		tmp = t_3;
	elseif (k <= -1.06e-159)
		tmp = x * t_4;
	elseif (k <= -1.18e-222)
		tmp = t_3;
	elseif (k <= 2.5e-286)
		tmp = x * (((y * ((a * b) - (c * i))) + t_4) + (j * t_1));
	elseif (k <= 1.9e+44)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = 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 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -5.2e+185], N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -6.6e+107], N[(b * N[(z * N[(N[(k * y0), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -8.5e+39], N[(y4 * N[(N[(N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -9.5e-8], t$95$2, If[LessEqual[k, -5e-26], N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -5.8e-96], t$95$3, If[LessEqual[k, -1.06e-159], N[(x * t$95$4), $MachinePrecision], If[LessEqual[k, -1.18e-222], t$95$3, If[LessEqual[k, 2.5e-286], N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision] + N[(j * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.9e+44], t$95$3, t$95$2]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if k < -5.20000000000000001e185

   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%

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

   5. Taylor expanded in b around inf 46.7%

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

   6. Taylor expanded in k around -inf 73.8%

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

      1. associate-*r* 73.8%

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

      2. neg-mul-1 73.8%

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

      3. *-commutative 73.8%

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

   8. Simplified 73.8%

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

   if -5.20000000000000001e185 < k < -6.60000000000000064e107

   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%

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

   5. Taylor expanded in b around inf 29.1%

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

   6. Taylor expanded in z around -inf 64.5%

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

      1. associate-*r* 64.5%

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

      2. neg-mul-1 64.5%

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

      3. *-commutative 64.5%

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

   8. Simplified 64.5%

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

   if -6.60000000000000064e107 < k < -8.49999999999999971e39

   1. Initial program 41.7%

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

   3. Taylor expanded in y4 around inf 75.1%

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

   if -8.49999999999999971e39 < k < -9.50000000000000036e-8 or 1.9000000000000001e44 < k

   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%

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

   5. Taylor expanded in z around -inf 45.8%

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

   6. Taylor expanded in k around inf 55.7%

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

   if -9.50000000000000036e-8 < k < -5.00000000000000019e-26

   1. Initial program 27.6%

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

   3. Taylor expanded in y1 around inf 51.2%

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

   4. Taylor expanded in i around inf 76.2%

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

   if -5.00000000000000019e-26 < k < -5.79999999999999987e-96 or -1.06e-159 < k < -1.18000000000000007e-222 or 2.50000000000000018e-286 < k < 1.9000000000000001e44

   1. Initial program 30.7%

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

   3. Taylor expanded in j around inf 54.5%

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

   if -5.79999999999999987e-96 < k < -1.06e-159

   1. Initial program 44.1%

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

   3. Taylor expanded in y2 around inf 24.3%

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

   4. Taylor expanded in x around inf 56.6%

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

   if -1.18000000000000007e-222 < k < 2.50000000000000018e-286

   1. Initial program 42.5%

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

   3. Simplified 46.4%

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

   5. Taylor expanded in x around inf 61.9%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -5.2 \cdot 10^{+185}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq -6.6 \cdot 10^{+107}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0 - t \cdot a\right)\right)\\ \mathbf{elif}\;k \leq -8.5 \cdot 10^{+39}:\\ \;\;\;\;y4 \cdot \left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - b \cdot \left(y \cdot k - t \cdot j\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq -9.5 \cdot 10^{-8}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;k \leq -5 \cdot 10^{-26}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;k \leq -5.8 \cdot 10^{-96}:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq -1.06 \cdot 10^{-159}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;k \leq -1.18 \cdot 10^{-222}:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 2.5 \cdot 10^{-286}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 1.9 \cdot 10^{+44}:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 39.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + \left(z \cdot t\right) \cdot i\right) - t \cdot \left(y2 \cdot y4\right)\right)\\ t_2 := y4 \cdot \left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - b \cdot \left(y \cdot k - t \cdot j\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ t_3 := a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{if}\;y4 \leq -1.55 \cdot 10^{+71}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y4 \leq -1.55 \cdot 10^{-16}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y4 \leq -1.52 \cdot 10^{-170}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -2.9 \cdot 10^{-214}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y4 \leq 1.75 \cdot 10^{-243}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq 8 \cdot 10^{-146}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y4 \leq 1.26 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq 1.1 \cdot 10^{+89}:\\ \;\;\;\;\left(y0 \cdot y2\right) \cdot \left(x \cdot c - k \cdot y5\right)\\ \mathbf{elif}\;y4 \leq 4.5 \cdot 10^{+106}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          c
          (- (+ (* y0 (- (* x y2) (* z y3))) (* (* z t) i)) (* t (* y2 y4)))))
        (t_2
         (*
          y4
          (+
           (- (* y1 (- (* k y2) (* j y3))) (* b (- (* y k) (* t j))))
           (* c (- (* y y3) (* t y2))))))
        (t_3 (* a (* y (- (* x b) (* y3 y5))))))
   (if (<= y4 -1.55e+71)
     t_2
     (if (<= y4 -1.55e-16)
       t_3
       (if (<= y4 -1.52e-170)
         (*
          y2
          (+
           (+ (* k (- (* y1 y4) (* y0 y5))) (* x (- (* c y0) (* a y1))))
           (* t (- (* a y5) (* c y4)))))
         (if (<= y4 -2.9e-214)
           t_3
           (if (<= y4 1.75e-243)
             t_1
             (if (<= y4 8e-146)
               (* k (* z (- (* b y0) (* i y1))))
               (if (<= y4 1.26e+48)
                 t_1
                 (if (<= y4 1.1e+89)
                   (* (* y0 y2) (- (* x c) (* k y5)))
                   (if (<= y4 4.5e+106)
                     (* a (* z (- (* y1 y3) (* t b))))
                     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 * (((y0 * ((x * y2) - (z * y3))) + ((z * t) * i)) - (t * (y2 * y4)));
	double t_2 = y4 * (((y1 * ((k * y2) - (j * y3))) - (b * ((y * k) - (t * j)))) + (c * ((y * y3) - (t * y2))));
	double t_3 = a * (y * ((x * b) - (y3 * y5)));
	double tmp;
	if (y4 <= -1.55e+71) {
		tmp = t_2;
	} else if (y4 <= -1.55e-16) {
		tmp = t_3;
	} else if (y4 <= -1.52e-170) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else if (y4 <= -2.9e-214) {
		tmp = t_3;
	} else if (y4 <= 1.75e-243) {
		tmp = t_1;
	} else if (y4 <= 8e-146) {
		tmp = k * (z * ((b * y0) - (i * y1)));
	} else if (y4 <= 1.26e+48) {
		tmp = t_1;
	} else if (y4 <= 1.1e+89) {
		tmp = (y0 * y2) * ((x * c) - (k * y5));
	} else if (y4 <= 4.5e+106) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = c * (((y0 * ((x * y2) - (z * y3))) + ((z * t) * i)) - (t * (y2 * y4)))
    t_2 = y4 * (((y1 * ((k * y2) - (j * y3))) - (b * ((y * k) - (t * j)))) + (c * ((y * y3) - (t * y2))))
    t_3 = a * (y * ((x * b) - (y3 * y5)))
    if (y4 <= (-1.55d+71)) then
        tmp = t_2
    else if (y4 <= (-1.55d-16)) then
        tmp = t_3
    else if (y4 <= (-1.52d-170)) then
        tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
    else if (y4 <= (-2.9d-214)) then
        tmp = t_3
    else if (y4 <= 1.75d-243) then
        tmp = t_1
    else if (y4 <= 8d-146) then
        tmp = k * (z * ((b * y0) - (i * y1)))
    else if (y4 <= 1.26d+48) then
        tmp = t_1
    else if (y4 <= 1.1d+89) then
        tmp = (y0 * y2) * ((x * c) - (k * y5))
    else if (y4 <= 4.5d+106) then
        tmp = a * (z * ((y1 * y3) - (t * b)))
    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 * (((y0 * ((x * y2) - (z * y3))) + ((z * t) * i)) - (t * (y2 * y4)));
	double t_2 = y4 * (((y1 * ((k * y2) - (j * y3))) - (b * ((y * k) - (t * j)))) + (c * ((y * y3) - (t * y2))));
	double t_3 = a * (y * ((x * b) - (y3 * y5)));
	double tmp;
	if (y4 <= -1.55e+71) {
		tmp = t_2;
	} else if (y4 <= -1.55e-16) {
		tmp = t_3;
	} else if (y4 <= -1.52e-170) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else if (y4 <= -2.9e-214) {
		tmp = t_3;
	} else if (y4 <= 1.75e-243) {
		tmp = t_1;
	} else if (y4 <= 8e-146) {
		tmp = k * (z * ((b * y0) - (i * y1)));
	} else if (y4 <= 1.26e+48) {
		tmp = t_1;
	} else if (y4 <= 1.1e+89) {
		tmp = (y0 * y2) * ((x * c) - (k * y5));
	} else if (y4 <= 4.5e+106) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} 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 * (((y0 * ((x * y2) - (z * y3))) + ((z * t) * i)) - (t * (y2 * y4)))
	t_2 = y4 * (((y1 * ((k * y2) - (j * y3))) - (b * ((y * k) - (t * j)))) + (c * ((y * y3) - (t * y2))))
	t_3 = a * (y * ((x * b) - (y3 * y5)))
	tmp = 0
	if y4 <= -1.55e+71:
		tmp = t_2
	elif y4 <= -1.55e-16:
		tmp = t_3
	elif y4 <= -1.52e-170:
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
	elif y4 <= -2.9e-214:
		tmp = t_3
	elif y4 <= 1.75e-243:
		tmp = t_1
	elif y4 <= 8e-146:
		tmp = k * (z * ((b * y0) - (i * y1)))
	elif y4 <= 1.26e+48:
		tmp = t_1
	elif y4 <= 1.1e+89:
		tmp = (y0 * y2) * ((x * c) - (k * y5))
	elif y4 <= 4.5e+106:
		tmp = a * (z * ((y1 * y3) - (t * b)))
	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(Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(Float64(z * t) * i)) - Float64(t * Float64(y2 * y4))))
	t_2 = Float64(y4 * Float64(Float64(Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))) - Float64(b * Float64(Float64(y * k) - Float64(t * j)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))))
	t_3 = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))))
	tmp = 0.0
	if (y4 <= -1.55e+71)
		tmp = t_2;
	elseif (y4 <= -1.55e-16)
		tmp = t_3;
	elseif (y4 <= -1.52e-170)
		tmp = Float64(y2 * Float64(Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y4 <= -2.9e-214)
		tmp = t_3;
	elseif (y4 <= 1.75e-243)
		tmp = t_1;
	elseif (y4 <= 8e-146)
		tmp = Float64(k * Float64(z * Float64(Float64(b * y0) - Float64(i * y1))));
	elseif (y4 <= 1.26e+48)
		tmp = t_1;
	elseif (y4 <= 1.1e+89)
		tmp = Float64(Float64(y0 * y2) * Float64(Float64(x * c) - Float64(k * y5)));
	elseif (y4 <= 4.5e+106)
		tmp = Float64(a * Float64(z * Float64(Float64(y1 * y3) - Float64(t * b))));
	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 * (((y0 * ((x * y2) - (z * y3))) + ((z * t) * i)) - (t * (y2 * y4)));
	t_2 = y4 * (((y1 * ((k * y2) - (j * y3))) - (b * ((y * k) - (t * j)))) + (c * ((y * y3) - (t * y2))));
	t_3 = a * (y * ((x * b) - (y3 * y5)));
	tmp = 0.0;
	if (y4 <= -1.55e+71)
		tmp = t_2;
	elseif (y4 <= -1.55e-16)
		tmp = t_3;
	elseif (y4 <= -1.52e-170)
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	elseif (y4 <= -2.9e-214)
		tmp = t_3;
	elseif (y4 <= 1.75e-243)
		tmp = t_1;
	elseif (y4 <= 8e-146)
		tmp = k * (z * ((b * y0) - (i * y1)));
	elseif (y4 <= 1.26e+48)
		tmp = t_1;
	elseif (y4 <= 1.1e+89)
		tmp = (y0 * y2) * ((x * c) - (k * y5));
	elseif (y4 <= 4.5e+106)
		tmp = a * (z * ((y1 * y3) - (t * b)));
	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[(N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(t * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y4 * N[(N[(N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -1.55e+71], t$95$2, If[LessEqual[y4, -1.55e-16], t$95$3, If[LessEqual[y4, -1.52e-170], N[(y2 * N[(N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -2.9e-214], t$95$3, If[LessEqual[y4, 1.75e-243], t$95$1, If[LessEqual[y4, 8e-146], N[(k * N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 1.26e+48], t$95$1, If[LessEqual[y4, 1.1e+89], N[(N[(y0 * y2), $MachinePrecision] * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 4.5e+106], N[(a * N[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y4 < -1.55000000000000009e71 or 4.4999999999999997e106 < y4

   1. Initial program 25.4%

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

   3. Taylor expanded in y4 around inf 66.9%

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

   if -1.55000000000000009e71 < y4 < -1.55e-16 or -1.52000000000000009e-170 < y4 < -2.89999999999999985e-214

   1. Initial program 26.7%

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

   3. Simplified 26.6%

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

   5. Taylor expanded in a around inf 49.3%

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

   6. Taylor expanded in y around inf 64.8%

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

   if -1.55e-16 < y4 < -1.52000000000000009e-170

   1. Initial program 40.2%

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

   3. Taylor expanded in y2 around inf 49.6%

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

   if -2.89999999999999985e-214 < y4 < 1.74999999999999989e-243 or 8.00000000000000021e-146 < y4 < 1.26000000000000001e48

   1. Initial program 33.6%

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

   3. Simplified 33.6%

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

   5. Taylor expanded in c around inf 40.9%

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

   6. Taylor expanded in y around 0 46.0%

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

   if 1.74999999999999989e-243 < y4 < 8.00000000000000021e-146

   1. Initial program 33.3%

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

   3. Simplified 33.3%

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

   5. Taylor expanded in z around -inf 50.5%

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

   6. Taylor expanded in k around inf 59.0%

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

   if 1.26000000000000001e48 < y4 < 1.1e89

   1. Initial program 16.1%

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

   3. Taylor expanded in y2 around inf 53.9%

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

   4. Taylor expanded in y0 around inf 69.6%

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

      1. associate-*r* 69.6%

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

      2. +-commutative 69.6%

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

      3. mul-1-neg 69.6%

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

      4. unsub-neg 69.6%

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

      5. *-commutative 69.6%

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

   6. Simplified 69.6%

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

   if 1.1e89 < y4 < 4.4999999999999997e106

   1. Initial program 25.0%

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

   3. Simplified 25.0%

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

   5. Taylor expanded in a around inf 75.1%

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

   6. Taylor expanded in z around -inf 75.3%

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

      1. associate-*r* 75.3%

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

      2. neg-mul-1 75.3%

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

      3. +-commutative 75.3%

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

      4. mul-1-neg 75.3%

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

      5. unsub-neg 75.3%

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

   8. Simplified 75.3%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -1.55 \cdot 10^{+71}:\\ \;\;\;\;y4 \cdot \left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - b \cdot \left(y \cdot k - t \cdot j\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq -1.55 \cdot 10^{-16}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq -1.52 \cdot 10^{-170}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -2.9 \cdot 10^{-214}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq 1.75 \cdot 10^{-243}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + \left(z \cdot t\right) \cdot i\right) - t \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq 8 \cdot 10^{-146}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y4 \leq 1.26 \cdot 10^{+48}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + \left(z \cdot t\right) \cdot i\right) - t \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq 1.1 \cdot 10^{+89}:\\ \;\;\;\;\left(y0 \cdot y2\right) \cdot \left(x \cdot c - k \cdot y5\right)\\ \mathbf{elif}\;y4 \leq 4.5 \cdot 10^{+106}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - b \cdot \left(y \cdot k - t \cdot j\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 39.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot k - t \cdot j\\ t_2 := y4 \cdot \left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - b \cdot t\_1\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ t_3 := a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ t_4 := c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + \left(z \cdot t\right) \cdot i\right) - t \cdot \left(y2 \cdot y4\right)\right)\\ t_5 := y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot t\_1 + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{if}\;y4 \leq -4.35 \cdot 10^{+71}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y4 \leq -5.6 \cdot 10^{-15}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y4 \leq -7 \cdot 10^{-171}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -1.95 \cdot 10^{-208}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y4 \leq 6.8 \cdot 10^{-184}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y4 \leq 9.6 \cdot 10^{-96}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;y4 \leq 2 \cdot 10^{+49}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y4 \leq 3 \cdot 10^{+88}:\\ \;\;\;\;\left(y0 \cdot y2\right) \cdot \left(x \cdot c - k \cdot y5\right)\\ \mathbf{elif}\;y4 \leq 1.9 \cdot 10^{+152}:\\ \;\;\;\;t\_5\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y k) (* t j)))
        (t_2
         (*
          y4
          (+
           (- (* y1 (- (* k y2) (* j y3))) (* b t_1))
           (* c (- (* y y3) (* t y2))))))
        (t_3 (* a (* y (- (* x b) (* y3 y5)))))
        (t_4
         (*
          c
          (- (+ (* y0 (- (* x y2) (* z y3))) (* (* z t) i)) (* t (* y2 y4)))))
        (t_5
         (*
          y5
          (+
           (* a (- (* t y2) (* y y3)))
           (+ (* i t_1) (* y0 (- (* j y3) (* k y2))))))))
   (if (<= y4 -4.35e+71)
     t_2
     (if (<= y4 -5.6e-15)
       t_3
       (if (<= y4 -7e-171)
         (*
          y2
          (+
           (+ (* k (- (* y1 y4) (* y0 y5))) (* x (- (* c y0) (* a y1))))
           (* t (- (* a y5) (* c y4)))))
         (if (<= y4 -1.95e-208)
           t_3
           (if (<= y4 6.8e-184)
             t_4
             (if (<= y4 9.6e-96)
               t_5
               (if (<= y4 2e+49)
                 t_4
                 (if (<= y4 3e+88)
                   (* (* y0 y2) (- (* x c) (* k y5)))
                   (if (<= y4 1.9e+152) t_5 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 = (y * k) - (t * j);
	double t_2 = y4 * (((y1 * ((k * y2) - (j * y3))) - (b * t_1)) + (c * ((y * y3) - (t * y2))));
	double t_3 = a * (y * ((x * b) - (y3 * y5)));
	double t_4 = c * (((y0 * ((x * y2) - (z * y3))) + ((z * t) * i)) - (t * (y2 * y4)));
	double t_5 = y5 * ((a * ((t * y2) - (y * y3))) + ((i * t_1) + (y0 * ((j * y3) - (k * y2)))));
	double tmp;
	if (y4 <= -4.35e+71) {
		tmp = t_2;
	} else if (y4 <= -5.6e-15) {
		tmp = t_3;
	} else if (y4 <= -7e-171) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else if (y4 <= -1.95e-208) {
		tmp = t_3;
	} else if (y4 <= 6.8e-184) {
		tmp = t_4;
	} else if (y4 <= 9.6e-96) {
		tmp = t_5;
	} else if (y4 <= 2e+49) {
		tmp = t_4;
	} else if (y4 <= 3e+88) {
		tmp = (y0 * y2) * ((x * c) - (k * y5));
	} else if (y4 <= 1.9e+152) {
		tmp = t_5;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = (y * k) - (t * j)
    t_2 = y4 * (((y1 * ((k * y2) - (j * y3))) - (b * t_1)) + (c * ((y * y3) - (t * y2))))
    t_3 = a * (y * ((x * b) - (y3 * y5)))
    t_4 = c * (((y0 * ((x * y2) - (z * y3))) + ((z * t) * i)) - (t * (y2 * y4)))
    t_5 = y5 * ((a * ((t * y2) - (y * y3))) + ((i * t_1) + (y0 * ((j * y3) - (k * y2)))))
    if (y4 <= (-4.35d+71)) then
        tmp = t_2
    else if (y4 <= (-5.6d-15)) then
        tmp = t_3
    else if (y4 <= (-7d-171)) then
        tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
    else if (y4 <= (-1.95d-208)) then
        tmp = t_3
    else if (y4 <= 6.8d-184) then
        tmp = t_4
    else if (y4 <= 9.6d-96) then
        tmp = t_5
    else if (y4 <= 2d+49) then
        tmp = t_4
    else if (y4 <= 3d+88) then
        tmp = (y0 * y2) * ((x * c) - (k * y5))
    else if (y4 <= 1.9d+152) then
        tmp = t_5
    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 = (y * k) - (t * j);
	double t_2 = y4 * (((y1 * ((k * y2) - (j * y3))) - (b * t_1)) + (c * ((y * y3) - (t * y2))));
	double t_3 = a * (y * ((x * b) - (y3 * y5)));
	double t_4 = c * (((y0 * ((x * y2) - (z * y3))) + ((z * t) * i)) - (t * (y2 * y4)));
	double t_5 = y5 * ((a * ((t * y2) - (y * y3))) + ((i * t_1) + (y0 * ((j * y3) - (k * y2)))));
	double tmp;
	if (y4 <= -4.35e+71) {
		tmp = t_2;
	} else if (y4 <= -5.6e-15) {
		tmp = t_3;
	} else if (y4 <= -7e-171) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else if (y4 <= -1.95e-208) {
		tmp = t_3;
	} else if (y4 <= 6.8e-184) {
		tmp = t_4;
	} else if (y4 <= 9.6e-96) {
		tmp = t_5;
	} else if (y4 <= 2e+49) {
		tmp = t_4;
	} else if (y4 <= 3e+88) {
		tmp = (y0 * y2) * ((x * c) - (k * y5));
	} else if (y4 <= 1.9e+152) {
		tmp = t_5;
	} 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 = (y * k) - (t * j)
	t_2 = y4 * (((y1 * ((k * y2) - (j * y3))) - (b * t_1)) + (c * ((y * y3) - (t * y2))))
	t_3 = a * (y * ((x * b) - (y3 * y5)))
	t_4 = c * (((y0 * ((x * y2) - (z * y3))) + ((z * t) * i)) - (t * (y2 * y4)))
	t_5 = y5 * ((a * ((t * y2) - (y * y3))) + ((i * t_1) + (y0 * ((j * y3) - (k * y2)))))
	tmp = 0
	if y4 <= -4.35e+71:
		tmp = t_2
	elif y4 <= -5.6e-15:
		tmp = t_3
	elif y4 <= -7e-171:
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
	elif y4 <= -1.95e-208:
		tmp = t_3
	elif y4 <= 6.8e-184:
		tmp = t_4
	elif y4 <= 9.6e-96:
		tmp = t_5
	elif y4 <= 2e+49:
		tmp = t_4
	elif y4 <= 3e+88:
		tmp = (y0 * y2) * ((x * c) - (k * y5))
	elif y4 <= 1.9e+152:
		tmp = t_5
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y * k) - Float64(t * j))
	t_2 = Float64(y4 * Float64(Float64(Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))) - Float64(b * t_1)) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))))
	t_3 = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))))
	t_4 = Float64(c * Float64(Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(Float64(z * t) * i)) - Float64(t * Float64(y2 * y4))))
	t_5 = Float64(y5 * Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(Float64(i * t_1) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))))))
	tmp = 0.0
	if (y4 <= -4.35e+71)
		tmp = t_2;
	elseif (y4 <= -5.6e-15)
		tmp = t_3;
	elseif (y4 <= -7e-171)
		tmp = Float64(y2 * Float64(Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y4 <= -1.95e-208)
		tmp = t_3;
	elseif (y4 <= 6.8e-184)
		tmp = t_4;
	elseif (y4 <= 9.6e-96)
		tmp = t_5;
	elseif (y4 <= 2e+49)
		tmp = t_4;
	elseif (y4 <= 3e+88)
		tmp = Float64(Float64(y0 * y2) * Float64(Float64(x * c) - Float64(k * y5)));
	elseif (y4 <= 1.9e+152)
		tmp = t_5;
	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 = (y * k) - (t * j);
	t_2 = y4 * (((y1 * ((k * y2) - (j * y3))) - (b * t_1)) + (c * ((y * y3) - (t * y2))));
	t_3 = a * (y * ((x * b) - (y3 * y5)));
	t_4 = c * (((y0 * ((x * y2) - (z * y3))) + ((z * t) * i)) - (t * (y2 * y4)));
	t_5 = y5 * ((a * ((t * y2) - (y * y3))) + ((i * t_1) + (y0 * ((j * y3) - (k * y2)))));
	tmp = 0.0;
	if (y4 <= -4.35e+71)
		tmp = t_2;
	elseif (y4 <= -5.6e-15)
		tmp = t_3;
	elseif (y4 <= -7e-171)
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	elseif (y4 <= -1.95e-208)
		tmp = t_3;
	elseif (y4 <= 6.8e-184)
		tmp = t_4;
	elseif (y4 <= 9.6e-96)
		tmp = t_5;
	elseif (y4 <= 2e+49)
		tmp = t_4;
	elseif (y4 <= 3e+88)
		tmp = (y0 * y2) * ((x * c) - (k * y5));
	elseif (y4 <= 1.9e+152)
		tmp = t_5;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y4 * N[(N[(N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(c * N[(N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(t * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y5 * N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(i * t$95$1), $MachinePrecision] + N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -4.35e+71], t$95$2, If[LessEqual[y4, -5.6e-15], t$95$3, If[LessEqual[y4, -7e-171], N[(y2 * N[(N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -1.95e-208], t$95$3, If[LessEqual[y4, 6.8e-184], t$95$4, If[LessEqual[y4, 9.6e-96], t$95$5, If[LessEqual[y4, 2e+49], t$95$4, If[LessEqual[y4, 3e+88], N[(N[(y0 * y2), $MachinePrecision] * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 1.9e+152], t$95$5, t$95$2]]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y4 < -4.3499999999999999e71 or 1.9e152 < y4

   1. Initial program 20.3%

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

   3. Taylor expanded in y4 around inf 70.9%

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

   if -4.3499999999999999e71 < y4 < -5.60000000000000028e-15 or -6.99999999999999988e-171 < y4 < -1.95000000000000002e-208

   1. Initial program 26.7%

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

   3. Simplified 26.6%

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

   5. Taylor expanded in a around inf 49.3%

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

   6. Taylor expanded in y around inf 64.8%

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

   if -5.60000000000000028e-15 < y4 < -6.99999999999999988e-171

   1. Initial program 40.2%

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

   3. Taylor expanded in y2 around inf 49.6%

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

   if -1.95000000000000002e-208 < y4 < 6.80000000000000008e-184 or 9.60000000000000076e-96 < y4 < 1.99999999999999989e49

   1. Initial program 30.4%

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

   3. Simplified 30.4%

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

   5. Taylor expanded in c around inf 42.8%

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

   6. Taylor expanded in y around 0 48.5%

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

   if 6.80000000000000008e-184 < y4 < 9.60000000000000076e-96 or 3.00000000000000005e88 < y4 < 1.9e152

   1. Initial program 51.9%

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

   3. Taylor expanded in y5 around -inf 59.6%

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

   if 1.99999999999999989e49 < y4 < 3.00000000000000005e88

   1. Initial program 16.1%

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

   3. Taylor expanded in y2 around inf 53.9%

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

   4. Taylor expanded in y0 around inf 69.6%

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

      1. associate-*r* 69.6%

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

      2. +-commutative 69.6%

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

      3. mul-1-neg 69.6%

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

      4. unsub-neg 69.6%

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

      5. *-commutative 69.6%

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

   6. Simplified 69.6%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -4.35 \cdot 10^{+71}:\\ \;\;\;\;y4 \cdot \left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - b \cdot \left(y \cdot k - t \cdot j\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq -5.6 \cdot 10^{-15}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq -7 \cdot 10^{-171}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -1.95 \cdot 10^{-208}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq 6.8 \cdot 10^{-184}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + \left(z \cdot t\right) \cdot i\right) - t \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq 9.6 \cdot 10^{-96}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 2 \cdot 10^{+49}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + \left(z \cdot t\right) \cdot i\right) - t \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq 3 \cdot 10^{+88}:\\ \;\;\;\;\left(y0 \cdot y2\right) \cdot \left(x \cdot c - k \cdot y5\right)\\ \mathbf{elif}\;y4 \leq 1.9 \cdot 10^{+152}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - b \cdot \left(y \cdot k - t \cdot j\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 36.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot y1 - b \cdot y0\\ t_2 := k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ t_3 := j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot t\_1\right)\\ \mathbf{if}\;k \leq -2.2 \cdot 10^{+185}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq -2 \cdot 10^{+108}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0 - t \cdot a\right)\right)\\ \mathbf{elif}\;k \leq -6 \cdot 10^{+39}:\\ \;\;\;\;y4 \cdot \left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - b \cdot \left(y \cdot k - t \cdot j\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq -1.45 \cdot 10^{-7}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;k \leq -2.1 \cdot 10^{-25}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;k \leq -7 \cdot 10^{-84}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;k \leq -2 \cdot 10^{-224}:\\ \;\;\;\;y0 \cdot \left(\left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;k \leq 2.4 \cdot 10^{-278}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot t\_1\right)\\ \mathbf{elif}\;k \leq 1.26 \cdot 10^{+44}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* i y1) (* b y0)))
        (t_2 (* k (* z (- (* b y0) (* i y1)))))
        (t_3
         (*
          j
          (+
           (+ (* y3 (- (* y0 y5) (* y1 y4))) (* t (- (* b y4) (* i y5))))
           (* x t_1)))))
   (if (<= k -2.2e+185)
     (* b (* k (- (* z y0) (* y y4))))
     (if (<= k -2e+108)
       (* b (* z (- (* k y0) (* t a))))
       (if (<= k -6e+39)
         (*
          y4
          (+
           (- (* y1 (- (* k y2) (* j y3))) (* b (- (* y k) (* t j))))
           (* c (- (* y y3) (* t y2)))))
         (if (<= k -1.45e-7)
           t_2
           (if (<= k -2.1e-25)
             (* i (* y1 (- (* x j) (* z k))))
             (if (<= k -7e-84)
               t_3
               (if (<= k -2e-224)
                 (*
                  y0
                  (+
                   (+ (* y5 (- (* j y3) (* k y2))) (* c (- (* x y2) (* z y3))))
                   (* b (- (* z k) (* x j)))))
                 (if (<= k 2.4e-278)
                   (*
                    x
                    (+
                     (+ (* y (- (* a b) (* c i))) (* y2 (- (* c y0) (* a y1))))
                     (* j t_1)))
                   (if (<= k 1.26e+44) t_3 t_2)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (i * y1) - (b * y0);
	double t_2 = k * (z * ((b * y0) - (i * y1)));
	double t_3 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * t_1));
	double tmp;
	if (k <= -2.2e+185) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (k <= -2e+108) {
		tmp = b * (z * ((k * y0) - (t * a)));
	} else if (k <= -6e+39) {
		tmp = y4 * (((y1 * ((k * y2) - (j * y3))) - (b * ((y * k) - (t * j)))) + (c * ((y * y3) - (t * y2))));
	} else if (k <= -1.45e-7) {
		tmp = t_2;
	} else if (k <= -2.1e-25) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (k <= -7e-84) {
		tmp = t_3;
	} else if (k <= -2e-224) {
		tmp = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * ((x * y2) - (z * y3)))) + (b * ((z * k) - (x * j))));
	} else if (k <= 2.4e-278) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_1));
	} else if (k <= 1.26e+44) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (i * y1) - (b * y0)
    t_2 = k * (z * ((b * y0) - (i * y1)))
    t_3 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * t_1))
    if (k <= (-2.2d+185)) then
        tmp = b * (k * ((z * y0) - (y * y4)))
    else if (k <= (-2d+108)) then
        tmp = b * (z * ((k * y0) - (t * a)))
    else if (k <= (-6d+39)) then
        tmp = y4 * (((y1 * ((k * y2) - (j * y3))) - (b * ((y * k) - (t * j)))) + (c * ((y * y3) - (t * y2))))
    else if (k <= (-1.45d-7)) then
        tmp = t_2
    else if (k <= (-2.1d-25)) then
        tmp = i * (y1 * ((x * j) - (z * k)))
    else if (k <= (-7d-84)) then
        tmp = t_3
    else if (k <= (-2d-224)) then
        tmp = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * ((x * y2) - (z * y3)))) + (b * ((z * k) - (x * j))))
    else if (k <= 2.4d-278) then
        tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_1))
    else if (k <= 1.26d+44) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (i * y1) - (b * y0);
	double t_2 = k * (z * ((b * y0) - (i * y1)));
	double t_3 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * t_1));
	double tmp;
	if (k <= -2.2e+185) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (k <= -2e+108) {
		tmp = b * (z * ((k * y0) - (t * a)));
	} else if (k <= -6e+39) {
		tmp = y4 * (((y1 * ((k * y2) - (j * y3))) - (b * ((y * k) - (t * j)))) + (c * ((y * y3) - (t * y2))));
	} else if (k <= -1.45e-7) {
		tmp = t_2;
	} else if (k <= -2.1e-25) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (k <= -7e-84) {
		tmp = t_3;
	} else if (k <= -2e-224) {
		tmp = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * ((x * y2) - (z * y3)))) + (b * ((z * k) - (x * j))));
	} else if (k <= 2.4e-278) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_1));
	} else if (k <= 1.26e+44) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (i * y1) - (b * y0)
	t_2 = k * (z * ((b * y0) - (i * y1)))
	t_3 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * t_1))
	tmp = 0
	if k <= -2.2e+185:
		tmp = b * (k * ((z * y0) - (y * y4)))
	elif k <= -2e+108:
		tmp = b * (z * ((k * y0) - (t * a)))
	elif k <= -6e+39:
		tmp = y4 * (((y1 * ((k * y2) - (j * y3))) - (b * ((y * k) - (t * j)))) + (c * ((y * y3) - (t * y2))))
	elif k <= -1.45e-7:
		tmp = t_2
	elif k <= -2.1e-25:
		tmp = i * (y1 * ((x * j) - (z * k)))
	elif k <= -7e-84:
		tmp = t_3
	elif k <= -2e-224:
		tmp = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * ((x * y2) - (z * y3)))) + (b * ((z * k) - (x * j))))
	elif k <= 2.4e-278:
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_1))
	elif k <= 1.26e+44:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(i * y1) - Float64(b * y0))
	t_2 = Float64(k * Float64(z * Float64(Float64(b * y0) - Float64(i * y1))))
	t_3 = Float64(j * Float64(Float64(Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(t * Float64(Float64(b * y4) - Float64(i * y5)))) + Float64(x * t_1)))
	tmp = 0.0
	if (k <= -2.2e+185)
		tmp = Float64(b * Float64(k * Float64(Float64(z * y0) - Float64(y * y4))));
	elseif (k <= -2e+108)
		tmp = Float64(b * Float64(z * Float64(Float64(k * y0) - Float64(t * a))));
	elseif (k <= -6e+39)
		tmp = Float64(y4 * Float64(Float64(Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))) - Float64(b * Float64(Float64(y * k) - Float64(t * j)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (k <= -1.45e-7)
		tmp = t_2;
	elseif (k <= -2.1e-25)
		tmp = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))));
	elseif (k <= -7e-84)
		tmp = t_3;
	elseif (k <= -2e-224)
		tmp = Float64(y0 * Float64(Float64(Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))) + Float64(c * Float64(Float64(x * y2) - Float64(z * y3)))) + Float64(b * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (k <= 2.4e-278)
		tmp = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * t_1)));
	elseif (k <= 1.26e+44)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (i * y1) - (b * y0);
	t_2 = k * (z * ((b * y0) - (i * y1)));
	t_3 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * t_1));
	tmp = 0.0;
	if (k <= -2.2e+185)
		tmp = b * (k * ((z * y0) - (y * y4)));
	elseif (k <= -2e+108)
		tmp = b * (z * ((k * y0) - (t * a)));
	elseif (k <= -6e+39)
		tmp = y4 * (((y1 * ((k * y2) - (j * y3))) - (b * ((y * k) - (t * j)))) + (c * ((y * y3) - (t * y2))));
	elseif (k <= -1.45e-7)
		tmp = t_2;
	elseif (k <= -2.1e-25)
		tmp = i * (y1 * ((x * j) - (z * k)));
	elseif (k <= -7e-84)
		tmp = t_3;
	elseif (k <= -2e-224)
		tmp = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * ((x * y2) - (z * y3)))) + (b * ((z * k) - (x * j))));
	elseif (k <= 2.4e-278)
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_1));
	elseif (k <= 1.26e+44)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = 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 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -2.2e+185], N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -2e+108], N[(b * N[(z * N[(N[(k * y0), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -6e+39], N[(y4 * N[(N[(N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -1.45e-7], t$95$2, If[LessEqual[k, -2.1e-25], N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -7e-84], t$95$3, If[LessEqual[k, -2e-224], N[(y0 * N[(N[(N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.4e-278], N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.26e+44], t$95$3, t$95$2]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if k < -2.2000000000000001e185

   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%

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

   5. Taylor expanded in b around inf 46.7%

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

   6. Taylor expanded in k around -inf 73.8%

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

      1. associate-*r* 73.8%

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

      2. neg-mul-1 73.8%

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

      3. *-commutative 73.8%

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

   8. Simplified 73.8%

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

   if -2.2000000000000001e185 < k < -2.0000000000000001e108

   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%

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

   5. Taylor expanded in b around inf 29.1%

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

   6. Taylor expanded in z around -inf 64.5%

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

      1. associate-*r* 64.5%

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

      2. neg-mul-1 64.5%

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

      3. *-commutative 64.5%

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

   8. Simplified 64.5%

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

   if -2.0000000000000001e108 < k < -5.9999999999999999e39

   1. Initial program 41.7%

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

   3. Taylor expanded in y4 around inf 75.1%

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

   if -5.9999999999999999e39 < k < -1.4499999999999999e-7 or 1.25999999999999996e44 < k

   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%

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

   5. Taylor expanded in z around -inf 45.8%

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

   6. Taylor expanded in k around inf 55.7%

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

   if -1.4499999999999999e-7 < k < -2.10000000000000002e-25

   1. Initial program 27.6%

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

   3. Taylor expanded in y1 around inf 51.2%

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

   4. Taylor expanded in i around inf 76.2%

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

   if -2.10000000000000002e-25 < k < -7.0000000000000002e-84 or 2.4e-278 < k < 1.25999999999999996e44

   1. Initial program 26.4%

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

   3. Taylor expanded in j around inf 52.9%

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

   if -7.0000000000000002e-84 < k < -2e-224

   1. Initial program 47.9%

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

   3. Taylor expanded in y0 around inf 55.6%

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

   if -2e-224 < k < 2.4e-278

   1. Initial program 42.5%

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

   3. Simplified 46.4%

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

   5. Taylor expanded in x around inf 61.9%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -2.2 \cdot 10^{+185}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq -2 \cdot 10^{+108}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0 - t \cdot a\right)\right)\\ \mathbf{elif}\;k \leq -6 \cdot 10^{+39}:\\ \;\;\;\;y4 \cdot \left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - b \cdot \left(y \cdot k - t \cdot j\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq -1.45 \cdot 10^{-7}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;k \leq -2.1 \cdot 10^{-25}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;k \leq -7 \cdot 10^{-84}:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq -2 \cdot 10^{-224}:\\ \;\;\;\;y0 \cdot \left(\left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;k \leq 2.4 \cdot 10^{-278}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 1.26 \cdot 10^{+44}:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 35.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ t_2 := j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ t_3 := y \cdot k - t \cdot j\\ t_4 := y1 \cdot \left(x \cdot j - z \cdot k\right)\\ \mathbf{if}\;k \leq -1.45 \cdot 10^{+187}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq -2 \cdot 10^{+108}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0 - t \cdot a\right)\right)\\ \mathbf{elif}\;k \leq -6 \cdot 10^{+39}:\\ \;\;\;\;y4 \cdot \left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - b \cdot t\_3\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq -4.5 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq -2.1 \cdot 10^{-25}:\\ \;\;\;\;i \cdot t\_4\\ \mathbf{elif}\;k \leq -5 \cdot 10^{-84}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;k \leq -2.6 \cdot 10^{-242}:\\ \;\;\;\;y0 \cdot \left(\left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;k \leq 2.5 \cdot 10^{-254}:\\ \;\;\;\;i \cdot \left(t\_4 + \left(c \cdot \left(z \cdot t - x \cdot y\right) + y5 \cdot t\_3\right)\right)\\ \mathbf{elif}\;k \leq 1.55 \cdot 10^{+48}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (* z (- (* b y0) (* i y1)))))
        (t_2
         (*
          j
          (+
           (+ (* y3 (- (* y0 y5) (* y1 y4))) (* t (- (* b y4) (* i y5))))
           (* x (- (* i y1) (* b y0))))))
        (t_3 (- (* y k) (* t j)))
        (t_4 (* y1 (- (* x j) (* z k)))))
   (if (<= k -1.45e+187)
     (* b (* k (- (* z y0) (* y y4))))
     (if (<= k -2e+108)
       (* b (* z (- (* k y0) (* t a))))
       (if (<= k -6e+39)
         (*
          y4
          (+
           (- (* y1 (- (* k y2) (* j y3))) (* b t_3))
           (* c (- (* y y3) (* t y2)))))
         (if (<= k -4.5e-7)
           t_1
           (if (<= k -2.1e-25)
             (* i t_4)
             (if (<= k -5e-84)
               t_2
               (if (<= k -2.6e-242)
                 (*
                  y0
                  (+
                   (+ (* y5 (- (* j y3) (* k y2))) (* c (- (* x y2) (* z y3))))
                   (* b (- (* z k) (* x j)))))
                 (if (<= k 2.5e-254)
                   (* i (+ t_4 (+ (* c (- (* z t) (* x y))) (* y5 t_3))))
                   (if (<= k 1.55e+48) t_2 t_1)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (z * ((b * y0) - (i * y1)));
	double t_2 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))));
	double t_3 = (y * k) - (t * j);
	double t_4 = y1 * ((x * j) - (z * k));
	double tmp;
	if (k <= -1.45e+187) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (k <= -2e+108) {
		tmp = b * (z * ((k * y0) - (t * a)));
	} else if (k <= -6e+39) {
		tmp = y4 * (((y1 * ((k * y2) - (j * y3))) - (b * t_3)) + (c * ((y * y3) - (t * y2))));
	} else if (k <= -4.5e-7) {
		tmp = t_1;
	} else if (k <= -2.1e-25) {
		tmp = i * t_4;
	} else if (k <= -5e-84) {
		tmp = t_2;
	} else if (k <= -2.6e-242) {
		tmp = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * ((x * y2) - (z * y3)))) + (b * ((z * k) - (x * j))));
	} else if (k <= 2.5e-254) {
		tmp = i * (t_4 + ((c * ((z * t) - (x * y))) + (y5 * t_3)));
	} else if (k <= 1.55e+48) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = k * (z * ((b * y0) - (i * y1)))
    t_2 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))))
    t_3 = (y * k) - (t * j)
    t_4 = y1 * ((x * j) - (z * k))
    if (k <= (-1.45d+187)) then
        tmp = b * (k * ((z * y0) - (y * y4)))
    else if (k <= (-2d+108)) then
        tmp = b * (z * ((k * y0) - (t * a)))
    else if (k <= (-6d+39)) then
        tmp = y4 * (((y1 * ((k * y2) - (j * y3))) - (b * t_3)) + (c * ((y * y3) - (t * y2))))
    else if (k <= (-4.5d-7)) then
        tmp = t_1
    else if (k <= (-2.1d-25)) then
        tmp = i * t_4
    else if (k <= (-5d-84)) then
        tmp = t_2
    else if (k <= (-2.6d-242)) then
        tmp = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * ((x * y2) - (z * y3)))) + (b * ((z * k) - (x * j))))
    else if (k <= 2.5d-254) then
        tmp = i * (t_4 + ((c * ((z * t) - (x * y))) + (y5 * t_3)))
    else if (k <= 1.55d+48) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (z * ((b * y0) - (i * y1)));
	double t_2 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))));
	double t_3 = (y * k) - (t * j);
	double t_4 = y1 * ((x * j) - (z * k));
	double tmp;
	if (k <= -1.45e+187) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (k <= -2e+108) {
		tmp = b * (z * ((k * y0) - (t * a)));
	} else if (k <= -6e+39) {
		tmp = y4 * (((y1 * ((k * y2) - (j * y3))) - (b * t_3)) + (c * ((y * y3) - (t * y2))));
	} else if (k <= -4.5e-7) {
		tmp = t_1;
	} else if (k <= -2.1e-25) {
		tmp = i * t_4;
	} else if (k <= -5e-84) {
		tmp = t_2;
	} else if (k <= -2.6e-242) {
		tmp = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * ((x * y2) - (z * y3)))) + (b * ((z * k) - (x * j))));
	} else if (k <= 2.5e-254) {
		tmp = i * (t_4 + ((c * ((z * t) - (x * y))) + (y5 * t_3)));
	} else if (k <= 1.55e+48) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = k * (z * ((b * y0) - (i * y1)))
	t_2 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))))
	t_3 = (y * k) - (t * j)
	t_4 = y1 * ((x * j) - (z * k))
	tmp = 0
	if k <= -1.45e+187:
		tmp = b * (k * ((z * y0) - (y * y4)))
	elif k <= -2e+108:
		tmp = b * (z * ((k * y0) - (t * a)))
	elif k <= -6e+39:
		tmp = y4 * (((y1 * ((k * y2) - (j * y3))) - (b * t_3)) + (c * ((y * y3) - (t * y2))))
	elif k <= -4.5e-7:
		tmp = t_1
	elif k <= -2.1e-25:
		tmp = i * t_4
	elif k <= -5e-84:
		tmp = t_2
	elif k <= -2.6e-242:
		tmp = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * ((x * y2) - (z * y3)))) + (b * ((z * k) - (x * j))))
	elif k <= 2.5e-254:
		tmp = i * (t_4 + ((c * ((z * t) - (x * y))) + (y5 * t_3)))
	elif k <= 1.55e+48:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(k * Float64(z * Float64(Float64(b * y0) - Float64(i * y1))))
	t_2 = Float64(j * Float64(Float64(Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(t * Float64(Float64(b * y4) - Float64(i * y5)))) + Float64(x * Float64(Float64(i * y1) - Float64(b * y0)))))
	t_3 = Float64(Float64(y * k) - Float64(t * j))
	t_4 = Float64(y1 * Float64(Float64(x * j) - Float64(z * k)))
	tmp = 0.0
	if (k <= -1.45e+187)
		tmp = Float64(b * Float64(k * Float64(Float64(z * y0) - Float64(y * y4))));
	elseif (k <= -2e+108)
		tmp = Float64(b * Float64(z * Float64(Float64(k * y0) - Float64(t * a))));
	elseif (k <= -6e+39)
		tmp = Float64(y4 * Float64(Float64(Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))) - Float64(b * t_3)) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (k <= -4.5e-7)
		tmp = t_1;
	elseif (k <= -2.1e-25)
		tmp = Float64(i * t_4);
	elseif (k <= -5e-84)
		tmp = t_2;
	elseif (k <= -2.6e-242)
		tmp = Float64(y0 * Float64(Float64(Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))) + Float64(c * Float64(Float64(x * y2) - Float64(z * y3)))) + Float64(b * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (k <= 2.5e-254)
		tmp = Float64(i * Float64(t_4 + Float64(Float64(c * Float64(Float64(z * t) - Float64(x * y))) + Float64(y5 * t_3))));
	elseif (k <= 1.55e+48)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = k * (z * ((b * y0) - (i * y1)));
	t_2 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))));
	t_3 = (y * k) - (t * j);
	t_4 = y1 * ((x * j) - (z * k));
	tmp = 0.0;
	if (k <= -1.45e+187)
		tmp = b * (k * ((z * y0) - (y * y4)));
	elseif (k <= -2e+108)
		tmp = b * (z * ((k * y0) - (t * a)));
	elseif (k <= -6e+39)
		tmp = y4 * (((y1 * ((k * y2) - (j * y3))) - (b * t_3)) + (c * ((y * y3) - (t * y2))));
	elseif (k <= -4.5e-7)
		tmp = t_1;
	elseif (k <= -2.1e-25)
		tmp = i * t_4;
	elseif (k <= -5e-84)
		tmp = t_2;
	elseif (k <= -2.6e-242)
		tmp = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * ((x * y2) - (z * y3)))) + (b * ((z * k) - (x * j))));
	elseif (k <= 2.5e-254)
		tmp = i * (t_4 + ((c * ((z * t) - (x * y))) + (y5 * t_3)));
	elseif (k <= 1.55e+48)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(k * N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -1.45e+187], N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -2e+108], N[(b * N[(z * N[(N[(k * y0), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -6e+39], N[(y4 * N[(N[(N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -4.5e-7], t$95$1, If[LessEqual[k, -2.1e-25], N[(i * t$95$4), $MachinePrecision], If[LessEqual[k, -5e-84], t$95$2, If[LessEqual[k, -2.6e-242], N[(y0 * N[(N[(N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.5e-254], N[(i * N[(t$95$4 + N[(N[(c * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.55e+48], t$95$2, t$95$1]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if k < -1.45e187

   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%

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

   5. Taylor expanded in b around inf 46.7%

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

   6. Taylor expanded in k around -inf 73.8%

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

      1. associate-*r* 73.8%

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

      2. neg-mul-1 73.8%

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

      3. *-commutative 73.8%

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

   8. Simplified 73.8%

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

   if -1.45e187 < k < -2.0000000000000001e108

   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%

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

   5. Taylor expanded in b around inf 29.1%

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

   6. Taylor expanded in z around -inf 64.5%

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

      1. associate-*r* 64.5%

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

      2. neg-mul-1 64.5%

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

      3. *-commutative 64.5%

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

   8. Simplified 64.5%

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

   if -2.0000000000000001e108 < k < -5.9999999999999999e39

   1. Initial program 41.7%

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

   3. Taylor expanded in y4 around inf 75.1%

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

   if -5.9999999999999999e39 < k < -4.4999999999999998e-7 or 1.55000000000000003e48 < k

   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%

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

   5. Taylor expanded in z around -inf 45.8%

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

   6. Taylor expanded in k around inf 55.7%

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

   if -4.4999999999999998e-7 < k < -2.10000000000000002e-25

   1. Initial program 27.6%

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

   3. Taylor expanded in y1 around inf 51.2%

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

   4. Taylor expanded in i around inf 76.2%

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

   if -2.10000000000000002e-25 < k < -5.0000000000000002e-84 or 2.5000000000000002e-254 < k < 1.55000000000000003e48

   1. Initial program 23.2%

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

   3. Taylor expanded in j around inf 53.1%

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

   if -5.0000000000000002e-84 < k < -2.60000000000000017e-242

   1. Initial program 48.2%

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

   3. Taylor expanded in y0 around inf 55.0%

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

   if -2.60000000000000017e-242 < k < 2.5000000000000002e-254

   1. Initial program 46.6%

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

   3. Simplified 50.1%

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

   5. Taylor expanded in i around -inf 61.4%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.45 \cdot 10^{+187}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq -2 \cdot 10^{+108}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0 - t \cdot a\right)\right)\\ \mathbf{elif}\;k \leq -6 \cdot 10^{+39}:\\ \;\;\;\;y4 \cdot \left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - b \cdot \left(y \cdot k - t \cdot j\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq -4.5 \cdot 10^{-7}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;k \leq -2.1 \cdot 10^{-25}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;k \leq -5 \cdot 10^{-84}:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq -2.6 \cdot 10^{-242}:\\ \;\;\;\;y0 \cdot \left(\left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;k \leq 2.5 \cdot 10^{-254}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(c \cdot \left(z \cdot t - x \cdot y\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\right)\\ \mathbf{elif}\;k \leq 1.55 \cdot 10^{+48}:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 39.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(c \cdot \left(z \cdot t - x \cdot y\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\right)\\ t_2 := b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ t_3 := b \cdot y0 - i \cdot y1\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{+123}:\\ \;\;\;\;k \cdot \left(z \cdot t\_3\right)\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+20}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-130}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-244}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+143}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(k \cdot t\_3 + \left(t \cdot \left(c \cdot i - a \cdot b\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          i
          (+
           (* y1 (- (* x j) (* z k)))
           (+ (* c (- (* z t) (* x y))) (* y5 (- (* y k) (* t j)))))))
        (t_2
         (*
          b
          (+
           (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
           (* y0 (- (* z k) (* x j))))))
        (t_3 (- (* b y0) (* i y1))))
   (if (<= z -1.55e+123)
     (* k (* z t_3))
     (if (<= z -1.55e+39)
       (*
        x
        (+
         (+ (* y (- (* a b) (* c i))) (* y2 (- (* c y0) (* a y1))))
         (* j (- (* i y1) (* b y0)))))
       (if (<= z -6e+20)
         (* b (* k (- (* z y0) (* y y4))))
         (if (<= z -1.65e-130)
           t_1
           (if (<= z -1.6e-244)
             t_2
             (if (<= z 1.8e+63)
               t_1
               (if (<= z 9.5e+143)
                 t_2
                 (*
                  z
                  (+
                   (* k t_3)
                   (+
                    (* t (- (* c i) (* a b)))
                    (* y3 (- (* a y1) (* c y0)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * ((y1 * ((x * j) - (z * k))) + ((c * ((z * t) - (x * y))) + (y5 * ((y * k) - (t * j)))));
	double t_2 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double t_3 = (b * y0) - (i * y1);
	double tmp;
	if (z <= -1.55e+123) {
		tmp = k * (z * t_3);
	} else if (z <= -1.55e+39) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	} else if (z <= -6e+20) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (z <= -1.65e-130) {
		tmp = t_1;
	} else if (z <= -1.6e-244) {
		tmp = t_2;
	} else if (z <= 1.8e+63) {
		tmp = t_1;
	} else if (z <= 9.5e+143) {
		tmp = t_2;
	} else {
		tmp = z * ((k * t_3) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = i * ((y1 * ((x * j) - (z * k))) + ((c * ((z * t) - (x * y))) + (y5 * ((y * k) - (t * j)))))
    t_2 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    t_3 = (b * y0) - (i * y1)
    if (z <= (-1.55d+123)) then
        tmp = k * (z * t_3)
    else if (z <= (-1.55d+39)) then
        tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
    else if (z <= (-6d+20)) then
        tmp = b * (k * ((z * y0) - (y * y4)))
    else if (z <= (-1.65d-130)) then
        tmp = t_1
    else if (z <= (-1.6d-244)) then
        tmp = t_2
    else if (z <= 1.8d+63) then
        tmp = t_1
    else if (z <= 9.5d+143) then
        tmp = t_2
    else
        tmp = z * ((k * t_3) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * ((y1 * ((x * j) - (z * k))) + ((c * ((z * t) - (x * y))) + (y5 * ((y * k) - (t * j)))));
	double t_2 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double t_3 = (b * y0) - (i * y1);
	double tmp;
	if (z <= -1.55e+123) {
		tmp = k * (z * t_3);
	} else if (z <= -1.55e+39) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	} else if (z <= -6e+20) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (z <= -1.65e-130) {
		tmp = t_1;
	} else if (z <= -1.6e-244) {
		tmp = t_2;
	} else if (z <= 1.8e+63) {
		tmp = t_1;
	} else if (z <= 9.5e+143) {
		tmp = t_2;
	} else {
		tmp = z * ((k * t_3) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = i * ((y1 * ((x * j) - (z * k))) + ((c * ((z * t) - (x * y))) + (y5 * ((y * k) - (t * j)))))
	t_2 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	t_3 = (b * y0) - (i * y1)
	tmp = 0
	if z <= -1.55e+123:
		tmp = k * (z * t_3)
	elif z <= -1.55e+39:
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
	elif z <= -6e+20:
		tmp = b * (k * ((z * y0) - (y * y4)))
	elif z <= -1.65e-130:
		tmp = t_1
	elif z <= -1.6e-244:
		tmp = t_2
	elif z <= 1.8e+63:
		tmp = t_1
	elif z <= 9.5e+143:
		tmp = t_2
	else:
		tmp = z * ((k * t_3) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(i * Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) + Float64(Float64(c * Float64(Float64(z * t) - Float64(x * y))) + Float64(y5 * Float64(Float64(y * k) - Float64(t * j))))))
	t_2 = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))))
	t_3 = Float64(Float64(b * y0) - Float64(i * y1))
	tmp = 0.0
	if (z <= -1.55e+123)
		tmp = Float64(k * Float64(z * t_3));
	elseif (z <= -1.55e+39)
		tmp = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (z <= -6e+20)
		tmp = Float64(b * Float64(k * Float64(Float64(z * y0) - Float64(y * y4))));
	elseif (z <= -1.65e-130)
		tmp = t_1;
	elseif (z <= -1.6e-244)
		tmp = t_2;
	elseif (z <= 1.8e+63)
		tmp = t_1;
	elseif (z <= 9.5e+143)
		tmp = t_2;
	else
		tmp = Float64(z * Float64(Float64(k * t_3) + Float64(Float64(t * Float64(Float64(c * i) - Float64(a * b))) + Float64(y3 * Float64(Float64(a * y1) - Float64(c * y0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = i * ((y1 * ((x * j) - (z * k))) + ((c * ((z * t) - (x * y))) + (y5 * ((y * k) - (t * j)))));
	t_2 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	t_3 = (b * y0) - (i * y1);
	tmp = 0.0;
	if (z <= -1.55e+123)
		tmp = k * (z * t_3);
	elseif (z <= -1.55e+39)
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	elseif (z <= -6e+20)
		tmp = b * (k * ((z * y0) - (y * y4)));
	elseif (z <= -1.65e-130)
		tmp = t_1;
	elseif (z <= -1.6e-244)
		tmp = t_2;
	elseif (z <= 1.8e+63)
		tmp = t_1;
	elseif (z <= 9.5e+143)
		tmp = t_2;
	else
		tmp = z * ((k * t_3) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(i * N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(c * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.55e+123], N[(k * N[(z * t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.55e+39], N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6e+20], N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.65e-130], t$95$1, If[LessEqual[z, -1.6e-244], t$95$2, If[LessEqual[z, 1.8e+63], t$95$1, If[LessEqual[z, 9.5e+143], t$95$2, N[(z * N[(N[(k * t$95$3), $MachinePrecision] + N[(N[(t * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.55000000000000003e123

   1. Initial program 29.9%

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

   3. Simplified 32.6%

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

   5. Taylor expanded in z around -inf 59.5%

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

   6. Taylor expanded in k around inf 62.5%

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

   if -1.55000000000000003e123 < z < -1.5500000000000001e39

   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 26.3%

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

   5. Taylor expanded in x around inf 57.9%

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

   if -1.5500000000000001e39 < z < -6e20

   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%

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

   5. Taylor expanded in b around inf 15.0%

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

   6. Taylor expanded in k around -inf 72.4%

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

      1. associate-*r* 72.4%

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

      2. neg-mul-1 72.4%

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

      3. *-commutative 72.4%

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

   8. Simplified 72.4%

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

   if -6e20 < z < -1.6499999999999999e-130 or -1.5999999999999999e-244 < z < 1.79999999999999999e63

   1. Initial program 39.0%

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

   3. Simplified 39.0%

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

   5. Taylor expanded in i around -inf 51.5%

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

   if -1.6499999999999999e-130 < z < -1.5999999999999999e-244 or 1.79999999999999999e63 < z < 9.50000000000000066e143

   1. Initial program 20.4%

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

   3. Simplified 20.4%

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

   5. Taylor expanded in b around inf 68.0%

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

   if 9.50000000000000066e143 < z

   1. Initial program 17.2%

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

   3. Simplified 17.2%

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

   5. Taylor expanded in z around -inf 65.5%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+123}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+20}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-130}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(c \cdot \left(z \cdot t - x \cdot y\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\right)\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-244}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+63}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(c \cdot \left(z \cdot t - x \cdot y\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+143}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot \left(c \cdot i - a \cdot b\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 39.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ t_2 := b \cdot y0 - i \cdot y1\\ t_3 := z \cdot t - x \cdot y\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{+124}:\\ \;\;\;\;k \cdot \left(z \cdot t\_2\right)\\ \mathbf{elif}\;z \leq -3.15 \cdot 10^{+72}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-56}:\\ \;\;\;\;c \cdot \left(\left(i \cdot t\_3 + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-129}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-242}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{+59}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(c \cdot t\_3 + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+144}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(k \cdot t\_2 + \left(t \cdot \left(c \cdot i - a \cdot b\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          b
          (+
           (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
           (* y0 (- (* z k) (* x j))))))
        (t_2 (- (* b y0) (* i y1)))
        (t_3 (- (* z t) (* x y))))
   (if (<= z -1.65e+124)
     (* k (* z t_2))
     (if (<= z -3.15e+72)
       (*
        x
        (+
         (+ (* y (- (* a b) (* c i))) (* y2 (- (* c y0) (* a y1))))
         (* j (- (* i y1) (* b y0)))))
       (if (<= z -2.9e-56)
         (*
          c
          (+
           (+ (* i t_3) (* y0 (- (* x y2) (* z y3))))
           (* y4 (- (* y y3) (* t y2)))))
         (if (<= z -1.02e-129)
           (* j (* t (- (* b y4) (* i y5))))
           (if (<= z -1.5e-242)
             t_1
             (if (<= z 1.18e+59)
               (*
                i
                (+
                 (* y1 (- (* x j) (* z k)))
                 (+ (* c t_3) (* y5 (- (* y k) (* t j))))))
               (if (<= z 1.2e+144)
                 t_1
                 (*
                  z
                  (+
                   (* k t_2)
                   (+
                    (* t (- (* c i) (* a b)))
                    (* y3 (- (* a y1) (* c y0)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double t_2 = (b * y0) - (i * y1);
	double t_3 = (z * t) - (x * y);
	double tmp;
	if (z <= -1.65e+124) {
		tmp = k * (z * t_2);
	} else if (z <= -3.15e+72) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	} else if (z <= -2.9e-56) {
		tmp = c * (((i * t_3) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (z <= -1.02e-129) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (z <= -1.5e-242) {
		tmp = t_1;
	} else if (z <= 1.18e+59) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((c * t_3) + (y5 * ((y * k) - (t * j)))));
	} else if (z <= 1.2e+144) {
		tmp = t_1;
	} else {
		tmp = z * ((k * t_2) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    t_2 = (b * y0) - (i * y1)
    t_3 = (z * t) - (x * y)
    if (z <= (-1.65d+124)) then
        tmp = k * (z * t_2)
    else if (z <= (-3.15d+72)) then
        tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
    else if (z <= (-2.9d-56)) then
        tmp = c * (((i * t_3) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))))
    else if (z <= (-1.02d-129)) then
        tmp = j * (t * ((b * y4) - (i * y5)))
    else if (z <= (-1.5d-242)) then
        tmp = t_1
    else if (z <= 1.18d+59) then
        tmp = i * ((y1 * ((x * j) - (z * k))) + ((c * t_3) + (y5 * ((y * k) - (t * j)))))
    else if (z <= 1.2d+144) then
        tmp = t_1
    else
        tmp = z * ((k * t_2) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double t_2 = (b * y0) - (i * y1);
	double t_3 = (z * t) - (x * y);
	double tmp;
	if (z <= -1.65e+124) {
		tmp = k * (z * t_2);
	} else if (z <= -3.15e+72) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	} else if (z <= -2.9e-56) {
		tmp = c * (((i * t_3) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (z <= -1.02e-129) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (z <= -1.5e-242) {
		tmp = t_1;
	} else if (z <= 1.18e+59) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((c * t_3) + (y5 * ((y * k) - (t * j)))));
	} else if (z <= 1.2e+144) {
		tmp = t_1;
	} else {
		tmp = z * ((k * t_2) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	t_2 = (b * y0) - (i * y1)
	t_3 = (z * t) - (x * y)
	tmp = 0
	if z <= -1.65e+124:
		tmp = k * (z * t_2)
	elif z <= -3.15e+72:
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
	elif z <= -2.9e-56:
		tmp = c * (((i * t_3) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))))
	elif z <= -1.02e-129:
		tmp = j * (t * ((b * y4) - (i * y5)))
	elif z <= -1.5e-242:
		tmp = t_1
	elif z <= 1.18e+59:
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((c * t_3) + (y5 * ((y * k) - (t * j)))))
	elif z <= 1.2e+144:
		tmp = t_1
	else:
		tmp = z * ((k * t_2) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))))
	t_2 = Float64(Float64(b * y0) - Float64(i * y1))
	t_3 = Float64(Float64(z * t) - Float64(x * y))
	tmp = 0.0
	if (z <= -1.65e+124)
		tmp = Float64(k * Float64(z * t_2));
	elseif (z <= -3.15e+72)
		tmp = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (z <= -2.9e-56)
		tmp = Float64(c * Float64(Float64(Float64(i * t_3) + Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3)))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (z <= -1.02e-129)
		tmp = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))));
	elseif (z <= -1.5e-242)
		tmp = t_1;
	elseif (z <= 1.18e+59)
		tmp = Float64(i * Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) + Float64(Float64(c * t_3) + Float64(y5 * Float64(Float64(y * k) - Float64(t * j))))));
	elseif (z <= 1.2e+144)
		tmp = t_1;
	else
		tmp = Float64(z * Float64(Float64(k * t_2) + Float64(Float64(t * Float64(Float64(c * i) - Float64(a * b))) + Float64(y3 * Float64(Float64(a * y1) - Float64(c * y0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	t_2 = (b * y0) - (i * y1);
	t_3 = (z * t) - (x * y);
	tmp = 0.0;
	if (z <= -1.65e+124)
		tmp = k * (z * t_2);
	elseif (z <= -3.15e+72)
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	elseif (z <= -2.9e-56)
		tmp = c * (((i * t_3) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	elseif (z <= -1.02e-129)
		tmp = j * (t * ((b * y4) - (i * y5)));
	elseif (z <= -1.5e-242)
		tmp = t_1;
	elseif (z <= 1.18e+59)
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((c * t_3) + (y5 * ((y * k) - (t * j)))));
	elseif (z <= 1.2e+144)
		tmp = t_1;
	else
		tmp = z * ((k * t_2) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.65e+124], N[(k * N[(z * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.15e+72], N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.9e-56], N[(c * N[(N[(N[(i * t$95$3), $MachinePrecision] + N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.02e-129], N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.5e-242], t$95$1, If[LessEqual[z, 1.18e+59], N[(i * N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(c * t$95$3), $MachinePrecision] + N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e+144], t$95$1, N[(z * N[(N[(k * t$95$2), $MachinePrecision] + N[(N[(t * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -1.65000000000000007e124

   1. Initial program 29.9%

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

   3. Simplified 32.6%

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

   5. Taylor expanded in z around -inf 59.5%

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

   6. Taylor expanded in k around inf 62.5%

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

   if -1.65000000000000007e124 < z < -3.14999999999999981e72

   1. Initial program 9.1%

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

   3. Simplified 9.1%

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

   5. Taylor expanded in x around inf 72.7%

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

   if -3.14999999999999981e72 < z < -2.89999999999999991e-56

   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%

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

   5. Taylor expanded in c around inf 53.6%

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

   if -2.89999999999999991e-56 < z < -1.02e-129

   1. Initial program 25.0%

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

   3. Taylor expanded in j around inf 50.1%

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

   4. Taylor expanded in t around inf 67.2%

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

   if -1.02e-129 < z < -1.5e-242 or 1.17999999999999994e59 < z < 1.2e144

   1. Initial program 20.4%

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

   3. Simplified 20.4%

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

   5. Taylor expanded in b around inf 68.0%

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

   if -1.5e-242 < z < 1.17999999999999994e59

   1. Initial program 39.4%

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

   3. Simplified 39.4%

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

   5. Taylor expanded in i around -inf 50.7%

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

   if 1.2e144 < z

   1. Initial program 17.2%

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

   3. Simplified 17.2%

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

   5. Taylor expanded in z around -inf 65.5%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+124}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;z \leq -3.15 \cdot 10^{+72}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-56}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-129}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-242}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{+59}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(c \cdot \left(z \cdot t - x \cdot y\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+144}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot \left(c \cdot i - a \cdot b\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 31.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(z \cdot \left(k \cdot y0 - t \cdot a\right)\right)\\ \mathbf{if}\;z \leq -3.45 \cdot 10^{-43}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-161}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-248}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-140}:\\ \;\;\;\;\left(j \cdot y5\right) \cdot \left(y0 \cdot y3 - t \cdot i\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-48}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+47}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+105}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + \left(z \cdot t\right) \cdot i\right) - t \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* z (- (* k y0) (* t a))))))
   (if (<= z -3.45e-43)
     (* k (* z (- (* b y0) (* i y1))))
     (if (<= z -9.5e-161)
       (* j (* t (- (* b y4) (* i y5))))
       (if (<= z 2.8e-248)
         (* x (* y2 (- (* c y0) (* a y1))))
         (if (<= z 5.8e-140)
           (* (* j y5) (- (* y0 y3) (* t i)))
           (if (<= z 3e-100)
             t_1
             (if (<= z 8e-48)
               (* a (* y (- (* x b) (* y3 y5))))
               (if (<= z 2.3e+47)
                 (* b (* k (- (* z y0) (* y y4))))
                 (if (<= z 2.9e+105)
                   (*
                    c
                    (-
                     (+ (* y0 (- (* x y2) (* z y3))) (* (* z t) i))
                     (* t (* y2 y4))))
                   t_1))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (z * ((k * y0) - (t * a)));
	double tmp;
	if (z <= -3.45e-43) {
		tmp = k * (z * ((b * y0) - (i * y1)));
	} else if (z <= -9.5e-161) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (z <= 2.8e-248) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (z <= 5.8e-140) {
		tmp = (j * y5) * ((y0 * y3) - (t * i));
	} else if (z <= 3e-100) {
		tmp = t_1;
	} else if (z <= 8e-48) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (z <= 2.3e+47) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (z <= 2.9e+105) {
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + ((z * t) * i)) - (t * (y2 * y4)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (z * ((k * y0) - (t * a)))
    if (z <= (-3.45d-43)) then
        tmp = k * (z * ((b * y0) - (i * y1)))
    else if (z <= (-9.5d-161)) then
        tmp = j * (t * ((b * y4) - (i * y5)))
    else if (z <= 2.8d-248) then
        tmp = x * (y2 * ((c * y0) - (a * y1)))
    else if (z <= 5.8d-140) then
        tmp = (j * y5) * ((y0 * y3) - (t * i))
    else if (z <= 3d-100) then
        tmp = t_1
    else if (z <= 8d-48) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (z <= 2.3d+47) then
        tmp = b * (k * ((z * y0) - (y * y4)))
    else if (z <= 2.9d+105) then
        tmp = c * (((y0 * ((x * y2) - (z * y3))) + ((z * t) * i)) - (t * (y2 * y4)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (z * ((k * y0) - (t * a)));
	double tmp;
	if (z <= -3.45e-43) {
		tmp = k * (z * ((b * y0) - (i * y1)));
	} else if (z <= -9.5e-161) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (z <= 2.8e-248) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (z <= 5.8e-140) {
		tmp = (j * y5) * ((y0 * y3) - (t * i));
	} else if (z <= 3e-100) {
		tmp = t_1;
	} else if (z <= 8e-48) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (z <= 2.3e+47) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (z <= 2.9e+105) {
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + ((z * t) * i)) - (t * (y2 * y4)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (z * ((k * y0) - (t * a)))
	tmp = 0
	if z <= -3.45e-43:
		tmp = k * (z * ((b * y0) - (i * y1)))
	elif z <= -9.5e-161:
		tmp = j * (t * ((b * y4) - (i * y5)))
	elif z <= 2.8e-248:
		tmp = x * (y2 * ((c * y0) - (a * y1)))
	elif z <= 5.8e-140:
		tmp = (j * y5) * ((y0 * y3) - (t * i))
	elif z <= 3e-100:
		tmp = t_1
	elif z <= 8e-48:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif z <= 2.3e+47:
		tmp = b * (k * ((z * y0) - (y * y4)))
	elif z <= 2.9e+105:
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + ((z * t) * i)) - (t * (y2 * y4)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(z * Float64(Float64(k * y0) - Float64(t * a))))
	tmp = 0.0
	if (z <= -3.45e-43)
		tmp = Float64(k * Float64(z * Float64(Float64(b * y0) - Float64(i * y1))));
	elseif (z <= -9.5e-161)
		tmp = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))));
	elseif (z <= 2.8e-248)
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (z <= 5.8e-140)
		tmp = Float64(Float64(j * y5) * Float64(Float64(y0 * y3) - Float64(t * i)));
	elseif (z <= 3e-100)
		tmp = t_1;
	elseif (z <= 8e-48)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (z <= 2.3e+47)
		tmp = Float64(b * Float64(k * Float64(Float64(z * y0) - Float64(y * y4))));
	elseif (z <= 2.9e+105)
		tmp = Float64(c * Float64(Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(Float64(z * t) * i)) - Float64(t * Float64(y2 * y4))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (z * ((k * y0) - (t * a)));
	tmp = 0.0;
	if (z <= -3.45e-43)
		tmp = k * (z * ((b * y0) - (i * y1)));
	elseif (z <= -9.5e-161)
		tmp = j * (t * ((b * y4) - (i * y5)));
	elseif (z <= 2.8e-248)
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	elseif (z <= 5.8e-140)
		tmp = (j * y5) * ((y0 * y3) - (t * i));
	elseif (z <= 3e-100)
		tmp = t_1;
	elseif (z <= 8e-48)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (z <= 2.3e+47)
		tmp = b * (k * ((z * y0) - (y * y4)));
	elseif (z <= 2.9e+105)
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + ((z * t) * i)) - (t * (y2 * y4)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(z * N[(N[(k * y0), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.45e-43], N[(k * N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9.5e-161], N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e-248], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e-140], N[(N[(j * y5), $MachinePrecision] * N[(N[(y0 * y3), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e-100], t$95$1, If[LessEqual[z, 8e-48], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.3e+47], N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e+105], N[(c * N[(N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(t * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if z < -3.44999999999999982e-43

   1. Initial program 27.3%

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

   3. Simplified 28.6%

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

   5. Taylor expanded in z around -inf 48.2%

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

   6. Taylor expanded in k around inf 51.3%

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

   if -3.44999999999999982e-43 < z < -9.4999999999999996e-161

   1. Initial program 32.4%

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

   3. Taylor expanded in j around inf 46.7%

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

   4. Taylor expanded in t around inf 59.9%

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

   if -9.4999999999999996e-161 < z < 2.8000000000000001e-248

   1. Initial program 25.1%

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

   3. Taylor expanded in y2 around inf 33.0%

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

   4. Taylor expanded in x around inf 43.8%

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

   if 2.8000000000000001e-248 < z < 5.79999999999999995e-140

   1. Initial program 54.8%

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

   3. Taylor expanded in j around inf 60.3%

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

   4. Taylor expanded in y5 around inf 55.9%

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

      1. associate-*r* 60.1%

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

      2. +-commutative 60.1%

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

      3. mul-1-neg 60.1%

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

      4. unsub-neg 60.1%

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

      5. *-commutative 60.1%

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

   6. Simplified 60.1%

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

   if 5.79999999999999995e-140 < z < 3.0000000000000001e-100 or 2.9000000000000001e105 < z

   1. Initial program 19.7%

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

   3. Simplified 19.7%

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

   5. Taylor expanded in b around inf 43.6%

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

   6. Taylor expanded in z around -inf 57.5%

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

      1. associate-*r* 57.5%

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

      2. neg-mul-1 57.5%

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

      3. *-commutative 57.5%

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

   8. Simplified 57.5%

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

   if 3.0000000000000001e-100 < z < 7.9999999999999998e-48

   1. Initial program 40.0%

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

   3. Simplified 39.9%

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

   5. Taylor expanded in a around inf 37.3%

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

   6. Taylor expanded in y around inf 41.8%

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

   if 7.9999999999999998e-48 < z < 2.2999999999999999e47

   1. Initial program 41.3%

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

   3. Simplified 41.3%

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

   5. Taylor expanded in b around inf 28.6%

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

   6. Taylor expanded in k around -inf 51.0%

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

      1. associate-*r* 51.0%

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

      2. neg-mul-1 51.0%

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

      3. *-commutative 51.0%

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

   8. Simplified 51.0%

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

   if 2.2999999999999999e47 < z < 2.9000000000000001e105

   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%

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

   5. Taylor expanded in c around inf 67.2%

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

   6. Taylor expanded in y around 0 67.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(i \cdot \left(t \cdot z\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - t \cdot \left(y2 \cdot y4\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.45 \cdot 10^{-43}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-161}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-248}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-140}:\\ \;\;\;\;\left(j \cdot y5\right) \cdot \left(y0 \cdot y3 - t \cdot i\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-100}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0 - t \cdot a\right)\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-48}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+47}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+105}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + \left(z \cdot t\right) \cdot i\right) - t \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0 - t \cdot a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 30.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ t_2 := x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{if}\;x \leq -1.72 \cdot 10^{+180}:\\ \;\;\;\;\left(x \cdot c\right) \cdot \left(y0 \cdot y2 - y \cdot i\right)\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{+90}:\\ \;\;\;\;\left(x \cdot j\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{+49}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-48}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-149}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-241}:\\ \;\;\;\;t \cdot \left(b \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-68}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{+68}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+160}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* t (- (* b y4) (* i y5)))))
        (t_2 (* x (* y2 (- (* c y0) (* a y1))))))
   (if (<= x -1.72e+180)
     (* (* x c) (- (* y0 y2) (* y i)))
     (if (<= x -3.8e+90)
       (* (* x j) (- (* i y1) (* b y0)))
       (if (<= x -3.3e+49)
         t_2
         (if (<= x -3.1e-48)
           (* y1 (* y4 (- (* k y2) (* j y3))))
           (if (<= x -8e-149)
             (* c (* t (- (* z i) (* y2 y4))))
             (if (<= x 2.3e-241)
               (* t (* b (- (* j y4) (* z a))))
               (if (<= x 7.5e-68)
                 t_1
                 (if (<= x 1.02e+68)
                   (* a (* y (- (* x b) (* y3 y5))))
                   (if (<= x 2.2e+160) 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 = j * (t * ((b * y4) - (i * y5)));
	double t_2 = x * (y2 * ((c * y0) - (a * y1)));
	double tmp;
	if (x <= -1.72e+180) {
		tmp = (x * c) * ((y0 * y2) - (y * i));
	} else if (x <= -3.8e+90) {
		tmp = (x * j) * ((i * y1) - (b * y0));
	} else if (x <= -3.3e+49) {
		tmp = t_2;
	} else if (x <= -3.1e-48) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else if (x <= -8e-149) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (x <= 2.3e-241) {
		tmp = t * (b * ((j * y4) - (z * a)));
	} else if (x <= 7.5e-68) {
		tmp = t_1;
	} else if (x <= 1.02e+68) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (x <= 2.2e+160) {
		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 = j * (t * ((b * y4) - (i * y5)))
    t_2 = x * (y2 * ((c * y0) - (a * y1)))
    if (x <= (-1.72d+180)) then
        tmp = (x * c) * ((y0 * y2) - (y * i))
    else if (x <= (-3.8d+90)) then
        tmp = (x * j) * ((i * y1) - (b * y0))
    else if (x <= (-3.3d+49)) then
        tmp = t_2
    else if (x <= (-3.1d-48)) then
        tmp = y1 * (y4 * ((k * y2) - (j * y3)))
    else if (x <= (-8d-149)) then
        tmp = c * (t * ((z * i) - (y2 * y4)))
    else if (x <= 2.3d-241) then
        tmp = t * (b * ((j * y4) - (z * a)))
    else if (x <= 7.5d-68) then
        tmp = t_1
    else if (x <= 1.02d+68) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (x <= 2.2d+160) 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 = j * (t * ((b * y4) - (i * y5)));
	double t_2 = x * (y2 * ((c * y0) - (a * y1)));
	double tmp;
	if (x <= -1.72e+180) {
		tmp = (x * c) * ((y0 * y2) - (y * i));
	} else if (x <= -3.8e+90) {
		tmp = (x * j) * ((i * y1) - (b * y0));
	} else if (x <= -3.3e+49) {
		tmp = t_2;
	} else if (x <= -3.1e-48) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else if (x <= -8e-149) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (x <= 2.3e-241) {
		tmp = t * (b * ((j * y4) - (z * a)));
	} else if (x <= 7.5e-68) {
		tmp = t_1;
	} else if (x <= 1.02e+68) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (x <= 2.2e+160) {
		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 = j * (t * ((b * y4) - (i * y5)))
	t_2 = x * (y2 * ((c * y0) - (a * y1)))
	tmp = 0
	if x <= -1.72e+180:
		tmp = (x * c) * ((y0 * y2) - (y * i))
	elif x <= -3.8e+90:
		tmp = (x * j) * ((i * y1) - (b * y0))
	elif x <= -3.3e+49:
		tmp = t_2
	elif x <= -3.1e-48:
		tmp = y1 * (y4 * ((k * y2) - (j * y3)))
	elif x <= -8e-149:
		tmp = c * (t * ((z * i) - (y2 * y4)))
	elif x <= 2.3e-241:
		tmp = t * (b * ((j * y4) - (z * a)))
	elif x <= 7.5e-68:
		tmp = t_1
	elif x <= 1.02e+68:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif x <= 2.2e+160:
		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(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))))
	t_2 = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))))
	tmp = 0.0
	if (x <= -1.72e+180)
		tmp = Float64(Float64(x * c) * Float64(Float64(y0 * y2) - Float64(y * i)));
	elseif (x <= -3.8e+90)
		tmp = Float64(Float64(x * j) * Float64(Float64(i * y1) - Float64(b * y0)));
	elseif (x <= -3.3e+49)
		tmp = t_2;
	elseif (x <= -3.1e-48)
		tmp = Float64(y1 * Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif (x <= -8e-149)
		tmp = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (x <= 2.3e-241)
		tmp = Float64(t * Float64(b * Float64(Float64(j * y4) - Float64(z * a))));
	elseif (x <= 7.5e-68)
		tmp = t_1;
	elseif (x <= 1.02e+68)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (x <= 2.2e+160)
		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 = j * (t * ((b * y4) - (i * y5)));
	t_2 = x * (y2 * ((c * y0) - (a * y1)));
	tmp = 0.0;
	if (x <= -1.72e+180)
		tmp = (x * c) * ((y0 * y2) - (y * i));
	elseif (x <= -3.8e+90)
		tmp = (x * j) * ((i * y1) - (b * y0));
	elseif (x <= -3.3e+49)
		tmp = t_2;
	elseif (x <= -3.1e-48)
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	elseif (x <= -8e-149)
		tmp = c * (t * ((z * i) - (y2 * y4)));
	elseif (x <= 2.3e-241)
		tmp = t * (b * ((j * y4) - (z * a)));
	elseif (x <= 7.5e-68)
		tmp = t_1;
	elseif (x <= 1.02e+68)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (x <= 2.2e+160)
		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[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.72e+180], N[(N[(x * c), $MachinePrecision] * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.8e+90], N[(N[(x * j), $MachinePrecision] * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.3e+49], t$95$2, If[LessEqual[x, -3.1e-48], N[(y1 * N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -8e-149], N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.3e-241], N[(t * N[(b * N[(N[(j * y4), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.5e-68], t$95$1, If[LessEqual[x, 1.02e+68], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.2e+160], t$95$1, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if x < -1.72e180

   1. Initial program 30.4%

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

   3. Simplified 30.4%

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

   5. Taylor expanded in c around inf 36.3%

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

   6. Taylor expanded in x around inf 58.4%

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

      1. associate-*r* 48.8%

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

      2. +-commutative 48.8%

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

      3. mul-1-neg 48.8%

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

      4. unsub-neg 48.8%

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

      5. *-commutative 48.8%

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

   8. Simplified 48.8%

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

   if -1.72e180 < x < -3.8000000000000001e90

   1. Initial program 30.4%

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

   3. Taylor expanded in j around inf 49.4%

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

   4. Taylor expanded in x around inf 44.8%

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

      1. associate-*r* 52.9%

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

      2. *-commutative 52.9%

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

   6. Simplified 52.9%

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

   if -3.8000000000000001e90 < x < -3.2999999999999998e49 or 2.19999999999999992e160 < x

   1. Initial program 21.2%

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

   3. Taylor expanded in y2 around inf 42.7%

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

   4. Taylor expanded in x around inf 61.3%

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

   if -3.2999999999999998e49 < x < -3.10000000000000016e-48

   1. Initial program 36.9%

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

   3. Taylor expanded in y1 around inf 44.2%

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

   4. Taylor expanded in y4 around inf 52.8%

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

   if -3.10000000000000016e-48 < x < -7.99999999999999983e-149

   1. Initial program 39.4%

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

   3. Simplified 39.3%

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

   5. Taylor expanded in c around inf 53.5%

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

   6. Taylor expanded in t around inf 62.0%

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

   if -7.99999999999999983e-149 < x < 2.2999999999999999e-241

   1. Initial program 26.8%

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

   3. Simplified 26.8%

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

   5. Taylor expanded in b around inf 52.8%

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

   6. Taylor expanded in t around inf 41.5%

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

      1. associate-*r* 41.4%

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

      2. +-commutative 41.4%

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

      3. mul-1-neg 41.4%

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

      4. unsub-neg 41.4%

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

      5. *-commutative 41.4%

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

      6. *-commutative 41.4%

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

   8. Simplified 41.4%

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

   9. Taylor expanded in b around 0 41.5%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot \left(j \cdot y4 - a \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 41.4%

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

       2. *-commutative 41.4%

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

       3. *-commutative 41.4%

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

       4. associate-*l* 41.5%

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

       5. *-commutative 41.5%

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

   11. Simplified 41.5%

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

   if 2.2999999999999999e-241 < x < 7.50000000000000081e-68 or 1.02e68 < x < 2.19999999999999992e160

   1. Initial program 31.2%

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

   3. Taylor expanded in j around inf 35.1%

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

   4. Taylor expanded in t around inf 47.9%

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

   if 7.50000000000000081e-68 < x < 1.02e68

   1. Initial program 31.0%

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

   3. Simplified 31.0%

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

   5. Taylor expanded in a around inf 40.5%

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

   6. Taylor expanded in y around inf 40.7%

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

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.72 \cdot 10^{+180}:\\ \;\;\;\;\left(x \cdot c\right) \cdot \left(y0 \cdot y2 - y \cdot i\right)\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{+90}:\\ \;\;\;\;\left(x \cdot j\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-48}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-149}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-241}:\\ \;\;\;\;t \cdot \left(b \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-68}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{+68}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+160}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 30.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ t_2 := x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{if}\;x \leq -3.7 \cdot 10^{+182}:\\ \;\;\;\;\left(x \cdot c\right) \cdot \left(y0 \cdot y2 - y \cdot i\right)\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{+92}:\\ \;\;\;\;\left(x \cdot j\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\\ \mathbf{elif}\;x \leq -1.16 \cdot 10^{+49}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-49}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-156}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-276}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+67}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{+160}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* t (- (* b y4) (* i y5)))))
        (t_2 (* x (* y2 (- (* c y0) (* a y1))))))
   (if (<= x -3.7e+182)
     (* (* x c) (- (* y0 y2) (* y i)))
     (if (<= x -5.2e+92)
       (* (* x j) (- (* i y1) (* b y0)))
       (if (<= x -1.16e+49)
         t_2
         (if (<= x -2.8e-49)
           (* y1 (* y4 (- (* k y2) (* j y3))))
           (if (<= x -6.2e-156)
             (* c (* t (- (* z i) (* y2 y4))))
             (if (<= x 5.8e-276)
               (* a (* z (- (* y1 y3) (* t b))))
               (if (<= x 8e-65)
                 t_1
                 (if (<= x 4.5e+67)
                   (* a (* y (- (* x b) (* y3 y5))))
                   (if (<= x 1.12e+160) 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 = j * (t * ((b * y4) - (i * y5)));
	double t_2 = x * (y2 * ((c * y0) - (a * y1)));
	double tmp;
	if (x <= -3.7e+182) {
		tmp = (x * c) * ((y0 * y2) - (y * i));
	} else if (x <= -5.2e+92) {
		tmp = (x * j) * ((i * y1) - (b * y0));
	} else if (x <= -1.16e+49) {
		tmp = t_2;
	} else if (x <= -2.8e-49) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else if (x <= -6.2e-156) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (x <= 5.8e-276) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (x <= 8e-65) {
		tmp = t_1;
	} else if (x <= 4.5e+67) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (x <= 1.12e+160) {
		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 = j * (t * ((b * y4) - (i * y5)))
    t_2 = x * (y2 * ((c * y0) - (a * y1)))
    if (x <= (-3.7d+182)) then
        tmp = (x * c) * ((y0 * y2) - (y * i))
    else if (x <= (-5.2d+92)) then
        tmp = (x * j) * ((i * y1) - (b * y0))
    else if (x <= (-1.16d+49)) then
        tmp = t_2
    else if (x <= (-2.8d-49)) then
        tmp = y1 * (y4 * ((k * y2) - (j * y3)))
    else if (x <= (-6.2d-156)) then
        tmp = c * (t * ((z * i) - (y2 * y4)))
    else if (x <= 5.8d-276) then
        tmp = a * (z * ((y1 * y3) - (t * b)))
    else if (x <= 8d-65) then
        tmp = t_1
    else if (x <= 4.5d+67) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (x <= 1.12d+160) 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 = j * (t * ((b * y4) - (i * y5)));
	double t_2 = x * (y2 * ((c * y0) - (a * y1)));
	double tmp;
	if (x <= -3.7e+182) {
		tmp = (x * c) * ((y0 * y2) - (y * i));
	} else if (x <= -5.2e+92) {
		tmp = (x * j) * ((i * y1) - (b * y0));
	} else if (x <= -1.16e+49) {
		tmp = t_2;
	} else if (x <= -2.8e-49) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else if (x <= -6.2e-156) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (x <= 5.8e-276) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (x <= 8e-65) {
		tmp = t_1;
	} else if (x <= 4.5e+67) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (x <= 1.12e+160) {
		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 = j * (t * ((b * y4) - (i * y5)))
	t_2 = x * (y2 * ((c * y0) - (a * y1)))
	tmp = 0
	if x <= -3.7e+182:
		tmp = (x * c) * ((y0 * y2) - (y * i))
	elif x <= -5.2e+92:
		tmp = (x * j) * ((i * y1) - (b * y0))
	elif x <= -1.16e+49:
		tmp = t_2
	elif x <= -2.8e-49:
		tmp = y1 * (y4 * ((k * y2) - (j * y3)))
	elif x <= -6.2e-156:
		tmp = c * (t * ((z * i) - (y2 * y4)))
	elif x <= 5.8e-276:
		tmp = a * (z * ((y1 * y3) - (t * b)))
	elif x <= 8e-65:
		tmp = t_1
	elif x <= 4.5e+67:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif x <= 1.12e+160:
		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(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))))
	t_2 = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))))
	tmp = 0.0
	if (x <= -3.7e+182)
		tmp = Float64(Float64(x * c) * Float64(Float64(y0 * y2) - Float64(y * i)));
	elseif (x <= -5.2e+92)
		tmp = Float64(Float64(x * j) * Float64(Float64(i * y1) - Float64(b * y0)));
	elseif (x <= -1.16e+49)
		tmp = t_2;
	elseif (x <= -2.8e-49)
		tmp = Float64(y1 * Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif (x <= -6.2e-156)
		tmp = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (x <= 5.8e-276)
		tmp = Float64(a * Float64(z * Float64(Float64(y1 * y3) - Float64(t * b))));
	elseif (x <= 8e-65)
		tmp = t_1;
	elseif (x <= 4.5e+67)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (x <= 1.12e+160)
		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 = j * (t * ((b * y4) - (i * y5)));
	t_2 = x * (y2 * ((c * y0) - (a * y1)));
	tmp = 0.0;
	if (x <= -3.7e+182)
		tmp = (x * c) * ((y0 * y2) - (y * i));
	elseif (x <= -5.2e+92)
		tmp = (x * j) * ((i * y1) - (b * y0));
	elseif (x <= -1.16e+49)
		tmp = t_2;
	elseif (x <= -2.8e-49)
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	elseif (x <= -6.2e-156)
		tmp = c * (t * ((z * i) - (y2 * y4)));
	elseif (x <= 5.8e-276)
		tmp = a * (z * ((y1 * y3) - (t * b)));
	elseif (x <= 8e-65)
		tmp = t_1;
	elseif (x <= 4.5e+67)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (x <= 1.12e+160)
		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[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.7e+182], N[(N[(x * c), $MachinePrecision] * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.2e+92], N[(N[(x * j), $MachinePrecision] * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.16e+49], t$95$2, If[LessEqual[x, -2.8e-49], N[(y1 * N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.2e-156], N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.8e-276], N[(a * N[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8e-65], t$95$1, If[LessEqual[x, 4.5e+67], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.12e+160], t$95$1, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if x < -3.69999999999999977e182

   1. Initial program 30.4%

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

   3. Simplified 30.4%

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

   5. Taylor expanded in c around inf 36.3%

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

   6. Taylor expanded in x around inf 58.4%

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

      1. associate-*r* 48.8%

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

      2. +-commutative 48.8%

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

      3. mul-1-neg 48.8%

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

      4. unsub-neg 48.8%

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

      5. *-commutative 48.8%

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

   8. Simplified 48.8%

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

   if -3.69999999999999977e182 < x < -5.1999999999999998e92

   1. Initial program 30.4%

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

   3. Taylor expanded in j around inf 49.4%

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

   4. Taylor expanded in x around inf 44.8%

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

      1. associate-*r* 52.9%

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

      2. *-commutative 52.9%

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

   6. Simplified 52.9%

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

   if -5.1999999999999998e92 < x < -1.16e49 or 1.12e160 < x

   1. Initial program 21.2%

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

   3. Taylor expanded in y2 around inf 42.7%

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

   4. Taylor expanded in x around inf 61.3%

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

   if -1.16e49 < x < -2.79999999999999997e-49

   1. Initial program 36.9%

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

   3. Taylor expanded in y1 around inf 44.2%

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

   4. Taylor expanded in y4 around inf 52.8%

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

   if -2.79999999999999997e-49 < x < -6.1999999999999996e-156

   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 41.8%

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

   5. Taylor expanded in c around inf 51.4%

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

   6. Taylor expanded in t around inf 59.6%

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

   if -6.1999999999999996e-156 < x < 5.79999999999999975e-276

   1. Initial program 29.3%

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

   3. Simplified 29.3%

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

   5. Taylor expanded in a around inf 38.0%

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

   6. Taylor expanded in z around -inf 43.7%

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

      1. associate-*r* 43.7%

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

      2. neg-mul-1 43.7%

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

      3. +-commutative 43.7%

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

      4. mul-1-neg 43.7%

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

      5. unsub-neg 43.7%

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

   8. Simplified 43.7%

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

   if 5.79999999999999975e-276 < x < 7.99999999999999939e-65 or 4.4999999999999998e67 < x < 1.12e160

   1. Initial program 28.5%

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

   3. Taylor expanded in j around inf 33.6%

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

   4. Taylor expanded in t around inf 46.8%

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

   if 7.99999999999999939e-65 < x < 4.4999999999999998e67

   1. Initial program 31.0%

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

   3. Simplified 31.0%

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

   5. Taylor expanded in a around inf 40.5%

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

   6. Taylor expanded in y around inf 40.7%

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

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{+182}:\\ \;\;\;\;\left(x \cdot c\right) \cdot \left(y0 \cdot y2 - y \cdot i\right)\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{+92}:\\ \;\;\;\;\left(x \cdot j\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\\ \mathbf{elif}\;x \leq -1.16 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-49}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-156}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-276}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-65}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+67}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{+160}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 34.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot y0 - a \cdot y1\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{-42}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-160}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-243}:\\ \;\;\;\;x \cdot \left(y2 \cdot t\_1\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-230}:\\ \;\;\;\;\left(j \cdot y5\right) \cdot \left(y0 \cdot y3 - t \cdot i\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-18}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot t\_1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+105}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + \left(z \cdot t\right) \cdot i\right) - t \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0 - t \cdot a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* c y0) (* a y1))))
   (if (<= z -1.35e-42)
     (* k (* z (- (* b y0) (* i y1))))
     (if (<= z -2.9e-160)
       (* j (* t (- (* b y4) (* i y5))))
       (if (<= z 2.2e-243)
         (* x (* y2 t_1))
         (if (<= z 1.3e-230)
           (* (* j y5) (- (* y0 y3) (* t i)))
           (if (<= z 4.6e-18)
             (*
              y2
              (+
               (+ (* k (- (* y1 y4) (* y0 y5))) (* x t_1))
               (* t (- (* a y5) (* c y4)))))
             (if (<= z 7.5e+105)
               (*
                c
                (-
                 (+ (* y0 (- (* x y2) (* z y3))) (* (* z t) i))
                 (* t (* y2 y4))))
               (* b (* z (- (* k y0) (* t 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 = (c * y0) - (a * y1);
	double tmp;
	if (z <= -1.35e-42) {
		tmp = k * (z * ((b * y0) - (i * y1)));
	} else if (z <= -2.9e-160) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (z <= 2.2e-243) {
		tmp = x * (y2 * t_1);
	} else if (z <= 1.3e-230) {
		tmp = (j * y5) * ((y0 * y3) - (t * i));
	} else if (z <= 4.6e-18) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_1)) + (t * ((a * y5) - (c * y4))));
	} else if (z <= 7.5e+105) {
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + ((z * t) * i)) - (t * (y2 * y4)));
	} else {
		tmp = b * (z * ((k * y0) - (t * 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 = (c * y0) - (a * y1)
    if (z <= (-1.35d-42)) then
        tmp = k * (z * ((b * y0) - (i * y1)))
    else if (z <= (-2.9d-160)) then
        tmp = j * (t * ((b * y4) - (i * y5)))
    else if (z <= 2.2d-243) then
        tmp = x * (y2 * t_1)
    else if (z <= 1.3d-230) then
        tmp = (j * y5) * ((y0 * y3) - (t * i))
    else if (z <= 4.6d-18) then
        tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_1)) + (t * ((a * y5) - (c * y4))))
    else if (z <= 7.5d+105) then
        tmp = c * (((y0 * ((x * y2) - (z * y3))) + ((z * t) * i)) - (t * (y2 * y4)))
    else
        tmp = b * (z * ((k * y0) - (t * 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 = (c * y0) - (a * y1);
	double tmp;
	if (z <= -1.35e-42) {
		tmp = k * (z * ((b * y0) - (i * y1)));
	} else if (z <= -2.9e-160) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (z <= 2.2e-243) {
		tmp = x * (y2 * t_1);
	} else if (z <= 1.3e-230) {
		tmp = (j * y5) * ((y0 * y3) - (t * i));
	} else if (z <= 4.6e-18) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_1)) + (t * ((a * y5) - (c * y4))));
	} else if (z <= 7.5e+105) {
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + ((z * t) * i)) - (t * (y2 * y4)));
	} else {
		tmp = b * (z * ((k * y0) - (t * a)));
	}
	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)
	tmp = 0
	if z <= -1.35e-42:
		tmp = k * (z * ((b * y0) - (i * y1)))
	elif z <= -2.9e-160:
		tmp = j * (t * ((b * y4) - (i * y5)))
	elif z <= 2.2e-243:
		tmp = x * (y2 * t_1)
	elif z <= 1.3e-230:
		tmp = (j * y5) * ((y0 * y3) - (t * i))
	elif z <= 4.6e-18:
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_1)) + (t * ((a * y5) - (c * y4))))
	elif z <= 7.5e+105:
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + ((z * t) * i)) - (t * (y2 * y4)))
	else:
		tmp = b * (z * ((k * y0) - (t * 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(Float64(c * y0) - Float64(a * y1))
	tmp = 0.0
	if (z <= -1.35e-42)
		tmp = Float64(k * Float64(z * Float64(Float64(b * y0) - Float64(i * y1))));
	elseif (z <= -2.9e-160)
		tmp = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))));
	elseif (z <= 2.2e-243)
		tmp = Float64(x * Float64(y2 * t_1));
	elseif (z <= 1.3e-230)
		tmp = Float64(Float64(j * y5) * Float64(Float64(y0 * y3) - Float64(t * i)));
	elseif (z <= 4.6e-18)
		tmp = Float64(y2 * Float64(Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(x * t_1)) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (z <= 7.5e+105)
		tmp = Float64(c * Float64(Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(Float64(z * t) * i)) - Float64(t * Float64(y2 * y4))));
	else
		tmp = Float64(b * Float64(z * Float64(Float64(k * y0) - Float64(t * 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 = (c * y0) - (a * y1);
	tmp = 0.0;
	if (z <= -1.35e-42)
		tmp = k * (z * ((b * y0) - (i * y1)));
	elseif (z <= -2.9e-160)
		tmp = j * (t * ((b * y4) - (i * y5)));
	elseif (z <= 2.2e-243)
		tmp = x * (y2 * t_1);
	elseif (z <= 1.3e-230)
		tmp = (j * y5) * ((y0 * y3) - (t * i));
	elseif (z <= 4.6e-18)
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_1)) + (t * ((a * y5) - (c * y4))));
	elseif (z <= 7.5e+105)
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + ((z * t) * i)) - (t * (y2 * y4)));
	else
		tmp = b * (z * ((k * y0) - (t * 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[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e-42], N[(k * N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.9e-160], N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e-243], N[(x * N[(y2 * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e-230], N[(N[(j * y5), $MachinePrecision] * N[(N[(y0 * y3), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e-18], N[(y2 * N[(N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e+105], N[(c * N[(N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(t * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(z * N[(N[(k * y0), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -1.35e-42

   1. Initial program 27.3%

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

   3. Simplified 28.6%

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

   5. Taylor expanded in z around -inf 48.2%

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

   6. Taylor expanded in k around inf 51.3%

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

   if -1.35e-42 < z < -2.8999999999999999e-160

   1. Initial program 32.4%

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

   3. Taylor expanded in j around inf 46.7%

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

   4. Taylor expanded in t around inf 59.9%

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

   if -2.8999999999999999e-160 < z < 2.1999999999999999e-243

   1. Initial program 25.1%

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

   3. Taylor expanded in y2 around inf 33.0%

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

   4. Taylor expanded in x around inf 43.8%

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

   if 2.1999999999999999e-243 < z < 1.3000000000000001e-230

   1. Initial program 21.3%

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

   3. Taylor expanded in j around inf 61.3%

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

   4. Taylor expanded in y5 around inf 61.4%

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

      1. associate-*r* 80.1%

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

      2. +-commutative 80.1%

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

      3. mul-1-neg 80.1%

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

      4. unsub-neg 80.1%

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

      5. *-commutative 80.1%

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

   6. Simplified 80.1%

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

   if 1.3000000000000001e-230 < z < 4.6000000000000002e-18

   1. Initial program 44.2%

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

   3. Taylor expanded in y2 around inf 52.7%

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

   if 4.6000000000000002e-18 < z < 7.5000000000000002e105

   1. Initial program 39.5%

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

   3. Simplified 39.5%

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

   5. Taylor expanded in c around inf 52.2%

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

   6. Taylor expanded in y around 0 45.2%

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

   if 7.5000000000000002e105 < z

   1. Initial program 16.8%

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

   3. Simplified 16.8%

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

   5. Taylor expanded in b around inf 44.7%

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

   6. Taylor expanded in z around -inf 61.6%

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

      1. associate-*r* 61.6%

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

      2. neg-mul-1 61.6%

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

      3. *-commutative 61.6%

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

   8. Simplified 61.6%

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

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-42}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-160}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-243}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-230}:\\ \;\;\;\;\left(j \cdot y5\right) \cdot \left(y0 \cdot y3 - t \cdot i\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-18}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+105}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + \left(z \cdot t\right) \cdot i\right) - t \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0 - t \cdot a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 36.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{-38}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-130}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-239}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.85:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+206}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0 - t \cdot a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          b
          (+
           (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
           (* y0 (- (* z k) (* x j)))))))
   (if (<= z -6.2e-38)
     (* k (* z (- (* b y0) (* i y1))))
     (if (<= z -1.7e-130)
       (*
        y5
        (+
         (* a (- (* t y2) (* y y3)))
         (+ (* i (- (* y k) (* t j))) (* y0 (- (* j y3) (* k y2))))))
       (if (<= z 1.9e-239)
         t_1
         (if (<= z 0.85)
           (*
            y2
            (+
             (+ (* k (- (* y1 y4) (* y0 y5))) (* x (- (* c y0) (* a y1))))
             (* t (- (* a y5) (* c y4)))))
           (if (<= z 2e+206) t_1 (* b (* z (- (* k y0) (* t a)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double tmp;
	if (z <= -6.2e-38) {
		tmp = k * (z * ((b * y0) - (i * y1)));
	} else if (z <= -1.7e-130) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	} else if (z <= 1.9e-239) {
		tmp = t_1;
	} else if (z <= 0.85) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else if (z <= 2e+206) {
		tmp = t_1;
	} else {
		tmp = b * (z * ((k * y0) - (t * 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 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    if (z <= (-6.2d-38)) then
        tmp = k * (z * ((b * y0) - (i * y1)))
    else if (z <= (-1.7d-130)) then
        tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))))
    else if (z <= 1.9d-239) then
        tmp = t_1
    else if (z <= 0.85d0) then
        tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
    else if (z <= 2d+206) then
        tmp = t_1
    else
        tmp = b * (z * ((k * y0) - (t * a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double tmp;
	if (z <= -6.2e-38) {
		tmp = k * (z * ((b * y0) - (i * y1)));
	} else if (z <= -1.7e-130) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	} else if (z <= 1.9e-239) {
		tmp = t_1;
	} else if (z <= 0.85) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else if (z <= 2e+206) {
		tmp = t_1;
	} else {
		tmp = b * (z * ((k * y0) - (t * a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	tmp = 0
	if z <= -6.2e-38:
		tmp = k * (z * ((b * y0) - (i * y1)))
	elif z <= -1.7e-130:
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))))
	elif z <= 1.9e-239:
		tmp = t_1
	elif z <= 0.85:
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
	elif z <= 2e+206:
		tmp = t_1
	else:
		tmp = b * (z * ((k * y0) - (t * a)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))))
	tmp = 0.0
	if (z <= -6.2e-38)
		tmp = Float64(k * Float64(z * Float64(Float64(b * y0) - Float64(i * y1))));
	elseif (z <= -1.7e-130)
		tmp = Float64(y5 * Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(Float64(i * Float64(Float64(y * k) - Float64(t * j))) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))))));
	elseif (z <= 1.9e-239)
		tmp = t_1;
	elseif (z <= 0.85)
		tmp = Float64(y2 * Float64(Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (z <= 2e+206)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(z * Float64(Float64(k * y0) - Float64(t * a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	tmp = 0.0;
	if (z <= -6.2e-38)
		tmp = k * (z * ((b * y0) - (i * y1)));
	elseif (z <= -1.7e-130)
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	elseif (z <= 1.9e-239)
		tmp = t_1;
	elseif (z <= 0.85)
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	elseif (z <= 2e+206)
		tmp = t_1;
	else
		tmp = b * (z * ((k * y0) - (t * a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.2e-38], N[(k * N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.7e-130], N[(y5 * N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e-239], t$95$1, If[LessEqual[z, 0.85], N[(y2 * N[(N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+206], t$95$1, N[(b * N[(z * N[(N[(k * y0), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.19999999999999966e-38

   1. Initial program 27.3%

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

   3. Simplified 28.6%

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

   5. Taylor expanded in z around -inf 48.2%

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

   6. Taylor expanded in k around inf 51.3%

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

   if -6.19999999999999966e-38 < z < -1.70000000000000003e-130

   1. Initial program 39.9%

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

   3. Taylor expanded in y5 around -inf 61.1%

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

   if -1.70000000000000003e-130 < z < 1.9000000000000001e-239 or 0.849999999999999978 < z < 2.0000000000000001e206

   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%

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

   5. Taylor expanded in b around inf 52.4%

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

   if 1.9000000000000001e-239 < z < 0.849999999999999978

   1. Initial program 45.0%

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

   3. Taylor expanded in y2 around inf 49.2%

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

   if 2.0000000000000001e206 < z

   1. Initial program 17.4%

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

   3. Simplified 17.4%

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

   5. Taylor expanded in b around inf 30.8%

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

   6. Taylor expanded in z around -inf 65.6%

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

      1. associate-*r* 65.6%

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

      2. neg-mul-1 65.6%

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

      3. *-commutative 65.6%

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

   8. Simplified 65.6%

      \[\leadsto \color{blue}{\left(-b\right) \cdot \left(z \cdot \left(t \cdot a - k \cdot y0\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-38}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-130}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-239}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;z \leq 0.85:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+206}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0 - t \cdot a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 28.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{if}\;x \leq -1.02 \cdot 10^{+191}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{+75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -130000000000:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-11}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.08 \cdot 10^{-47}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-149}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-246}:\\ \;\;\;\;t \cdot \left(b \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{+160}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* y1 (- (* x j) (* z k))))))
   (if (<= x -1.02e+191)
     (* a (* b (- (* x y) (* z t))))
     (if (<= x -2.4e+75)
       t_1
       (if (<= x -130000000000.0)
         (* k (* z (* b y0)))
         (if (<= x -6.8e-11)
           t_1
           (if (<= x -1.08e-47)
             (* t (* y2 (- (* a y5) (* c y4))))
             (if (<= x -2.7e-149)
               (* c (* t (- (* z i) (* y2 y4))))
               (if (<= x 3e-246)
                 (* t (* b (- (* j y4) (* z a))))
                 (if (<= x 1.12e+160)
                   (* j (* t (- (* b y4) (* i y5))))
                   (* c (* x (* y0 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 = i * (y1 * ((x * j) - (z * k)));
	double tmp;
	if (x <= -1.02e+191) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (x <= -2.4e+75) {
		tmp = t_1;
	} else if (x <= -130000000000.0) {
		tmp = k * (z * (b * y0));
	} else if (x <= -6.8e-11) {
		tmp = t_1;
	} else if (x <= -1.08e-47) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (x <= -2.7e-149) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (x <= 3e-246) {
		tmp = t * (b * ((j * y4) - (z * a)));
	} else if (x <= 1.12e+160) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else {
		tmp = c * (x * (y0 * 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) :: tmp
    t_1 = i * (y1 * ((x * j) - (z * k)))
    if (x <= (-1.02d+191)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (x <= (-2.4d+75)) then
        tmp = t_1
    else if (x <= (-130000000000.0d0)) then
        tmp = k * (z * (b * y0))
    else if (x <= (-6.8d-11)) then
        tmp = t_1
    else if (x <= (-1.08d-47)) then
        tmp = t * (y2 * ((a * y5) - (c * y4)))
    else if (x <= (-2.7d-149)) then
        tmp = c * (t * ((z * i) - (y2 * y4)))
    else if (x <= 3d-246) then
        tmp = t * (b * ((j * y4) - (z * a)))
    else if (x <= 1.12d+160) then
        tmp = j * (t * ((b * y4) - (i * y5)))
    else
        tmp = c * (x * (y0 * 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 = i * (y1 * ((x * j) - (z * k)));
	double tmp;
	if (x <= -1.02e+191) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (x <= -2.4e+75) {
		tmp = t_1;
	} else if (x <= -130000000000.0) {
		tmp = k * (z * (b * y0));
	} else if (x <= -6.8e-11) {
		tmp = t_1;
	} else if (x <= -1.08e-47) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (x <= -2.7e-149) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (x <= 3e-246) {
		tmp = t * (b * ((j * y4) - (z * a)));
	} else if (x <= 1.12e+160) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else {
		tmp = c * (x * (y0 * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = i * (y1 * ((x * j) - (z * k)))
	tmp = 0
	if x <= -1.02e+191:
		tmp = a * (b * ((x * y) - (z * t)))
	elif x <= -2.4e+75:
		tmp = t_1
	elif x <= -130000000000.0:
		tmp = k * (z * (b * y0))
	elif x <= -6.8e-11:
		tmp = t_1
	elif x <= -1.08e-47:
		tmp = t * (y2 * ((a * y5) - (c * y4)))
	elif x <= -2.7e-149:
		tmp = c * (t * ((z * i) - (y2 * y4)))
	elif x <= 3e-246:
		tmp = t * (b * ((j * y4) - (z * a)))
	elif x <= 1.12e+160:
		tmp = j * (t * ((b * y4) - (i * y5)))
	else:
		tmp = c * (x * (y0 * 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(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))))
	tmp = 0.0
	if (x <= -1.02e+191)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (x <= -2.4e+75)
		tmp = t_1;
	elseif (x <= -130000000000.0)
		tmp = Float64(k * Float64(z * Float64(b * y0)));
	elseif (x <= -6.8e-11)
		tmp = t_1;
	elseif (x <= -1.08e-47)
		tmp = Float64(t * Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))));
	elseif (x <= -2.7e-149)
		tmp = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (x <= 3e-246)
		tmp = Float64(t * Float64(b * Float64(Float64(j * y4) - Float64(z * a))));
	elseif (x <= 1.12e+160)
		tmp = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))));
	else
		tmp = Float64(c * Float64(x * Float64(y0 * 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 = i * (y1 * ((x * j) - (z * k)));
	tmp = 0.0;
	if (x <= -1.02e+191)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (x <= -2.4e+75)
		tmp = t_1;
	elseif (x <= -130000000000.0)
		tmp = k * (z * (b * y0));
	elseif (x <= -6.8e-11)
		tmp = t_1;
	elseif (x <= -1.08e-47)
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	elseif (x <= -2.7e-149)
		tmp = c * (t * ((z * i) - (y2 * y4)));
	elseif (x <= 3e-246)
		tmp = t * (b * ((j * y4) - (z * a)));
	elseif (x <= 1.12e+160)
		tmp = j * (t * ((b * y4) - (i * y5)));
	else
		tmp = c * (x * (y0 * 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[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.02e+191], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.4e+75], t$95$1, If[LessEqual[x, -130000000000.0], N[(k * N[(z * N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.8e-11], t$95$1, If[LessEqual[x, -1.08e-47], N[(t * N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.7e-149], N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3e-246], N[(t * N[(b * N[(N[(j * y4), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.12e+160], N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if x < -1.02000000000000006e191

   1. Initial program 31.8%

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

   3. Simplified 31.8%

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

   5. Taylor expanded in b around inf 37.7%

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

   6. Taylor expanded in a around inf 50.5%

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

      1. neg-mul-1 50.5%

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

      2. +-commutative 50.5%

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

      3. unsub-neg 50.5%

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

      4. *-commutative 50.5%

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

   8. Simplified 50.5%

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

   if -1.02000000000000006e191 < x < -2.4e75 or -1.3e11 < x < -6.7999999999999998e-11

   1. Initial program 34.6%

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

   3. Taylor expanded in y1 around inf 53.2%

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

   4. Taylor expanded in i around inf 50.9%

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

   if -2.4e75 < x < -1.3e11

   1. Initial program 40.5%

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

   3. Simplified 40.5%

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

   5. Taylor expanded in z around -inf 47.1%

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

   6. Taylor expanded in k around inf 54.4%

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

   7. Taylor expanded in i around 0 54.1%

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

      1. neg-mul-1 54.1%

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

      2. distribute-rgt-neg-in 54.1%

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

   9. Simplified 54.1%

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

   if -6.7999999999999998e-11 < x < -1.08000000000000005e-47

   1. Initial program 20.7%

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

   3. Taylor expanded in y2 around inf 60.7%

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

   4. Taylor expanded in t around inf 60.6%

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

   if -1.08000000000000005e-47 < x < -2.70000000000000014e-149

   1. Initial program 39.4%

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

   3. Simplified 39.3%

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

   5. Taylor expanded in c around inf 53.5%

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

   6. Taylor expanded in t around inf 62.0%

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

   if -2.70000000000000014e-149 < x < 3e-246

   1. Initial program 26.8%

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

   3. Simplified 26.8%

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

   5. Taylor expanded in b around inf 52.8%

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

   6. Taylor expanded in t around inf 41.5%

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

      1. associate-*r* 41.4%

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

      2. +-commutative 41.4%

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

      3. mul-1-neg 41.4%

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

      4. unsub-neg 41.4%

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

      5. *-commutative 41.4%

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

      6. *-commutative 41.4%

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

   8. Simplified 41.4%

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

   9. Taylor expanded in b around 0 41.5%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot \left(j \cdot y4 - a \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 41.4%

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

       2. *-commutative 41.4%

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

       3. *-commutative 41.4%

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

       4. associate-*l* 41.5%

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

       5. *-commutative 41.5%

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

   11. Simplified 41.5%

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

   if 3e-246 < x < 1.12e160

   1. Initial program 31.1%

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

   3. Taylor expanded in j around inf 34.7%

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

   4. Taylor expanded in t around inf 40.1%

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

   if 1.12e160 < x

   1. Initial program 16.0%

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

   3. Taylor expanded in y2 around inf 48.4%

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

   4. Taylor expanded in x around inf 52.8%

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

   5. Taylor expanded in c around inf 48.9%

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

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+191}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{+75}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;x \leq -130000000000:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-11}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;x \leq -1.08 \cdot 10^{-47}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-149}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-246}:\\ \;\;\;\;t \cdot \left(b \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{+160}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 29.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ t_2 := j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ t_3 := x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{if}\;x \leq -1.25 \cdot 10^{+58}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq -160:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-49}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-150}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{-247}:\\ \;\;\;\;t \cdot \left(b \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-66}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+68}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+160}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* t (- (* z i) (* y2 y4)))))
        (t_2 (* j (* t (- (* b y4) (* i y5)))))
        (t_3 (* x (* y2 (- (* c y0) (* a y1))))))
   (if (<= x -1.25e+58)
     t_3
     (if (<= x -160.0)
       t_1
       (if (<= x -2.3e-49)
         (* t (* y2 (- (* a y5) (* c y4))))
         (if (<= x -6.5e-150)
           t_1
           (if (<= x 8.8e-247)
             (* t (* b (- (* j y4) (* z a))))
             (if (<= x 1.95e-66)
               t_2
               (if (<= x 1.15e+68)
                 (* a (* y (- (* x b) (* y3 y5))))
                 (if (<= x 4.2e+160) t_2 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 = c * (t * ((z * i) - (y2 * y4)));
	double t_2 = j * (t * ((b * y4) - (i * y5)));
	double t_3 = x * (y2 * ((c * y0) - (a * y1)));
	double tmp;
	if (x <= -1.25e+58) {
		tmp = t_3;
	} else if (x <= -160.0) {
		tmp = t_1;
	} else if (x <= -2.3e-49) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (x <= -6.5e-150) {
		tmp = t_1;
	} else if (x <= 8.8e-247) {
		tmp = t * (b * ((j * y4) - (z * a)));
	} else if (x <= 1.95e-66) {
		tmp = t_2;
	} else if (x <= 1.15e+68) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (x <= 4.2e+160) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = c * (t * ((z * i) - (y2 * y4)))
    t_2 = j * (t * ((b * y4) - (i * y5)))
    t_3 = x * (y2 * ((c * y0) - (a * y1)))
    if (x <= (-1.25d+58)) then
        tmp = t_3
    else if (x <= (-160.0d0)) then
        tmp = t_1
    else if (x <= (-2.3d-49)) then
        tmp = t * (y2 * ((a * y5) - (c * y4)))
    else if (x <= (-6.5d-150)) then
        tmp = t_1
    else if (x <= 8.8d-247) then
        tmp = t * (b * ((j * y4) - (z * a)))
    else if (x <= 1.95d-66) then
        tmp = t_2
    else if (x <= 1.15d+68) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (x <= 4.2d+160) then
        tmp = t_2
    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 = c * (t * ((z * i) - (y2 * y4)));
	double t_2 = j * (t * ((b * y4) - (i * y5)));
	double t_3 = x * (y2 * ((c * y0) - (a * y1)));
	double tmp;
	if (x <= -1.25e+58) {
		tmp = t_3;
	} else if (x <= -160.0) {
		tmp = t_1;
	} else if (x <= -2.3e-49) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (x <= -6.5e-150) {
		tmp = t_1;
	} else if (x <= 8.8e-247) {
		tmp = t * (b * ((j * y4) - (z * a)));
	} else if (x <= 1.95e-66) {
		tmp = t_2;
	} else if (x <= 1.15e+68) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (x <= 4.2e+160) {
		tmp = t_2;
	} 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 = c * (t * ((z * i) - (y2 * y4)))
	t_2 = j * (t * ((b * y4) - (i * y5)))
	t_3 = x * (y2 * ((c * y0) - (a * y1)))
	tmp = 0
	if x <= -1.25e+58:
		tmp = t_3
	elif x <= -160.0:
		tmp = t_1
	elif x <= -2.3e-49:
		tmp = t * (y2 * ((a * y5) - (c * y4)))
	elif x <= -6.5e-150:
		tmp = t_1
	elif x <= 8.8e-247:
		tmp = t * (b * ((j * y4) - (z * a)))
	elif x <= 1.95e-66:
		tmp = t_2
	elif x <= 1.15e+68:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif x <= 4.2e+160:
		tmp = t_2
	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(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))))
	t_2 = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))))
	t_3 = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))))
	tmp = 0.0
	if (x <= -1.25e+58)
		tmp = t_3;
	elseif (x <= -160.0)
		tmp = t_1;
	elseif (x <= -2.3e-49)
		tmp = Float64(t * Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))));
	elseif (x <= -6.5e-150)
		tmp = t_1;
	elseif (x <= 8.8e-247)
		tmp = Float64(t * Float64(b * Float64(Float64(j * y4) - Float64(z * a))));
	elseif (x <= 1.95e-66)
		tmp = t_2;
	elseif (x <= 1.15e+68)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (x <= 4.2e+160)
		tmp = t_2;
	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 = c * (t * ((z * i) - (y2 * y4)));
	t_2 = j * (t * ((b * y4) - (i * y5)));
	t_3 = x * (y2 * ((c * y0) - (a * y1)));
	tmp = 0.0;
	if (x <= -1.25e+58)
		tmp = t_3;
	elseif (x <= -160.0)
		tmp = t_1;
	elseif (x <= -2.3e-49)
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	elseif (x <= -6.5e-150)
		tmp = t_1;
	elseif (x <= 8.8e-247)
		tmp = t * (b * ((j * y4) - (z * a)));
	elseif (x <= 1.95e-66)
		tmp = t_2;
	elseif (x <= 1.15e+68)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (x <= 4.2e+160)
		tmp = t_2;
	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[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.25e+58], t$95$3, If[LessEqual[x, -160.0], t$95$1, If[LessEqual[x, -2.3e-49], N[(t * N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.5e-150], t$95$1, If[LessEqual[x, 8.8e-247], N[(t * N[(b * N[(N[(j * y4), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.95e-66], t$95$2, If[LessEqual[x, 1.15e+68], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.2e+160], t$95$2, t$95$3]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -1.24999999999999996e58 or 4.19999999999999993e160 < x

   1. Initial program 26.6%

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

   3. Taylor expanded in y2 around inf 33.6%

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

   4. Taylor expanded in x around inf 49.1%

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

   if -1.24999999999999996e58 < x < -160 or -2.2999999999999999e-49 < x < -6.49999999999999997e-150

   1. Initial program 41.6%

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

   3. Simplified 41.5%

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

   5. Taylor expanded in c around inf 51.1%

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

   6. Taylor expanded in t around inf 62.8%

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

   if -160 < x < -2.2999999999999999e-49

   1. Initial program 29.7%

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

   3. Taylor expanded in y2 around inf 50.5%

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

   4. Taylor expanded in t around inf 43.4%

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

   if -6.49999999999999997e-150 < x < 8.79999999999999966e-247

   1. Initial program 26.8%

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

   3. Simplified 26.8%

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

   5. Taylor expanded in b around inf 52.8%

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

   6. Taylor expanded in t around inf 41.5%

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

      1. associate-*r* 41.4%

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

      2. +-commutative 41.4%

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

      3. mul-1-neg 41.4%

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

      4. unsub-neg 41.4%

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

      5. *-commutative 41.4%

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

      6. *-commutative 41.4%

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

   8. Simplified 41.4%

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

   9. Taylor expanded in b around 0 41.5%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot \left(j \cdot y4 - a \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 41.4%

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

       2. *-commutative 41.4%

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

       3. *-commutative 41.4%

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

       4. associate-*l* 41.5%

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

       5. *-commutative 41.5%

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

   11. Simplified 41.5%

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

   if 8.79999999999999966e-247 < x < 1.94999999999999991e-66 or 1.15e68 < x < 4.19999999999999993e160

   1. Initial program 31.2%

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

   3. Taylor expanded in j around inf 35.1%

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

   4. Taylor expanded in t around inf 47.9%

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

   if 1.94999999999999991e-66 < x < 1.15e68

   1. Initial program 31.0%

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

   3. Simplified 31.0%

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

   5. Taylor expanded in a around inf 40.5%

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

   6. Taylor expanded in y around inf 40.7%

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

4. Final simplification 48.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+58}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -160:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-49}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-150}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{-247}:\\ \;\;\;\;t \cdot \left(b \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-66}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+68}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+160}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 29.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ t_2 := x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{if}\;x \leq -2.06 \cdot 10^{+55}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-49}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-146}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-248}:\\ \;\;\;\;t \cdot \left(b \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+68}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+160}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* t (- (* b y4) (* i y5)))))
        (t_2 (* x (* y2 (- (* c y0) (* a y1))))))
   (if (<= x -2.06e+55)
     t_2
     (if (<= x -4.5e-49)
       (* y1 (* y4 (- (* k y2) (* j y3))))
       (if (<= x -2.1e-146)
         (* c (* t (- (* z i) (* y2 y4))))
         (if (<= x 9.2e-248)
           (* t (* b (- (* j y4) (* z a))))
           (if (<= x 1.2e-65)
             t_1
             (if (<= x 1.4e+68)
               (* a (* y (- (* x b) (* y3 y5))))
               (if (<= x 5.8e+160) 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 = j * (t * ((b * y4) - (i * y5)));
	double t_2 = x * (y2 * ((c * y0) - (a * y1)));
	double tmp;
	if (x <= -2.06e+55) {
		tmp = t_2;
	} else if (x <= -4.5e-49) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else if (x <= -2.1e-146) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (x <= 9.2e-248) {
		tmp = t * (b * ((j * y4) - (z * a)));
	} else if (x <= 1.2e-65) {
		tmp = t_1;
	} else if (x <= 1.4e+68) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (x <= 5.8e+160) {
		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 = j * (t * ((b * y4) - (i * y5)))
    t_2 = x * (y2 * ((c * y0) - (a * y1)))
    if (x <= (-2.06d+55)) then
        tmp = t_2
    else if (x <= (-4.5d-49)) then
        tmp = y1 * (y4 * ((k * y2) - (j * y3)))
    else if (x <= (-2.1d-146)) then
        tmp = c * (t * ((z * i) - (y2 * y4)))
    else if (x <= 9.2d-248) then
        tmp = t * (b * ((j * y4) - (z * a)))
    else if (x <= 1.2d-65) then
        tmp = t_1
    else if (x <= 1.4d+68) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (x <= 5.8d+160) 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 = j * (t * ((b * y4) - (i * y5)));
	double t_2 = x * (y2 * ((c * y0) - (a * y1)));
	double tmp;
	if (x <= -2.06e+55) {
		tmp = t_2;
	} else if (x <= -4.5e-49) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else if (x <= -2.1e-146) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (x <= 9.2e-248) {
		tmp = t * (b * ((j * y4) - (z * a)));
	} else if (x <= 1.2e-65) {
		tmp = t_1;
	} else if (x <= 1.4e+68) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (x <= 5.8e+160) {
		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 = j * (t * ((b * y4) - (i * y5)))
	t_2 = x * (y2 * ((c * y0) - (a * y1)))
	tmp = 0
	if x <= -2.06e+55:
		tmp = t_2
	elif x <= -4.5e-49:
		tmp = y1 * (y4 * ((k * y2) - (j * y3)))
	elif x <= -2.1e-146:
		tmp = c * (t * ((z * i) - (y2 * y4)))
	elif x <= 9.2e-248:
		tmp = t * (b * ((j * y4) - (z * a)))
	elif x <= 1.2e-65:
		tmp = t_1
	elif x <= 1.4e+68:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif x <= 5.8e+160:
		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(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))))
	t_2 = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))))
	tmp = 0.0
	if (x <= -2.06e+55)
		tmp = t_2;
	elseif (x <= -4.5e-49)
		tmp = Float64(y1 * Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif (x <= -2.1e-146)
		tmp = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (x <= 9.2e-248)
		tmp = Float64(t * Float64(b * Float64(Float64(j * y4) - Float64(z * a))));
	elseif (x <= 1.2e-65)
		tmp = t_1;
	elseif (x <= 1.4e+68)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (x <= 5.8e+160)
		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 = j * (t * ((b * y4) - (i * y5)));
	t_2 = x * (y2 * ((c * y0) - (a * y1)));
	tmp = 0.0;
	if (x <= -2.06e+55)
		tmp = t_2;
	elseif (x <= -4.5e-49)
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	elseif (x <= -2.1e-146)
		tmp = c * (t * ((z * i) - (y2 * y4)));
	elseif (x <= 9.2e-248)
		tmp = t * (b * ((j * y4) - (z * a)));
	elseif (x <= 1.2e-65)
		tmp = t_1;
	elseif (x <= 1.4e+68)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (x <= 5.8e+160)
		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[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.06e+55], t$95$2, If[LessEqual[x, -4.5e-49], N[(y1 * N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.1e-146], N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.2e-248], N[(t * N[(b * N[(N[(j * y4), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.2e-65], t$95$1, If[LessEqual[x, 1.4e+68], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.8e+160], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -2.06e55 or 5.7999999999999998e160 < x

   1. Initial program 26.6%

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

   3. Taylor expanded in y2 around inf 33.6%

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

   4. Taylor expanded in x around inf 49.1%

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

   if -2.06e55 < x < -4.5000000000000002e-49

   1. Initial program 36.9%

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

   3. Taylor expanded in y1 around inf 44.2%

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

   4. Taylor expanded in y4 around inf 52.8%

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

   if -4.5000000000000002e-49 < x < -2.0999999999999999e-146

   1. Initial program 39.4%

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

   3. Simplified 39.3%

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

   5. Taylor expanded in c around inf 53.5%

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

   6. Taylor expanded in t around inf 62.0%

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

   if -2.0999999999999999e-146 < x < 9.2000000000000001e-248

   1. Initial program 26.8%

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

   3. Simplified 26.8%

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

   5. Taylor expanded in b around inf 52.8%

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

   6. Taylor expanded in t around inf 41.5%

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

      1. associate-*r* 41.4%

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

      2. +-commutative 41.4%

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

      3. mul-1-neg 41.4%

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

      4. unsub-neg 41.4%

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

      5. *-commutative 41.4%

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

      6. *-commutative 41.4%

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

   8. Simplified 41.4%

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

   9. Taylor expanded in b around 0 41.5%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot \left(j \cdot y4 - a \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 41.4%

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

       2. *-commutative 41.4%

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

       3. *-commutative 41.4%

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

       4. associate-*l* 41.5%

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

       5. *-commutative 41.5%

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

   11. Simplified 41.5%

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

   if 9.2000000000000001e-248 < x < 1.2000000000000001e-65 or 1.4e68 < x < 5.7999999999999998e160

   1. Initial program 31.2%

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

   3. Taylor expanded in j around inf 35.1%

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

   4. Taylor expanded in t around inf 47.9%

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

   if 1.2000000000000001e-65 < x < 1.4e68

   1. Initial program 31.0%

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

   3. Simplified 31.0%

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

   5. Taylor expanded in a around inf 40.5%

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

   6. Taylor expanded in y around inf 40.7%

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

4. Final simplification 48.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.06 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-49}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-146}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-248}:\\ \;\;\;\;t \cdot \left(b \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-65}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+68}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+160}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 31.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{+150}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.55 \cdot 10^{+17}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(t \cdot i - y0 \cdot y3\right)\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-10}:\\ \;\;\;\;\left(x \cdot c\right) \cdot \left(y0 \cdot y2 - y \cdot i\right)\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-124}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-254}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+157}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* t (- (* b y4) (* i y5))))))
   (if (<= y -4.5e+150)
     (* a (* y (- (* x b) (* y3 y5))))
     (if (<= y -1.05e+34)
       t_1
       (if (<= y -2.55e+17)
         (* (* z c) (- (* t i) (* y0 y3)))
         (if (<= y -1.1e-10)
           (* (* x c) (- (* y0 y2) (* y i)))
           (if (<= y -6.8e-124)
             (* i (* y1 (- (* x j) (* z k))))
             (if (<= y 4e-254)
               t_1
               (if (<= y 1.5e+157)
                 (* x (* y2 (- (* c y0) (* a y1))))
                 (* b (* k (- (* z y0) (* y y4)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (t * ((b * y4) - (i * y5)));
	double tmp;
	if (y <= -4.5e+150) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (y <= -1.05e+34) {
		tmp = t_1;
	} else if (y <= -2.55e+17) {
		tmp = (z * c) * ((t * i) - (y0 * y3));
	} else if (y <= -1.1e-10) {
		tmp = (x * c) * ((y0 * y2) - (y * i));
	} else if (y <= -6.8e-124) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (y <= 4e-254) {
		tmp = t_1;
	} else if (y <= 1.5e+157) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else {
		tmp = b * (k * ((z * y0) - (y * y4)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (t * ((b * y4) - (i * y5)))
    if (y <= (-4.5d+150)) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (y <= (-1.05d+34)) then
        tmp = t_1
    else if (y <= (-2.55d+17)) then
        tmp = (z * c) * ((t * i) - (y0 * y3))
    else if (y <= (-1.1d-10)) then
        tmp = (x * c) * ((y0 * y2) - (y * i))
    else if (y <= (-6.8d-124)) then
        tmp = i * (y1 * ((x * j) - (z * k)))
    else if (y <= 4d-254) then
        tmp = t_1
    else if (y <= 1.5d+157) then
        tmp = x * (y2 * ((c * y0) - (a * y1)))
    else
        tmp = b * (k * ((z * y0) - (y * y4)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (t * ((b * y4) - (i * y5)));
	double tmp;
	if (y <= -4.5e+150) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (y <= -1.05e+34) {
		tmp = t_1;
	} else if (y <= -2.55e+17) {
		tmp = (z * c) * ((t * i) - (y0 * y3));
	} else if (y <= -1.1e-10) {
		tmp = (x * c) * ((y0 * y2) - (y * i));
	} else if (y <= -6.8e-124) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (y <= 4e-254) {
		tmp = t_1;
	} else if (y <= 1.5e+157) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else {
		tmp = b * (k * ((z * y0) - (y * y4)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = j * (t * ((b * y4) - (i * y5)))
	tmp = 0
	if y <= -4.5e+150:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif y <= -1.05e+34:
		tmp = t_1
	elif y <= -2.55e+17:
		tmp = (z * c) * ((t * i) - (y0 * y3))
	elif y <= -1.1e-10:
		tmp = (x * c) * ((y0 * y2) - (y * i))
	elif y <= -6.8e-124:
		tmp = i * (y1 * ((x * j) - (z * k)))
	elif y <= 4e-254:
		tmp = t_1
	elif y <= 1.5e+157:
		tmp = x * (y2 * ((c * y0) - (a * y1)))
	else:
		tmp = b * (k * ((z * y0) - (y * y4)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))))
	tmp = 0.0
	if (y <= -4.5e+150)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (y <= -1.05e+34)
		tmp = t_1;
	elseif (y <= -2.55e+17)
		tmp = Float64(Float64(z * c) * Float64(Float64(t * i) - Float64(y0 * y3)));
	elseif (y <= -1.1e-10)
		tmp = Float64(Float64(x * c) * Float64(Float64(y0 * y2) - Float64(y * i)));
	elseif (y <= -6.8e-124)
		tmp = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))));
	elseif (y <= 4e-254)
		tmp = t_1;
	elseif (y <= 1.5e+157)
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	else
		tmp = Float64(b * Float64(k * Float64(Float64(z * y0) - Float64(y * y4))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = j * (t * ((b * y4) - (i * y5)));
	tmp = 0.0;
	if (y <= -4.5e+150)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (y <= -1.05e+34)
		tmp = t_1;
	elseif (y <= -2.55e+17)
		tmp = (z * c) * ((t * i) - (y0 * y3));
	elseif (y <= -1.1e-10)
		tmp = (x * c) * ((y0 * y2) - (y * i));
	elseif (y <= -6.8e-124)
		tmp = i * (y1 * ((x * j) - (z * k)));
	elseif (y <= 4e-254)
		tmp = t_1;
	elseif (y <= 1.5e+157)
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	else
		tmp = b * (k * ((z * y0) - (y * y4)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.5e+150], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.05e+34], t$95$1, If[LessEqual[y, -2.55e+17], N[(N[(z * c), $MachinePrecision] * N[(N[(t * i), $MachinePrecision] - N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.1e-10], N[(N[(x * c), $MachinePrecision] * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.8e-124], N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e-254], t$95$1, If[LessEqual[y, 1.5e+157], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -4.5e150

   1. Initial program 15.3%

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

   3. Simplified 18.3%

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

   5. Taylor expanded in a around inf 42.6%

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

   6. Taylor expanded in y around inf 45.9%

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

   if -4.5e150 < y < -1.05000000000000009e34 or -6.8000000000000001e-124 < y < 3.9999999999999996e-254

   1. Initial program 35.3%

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

   3. Taylor expanded in j around inf 43.6%

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

   4. Taylor expanded in t around inf 42.8%

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

   if -1.05000000000000009e34 < y < -2.55e17

   1. Initial program 66.4%

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

   3. Simplified 66.1%

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

   5. Taylor expanded in c around inf 33.7%

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

   6. Taylor expanded in z around inf 51.2%

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

      1. associate-*r* 51.2%

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

      2. +-commutative 51.2%

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

      3. mul-1-neg 51.2%

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

      4. unsub-neg 51.2%

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

      5. *-commutative 51.2%

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

   8. Simplified 51.2%

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

   if -2.55e17 < y < -1.09999999999999995e-10

   1. Initial program 28.6%

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

   3. Simplified 28.6%

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

   5. Taylor expanded in c around inf 100.0%

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

   6. Taylor expanded in x around inf 86.2%

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

      1. associate-*r* 86.2%

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

      2. +-commutative 86.2%

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

      3. mul-1-neg 86.2%

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

      4. unsub-neg 86.2%

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

      5. *-commutative 86.2%

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

   8. Simplified 86.2%

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

   if -1.09999999999999995e-10 < y < -6.8000000000000001e-124

   1. Initial program 45.6%

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

   3. Taylor expanded in y1 around inf 59.6%

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

   4. Taylor expanded in i around inf 55.7%

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

   if 3.9999999999999996e-254 < y < 1.50000000000000005e157

   1. Initial program 34.3%

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

   3. Taylor expanded in y2 around inf 45.2%

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

   4. Taylor expanded in x around inf 41.7%

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

   if 1.50000000000000005e157 < y

   1. Initial program 10.8%

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

   3. Simplified 10.8%

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

   5. Taylor expanded in b around inf 51.7%

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

   6. Taylor expanded in k around -inf 62.5%

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

      1. associate-*r* 62.5%

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

      2. neg-mul-1 62.5%

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

      3. *-commutative 62.5%

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

   8. Simplified 62.5%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+150}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{+34}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq -2.55 \cdot 10^{+17}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(t \cdot i - y0 \cdot y3\right)\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-10}:\\ \;\;\;\;\left(x \cdot c\right) \cdot \left(y0 \cdot y2 - y \cdot i\right)\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-124}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-254}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+157}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 31.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(z \cdot \left(k \cdot y0 - t \cdot a\right)\right)\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{-39}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-161}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-243}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-138}:\\ \;\;\;\;\left(j \cdot y5\right) \cdot \left(y0 \cdot y3 - t \cdot i\right)\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-42}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+88}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* z (- (* k y0) (* t a))))))
   (if (<= z -5.8e-39)
     (* k (* z (- (* b y0) (* i y1))))
     (if (<= z -5.8e-161)
       (* j (* t (- (* b y4) (* i y5))))
       (if (<= z 1.08e-243)
         (* x (* y2 (- (* c y0) (* a y1))))
         (if (<= z 1.75e-138)
           (* (* j y5) (- (* y0 y3) (* t i)))
           (if (<= z 1.95e-101)
             t_1
             (if (<= z 4.1e-42)
               (* a (* y (- (* x b) (* y3 y5))))
               (if (<= z 3.8e+88)
                 (* b (* k (- (* z y0) (* y y4))))
                 t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (z * ((k * y0) - (t * a)));
	double tmp;
	if (z <= -5.8e-39) {
		tmp = k * (z * ((b * y0) - (i * y1)));
	} else if (z <= -5.8e-161) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (z <= 1.08e-243) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (z <= 1.75e-138) {
		tmp = (j * y5) * ((y0 * y3) - (t * i));
	} else if (z <= 1.95e-101) {
		tmp = t_1;
	} else if (z <= 4.1e-42) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (z <= 3.8e+88) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (z * ((k * y0) - (t * a)))
    if (z <= (-5.8d-39)) then
        tmp = k * (z * ((b * y0) - (i * y1)))
    else if (z <= (-5.8d-161)) then
        tmp = j * (t * ((b * y4) - (i * y5)))
    else if (z <= 1.08d-243) then
        tmp = x * (y2 * ((c * y0) - (a * y1)))
    else if (z <= 1.75d-138) then
        tmp = (j * y5) * ((y0 * y3) - (t * i))
    else if (z <= 1.95d-101) then
        tmp = t_1
    else if (z <= 4.1d-42) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (z <= 3.8d+88) then
        tmp = b * (k * ((z * y0) - (y * y4)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (z * ((k * y0) - (t * a)));
	double tmp;
	if (z <= -5.8e-39) {
		tmp = k * (z * ((b * y0) - (i * y1)));
	} else if (z <= -5.8e-161) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (z <= 1.08e-243) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (z <= 1.75e-138) {
		tmp = (j * y5) * ((y0 * y3) - (t * i));
	} else if (z <= 1.95e-101) {
		tmp = t_1;
	} else if (z <= 4.1e-42) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (z <= 3.8e+88) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (z * ((k * y0) - (t * a)))
	tmp = 0
	if z <= -5.8e-39:
		tmp = k * (z * ((b * y0) - (i * y1)))
	elif z <= -5.8e-161:
		tmp = j * (t * ((b * y4) - (i * y5)))
	elif z <= 1.08e-243:
		tmp = x * (y2 * ((c * y0) - (a * y1)))
	elif z <= 1.75e-138:
		tmp = (j * y5) * ((y0 * y3) - (t * i))
	elif z <= 1.95e-101:
		tmp = t_1
	elif z <= 4.1e-42:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif z <= 3.8e+88:
		tmp = b * (k * ((z * y0) - (y * y4)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(z * Float64(Float64(k * y0) - Float64(t * a))))
	tmp = 0.0
	if (z <= -5.8e-39)
		tmp = Float64(k * Float64(z * Float64(Float64(b * y0) - Float64(i * y1))));
	elseif (z <= -5.8e-161)
		tmp = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))));
	elseif (z <= 1.08e-243)
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (z <= 1.75e-138)
		tmp = Float64(Float64(j * y5) * Float64(Float64(y0 * y3) - Float64(t * i)));
	elseif (z <= 1.95e-101)
		tmp = t_1;
	elseif (z <= 4.1e-42)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (z <= 3.8e+88)
		tmp = Float64(b * Float64(k * Float64(Float64(z * y0) - Float64(y * y4))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (z * ((k * y0) - (t * a)));
	tmp = 0.0;
	if (z <= -5.8e-39)
		tmp = k * (z * ((b * y0) - (i * y1)));
	elseif (z <= -5.8e-161)
		tmp = j * (t * ((b * y4) - (i * y5)));
	elseif (z <= 1.08e-243)
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	elseif (z <= 1.75e-138)
		tmp = (j * y5) * ((y0 * y3) - (t * i));
	elseif (z <= 1.95e-101)
		tmp = t_1;
	elseif (z <= 4.1e-42)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (z <= 3.8e+88)
		tmp = b * (k * ((z * y0) - (y * y4)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(z * N[(N[(k * y0), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.8e-39], N[(k * N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.8e-161], N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.08e-243], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e-138], N[(N[(j * y5), $MachinePrecision] * N[(N[(y0 * y3), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.95e-101], t$95$1, If[LessEqual[z, 4.1e-42], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e+88], N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -5.79999999999999975e-39

   1. Initial program 27.3%

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

   3. Simplified 28.6%

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

   5. Taylor expanded in z around -inf 48.2%

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

   6. Taylor expanded in k around inf 51.3%

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

   if -5.79999999999999975e-39 < z < -5.8e-161

   1. Initial program 32.4%

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

   3. Taylor expanded in j around inf 46.7%

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

   4. Taylor expanded in t around inf 59.9%

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

   if -5.8e-161 < z < 1.08e-243

   1. Initial program 25.1%

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

   3. Taylor expanded in y2 around inf 33.0%

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

   4. Taylor expanded in x around inf 43.8%

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

   if 1.08e-243 < z < 1.7499999999999999e-138

   1. Initial program 54.8%

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

   3. Taylor expanded in j around inf 60.3%

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

   4. Taylor expanded in y5 around inf 55.9%

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

      1. associate-*r* 60.1%

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

      2. +-commutative 60.1%

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

      3. mul-1-neg 60.1%

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

      4. unsub-neg 60.1%

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

      5. *-commutative 60.1%

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

   6. Simplified 60.1%

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

   if 1.7499999999999999e-138 < z < 1.95000000000000008e-101 or 3.7999999999999997e88 < z

   1. Initial program 18.6%

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

   3. Simplified 18.6%

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

   5. Taylor expanded in b around inf 46.7%

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

   6. Taylor expanded in z around -inf 56.2%

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

      1. associate-*r* 56.2%

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

      2. neg-mul-1 56.2%

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

      3. *-commutative 56.2%

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

   8. Simplified 56.2%

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

   if 1.95000000000000008e-101 < z < 4.1000000000000001e-42

   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 39.9%

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

   5. Taylor expanded in a around inf 37.3%

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

   6. Taylor expanded in y around inf 41.8%

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

   if 4.1000000000000001e-42 < z < 3.7999999999999997e88

   1. Initial program 43.1%

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

   3. Simplified 43.1%

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

   5. Taylor expanded in b around inf 26.3%

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

   6. Taylor expanded in k around -inf 43.9%

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

      1. associate-*r* 43.9%

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

      2. neg-mul-1 43.9%

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

      3. *-commutative 43.9%

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

   8. Simplified 43.9%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-39}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-161}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-243}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-138}:\\ \;\;\;\;\left(j \cdot y5\right) \cdot \left(y0 \cdot y3 - t \cdot i\right)\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-101}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0 - t \cdot a\right)\right)\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-42}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+88}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0 - t \cdot a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 30.0% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ t_2 := a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{if}\;y3 \leq -9 \cdot 10^{+210}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y3 \leq -1.7 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y3 \leq -8 \cdot 10^{-274}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq 7.5 \cdot 10^{-146}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y3 \leq 2.1 \cdot 10^{+66}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y3 \leq 4 \cdot 10^{+187}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* y4 (- (* t j) (* y k)))))
        (t_2 (* a (* y3 (- (* z y1) (* y y5))))))
   (if (<= y3 -9e+210)
     t_2
     (if (<= y3 -1.7e-39)
       t_1
       (if (<= y3 -8e-274)
         (* b (* x (- (* y a) (* j y0))))
         (if (<= y3 7.5e-146)
           t_1
           (if (<= y3 2.1e+66)
             (* j (* t (- (* b y4) (* i y5))))
             (if (<= y3 4e+187) (* a (* b (- (* x y) (* z t)))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (y4 * ((t * j) - (y * k)));
	double t_2 = a * (y3 * ((z * y1) - (y * y5)));
	double tmp;
	if (y3 <= -9e+210) {
		tmp = t_2;
	} else if (y3 <= -1.7e-39) {
		tmp = t_1;
	} else if (y3 <= -8e-274) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y3 <= 7.5e-146) {
		tmp = t_1;
	} else if (y3 <= 2.1e+66) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (y3 <= 4e+187) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (y4 * ((t * j) - (y * k)))
    t_2 = a * (y3 * ((z * y1) - (y * y5)))
    if (y3 <= (-9d+210)) then
        tmp = t_2
    else if (y3 <= (-1.7d-39)) then
        tmp = t_1
    else if (y3 <= (-8d-274)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (y3 <= 7.5d-146) then
        tmp = t_1
    else if (y3 <= 2.1d+66) then
        tmp = j * (t * ((b * y4) - (i * y5)))
    else if (y3 <= 4d+187) then
        tmp = a * (b * ((x * y) - (z * t)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (y4 * ((t * j) - (y * k)));
	double t_2 = a * (y3 * ((z * y1) - (y * y5)));
	double tmp;
	if (y3 <= -9e+210) {
		tmp = t_2;
	} else if (y3 <= -1.7e-39) {
		tmp = t_1;
	} else if (y3 <= -8e-274) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y3 <= 7.5e-146) {
		tmp = t_1;
	} else if (y3 <= 2.1e+66) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (y3 <= 4e+187) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (y4 * ((t * j) - (y * k)))
	t_2 = a * (y3 * ((z * y1) - (y * y5)))
	tmp = 0
	if y3 <= -9e+210:
		tmp = t_2
	elif y3 <= -1.7e-39:
		tmp = t_1
	elif y3 <= -8e-274:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif y3 <= 7.5e-146:
		tmp = t_1
	elif y3 <= 2.1e+66:
		tmp = j * (t * ((b * y4) - (i * y5)))
	elif y3 <= 4e+187:
		tmp = a * (b * ((x * y) - (z * t)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))))
	t_2 = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))))
	tmp = 0.0
	if (y3 <= -9e+210)
		tmp = t_2;
	elseif (y3 <= -1.7e-39)
		tmp = t_1;
	elseif (y3 <= -8e-274)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (y3 <= 7.5e-146)
		tmp = t_1;
	elseif (y3 <= 2.1e+66)
		tmp = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))));
	elseif (y3 <= 4e+187)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (y4 * ((t * j) - (y * k)));
	t_2 = a * (y3 * ((z * y1) - (y * y5)));
	tmp = 0.0;
	if (y3 <= -9e+210)
		tmp = t_2;
	elseif (y3 <= -1.7e-39)
		tmp = t_1;
	elseif (y3 <= -8e-274)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (y3 <= 7.5e-146)
		tmp = t_1;
	elseif (y3 <= 2.1e+66)
		tmp = j * (t * ((b * y4) - (i * y5)));
	elseif (y3 <= 4e+187)
		tmp = a * (b * ((x * y) - (z * t)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -9e+210], t$95$2, If[LessEqual[y3, -1.7e-39], t$95$1, If[LessEqual[y3, -8e-274], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 7.5e-146], t$95$1, If[LessEqual[y3, 2.1e+66], N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 4e+187], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y3 < -9.00000000000000007e210 or 3.99999999999999963e187 < y3

   1. Initial program 18.7%

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

   3. Simplified 18.7%

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

   5. Taylor expanded in a around inf 46.4%

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

   6. Taylor expanded in y3 around inf 60.5%

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

   if -9.00000000000000007e210 < y3 < -1.7e-39 or -7.99999999999999973e-274 < y3 < 7.49999999999999981e-146

   1. Initial program 29.9%

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

   3. Simplified 29.9%

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

   5. Taylor expanded in b around inf 43.7%

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

   6. Taylor expanded in y4 around inf 42.1%

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

   if -1.7e-39 < y3 < -7.99999999999999973e-274

   1. Initial program 42.5%

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

   3. Simplified 42.4%

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

   5. Taylor expanded in b around inf 38.4%

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

   6. Taylor expanded in x around inf 33.0%

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

   if 7.49999999999999981e-146 < y3 < 2.10000000000000005e66

   1. Initial program 37.5%

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

   3. Taylor expanded in j around inf 42.5%

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

   4. Taylor expanded in t around inf 47.4%

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

   if 2.10000000000000005e66 < y3 < 3.99999999999999963e187

   1. Initial program 18.9%

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

   3. Simplified 18.9%

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

   5. Taylor expanded in b around inf 44.0%

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

   6. Taylor expanded in a around inf 44.2%

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

      1. neg-mul-1 44.2%

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

      2. +-commutative 44.2%

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

      3. unsub-neg 44.2%

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

      4. *-commutative 44.2%

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

   8. Simplified 44.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -9 \cdot 10^{+210}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y3 \leq -1.7 \cdot 10^{-39}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y3 \leq -8 \cdot 10^{-274}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq 7.5 \cdot 10^{-146}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y3 \leq 2.1 \cdot 10^{+66}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y3 \leq 4 \cdot 10^{+187}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 20.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(\left(z \cdot t\right) \cdot \left(-b\right)\right)\\ \mathbf{if}\;t \leq -7 \cdot 10^{+213}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(y1 \cdot \left(-a\right)\right)\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-272}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0\right)\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+61}:\\ \;\;\;\;\left(z \cdot \left(i \cdot y1\right)\right) \cdot \left(-k\right)\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+180}:\\ \;\;\;\;a \cdot \left(z \cdot \left(t \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+255}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* (* z t) (- b)))))
   (if (<= t -7e+213)
     t_1
     (if (<= t -2.9e+24)
       (* x (* y2 (* y1 (- a))))
       (if (<= t 9e-272)
         (* k (* z (* b y0)))
         (if (<= t 2.4e+61)
           (* (* z (* i y1)) (- k))
           (if (<= t 3.8e+180)
             (* a (* z (* t (- b))))
             (if (<= t 1.1e+255) (* a (* (* x y) 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 * ((z * t) * -b);
	double tmp;
	if (t <= -7e+213) {
		tmp = t_1;
	} else if (t <= -2.9e+24) {
		tmp = x * (y2 * (y1 * -a));
	} else if (t <= 9e-272) {
		tmp = k * (z * (b * y0));
	} else if (t <= 2.4e+61) {
		tmp = (z * (i * y1)) * -k;
	} else if (t <= 3.8e+180) {
		tmp = a * (z * (t * -b));
	} else if (t <= 1.1e+255) {
		tmp = a * ((x * y) * 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) :: tmp
    t_1 = a * ((z * t) * -b)
    if (t <= (-7d+213)) then
        tmp = t_1
    else if (t <= (-2.9d+24)) then
        tmp = x * (y2 * (y1 * -a))
    else if (t <= 9d-272) then
        tmp = k * (z * (b * y0))
    else if (t <= 2.4d+61) then
        tmp = (z * (i * y1)) * -k
    else if (t <= 3.8d+180) then
        tmp = a * (z * (t * -b))
    else if (t <= 1.1d+255) then
        tmp = a * ((x * y) * 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 * ((z * t) * -b);
	double tmp;
	if (t <= -7e+213) {
		tmp = t_1;
	} else if (t <= -2.9e+24) {
		tmp = x * (y2 * (y1 * -a));
	} else if (t <= 9e-272) {
		tmp = k * (z * (b * y0));
	} else if (t <= 2.4e+61) {
		tmp = (z * (i * y1)) * -k;
	} else if (t <= 3.8e+180) {
		tmp = a * (z * (t * -b));
	} else if (t <= 1.1e+255) {
		tmp = a * ((x * y) * 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 * ((z * t) * -b)
	tmp = 0
	if t <= -7e+213:
		tmp = t_1
	elif t <= -2.9e+24:
		tmp = x * (y2 * (y1 * -a))
	elif t <= 9e-272:
		tmp = k * (z * (b * y0))
	elif t <= 2.4e+61:
		tmp = (z * (i * y1)) * -k
	elif t <= 3.8e+180:
		tmp = a * (z * (t * -b))
	elif t <= 1.1e+255:
		tmp = a * ((x * y) * 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(Float64(z * t) * Float64(-b)))
	tmp = 0.0
	if (t <= -7e+213)
		tmp = t_1;
	elseif (t <= -2.9e+24)
		tmp = Float64(x * Float64(y2 * Float64(y1 * Float64(-a))));
	elseif (t <= 9e-272)
		tmp = Float64(k * Float64(z * Float64(b * y0)));
	elseif (t <= 2.4e+61)
		tmp = Float64(Float64(z * Float64(i * y1)) * Float64(-k));
	elseif (t <= 3.8e+180)
		tmp = Float64(a * Float64(z * Float64(t * Float64(-b))));
	elseif (t <= 1.1e+255)
		tmp = Float64(a * Float64(Float64(x * y) * 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 * ((z * t) * -b);
	tmp = 0.0;
	if (t <= -7e+213)
		tmp = t_1;
	elseif (t <= -2.9e+24)
		tmp = x * (y2 * (y1 * -a));
	elseif (t <= 9e-272)
		tmp = k * (z * (b * y0));
	elseif (t <= 2.4e+61)
		tmp = (z * (i * y1)) * -k;
	elseif (t <= 3.8e+180)
		tmp = a * (z * (t * -b));
	elseif (t <= 1.1e+255)
		tmp = a * ((x * y) * 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[(N[(z * t), $MachinePrecision] * (-b)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7e+213], t$95$1, If[LessEqual[t, -2.9e+24], N[(x * N[(y2 * N[(y1 * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9e-272], N[(k * N[(z * N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e+61], N[(N[(z * N[(i * y1), $MachinePrecision]), $MachinePrecision] * (-k)), $MachinePrecision], If[LessEqual[t, 3.8e+180], N[(a * N[(z * N[(t * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.1e+255], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -6.9999999999999994e213 or 1.10000000000000001e255 < t

   1. Initial program 20.8%

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

   3. Simplified 20.8%

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

   5. Taylor expanded in b around inf 41.5%

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

   6. Taylor expanded in a around inf 50.9%

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

      1. neg-mul-1 50.9%

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

      2. +-commutative 50.9%

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

      3. unsub-neg 50.9%

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

      4. *-commutative 50.9%

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

   8. Simplified 50.9%

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

   9. Taylor expanded in y around 0 56.6%

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

       1. mul-1-neg 56.6%

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

       2. *-commutative 56.6%

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

       3. distribute-rgt-neg-in 56.6%

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

       4. *-commutative 56.6%

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

   11. Simplified 56.6%

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

   if -6.9999999999999994e213 < t < -2.89999999999999979e24

   1. Initial program 28.8%

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

   3. Taylor expanded in y2 around inf 43.7%

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

   4. Taylor expanded in x around inf 32.3%

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

   5. Taylor expanded in c around 0 27.5%

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

      1. mul-1-neg 27.5%

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

      2. associate-*r* 32.8%

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

      3. distribute-rgt-neg-in 32.8%

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

   7. Simplified 32.8%

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

   if -2.89999999999999979e24 < t < 8.9999999999999995e-272

   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 32.0%

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

   5. Taylor expanded in z around -inf 35.6%

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

   6. Taylor expanded in k around inf 38.4%

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

   7. Taylor expanded in i around 0 34.6%

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

      1. neg-mul-1 34.6%

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

      2. distribute-rgt-neg-in 34.6%

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

   9. Simplified 34.6%

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

   if 8.9999999999999995e-272 < t < 2.3999999999999999e61

   1. Initial program 40.6%

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

   3. Simplified 40.6%

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

   5. Taylor expanded in z around -inf 32.6%

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

   6. Taylor expanded in k around inf 32.7%

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

   7. Taylor expanded in i around inf 24.0%

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

      1. associate-*r* 26.8%

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

      2. *-commutative 26.8%

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

   9. Simplified 26.8%

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

   if 2.3999999999999999e61 < t < 3.8e180

   1. Initial program 21.7%

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

   3. Simplified 21.7%

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

   5. Taylor expanded in b around inf 50.5%

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

   6. Taylor expanded in a around inf 29.8%

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

      1. neg-mul-1 29.8%

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

      2. +-commutative 29.8%

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

      3. unsub-neg 29.8%

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

      4. *-commutative 29.8%

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

   8. Simplified 29.8%

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

   9. Taylor expanded in y around 0 33.4%

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

       1. mul-1-neg 33.4%

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

       2. *-commutative 33.4%

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

       3. distribute-rgt-neg-in 33.4%

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

       4. associate-*r* 36.9%

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

       5. *-commutative 36.9%

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

   11. Simplified 36.9%

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

   if 3.8e180 < t < 1.10000000000000001e255

   1. Initial program 9.1%

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

   3. Simplified 18.2%

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

   5. Taylor expanded in b around inf 18.2%

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

   6. Taylor expanded in a around inf 28.2%

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

      1. neg-mul-1 28.2%

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

      2. +-commutative 28.2%

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

      3. unsub-neg 28.2%

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

      4. *-commutative 28.2%

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

   8. Simplified 28.2%

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

   9. Taylor expanded in y around inf 55.8%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 55.8%

          \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot b\right)} \]

   11. Simplified 55.8%

       \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot b\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 36.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+213}:\\ \;\;\;\;a \cdot \left(\left(z \cdot t\right) \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(y1 \cdot \left(-a\right)\right)\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-272}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0\right)\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+61}:\\ \;\;\;\;\left(z \cdot \left(i \cdot y1\right)\right) \cdot \left(-k\right)\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+180}:\\ \;\;\;\;a \cdot \left(z \cdot \left(t \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+255}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(z \cdot t\right) \cdot \left(-b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 21.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{-47}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq 8.8 \cdot 10^{-287}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{-225}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(y1 \cdot \left(-a\right)\right)\right)\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-76}:\\ \;\;\;\;i \cdot \left(\left(z \cdot y1\right) \cdot \left(-k\right)\right)\\ \mathbf{elif}\;b \leq 1:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+118}:\\ \;\;\;\;\left(z \cdot \left(i \cdot y1\right)\right) \cdot \left(-k\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot \left(t \cdot \left(-b\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= b -1e-47)
   (* k (* z (* b y0)))
   (if (<= b 8.8e-287)
     (* c (* (* z t) i))
     (if (<= b 9.2e-225)
       (* x (* y2 (* y1 (- a))))
       (if (<= b 4.2e-76)
         (* i (* (* z y1) (- k)))
         (if (<= b 1.0)
           (* c (* x (* y0 y2)))
           (if (<= b 1.4e+118)
             (* (* z (* i y1)) (- k))
             (* a (* z (* 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 tmp;
	if (b <= -1e-47) {
		tmp = k * (z * (b * y0));
	} else if (b <= 8.8e-287) {
		tmp = c * ((z * t) * i);
	} else if (b <= 9.2e-225) {
		tmp = x * (y2 * (y1 * -a));
	} else if (b <= 4.2e-76) {
		tmp = i * ((z * y1) * -k);
	} else if (b <= 1.0) {
		tmp = c * (x * (y0 * y2));
	} else if (b <= 1.4e+118) {
		tmp = (z * (i * y1)) * -k;
	} else {
		tmp = a * (z * (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) :: tmp
    if (b <= (-1d-47)) then
        tmp = k * (z * (b * y0))
    else if (b <= 8.8d-287) then
        tmp = c * ((z * t) * i)
    else if (b <= 9.2d-225) then
        tmp = x * (y2 * (y1 * -a))
    else if (b <= 4.2d-76) then
        tmp = i * ((z * y1) * -k)
    else if (b <= 1.0d0) then
        tmp = c * (x * (y0 * y2))
    else if (b <= 1.4d+118) then
        tmp = (z * (i * y1)) * -k
    else
        tmp = a * (z * (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 tmp;
	if (b <= -1e-47) {
		tmp = k * (z * (b * y0));
	} else if (b <= 8.8e-287) {
		tmp = c * ((z * t) * i);
	} else if (b <= 9.2e-225) {
		tmp = x * (y2 * (y1 * -a));
	} else if (b <= 4.2e-76) {
		tmp = i * ((z * y1) * -k);
	} else if (b <= 1.0) {
		tmp = c * (x * (y0 * y2));
	} else if (b <= 1.4e+118) {
		tmp = (z * (i * y1)) * -k;
	} else {
		tmp = a * (z * (t * -b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if b <= -1e-47:
		tmp = k * (z * (b * y0))
	elif b <= 8.8e-287:
		tmp = c * ((z * t) * i)
	elif b <= 9.2e-225:
		tmp = x * (y2 * (y1 * -a))
	elif b <= 4.2e-76:
		tmp = i * ((z * y1) * -k)
	elif b <= 1.0:
		tmp = c * (x * (y0 * y2))
	elif b <= 1.4e+118:
		tmp = (z * (i * y1)) * -k
	else:
		tmp = a * (z * (t * -b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (b <= -1e-47)
		tmp = Float64(k * Float64(z * Float64(b * y0)));
	elseif (b <= 8.8e-287)
		tmp = Float64(c * Float64(Float64(z * t) * i));
	elseif (b <= 9.2e-225)
		tmp = Float64(x * Float64(y2 * Float64(y1 * Float64(-a))));
	elseif (b <= 4.2e-76)
		tmp = Float64(i * Float64(Float64(z * y1) * Float64(-k)));
	elseif (b <= 1.0)
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	elseif (b <= 1.4e+118)
		tmp = Float64(Float64(z * Float64(i * y1)) * Float64(-k));
	else
		tmp = Float64(a * Float64(z * Float64(t * Float64(-b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (b <= -1e-47)
		tmp = k * (z * (b * y0));
	elseif (b <= 8.8e-287)
		tmp = c * ((z * t) * i);
	elseif (b <= 9.2e-225)
		tmp = x * (y2 * (y1 * -a));
	elseif (b <= 4.2e-76)
		tmp = i * ((z * y1) * -k);
	elseif (b <= 1.0)
		tmp = c * (x * (y0 * y2));
	elseif (b <= 1.4e+118)
		tmp = (z * (i * y1)) * -k;
	else
		tmp = a * (z * (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_] := If[LessEqual[b, -1e-47], N[(k * N[(z * N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.8e-287], N[(c * N[(N[(z * t), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.2e-225], N[(x * N[(y2 * N[(y1 * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.2e-76], N[(i * N[(N[(z * y1), $MachinePrecision] * (-k)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.0], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.4e+118], N[(N[(z * N[(i * y1), $MachinePrecision]), $MachinePrecision] * (-k)), $MachinePrecision], N[(a * N[(z * N[(t * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -9.9999999999999997e-48

   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 32.5%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around -inf 39.9%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   6. Taylor expanded in k around inf 39.0%

      \[\leadsto -1 \cdot \color{blue}{\left(k \cdot \left(z \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)} \]

   7. Taylor expanded in i around 0 37.7%

      \[\leadsto -1 \cdot \left(k \cdot \left(z \cdot \color{blue}{\left(-1 \cdot \left(b \cdot y0\right)\right)}\right)\right) \]
   8. Step-by-step derivation

      1. neg-mul-1 37.7%

         \[\leadsto -1 \cdot \left(k \cdot \left(z \cdot \color{blue}{\left(-b \cdot y0\right)}\right)\right) \]

      2. distribute-rgt-neg-in 37.7%

         \[\leadsto -1 \cdot \left(k \cdot \left(z \cdot \color{blue}{\left(b \cdot \left(-y0\right)\right)}\right)\right) \]

   9. Simplified 37.7%

      \[\leadsto -1 \cdot \left(k \cdot \left(z \cdot \color{blue}{\left(b \cdot \left(-y0\right)\right)}\right)\right) \]

   if -9.9999999999999997e-48 < b < 8.8000000000000001e-287

   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%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around -inf 48.7%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   6. Taylor expanded in t around inf 34.2%

      \[\leadsto -1 \cdot \color{blue}{\left(t \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 28.5%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

      2. *-commutative 28.5%

         \[\leadsto -1 \cdot \left(\left(t \cdot z\right) \cdot \left(\color{blue}{b \cdot a} - c \cdot i\right)\right) \]

   8. Simplified 28.5%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot \left(b \cdot a - c \cdot i\right)\right)} \]

   9. Taylor expanded in b around 0 30.1%

      \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(i \cdot \left(t \cdot z\right)\right)\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 30.1%

          \[\leadsto -1 \cdot \color{blue}{\left(\left(-1 \cdot c\right) \cdot \left(i \cdot \left(t \cdot z\right)\right)\right)} \]

       2. neg-mul-1 30.1%

          \[\leadsto -1 \cdot \left(\color{blue}{\left(-c\right)} \cdot \left(i \cdot \left(t \cdot z\right)\right)\right) \]

       3. *-commutative 30.1%

          \[\leadsto -1 \cdot \left(\left(-c\right) \cdot \left(i \cdot \color{blue}{\left(z \cdot t\right)}\right)\right) \]

   11. Simplified 30.1%

       \[\leadsto -1 \cdot \color{blue}{\left(\left(-c\right) \cdot \left(i \cdot \left(z \cdot t\right)\right)\right)} \]

   if 8.8000000000000001e-287 < b < 9.1999999999999995e-225

   1. Initial program 35.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 52.9%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 47.8%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   5. Taylor expanded in c around 0 31.7%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot \left(y1 \cdot y2\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 31.7%

         \[\leadsto x \cdot \color{blue}{\left(-a \cdot \left(y1 \cdot y2\right)\right)} \]

      2. associate-*r* 37.2%

         \[\leadsto x \cdot \left(-\color{blue}{\left(a \cdot y1\right) \cdot y2}\right) \]

      3. distribute-rgt-neg-in 37.2%

         \[\leadsto x \cdot \color{blue}{\left(\left(a \cdot y1\right) \cdot \left(-y2\right)\right)} \]

   7. Simplified 37.2%

      \[\leadsto x \cdot \color{blue}{\left(\left(a \cdot y1\right) \cdot \left(-y2\right)\right)} \]

   if 9.1999999999999995e-225 < b < 4.19999999999999985e-76

   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 35.1%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around -inf 43.9%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   6. Taylor expanded in k around inf 31.4%

      \[\leadsto -1 \cdot \color{blue}{\left(k \cdot \left(z \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)} \]

   7. Taylor expanded in i around inf 36.0%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)\right)} \]

   if 4.19999999999999985e-76 < b < 1

   1. Initial program 43.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 44.4%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 44.5%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   5. Taylor expanded in c around inf 38.7%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]

   if 1 < b < 1.39999999999999993e118

   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%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around -inf 34.3%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   6. Taylor expanded in k around inf 54.7%

      \[\leadsto -1 \cdot \color{blue}{\left(k \cdot \left(z \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)} \]

   7. Taylor expanded in i around inf 26.5%

      \[\leadsto -1 \cdot \left(k \cdot \color{blue}{\left(i \cdot \left(y1 \cdot z\right)\right)}\right) \]
   8. Step-by-step derivation

      1. associate-*r* 34.5%

         \[\leadsto -1 \cdot \left(k \cdot \color{blue}{\left(\left(i \cdot y1\right) \cdot z\right)}\right) \]

      2. *-commutative 34.5%

         \[\leadsto -1 \cdot \left(k \cdot \left(\color{blue}{\left(y1 \cdot i\right)} \cdot z\right)\right) \]

   9. Simplified 34.5%

      \[\leadsto -1 \cdot \left(k \cdot \color{blue}{\left(\left(y1 \cdot i\right) \cdot z\right)}\right) \]

   if 1.39999999999999993e118 < b

   1. Initial program 20.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 20.3%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 41.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 36.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. neg-mul-1 36.5%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + x \cdot y\right)\right) \]

      2. +-commutative 36.5%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y + \left(-t \cdot z\right)\right)}\right) \]

      3. unsub-neg 36.5%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y - t \cdot z\right)}\right) \]

      4. *-commutative 36.5%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) \]

   8. Simplified 36.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   9. Taylor expanded in y around 0 29.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 29.9%

          \[\leadsto \color{blue}{-a \cdot \left(b \cdot \left(t \cdot z\right)\right)} \]

       2. *-commutative 29.9%

          \[\leadsto -\color{blue}{\left(b \cdot \left(t \cdot z\right)\right) \cdot a} \]

       3. distribute-rgt-neg-in 29.9%

          \[\leadsto \color{blue}{\left(b \cdot \left(t \cdot z\right)\right) \cdot \left(-a\right)} \]

       4. associate-*r* 33.6%

          \[\leadsto \color{blue}{\left(\left(b \cdot t\right) \cdot z\right)} \cdot \left(-a\right) \]

       5. *-commutative 33.6%

          \[\leadsto \left(\color{blue}{\left(t \cdot b\right)} \cdot z\right) \cdot \left(-a\right) \]

   11. Simplified 33.6%

       \[\leadsto \color{blue}{\left(\left(t \cdot b\right) \cdot z\right) \cdot \left(-a\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 35.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{-47}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq 8.8 \cdot 10^{-287}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{-225}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(y1 \cdot \left(-a\right)\right)\right)\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-76}:\\ \;\;\;\;i \cdot \left(\left(z \cdot y1\right) \cdot \left(-k\right)\right)\\ \mathbf{elif}\;b \leq 1:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+118}:\\ \;\;\;\;\left(z \cdot \left(i \cdot y1\right)\right) \cdot \left(-k\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot \left(t \cdot \left(-b\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 30.1% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ t_2 := a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{if}\;y3 \leq -2.3 \cdot 10^{+210}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y3 \leq -3.8 \cdot 10^{-42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y3 \leq -4.2 \cdot 10^{-270}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq 3.5 \cdot 10^{+66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y3 \leq 2.55 \cdot 10^{+188}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* y4 (- (* t j) (* y k)))))
        (t_2 (* a (* y3 (- (* z y1) (* y y5))))))
   (if (<= y3 -2.3e+210)
     t_2
     (if (<= y3 -3.8e-42)
       t_1
       (if (<= y3 -4.2e-270)
         (* b (* x (- (* y a) (* j y0))))
         (if (<= y3 3.5e+66)
           t_1
           (if (<= y3 2.55e+188) (* a (* b (- (* x y) (* z t)))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (y4 * ((t * j) - (y * k)));
	double t_2 = a * (y3 * ((z * y1) - (y * y5)));
	double tmp;
	if (y3 <= -2.3e+210) {
		tmp = t_2;
	} else if (y3 <= -3.8e-42) {
		tmp = t_1;
	} else if (y3 <= -4.2e-270) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y3 <= 3.5e+66) {
		tmp = t_1;
	} else if (y3 <= 2.55e+188) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (y4 * ((t * j) - (y * k)))
    t_2 = a * (y3 * ((z * y1) - (y * y5)))
    if (y3 <= (-2.3d+210)) then
        tmp = t_2
    else if (y3 <= (-3.8d-42)) then
        tmp = t_1
    else if (y3 <= (-4.2d-270)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (y3 <= 3.5d+66) then
        tmp = t_1
    else if (y3 <= 2.55d+188) then
        tmp = a * (b * ((x * y) - (z * t)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (y4 * ((t * j) - (y * k)));
	double t_2 = a * (y3 * ((z * y1) - (y * y5)));
	double tmp;
	if (y3 <= -2.3e+210) {
		tmp = t_2;
	} else if (y3 <= -3.8e-42) {
		tmp = t_1;
	} else if (y3 <= -4.2e-270) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y3 <= 3.5e+66) {
		tmp = t_1;
	} else if (y3 <= 2.55e+188) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (y4 * ((t * j) - (y * k)))
	t_2 = a * (y3 * ((z * y1) - (y * y5)))
	tmp = 0
	if y3 <= -2.3e+210:
		tmp = t_2
	elif y3 <= -3.8e-42:
		tmp = t_1
	elif y3 <= -4.2e-270:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif y3 <= 3.5e+66:
		tmp = t_1
	elif y3 <= 2.55e+188:
		tmp = a * (b * ((x * y) - (z * t)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))))
	t_2 = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))))
	tmp = 0.0
	if (y3 <= -2.3e+210)
		tmp = t_2;
	elseif (y3 <= -3.8e-42)
		tmp = t_1;
	elseif (y3 <= -4.2e-270)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (y3 <= 3.5e+66)
		tmp = t_1;
	elseif (y3 <= 2.55e+188)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (y4 * ((t * j) - (y * k)));
	t_2 = a * (y3 * ((z * y1) - (y * y5)));
	tmp = 0.0;
	if (y3 <= -2.3e+210)
		tmp = t_2;
	elseif (y3 <= -3.8e-42)
		tmp = t_1;
	elseif (y3 <= -4.2e-270)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (y3 <= 3.5e+66)
		tmp = t_1;
	elseif (y3 <= 2.55e+188)
		tmp = a * (b * ((x * y) - (z * t)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -2.3e+210], t$95$2, If[LessEqual[y3, -3.8e-42], t$95$1, If[LessEqual[y3, -4.2e-270], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 3.5e+66], t$95$1, If[LessEqual[y3, 2.55e+188], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y3 < -2.2999999999999999e210 or 2.5500000000000001e188 < y3

   1. Initial program 18.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 18.7%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 46.4%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in y3 around inf 60.5%

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]

   if -2.2999999999999999e210 < y3 < -3.80000000000000017e-42 or -4.19999999999999992e-270 < y3 < 3.4999999999999997e66

   1. Initial program 32.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 33.0%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 39.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y4 around inf 38.1%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   if -3.80000000000000017e-42 < y3 < -4.19999999999999992e-270

   1. Initial program 42.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 42.4%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 38.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 33.0%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   if 3.4999999999999997e66 < y3 < 2.5500000000000001e188

   1. Initial program 18.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 18.9%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 44.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 44.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. neg-mul-1 44.2%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + x \cdot y\right)\right) \]

      2. +-commutative 44.2%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y + \left(-t \cdot z\right)\right)}\right) \]

      3. unsub-neg 44.2%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y - t \cdot z\right)}\right) \]

      4. *-commutative 44.2%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) \]

   8. Simplified 44.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 41.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -2.3 \cdot 10^{+210}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y3 \leq -3.8 \cdot 10^{-42}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y3 \leq -4.2 \cdot 10^{-270}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq 3.5 \cdot 10^{+66}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y3 \leq 2.55 \cdot 10^{+188}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 29.6% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ t_2 := a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{if}\;y3 \leq -3.2 \cdot 10^{+215}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y3 \leq -9.6 \cdot 10^{-41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y3 \leq -3.5 \cdot 10^{-273}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq 8 \cdot 10^{-13}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y3 \leq 9 \cdot 10^{+187}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* y4 (- (* t j) (* y k)))))
        (t_2 (* a (* y3 (- (* z y1) (* y y5))))))
   (if (<= y3 -3.2e+215)
     t_2
     (if (<= y3 -9.6e-41)
       t_1
       (if (<= y3 -3.5e-273)
         (* b (* x (- (* y a) (* j y0))))
         (if (<= y3 8e-13)
           t_1
           (if (<= y3 9e+187) (* c (* t (- (* z i) (* y2 y4)))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (y4 * ((t * j) - (y * k)));
	double t_2 = a * (y3 * ((z * y1) - (y * y5)));
	double tmp;
	if (y3 <= -3.2e+215) {
		tmp = t_2;
	} else if (y3 <= -9.6e-41) {
		tmp = t_1;
	} else if (y3 <= -3.5e-273) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y3 <= 8e-13) {
		tmp = t_1;
	} else if (y3 <= 9e+187) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (y4 * ((t * j) - (y * k)))
    t_2 = a * (y3 * ((z * y1) - (y * y5)))
    if (y3 <= (-3.2d+215)) then
        tmp = t_2
    else if (y3 <= (-9.6d-41)) then
        tmp = t_1
    else if (y3 <= (-3.5d-273)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (y3 <= 8d-13) then
        tmp = t_1
    else if (y3 <= 9d+187) then
        tmp = c * (t * ((z * i) - (y2 * y4)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (y4 * ((t * j) - (y * k)));
	double t_2 = a * (y3 * ((z * y1) - (y * y5)));
	double tmp;
	if (y3 <= -3.2e+215) {
		tmp = t_2;
	} else if (y3 <= -9.6e-41) {
		tmp = t_1;
	} else if (y3 <= -3.5e-273) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y3 <= 8e-13) {
		tmp = t_1;
	} else if (y3 <= 9e+187) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (y4 * ((t * j) - (y * k)))
	t_2 = a * (y3 * ((z * y1) - (y * y5)))
	tmp = 0
	if y3 <= -3.2e+215:
		tmp = t_2
	elif y3 <= -9.6e-41:
		tmp = t_1
	elif y3 <= -3.5e-273:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif y3 <= 8e-13:
		tmp = t_1
	elif y3 <= 9e+187:
		tmp = c * (t * ((z * i) - (y2 * y4)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))))
	t_2 = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))))
	tmp = 0.0
	if (y3 <= -3.2e+215)
		tmp = t_2;
	elseif (y3 <= -9.6e-41)
		tmp = t_1;
	elseif (y3 <= -3.5e-273)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (y3 <= 8e-13)
		tmp = t_1;
	elseif (y3 <= 9e+187)
		tmp = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (y4 * ((t * j) - (y * k)));
	t_2 = a * (y3 * ((z * y1) - (y * y5)));
	tmp = 0.0;
	if (y3 <= -3.2e+215)
		tmp = t_2;
	elseif (y3 <= -9.6e-41)
		tmp = t_1;
	elseif (y3 <= -3.5e-273)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (y3 <= 8e-13)
		tmp = t_1;
	elseif (y3 <= 9e+187)
		tmp = c * (t * ((z * i) - (y2 * y4)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -3.2e+215], t$95$2, If[LessEqual[y3, -9.6e-41], t$95$1, If[LessEqual[y3, -3.5e-273], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 8e-13], t$95$1, If[LessEqual[y3, 9e+187], N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y3 < -3.1999999999999999e215 or 9.00000000000000052e187 < y3

   1. Initial program 18.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 18.7%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 46.4%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in y3 around inf 60.5%

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]

   if -3.1999999999999999e215 < y3 < -9.60000000000000087e-41 or -3.49999999999999992e-273 < y3 < 8.0000000000000002e-13

   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 32.1%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 43.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y4 around inf 40.2%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   if -9.60000000000000087e-41 < y3 < -3.49999999999999992e-273

   1. Initial program 42.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 42.4%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 38.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 33.0%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   if 8.0000000000000002e-13 < y3 < 9.00000000000000052e187

   1. Initial program 26.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 26.8%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 31.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   6. Taylor expanded in t around inf 40.0%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(i \cdot z - y2 \cdot y4\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -3.2 \cdot 10^{+215}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y3 \leq -9.6 \cdot 10^{-41}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y3 \leq -3.5 \cdot 10^{-273}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq 8 \cdot 10^{-13}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y3 \leq 9 \cdot 10^{+187}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 19.1% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -3.6 \cdot 10^{+86}:\\ \;\;\;\;i \cdot \left(\left(z \cdot y1\right) \cdot \left(-k\right)\right)\\ \mathbf{elif}\;i \leq 6.2 \cdot 10^{-140}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(y1 \cdot \left(-a\right)\right)\right)\\ \mathbf{elif}\;i \leq 14.5:\\ \;\;\;\;\left(t \cdot b\right) \cdot \left(j \cdot y4\right)\\ \mathbf{elif}\;i \leq 2.35 \cdot 10^{+149}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{+220}:\\ \;\;\;\;a \cdot \left(\left(z \cdot t\right) \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= i -3.6e+86)
   (* i (* (* z y1) (- k)))
   (if (<= i 6.2e-140)
     (* x (* y2 (* y1 (- a))))
     (if (<= i 14.5)
       (* (* t b) (* j y4))
       (if (<= i 2.35e+149)
         (* x (* y2 (* c y0)))
         (if (<= i 1.3e+220)
           (* a (* (* z t) (- b)))
           (* c (* x (* y0 y2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (i <= -3.6e+86) {
		tmp = i * ((z * y1) * -k);
	} else if (i <= 6.2e-140) {
		tmp = x * (y2 * (y1 * -a));
	} else if (i <= 14.5) {
		tmp = (t * b) * (j * y4);
	} else if (i <= 2.35e+149) {
		tmp = x * (y2 * (c * y0));
	} else if (i <= 1.3e+220) {
		tmp = a * ((z * t) * -b);
	} else {
		tmp = c * (x * (y0 * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (i <= (-3.6d+86)) then
        tmp = i * ((z * y1) * -k)
    else if (i <= 6.2d-140) then
        tmp = x * (y2 * (y1 * -a))
    else if (i <= 14.5d0) then
        tmp = (t * b) * (j * y4)
    else if (i <= 2.35d+149) then
        tmp = x * (y2 * (c * y0))
    else if (i <= 1.3d+220) then
        tmp = a * ((z * t) * -b)
    else
        tmp = c * (x * (y0 * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (i <= -3.6e+86) {
		tmp = i * ((z * y1) * -k);
	} else if (i <= 6.2e-140) {
		tmp = x * (y2 * (y1 * -a));
	} else if (i <= 14.5) {
		tmp = (t * b) * (j * y4);
	} else if (i <= 2.35e+149) {
		tmp = x * (y2 * (c * y0));
	} else if (i <= 1.3e+220) {
		tmp = a * ((z * t) * -b);
	} else {
		tmp = c * (x * (y0 * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if i <= -3.6e+86:
		tmp = i * ((z * y1) * -k)
	elif i <= 6.2e-140:
		tmp = x * (y2 * (y1 * -a))
	elif i <= 14.5:
		tmp = (t * b) * (j * y4)
	elif i <= 2.35e+149:
		tmp = x * (y2 * (c * y0))
	elif i <= 1.3e+220:
		tmp = a * ((z * t) * -b)
	else:
		tmp = c * (x * (y0 * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (i <= -3.6e+86)
		tmp = Float64(i * Float64(Float64(z * y1) * Float64(-k)));
	elseif (i <= 6.2e-140)
		tmp = Float64(x * Float64(y2 * Float64(y1 * Float64(-a))));
	elseif (i <= 14.5)
		tmp = Float64(Float64(t * b) * Float64(j * y4));
	elseif (i <= 2.35e+149)
		tmp = Float64(x * Float64(y2 * Float64(c * y0)));
	elseif (i <= 1.3e+220)
		tmp = Float64(a * Float64(Float64(z * t) * Float64(-b)));
	else
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (i <= -3.6e+86)
		tmp = i * ((z * y1) * -k);
	elseif (i <= 6.2e-140)
		tmp = x * (y2 * (y1 * -a));
	elseif (i <= 14.5)
		tmp = (t * b) * (j * y4);
	elseif (i <= 2.35e+149)
		tmp = x * (y2 * (c * y0));
	elseif (i <= 1.3e+220)
		tmp = a * ((z * t) * -b);
	else
		tmp = c * (x * (y0 * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[i, -3.6e+86], N[(i * N[(N[(z * y1), $MachinePrecision] * (-k)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 6.2e-140], N[(x * N[(y2 * N[(y1 * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 14.5], N[(N[(t * b), $MachinePrecision] * N[(j * y4), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.35e+149], N[(x * N[(y2 * N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.3e+220], N[(a * N[(N[(z * t), $MachinePrecision] * (-b)), $MachinePrecision]), $MachinePrecision], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -3.60000000000000005e86

   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 30.3%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around -inf 32.9%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   6. Taylor expanded in k around inf 45.0%

      \[\leadsto -1 \cdot \color{blue}{\left(k \cdot \left(z \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)} \]

   7. Taylor expanded in i around inf 31.3%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)\right)} \]

   if -3.60000000000000005e86 < i < 6.1999999999999998e-140

   1. Initial program 30.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 43.8%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 39.3%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   5. Taylor expanded in c around 0 23.6%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot \left(y1 \cdot y2\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 23.6%

         \[\leadsto x \cdot \color{blue}{\left(-a \cdot \left(y1 \cdot y2\right)\right)} \]

      2. associate-*r* 27.4%

         \[\leadsto x \cdot \left(-\color{blue}{\left(a \cdot y1\right) \cdot y2}\right) \]

      3. distribute-rgt-neg-in 27.4%

         \[\leadsto x \cdot \color{blue}{\left(\left(a \cdot y1\right) \cdot \left(-y2\right)\right)} \]

   7. Simplified 27.4%

      \[\leadsto x \cdot \color{blue}{\left(\left(a \cdot y1\right) \cdot \left(-y2\right)\right)} \]

   if 6.1999999999999998e-140 < i < 14.5

   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%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 51.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in t around inf 34.3%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 34.1%

         \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)} \]

      2. +-commutative 34.1%

         \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{\left(j \cdot y4 + -1 \cdot \left(a \cdot z\right)\right)} \]

      3. mul-1-neg 34.1%

         \[\leadsto \left(b \cdot t\right) \cdot \left(j \cdot y4 + \color{blue}{\left(-a \cdot z\right)}\right) \]

      4. unsub-neg 34.1%

         \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{\left(j \cdot y4 - a \cdot z\right)} \]

      5. *-commutative 34.1%

         \[\leadsto \left(b \cdot t\right) \cdot \left(\color{blue}{y4 \cdot j} - a \cdot z\right) \]

      6. *-commutative 34.1%

         \[\leadsto \left(b \cdot t\right) \cdot \left(y4 \cdot j - \color{blue}{z \cdot a}\right) \]

   8. Simplified 34.1%

      \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \left(y4 \cdot j - z \cdot a\right)} \]

   9. Taylor expanded in y4 around inf 26.6%

      \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{\left(j \cdot y4\right)} \]
   10. Step-by-step derivation

       1. *-commutative 26.6%

          \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{\left(y4 \cdot j\right)} \]

   11. Simplified 26.6%

       \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{\left(y4 \cdot j\right)} \]

   if 14.5 < i < 2.3500000000000002e149

   1. Initial program 28.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 40.0%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 29.2%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   5. Taylor expanded in c around inf 29.1%

      \[\leadsto x \cdot \left(y2 \cdot \color{blue}{\left(c \cdot y0\right)}\right) \]

   if 2.3500000000000002e149 < i < 1.29999999999999997e220

   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%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 39.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 40.7%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. neg-mul-1 40.7%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + x \cdot y\right)\right) \]

      2. +-commutative 40.7%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y + \left(-t \cdot z\right)\right)}\right) \]

      3. unsub-neg 40.7%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y - t \cdot z\right)}\right) \]

      4. *-commutative 40.7%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) \]

   8. Simplified 40.7%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   9. Taylor expanded in y around 0 40.2%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 40.2%

          \[\leadsto a \cdot \color{blue}{\left(-b \cdot \left(t \cdot z\right)\right)} \]

       2. *-commutative 40.2%

          \[\leadsto a \cdot \left(-\color{blue}{\left(t \cdot z\right) \cdot b}\right) \]

       3. distribute-rgt-neg-in 40.2%

          \[\leadsto a \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot \left(-b\right)\right)} \]

       4. *-commutative 40.2%

          \[\leadsto a \cdot \left(\color{blue}{\left(z \cdot t\right)} \cdot \left(-b\right)\right) \]

   11. Simplified 40.2%

       \[\leadsto a \cdot \color{blue}{\left(\left(z \cdot t\right) \cdot \left(-b\right)\right)} \]

   if 1.29999999999999997e220 < i

   1. Initial program 28.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 35.3%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 34.9%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   5. Taylor expanded in c around inf 40.3%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 30.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.6 \cdot 10^{+86}:\\ \;\;\;\;i \cdot \left(\left(z \cdot y1\right) \cdot \left(-k\right)\right)\\ \mathbf{elif}\;i \leq 6.2 \cdot 10^{-140}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(y1 \cdot \left(-a\right)\right)\right)\\ \mathbf{elif}\;i \leq 14.5:\\ \;\;\;\;\left(t \cdot b\right) \cdot \left(j \cdot y4\right)\\ \mathbf{elif}\;i \leq 2.35 \cdot 10^{+149}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{+220}:\\ \;\;\;\;a \cdot \left(\left(z \cdot t\right) \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 20.3% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.3 \cdot 10^{+27}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-60}:\\ \;\;\;\;i \cdot \left(\left(k \cdot y1\right) \cdot \left(-z\right)\right)\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-81}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+146}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(y1 \cdot \left(-a\right)\right)\right)\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+269}:\\ \;\;\;\;a \cdot \left(\left(z \cdot t\right) \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot a\right) \cdot \left(y1 \cdot y3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= a -7.3e+27)
   (* a (* (* x y) b))
   (if (<= a -3.8e-60)
     (* i (* (* k y1) (- z)))
     (if (<= a 1.4e-81)
       (* x (* y2 (* c y0)))
       (if (<= a 8.5e+146)
         (* x (* y2 (* y1 (- a))))
         (if (<= a 2.7e+269)
           (* a (* (* z t) (- b)))
           (* (* z a) (* y1 y3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (a <= -7.3e+27) {
		tmp = a * ((x * y) * b);
	} else if (a <= -3.8e-60) {
		tmp = i * ((k * y1) * -z);
	} else if (a <= 1.4e-81) {
		tmp = x * (y2 * (c * y0));
	} else if (a <= 8.5e+146) {
		tmp = x * (y2 * (y1 * -a));
	} else if (a <= 2.7e+269) {
		tmp = a * ((z * t) * -b);
	} else {
		tmp = (z * a) * (y1 * y3);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (a <= (-7.3d+27)) then
        tmp = a * ((x * y) * b)
    else if (a <= (-3.8d-60)) then
        tmp = i * ((k * y1) * -z)
    else if (a <= 1.4d-81) then
        tmp = x * (y2 * (c * y0))
    else if (a <= 8.5d+146) then
        tmp = x * (y2 * (y1 * -a))
    else if (a <= 2.7d+269) then
        tmp = a * ((z * t) * -b)
    else
        tmp = (z * a) * (y1 * y3)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (a <= -7.3e+27) {
		tmp = a * ((x * y) * b);
	} else if (a <= -3.8e-60) {
		tmp = i * ((k * y1) * -z);
	} else if (a <= 1.4e-81) {
		tmp = x * (y2 * (c * y0));
	} else if (a <= 8.5e+146) {
		tmp = x * (y2 * (y1 * -a));
	} else if (a <= 2.7e+269) {
		tmp = a * ((z * t) * -b);
	} else {
		tmp = (z * a) * (y1 * y3);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if a <= -7.3e+27:
		tmp = a * ((x * y) * b)
	elif a <= -3.8e-60:
		tmp = i * ((k * y1) * -z)
	elif a <= 1.4e-81:
		tmp = x * (y2 * (c * y0))
	elif a <= 8.5e+146:
		tmp = x * (y2 * (y1 * -a))
	elif a <= 2.7e+269:
		tmp = a * ((z * t) * -b)
	else:
		tmp = (z * a) * (y1 * y3)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (a <= -7.3e+27)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	elseif (a <= -3.8e-60)
		tmp = Float64(i * Float64(Float64(k * y1) * Float64(-z)));
	elseif (a <= 1.4e-81)
		tmp = Float64(x * Float64(y2 * Float64(c * y0)));
	elseif (a <= 8.5e+146)
		tmp = Float64(x * Float64(y2 * Float64(y1 * Float64(-a))));
	elseif (a <= 2.7e+269)
		tmp = Float64(a * Float64(Float64(z * t) * Float64(-b)));
	else
		tmp = Float64(Float64(z * a) * Float64(y1 * y3));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (a <= -7.3e+27)
		tmp = a * ((x * y) * b);
	elseif (a <= -3.8e-60)
		tmp = i * ((k * y1) * -z);
	elseif (a <= 1.4e-81)
		tmp = x * (y2 * (c * y0));
	elseif (a <= 8.5e+146)
		tmp = x * (y2 * (y1 * -a));
	elseif (a <= 2.7e+269)
		tmp = a * ((z * t) * -b);
	else
		tmp = (z * a) * (y1 * y3);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[a, -7.3e+27], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.8e-60], N[(i * N[(N[(k * y1), $MachinePrecision] * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.4e-81], N[(x * N[(y2 * N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.5e+146], N[(x * N[(y2 * N[(y1 * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.7e+269], N[(a * N[(N[(z * t), $MachinePrecision] * (-b)), $MachinePrecision]), $MachinePrecision], N[(N[(z * a), $MachinePrecision] * N[(y1 * y3), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -7.2999999999999998e27

   1. Initial program 28.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.7%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 42.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 38.7%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. neg-mul-1 38.7%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + x \cdot y\right)\right) \]

      2. +-commutative 38.7%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y + \left(-t \cdot z\right)\right)}\right) \]

      3. unsub-neg 38.7%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y - t \cdot z\right)}\right) \]

      4. *-commutative 38.7%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) \]

   8. Simplified 38.7%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   9. Taylor expanded in y around inf 34.8%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 34.8%

          \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot b\right)} \]

   11. Simplified 34.8%

       \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot b\right)} \]

   if -7.2999999999999998e27 < a < -3.79999999999999994e-60

   1. Initial program 38.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 38.9%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around -inf 44.6%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   6. Taylor expanded in k around inf 45.5%

      \[\leadsto -1 \cdot \color{blue}{\left(k \cdot \left(z \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)} \]

   7. Taylor expanded in i around inf 39.7%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 44.8%

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(k \cdot y1\right) \cdot z\right)}\right) \]

   9. Simplified 44.8%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(\left(k \cdot y1\right) \cdot z\right)\right)} \]

   if -3.79999999999999994e-60 < a < 1.3999999999999999e-81

   1. Initial program 36.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 36.1%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 25.1%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   5. Taylor expanded in c around inf 24.2%

      \[\leadsto x \cdot \left(y2 \cdot \color{blue}{\left(c \cdot y0\right)}\right) \]

   if 1.3999999999999999e-81 < a < 8.5e146

   1. Initial program 25.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 33.6%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 41.4%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   5. Taylor expanded in c around 0 31.7%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot \left(y1 \cdot y2\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 31.7%

         \[\leadsto x \cdot \color{blue}{\left(-a \cdot \left(y1 \cdot y2\right)\right)} \]

      2. associate-*r* 36.1%

         \[\leadsto x \cdot \left(-\color{blue}{\left(a \cdot y1\right) \cdot y2}\right) \]

      3. distribute-rgt-neg-in 36.1%

         \[\leadsto x \cdot \color{blue}{\left(\left(a \cdot y1\right) \cdot \left(-y2\right)\right)} \]

   7. Simplified 36.1%

      \[\leadsto x \cdot \color{blue}{\left(\left(a \cdot y1\right) \cdot \left(-y2\right)\right)} \]

   if 8.5e146 < a < 2.6999999999999999e269

   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 23.1%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 49.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 40.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. neg-mul-1 40.0%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + x \cdot y\right)\right) \]

      2. +-commutative 40.0%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y + \left(-t \cdot z\right)\right)}\right) \]

      3. unsub-neg 40.0%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y - t \cdot z\right)}\right) \]

      4. *-commutative 40.0%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) \]

   8. Simplified 40.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   9. Taylor expanded in y around 0 38.4%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 38.4%

          \[\leadsto a \cdot \color{blue}{\left(-b \cdot \left(t \cdot z\right)\right)} \]

       2. *-commutative 38.4%

          \[\leadsto a \cdot \left(-\color{blue}{\left(t \cdot z\right) \cdot b}\right) \]

       3. distribute-rgt-neg-in 38.4%

          \[\leadsto a \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot \left(-b\right)\right)} \]

       4. *-commutative 38.4%

          \[\leadsto a \cdot \left(\color{blue}{\left(z \cdot t\right)} \cdot \left(-b\right)\right) \]

   11. Simplified 38.4%

       \[\leadsto a \cdot \color{blue}{\left(\left(z \cdot t\right) \cdot \left(-b\right)\right)} \]

   if 2.6999999999999999e269 < a

   1. Initial program 6.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 6.7%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 67.2%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in z around inf 47.3%

      \[\leadsto \color{blue}{a \cdot \left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 47.3%

         \[\leadsto \color{blue}{\left(a \cdot z\right) \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)} \]

      2. *-commutative 47.3%

         \[\leadsto \color{blue}{\left(z \cdot a\right)} \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right) \]

      3. +-commutative 47.3%

         \[\leadsto \left(z \cdot a\right) \cdot \color{blue}{\left(y1 \cdot y3 + -1 \cdot \left(b \cdot t\right)\right)} \]

      4. mul-1-neg 47.3%

         \[\leadsto \left(z \cdot a\right) \cdot \left(y1 \cdot y3 + \color{blue}{\left(-b \cdot t\right)}\right) \]

      5. unsub-neg 47.3%

         \[\leadsto \left(z \cdot a\right) \cdot \color{blue}{\left(y1 \cdot y3 - b \cdot t\right)} \]

   8. Simplified 47.3%

      \[\leadsto \color{blue}{\left(z \cdot a\right) \cdot \left(y1 \cdot y3 - b \cdot t\right)} \]

   9. Taylor expanded in y1 around inf 53.8%

      \[\leadsto \left(z \cdot a\right) \cdot \color{blue}{\left(y1 \cdot y3\right)} \]
   10. Step-by-step derivation

       1. *-commutative 53.8%

          \[\leadsto \left(z \cdot a\right) \cdot \color{blue}{\left(y3 \cdot y1\right)} \]

   11. Simplified 53.8%

       \[\leadsto \left(z \cdot a\right) \cdot \color{blue}{\left(y3 \cdot y1\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 32.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.3 \cdot 10^{+27}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-60}:\\ \;\;\;\;i \cdot \left(\left(k \cdot y1\right) \cdot \left(-z\right)\right)\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-81}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+146}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(y1 \cdot \left(-a\right)\right)\right)\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+269}:\\ \;\;\;\;a \cdot \left(\left(z \cdot t\right) \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot a\right) \cdot \left(y1 \cdot y3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 21.8% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot \left(i \cdot y1\right)\right) \cdot \left(-k\right)\\ \mathbf{if}\;i \leq -2 \cdot 10^{+87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 5 \cdot 10^{-140}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(y1 \cdot \left(-a\right)\right)\right)\\ \mathbf{elif}\;i \leq 55000:\\ \;\;\;\;\left(t \cdot b\right) \cdot \left(j \cdot y4\right)\\ \mathbf{elif}\;i \leq 4.9 \cdot 10^{+149}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq 2.46 \cdot 10^{+213}:\\ \;\;\;\;a \cdot \left(\left(z \cdot t\right) \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* z (* i y1)) (- k))))
   (if (<= i -2e+87)
     t_1
     (if (<= i 5e-140)
       (* x (* y2 (* y1 (- a))))
       (if (<= i 55000.0)
         (* (* t b) (* j y4))
         (if (<= i 4.9e+149)
           (* x (* y2 (* c y0)))
           (if (<= i 2.46e+213) (* a (* (* z t) (- 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 = (z * (i * y1)) * -k;
	double tmp;
	if (i <= -2e+87) {
		tmp = t_1;
	} else if (i <= 5e-140) {
		tmp = x * (y2 * (y1 * -a));
	} else if (i <= 55000.0) {
		tmp = (t * b) * (j * y4);
	} else if (i <= 4.9e+149) {
		tmp = x * (y2 * (c * y0));
	} else if (i <= 2.46e+213) {
		tmp = a * ((z * t) * -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) :: tmp
    t_1 = (z * (i * y1)) * -k
    if (i <= (-2d+87)) then
        tmp = t_1
    else if (i <= 5d-140) then
        tmp = x * (y2 * (y1 * -a))
    else if (i <= 55000.0d0) then
        tmp = (t * b) * (j * y4)
    else if (i <= 4.9d+149) then
        tmp = x * (y2 * (c * y0))
    else if (i <= 2.46d+213) then
        tmp = a * ((z * t) * -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 = (z * (i * y1)) * -k;
	double tmp;
	if (i <= -2e+87) {
		tmp = t_1;
	} else if (i <= 5e-140) {
		tmp = x * (y2 * (y1 * -a));
	} else if (i <= 55000.0) {
		tmp = (t * b) * (j * y4);
	} else if (i <= 4.9e+149) {
		tmp = x * (y2 * (c * y0));
	} else if (i <= 2.46e+213) {
		tmp = a * ((z * t) * -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 = (z * (i * y1)) * -k
	tmp = 0
	if i <= -2e+87:
		tmp = t_1
	elif i <= 5e-140:
		tmp = x * (y2 * (y1 * -a))
	elif i <= 55000.0:
		tmp = (t * b) * (j * y4)
	elif i <= 4.9e+149:
		tmp = x * (y2 * (c * y0))
	elif i <= 2.46e+213:
		tmp = a * ((z * t) * -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(Float64(z * Float64(i * y1)) * Float64(-k))
	tmp = 0.0
	if (i <= -2e+87)
		tmp = t_1;
	elseif (i <= 5e-140)
		tmp = Float64(x * Float64(y2 * Float64(y1 * Float64(-a))));
	elseif (i <= 55000.0)
		tmp = Float64(Float64(t * b) * Float64(j * y4));
	elseif (i <= 4.9e+149)
		tmp = Float64(x * Float64(y2 * Float64(c * y0)));
	elseif (i <= 2.46e+213)
		tmp = Float64(a * Float64(Float64(z * t) * Float64(-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 = (z * (i * y1)) * -k;
	tmp = 0.0;
	if (i <= -2e+87)
		tmp = t_1;
	elseif (i <= 5e-140)
		tmp = x * (y2 * (y1 * -a));
	elseif (i <= 55000.0)
		tmp = (t * b) * (j * y4);
	elseif (i <= 4.9e+149)
		tmp = x * (y2 * (c * y0));
	elseif (i <= 2.46e+213)
		tmp = a * ((z * t) * -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[(N[(z * N[(i * y1), $MachinePrecision]), $MachinePrecision] * (-k)), $MachinePrecision]}, If[LessEqual[i, -2e+87], t$95$1, If[LessEqual[i, 5e-140], N[(x * N[(y2 * N[(y1 * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 55000.0], N[(N[(t * b), $MachinePrecision] * N[(j * y4), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.9e+149], N[(x * N[(y2 * N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.46e+213], N[(a * N[(N[(z * t), $MachinePrecision] * (-b)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -1.9999999999999999e87 or 2.4600000000000001e213 < i

   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 28.6%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around -inf 36.0%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   6. Taylor expanded in k around inf 44.5%

      \[\leadsto -1 \cdot \color{blue}{\left(k \cdot \left(z \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)} \]

   7. Taylor expanded in i around inf 36.1%

      \[\leadsto -1 \cdot \left(k \cdot \color{blue}{\left(i \cdot \left(y1 \cdot z\right)\right)}\right) \]
   8. Step-by-step derivation

      1. associate-*r* 38.8%

         \[\leadsto -1 \cdot \left(k \cdot \color{blue}{\left(\left(i \cdot y1\right) \cdot z\right)}\right) \]

      2. *-commutative 38.8%

         \[\leadsto -1 \cdot \left(k \cdot \left(\color{blue}{\left(y1 \cdot i\right)} \cdot z\right)\right) \]

   9. Simplified 38.8%

      \[\leadsto -1 \cdot \left(k \cdot \color{blue}{\left(\left(y1 \cdot i\right) \cdot z\right)}\right) \]

   if -1.9999999999999999e87 < i < 5.00000000000000015e-140

   1. Initial program 30.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 43.8%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 39.3%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   5. Taylor expanded in c around 0 23.6%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot \left(y1 \cdot y2\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 23.6%

         \[\leadsto x \cdot \color{blue}{\left(-a \cdot \left(y1 \cdot y2\right)\right)} \]

      2. associate-*r* 27.4%

         \[\leadsto x \cdot \left(-\color{blue}{\left(a \cdot y1\right) \cdot y2}\right) \]

      3. distribute-rgt-neg-in 27.4%

         \[\leadsto x \cdot \color{blue}{\left(\left(a \cdot y1\right) \cdot \left(-y2\right)\right)} \]

   7. Simplified 27.4%

      \[\leadsto x \cdot \color{blue}{\left(\left(a \cdot y1\right) \cdot \left(-y2\right)\right)} \]

   if 5.00000000000000015e-140 < i < 55000

   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%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 51.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in t around inf 34.3%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 34.1%

         \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)} \]

      2. +-commutative 34.1%

         \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{\left(j \cdot y4 + -1 \cdot \left(a \cdot z\right)\right)} \]

      3. mul-1-neg 34.1%

         \[\leadsto \left(b \cdot t\right) \cdot \left(j \cdot y4 + \color{blue}{\left(-a \cdot z\right)}\right) \]

      4. unsub-neg 34.1%

         \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{\left(j \cdot y4 - a \cdot z\right)} \]

      5. *-commutative 34.1%

         \[\leadsto \left(b \cdot t\right) \cdot \left(\color{blue}{y4 \cdot j} - a \cdot z\right) \]

      6. *-commutative 34.1%

         \[\leadsto \left(b \cdot t\right) \cdot \left(y4 \cdot j - \color{blue}{z \cdot a}\right) \]

   8. Simplified 34.1%

      \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \left(y4 \cdot j - z \cdot a\right)} \]

   9. Taylor expanded in y4 around inf 26.6%

      \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{\left(j \cdot y4\right)} \]
   10. Step-by-step derivation

       1. *-commutative 26.6%

          \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{\left(y4 \cdot j\right)} \]

   11. Simplified 26.6%

       \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{\left(y4 \cdot j\right)} \]

   if 55000 < i < 4.9000000000000001e149

   1. Initial program 28.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 40.0%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 29.2%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   5. Taylor expanded in c around inf 29.1%

      \[\leadsto x \cdot \left(y2 \cdot \color{blue}{\left(c \cdot y0\right)}\right) \]

   if 4.9000000000000001e149 < i < 2.4600000000000001e213

   1. Initial program 20.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 20.0%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 41.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 41.4%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. neg-mul-1 41.4%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + x \cdot y\right)\right) \]

      2. +-commutative 41.4%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y + \left(-t \cdot z\right)\right)}\right) \]

      3. unsub-neg 41.4%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y - t \cdot z\right)}\right) \]

      4. *-commutative 41.4%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) \]

   8. Simplified 41.4%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   9. Taylor expanded in y around 0 40.8%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 40.8%

          \[\leadsto a \cdot \color{blue}{\left(-b \cdot \left(t \cdot z\right)\right)} \]

       2. *-commutative 40.8%

          \[\leadsto a \cdot \left(-\color{blue}{\left(t \cdot z\right) \cdot b}\right) \]

       3. distribute-rgt-neg-in 40.8%

          \[\leadsto a \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot \left(-b\right)\right)} \]

       4. *-commutative 40.8%

          \[\leadsto a \cdot \left(\color{blue}{\left(z \cdot t\right)} \cdot \left(-b\right)\right) \]

   11. Simplified 40.8%

       \[\leadsto a \cdot \color{blue}{\left(\left(z \cdot t\right) \cdot \left(-b\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 31.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2 \cdot 10^{+87}:\\ \;\;\;\;\left(z \cdot \left(i \cdot y1\right)\right) \cdot \left(-k\right)\\ \mathbf{elif}\;i \leq 5 \cdot 10^{-140}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(y1 \cdot \left(-a\right)\right)\right)\\ \mathbf{elif}\;i \leq 55000:\\ \;\;\;\;\left(t \cdot b\right) \cdot \left(j \cdot y4\right)\\ \mathbf{elif}\;i \leq 4.9 \cdot 10^{+149}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq 2.46 \cdot 10^{+213}:\\ \;\;\;\;a \cdot \left(\left(z \cdot t\right) \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot \left(i \cdot y1\right)\right) \cdot \left(-k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 21.8% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y0 \leq -1.4 \cdot 10^{+81}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -2.5 \cdot 10^{-122}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq -4 \cdot 10^{-228}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y1 \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;y0 \leq -1.55 \cdot 10^{-253}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq 4.4 \cdot 10^{+44}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y0 -1.4e+81)
   (* k (* z (* b y0)))
   (if (<= y0 -2.5e-122)
     (* c (* x (* y0 y2)))
     (if (<= y0 -4e-228)
       (* a (* x (* y1 (- y2))))
       (if (<= y0 -1.55e-253)
         (* a (* y1 (* z y3)))
         (if (<= y0 4.4e+44) (* c (* (* z t) i)) (* b (* k (* z y0)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y0 <= -1.4e+81) {
		tmp = k * (z * (b * y0));
	} else if (y0 <= -2.5e-122) {
		tmp = c * (x * (y0 * y2));
	} else if (y0 <= -4e-228) {
		tmp = a * (x * (y1 * -y2));
	} else if (y0 <= -1.55e-253) {
		tmp = a * (y1 * (z * y3));
	} else if (y0 <= 4.4e+44) {
		tmp = c * ((z * t) * i);
	} else {
		tmp = b * (k * (z * y0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y0 <= (-1.4d+81)) then
        tmp = k * (z * (b * y0))
    else if (y0 <= (-2.5d-122)) then
        tmp = c * (x * (y0 * y2))
    else if (y0 <= (-4d-228)) then
        tmp = a * (x * (y1 * -y2))
    else if (y0 <= (-1.55d-253)) then
        tmp = a * (y1 * (z * y3))
    else if (y0 <= 4.4d+44) then
        tmp = c * ((z * t) * i)
    else
        tmp = b * (k * (z * y0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y0 <= -1.4e+81) {
		tmp = k * (z * (b * y0));
	} else if (y0 <= -2.5e-122) {
		tmp = c * (x * (y0 * y2));
	} else if (y0 <= -4e-228) {
		tmp = a * (x * (y1 * -y2));
	} else if (y0 <= -1.55e-253) {
		tmp = a * (y1 * (z * y3));
	} else if (y0 <= 4.4e+44) {
		tmp = c * ((z * t) * i);
	} else {
		tmp = b * (k * (z * y0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y0 <= -1.4e+81:
		tmp = k * (z * (b * y0))
	elif y0 <= -2.5e-122:
		tmp = c * (x * (y0 * y2))
	elif y0 <= -4e-228:
		tmp = a * (x * (y1 * -y2))
	elif y0 <= -1.55e-253:
		tmp = a * (y1 * (z * y3))
	elif y0 <= 4.4e+44:
		tmp = c * ((z * t) * i)
	else:
		tmp = b * (k * (z * y0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y0 <= -1.4e+81)
		tmp = Float64(k * Float64(z * Float64(b * y0)));
	elseif (y0 <= -2.5e-122)
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	elseif (y0 <= -4e-228)
		tmp = Float64(a * Float64(x * Float64(y1 * Float64(-y2))));
	elseif (y0 <= -1.55e-253)
		tmp = Float64(a * Float64(y1 * Float64(z * y3)));
	elseif (y0 <= 4.4e+44)
		tmp = Float64(c * Float64(Float64(z * t) * i));
	else
		tmp = Float64(b * Float64(k * Float64(z * y0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y0 <= -1.4e+81)
		tmp = k * (z * (b * y0));
	elseif (y0 <= -2.5e-122)
		tmp = c * (x * (y0 * y2));
	elseif (y0 <= -4e-228)
		tmp = a * (x * (y1 * -y2));
	elseif (y0 <= -1.55e-253)
		tmp = a * (y1 * (z * y3));
	elseif (y0 <= 4.4e+44)
		tmp = c * ((z * t) * i);
	else
		tmp = b * (k * (z * y0));
	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[y0, -1.4e+81], N[(k * N[(z * N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -2.5e-122], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -4e-228], N[(a * N[(x * N[(y1 * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1.55e-253], N[(a * N[(y1 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 4.4e+44], N[(c * N[(N[(z * t), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], N[(b * N[(k * N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y0 < -1.39999999999999997e81

   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%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around -inf 42.2%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   6. Taylor expanded in k around inf 47.9%

      \[\leadsto -1 \cdot \color{blue}{\left(k \cdot \left(z \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)} \]

   7. Taylor expanded in i around 0 42.9%

      \[\leadsto -1 \cdot \left(k \cdot \left(z \cdot \color{blue}{\left(-1 \cdot \left(b \cdot y0\right)\right)}\right)\right) \]
   8. Step-by-step derivation

      1. neg-mul-1 42.9%

         \[\leadsto -1 \cdot \left(k \cdot \left(z \cdot \color{blue}{\left(-b \cdot y0\right)}\right)\right) \]

      2. distribute-rgt-neg-in 42.9%

         \[\leadsto -1 \cdot \left(k \cdot \left(z \cdot \color{blue}{\left(b \cdot \left(-y0\right)\right)}\right)\right) \]

   9. Simplified 42.9%

      \[\leadsto -1 \cdot \left(k \cdot \left(z \cdot \color{blue}{\left(b \cdot \left(-y0\right)\right)}\right)\right) \]

   if -1.39999999999999997e81 < y0 < -2.4999999999999999e-122

   1. Initial program 31.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 25.9%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 33.0%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   5. Taylor expanded in c around inf 30.0%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]

   if -2.4999999999999999e-122 < y0 < -4.00000000000000013e-228

   1. Initial program 54.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 34.9%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 26.1%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   5. Taylor expanded in c around 0 30.5%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(x \cdot \left(y1 \cdot y2\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 30.5%

         \[\leadsto \color{blue}{-a \cdot \left(x \cdot \left(y1 \cdot y2\right)\right)} \]

      2. *-commutative 30.5%

         \[\leadsto -\color{blue}{\left(x \cdot \left(y1 \cdot y2\right)\right) \cdot a} \]

      3. distribute-rgt-neg-in 30.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y1 \cdot y2\right)\right) \cdot \left(-a\right)} \]

      4. *-commutative 30.5%

         \[\leadsto \left(x \cdot \color{blue}{\left(y2 \cdot y1\right)}\right) \cdot \left(-a\right) \]

   7. Simplified 30.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y2 \cdot y1\right)\right) \cdot \left(-a\right)} \]

   if -4.00000000000000013e-228 < y0 < -1.54999999999999998e-253

   1. Initial program 40.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 40.5%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 30.6%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in z around inf 41.0%

      \[\leadsto \color{blue}{a \cdot \left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 31.4%

         \[\leadsto \color{blue}{\left(a \cdot z\right) \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)} \]

      2. *-commutative 31.4%

         \[\leadsto \color{blue}{\left(z \cdot a\right)} \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right) \]

      3. +-commutative 31.4%

         \[\leadsto \left(z \cdot a\right) \cdot \color{blue}{\left(y1 \cdot y3 + -1 \cdot \left(b \cdot t\right)\right)} \]

      4. mul-1-neg 31.4%

         \[\leadsto \left(z \cdot a\right) \cdot \left(y1 \cdot y3 + \color{blue}{\left(-b \cdot t\right)}\right) \]

      5. unsub-neg 31.4%

         \[\leadsto \left(z \cdot a\right) \cdot \color{blue}{\left(y1 \cdot y3 - b \cdot t\right)} \]

   8. Simplified 31.4%

      \[\leadsto \color{blue}{\left(z \cdot a\right) \cdot \left(y1 \cdot y3 - b \cdot t\right)} \]

   9. Taylor expanded in y1 around inf 41.1%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]

   if -1.54999999999999998e-253 < y0 < 4.39999999999999991e44

   1. Initial program 27.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.3%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around -inf 32.9%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   6. Taylor expanded in t around inf 36.7%

      \[\leadsto -1 \cdot \color{blue}{\left(t \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 33.1%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

      2. *-commutative 33.1%

         \[\leadsto -1 \cdot \left(\left(t \cdot z\right) \cdot \left(\color{blue}{b \cdot a} - c \cdot i\right)\right) \]

   8. Simplified 33.1%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot \left(b \cdot a - c \cdot i\right)\right)} \]

   9. Taylor expanded in b around 0 25.6%

      \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(i \cdot \left(t \cdot z\right)\right)\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 25.6%

          \[\leadsto -1 \cdot \color{blue}{\left(\left(-1 \cdot c\right) \cdot \left(i \cdot \left(t \cdot z\right)\right)\right)} \]

       2. neg-mul-1 25.6%

          \[\leadsto -1 \cdot \left(\color{blue}{\left(-c\right)} \cdot \left(i \cdot \left(t \cdot z\right)\right)\right) \]

       3. *-commutative 25.6%

          \[\leadsto -1 \cdot \left(\left(-c\right) \cdot \left(i \cdot \color{blue}{\left(z \cdot t\right)}\right)\right) \]

   11. Simplified 25.6%

       \[\leadsto -1 \cdot \color{blue}{\left(\left(-c\right) \cdot \left(i \cdot \left(z \cdot t\right)\right)\right)} \]

   if 4.39999999999999991e44 < y0

   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 24.9%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around -inf 42.2%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   6. Taylor expanded in k around inf 46.4%

      \[\leadsto -1 \cdot \color{blue}{\left(k \cdot \left(z \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)} \]

   7. Taylor expanded in i around 0 42.4%

      \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot \left(b \cdot \left(k \cdot \left(y0 \cdot z\right)\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 42.4%

         \[\leadsto -1 \cdot \color{blue}{\left(-b \cdot \left(k \cdot \left(y0 \cdot z\right)\right)\right)} \]

      2. *-commutative 42.4%

         \[\leadsto -1 \cdot \left(-\color{blue}{\left(k \cdot \left(y0 \cdot z\right)\right) \cdot b}\right) \]

      3. distribute-rgt-neg-in 42.4%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(k \cdot \left(y0 \cdot z\right)\right) \cdot \left(-b\right)\right)} \]

      4. *-commutative 42.4%

         \[\leadsto -1 \cdot \left(\left(k \cdot \color{blue}{\left(z \cdot y0\right)}\right) \cdot \left(-b\right)\right) \]

   9. Simplified 42.4%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(k \cdot \left(z \cdot y0\right)\right) \cdot \left(-b\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 34.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -1.4 \cdot 10^{+81}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -2.5 \cdot 10^{-122}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq -4 \cdot 10^{-228}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y1 \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;y0 \leq -1.55 \cdot 10^{-253}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq 4.4 \cdot 10^{+44}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 31: 27.9% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{if}\;y0 \leq -3.6 \cdot 10^{+100}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -1.4 \cdot 10^{-181}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y0 \leq 1.75 \cdot 10^{-307}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(c \cdot i\right)\\ \mathbf{elif}\;y0 \leq 1.15 \cdot 10^{+71}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* b (- (* x y) (* z t))))))
   (if (<= y0 -3.6e+100)
     (* k (* z (* b y0)))
     (if (<= y0 -1.4e-181)
       t_1
       (if (<= y0 1.75e-307)
         (* (* z t) (* c i))
         (if (<= y0 1.15e+71) t_1 (* b (* k (* z y0)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (b * ((x * y) - (z * t)));
	double tmp;
	if (y0 <= -3.6e+100) {
		tmp = k * (z * (b * y0));
	} else if (y0 <= -1.4e-181) {
		tmp = t_1;
	} else if (y0 <= 1.75e-307) {
		tmp = (z * t) * (c * i);
	} else if (y0 <= 1.15e+71) {
		tmp = t_1;
	} else {
		tmp = b * (k * (z * y0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (b * ((x * y) - (z * t)))
    if (y0 <= (-3.6d+100)) then
        tmp = k * (z * (b * y0))
    else if (y0 <= (-1.4d-181)) then
        tmp = t_1
    else if (y0 <= 1.75d-307) then
        tmp = (z * t) * (c * i)
    else if (y0 <= 1.15d+71) then
        tmp = t_1
    else
        tmp = b * (k * (z * y0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (b * ((x * y) - (z * t)));
	double tmp;
	if (y0 <= -3.6e+100) {
		tmp = k * (z * (b * y0));
	} else if (y0 <= -1.4e-181) {
		tmp = t_1;
	} else if (y0 <= 1.75e-307) {
		tmp = (z * t) * (c * i);
	} else if (y0 <= 1.15e+71) {
		tmp = t_1;
	} else {
		tmp = b * (k * (z * y0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (b * ((x * y) - (z * t)))
	tmp = 0
	if y0 <= -3.6e+100:
		tmp = k * (z * (b * y0))
	elif y0 <= -1.4e-181:
		tmp = t_1
	elif y0 <= 1.75e-307:
		tmp = (z * t) * (c * i)
	elif y0 <= 1.15e+71:
		tmp = t_1
	else:
		tmp = b * (k * (z * y0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))))
	tmp = 0.0
	if (y0 <= -3.6e+100)
		tmp = Float64(k * Float64(z * Float64(b * y0)));
	elseif (y0 <= -1.4e-181)
		tmp = t_1;
	elseif (y0 <= 1.75e-307)
		tmp = Float64(Float64(z * t) * Float64(c * i));
	elseif (y0 <= 1.15e+71)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(k * Float64(z * y0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (b * ((x * y) - (z * t)));
	tmp = 0.0;
	if (y0 <= -3.6e+100)
		tmp = k * (z * (b * y0));
	elseif (y0 <= -1.4e-181)
		tmp = t_1;
	elseif (y0 <= 1.75e-307)
		tmp = (z * t) * (c * i);
	elseif (y0 <= 1.15e+71)
		tmp = t_1;
	else
		tmp = b * (k * (z * y0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -3.6e+100], N[(k * N[(z * N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1.4e-181], t$95$1, If[LessEqual[y0, 1.75e-307], N[(N[(z * t), $MachinePrecision] * N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.15e+71], t$95$1, N[(b * N[(k * N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y0 < -3.6e100

   1. Initial program 26.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 26.2%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around -inf 44.5%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   6. Taylor expanded in k around inf 52.6%

      \[\leadsto -1 \cdot \color{blue}{\left(k \cdot \left(z \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)} \]

   7. Taylor expanded in i around 0 47.0%

      \[\leadsto -1 \cdot \left(k \cdot \left(z \cdot \color{blue}{\left(-1 \cdot \left(b \cdot y0\right)\right)}\right)\right) \]
   8. Step-by-step derivation

      1. neg-mul-1 47.0%

         \[\leadsto -1 \cdot \left(k \cdot \left(z \cdot \color{blue}{\left(-b \cdot y0\right)}\right)\right) \]

      2. distribute-rgt-neg-in 47.0%

         \[\leadsto -1 \cdot \left(k \cdot \left(z \cdot \color{blue}{\left(b \cdot \left(-y0\right)\right)}\right)\right) \]

   9. Simplified 47.0%

      \[\leadsto -1 \cdot \left(k \cdot \left(z \cdot \color{blue}{\left(b \cdot \left(-y0\right)\right)}\right)\right) \]

   if -3.6e100 < y0 < -1.39999999999999993e-181 or 1.7500000000000001e-307 < y0 < 1.1500000000000001e71

   1. Initial program 30.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.4%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 35.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 31.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. neg-mul-1 31.2%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + x \cdot y\right)\right) \]

      2. +-commutative 31.2%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y + \left(-t \cdot z\right)\right)}\right) \]

      3. unsub-neg 31.2%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y - t \cdot z\right)}\right) \]

      4. *-commutative 31.2%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) \]

   8. Simplified 31.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   if -1.39999999999999993e-181 < y0 < 1.7500000000000001e-307

   1. Initial program 45.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 48.6%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around -inf 40.4%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   6. Taylor expanded in t around inf 37.6%

      \[\leadsto -1 \cdot \color{blue}{\left(t \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 37.6%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

      2. *-commutative 37.6%

         \[\leadsto -1 \cdot \left(\left(t \cdot z\right) \cdot \left(\color{blue}{b \cdot a} - c \cdot i\right)\right) \]

   8. Simplified 37.6%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot \left(b \cdot a - c \cdot i\right)\right)} \]

   9. Taylor expanded in b around 0 31.6%

      \[\leadsto -1 \cdot \left(\left(t \cdot z\right) \cdot \color{blue}{\left(-1 \cdot \left(c \cdot i\right)\right)}\right) \]
   10. Step-by-step derivation

       1. neg-mul-1 31.6%

          \[\leadsto -1 \cdot \left(\left(t \cdot z\right) \cdot \color{blue}{\left(-c \cdot i\right)}\right) \]

       2. distribute-rgt-neg-in 31.6%

          \[\leadsto -1 \cdot \left(\left(t \cdot z\right) \cdot \color{blue}{\left(c \cdot \left(-i\right)\right)}\right) \]

   11. Simplified 31.6%

       \[\leadsto -1 \cdot \left(\left(t \cdot z\right) \cdot \color{blue}{\left(c \cdot \left(-i\right)\right)}\right) \]

   if 1.1500000000000001e71 < y0

   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%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around -inf 43.3%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   6. Taylor expanded in k around inf 47.9%

      \[\leadsto -1 \cdot \color{blue}{\left(k \cdot \left(z \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)} \]

   7. Taylor expanded in i around 0 45.5%

      \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot \left(b \cdot \left(k \cdot \left(y0 \cdot z\right)\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 45.5%

         \[\leadsto -1 \cdot \color{blue}{\left(-b \cdot \left(k \cdot \left(y0 \cdot z\right)\right)\right)} \]

      2. *-commutative 45.5%

         \[\leadsto -1 \cdot \left(-\color{blue}{\left(k \cdot \left(y0 \cdot z\right)\right) \cdot b}\right) \]

      3. distribute-rgt-neg-in 45.5%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(k \cdot \left(y0 \cdot z\right)\right) \cdot \left(-b\right)\right)} \]

      4. *-commutative 45.5%

         \[\leadsto -1 \cdot \left(\left(k \cdot \color{blue}{\left(z \cdot y0\right)}\right) \cdot \left(-b\right)\right) \]

   9. Simplified 45.5%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(k \cdot \left(z \cdot y0\right)\right) \cdot \left(-b\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 37.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -3.6 \cdot 10^{+100}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -1.4 \cdot 10^{-181}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y0 \leq 1.75 \cdot 10^{-307}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(c \cdot i\right)\\ \mathbf{elif}\;y0 \leq 1.15 \cdot 10^{+71}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 32: 28.9% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y0 \leq -3.7 \cdot 10^{+98}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -4 \cdot 10^{-144}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 6 \cdot 10^{-306}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 5 \cdot 10^{+71}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y0 -3.7e+98)
   (* k (* z (* b y0)))
   (if (<= y0 -4e-144)
     (* a (* y (- (* x b) (* y3 y5))))
     (if (<= y0 6e-306)
       (* a (* y3 (- (* z y1) (* y y5))))
       (if (<= y0 5e+71)
         (* a (* b (- (* x y) (* z t))))
         (* b (* k (* z y0))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y0 <= -3.7e+98) {
		tmp = k * (z * (b * y0));
	} else if (y0 <= -4e-144) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (y0 <= 6e-306) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (y0 <= 5e+71) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = b * (k * (z * y0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y0 <= (-3.7d+98)) then
        tmp = k * (z * (b * y0))
    else if (y0 <= (-4d-144)) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (y0 <= 6d-306) then
        tmp = a * (y3 * ((z * y1) - (y * y5)))
    else if (y0 <= 5d+71) then
        tmp = a * (b * ((x * y) - (z * t)))
    else
        tmp = b * (k * (z * y0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y0 <= -3.7e+98) {
		tmp = k * (z * (b * y0));
	} else if (y0 <= -4e-144) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (y0 <= 6e-306) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (y0 <= 5e+71) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = b * (k * (z * y0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y0 <= -3.7e+98:
		tmp = k * (z * (b * y0))
	elif y0 <= -4e-144:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif y0 <= 6e-306:
		tmp = a * (y3 * ((z * y1) - (y * y5)))
	elif y0 <= 5e+71:
		tmp = a * (b * ((x * y) - (z * t)))
	else:
		tmp = b * (k * (z * y0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y0 <= -3.7e+98)
		tmp = Float64(k * Float64(z * Float64(b * y0)));
	elseif (y0 <= -4e-144)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (y0 <= 6e-306)
		tmp = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))));
	elseif (y0 <= 5e+71)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	else
		tmp = Float64(b * Float64(k * Float64(z * y0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y0 <= -3.7e+98)
		tmp = k * (z * (b * y0));
	elseif (y0 <= -4e-144)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (y0 <= 6e-306)
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	elseif (y0 <= 5e+71)
		tmp = a * (b * ((x * y) - (z * t)));
	else
		tmp = b * (k * (z * y0));
	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[y0, -3.7e+98], N[(k * N[(z * N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -4e-144], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 6e-306], N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 5e+71], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(k * N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y0 < -3.6999999999999999e98

   1. Initial program 26.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 26.2%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around -inf 44.5%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   6. Taylor expanded in k around inf 52.6%

      \[\leadsto -1 \cdot \color{blue}{\left(k \cdot \left(z \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)} \]

   7. Taylor expanded in i around 0 47.0%

      \[\leadsto -1 \cdot \left(k \cdot \left(z \cdot \color{blue}{\left(-1 \cdot \left(b \cdot y0\right)\right)}\right)\right) \]
   8. Step-by-step derivation

      1. neg-mul-1 47.0%

         \[\leadsto -1 \cdot \left(k \cdot \left(z \cdot \color{blue}{\left(-b \cdot y0\right)}\right)\right) \]

      2. distribute-rgt-neg-in 47.0%

         \[\leadsto -1 \cdot \left(k \cdot \left(z \cdot \color{blue}{\left(b \cdot \left(-y0\right)\right)}\right)\right) \]

   9. Simplified 47.0%

      \[\leadsto -1 \cdot \left(k \cdot \left(z \cdot \color{blue}{\left(b \cdot \left(-y0\right)\right)}\right)\right) \]

   if -3.6999999999999999e98 < y0 < -3.9999999999999998e-144

   1. Initial program 35.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 35.8%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 24.8%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in y around inf 30.1%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]

   if -3.9999999999999998e-144 < y0 < 6.00000000000000048e-306

   1. Initial program 40.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 43.0%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 32.8%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in y3 around inf 34.8%

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]

   if 6.00000000000000048e-306 < y0 < 4.99999999999999972e71

   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 28.3%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 32.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 31.4%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. neg-mul-1 31.4%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + x \cdot y\right)\right) \]

      2. +-commutative 31.4%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y + \left(-t \cdot z\right)\right)}\right) \]

      3. unsub-neg 31.4%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y - t \cdot z\right)}\right) \]

      4. *-commutative 31.4%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) \]

   8. Simplified 31.4%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   if 4.99999999999999972e71 < y0

   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%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around -inf 43.3%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   6. Taylor expanded in k around inf 47.9%

      \[\leadsto -1 \cdot \color{blue}{\left(k \cdot \left(z \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)} \]

   7. Taylor expanded in i around 0 45.5%

      \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot \left(b \cdot \left(k \cdot \left(y0 \cdot z\right)\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 45.5%

         \[\leadsto -1 \cdot \color{blue}{\left(-b \cdot \left(k \cdot \left(y0 \cdot z\right)\right)\right)} \]

      2. *-commutative 45.5%

         \[\leadsto -1 \cdot \left(-\color{blue}{\left(k \cdot \left(y0 \cdot z\right)\right) \cdot b}\right) \]

      3. distribute-rgt-neg-in 45.5%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(k \cdot \left(y0 \cdot z\right)\right) \cdot \left(-b\right)\right)} \]

      4. *-commutative 45.5%

         \[\leadsto -1 \cdot \left(\left(k \cdot \color{blue}{\left(z \cdot y0\right)}\right) \cdot \left(-b\right)\right) \]

   9. Simplified 45.5%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(k \cdot \left(z \cdot y0\right)\right) \cdot \left(-b\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -3.7 \cdot 10^{+98}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -4 \cdot 10^{-144}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 6 \cdot 10^{-306}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 5 \cdot 10^{+71}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 33: 29.4% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y0 \leq -2.8 \cdot 10^{+99}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -5 \cdot 10^{-146}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 2.2 \cdot 10^{-306}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 5 \cdot 10^{-36}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y0 -2.8e+99)
   (* k (* z (* b y0)))
   (if (<= y0 -5e-146)
     (* a (* y (- (* x b) (* y3 y5))))
     (if (<= y0 2.2e-306)
       (* a (* y3 (- (* z y1) (* y y5))))
       (if (<= y0 5e-36)
         (* a (* b (- (* x y) (* z t))))
         (* b (* x (- (* y a) (* j y0)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y0 <= -2.8e+99) {
		tmp = k * (z * (b * y0));
	} else if (y0 <= -5e-146) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (y0 <= 2.2e-306) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (y0 <= 5e-36) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = b * (x * ((y * a) - (j * y0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y0 <= (-2.8d+99)) then
        tmp = k * (z * (b * y0))
    else if (y0 <= (-5d-146)) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (y0 <= 2.2d-306) then
        tmp = a * (y3 * ((z * y1) - (y * y5)))
    else if (y0 <= 5d-36) then
        tmp = a * (b * ((x * y) - (z * t)))
    else
        tmp = b * (x * ((y * a) - (j * y0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y0 <= -2.8e+99) {
		tmp = k * (z * (b * y0));
	} else if (y0 <= -5e-146) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (y0 <= 2.2e-306) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (y0 <= 5e-36) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = b * (x * ((y * a) - (j * y0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y0 <= -2.8e+99:
		tmp = k * (z * (b * y0))
	elif y0 <= -5e-146:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif y0 <= 2.2e-306:
		tmp = a * (y3 * ((z * y1) - (y * y5)))
	elif y0 <= 5e-36:
		tmp = a * (b * ((x * y) - (z * t)))
	else:
		tmp = b * (x * ((y * a) - (j * y0)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y0 <= -2.8e+99)
		tmp = Float64(k * Float64(z * Float64(b * y0)));
	elseif (y0 <= -5e-146)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (y0 <= 2.2e-306)
		tmp = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))));
	elseif (y0 <= 5e-36)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	else
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y0 <= -2.8e+99)
		tmp = k * (z * (b * y0));
	elseif (y0 <= -5e-146)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (y0 <= 2.2e-306)
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	elseif (y0 <= 5e-36)
		tmp = a * (b * ((x * y) - (z * t)));
	else
		tmp = b * (x * ((y * a) - (j * y0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y0, -2.8e+99], N[(k * N[(z * N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -5e-146], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 2.2e-306], N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 5e-36], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y0 < -2.8e99

   1. Initial program 26.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 26.2%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around -inf 44.5%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   6. Taylor expanded in k around inf 52.6%

      \[\leadsto -1 \cdot \color{blue}{\left(k \cdot \left(z \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)} \]

   7. Taylor expanded in i around 0 47.0%

      \[\leadsto -1 \cdot \left(k \cdot \left(z \cdot \color{blue}{\left(-1 \cdot \left(b \cdot y0\right)\right)}\right)\right) \]
   8. Step-by-step derivation

      1. neg-mul-1 47.0%

         \[\leadsto -1 \cdot \left(k \cdot \left(z \cdot \color{blue}{\left(-b \cdot y0\right)}\right)\right) \]

      2. distribute-rgt-neg-in 47.0%

         \[\leadsto -1 \cdot \left(k \cdot \left(z \cdot \color{blue}{\left(b \cdot \left(-y0\right)\right)}\right)\right) \]

   9. Simplified 47.0%

      \[\leadsto -1 \cdot \left(k \cdot \left(z \cdot \color{blue}{\left(b \cdot \left(-y0\right)\right)}\right)\right) \]

   if -2.8e99 < y0 < -4.99999999999999957e-146

   1. Initial program 35.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 35.8%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 24.8%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in y around inf 30.1%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]

   if -4.99999999999999957e-146 < y0 < 2.20000000000000016e-306

   1. Initial program 40.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 43.0%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 32.8%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in y3 around inf 34.8%

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]

   if 2.20000000000000016e-306 < y0 < 5.00000000000000004e-36

   1. Initial program 30.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.4%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 33.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 32.4%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. neg-mul-1 32.4%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + x \cdot y\right)\right) \]

      2. +-commutative 32.4%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y + \left(-t \cdot z\right)\right)}\right) \]

      3. unsub-neg 32.4%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y - t \cdot z\right)}\right) \]

      4. *-commutative 32.4%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) \]

   8. Simplified 32.4%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   if 5.00000000000000004e-36 < y0

   1. Initial program 23.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 23.6%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 35.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 41.7%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 37.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -2.8 \cdot 10^{+99}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -5 \cdot 10^{-146}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 2.2 \cdot 10^{-306}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 5 \cdot 10^{-36}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 34: 20.3% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -620000:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-82}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+152}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(y1 \cdot \left(-a\right)\right)\right)\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{+269}:\\ \;\;\;\;a \cdot \left(\left(z \cdot t\right) \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot a\right) \cdot \left(y1 \cdot y3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= a -620000.0)
   (* a (* (* x y) b))
   (if (<= a 2.35e-82)
     (* x (* y2 (* c y0)))
     (if (<= a 1.65e+152)
       (* x (* y2 (* y1 (- a))))
       (if (<= a 1.12e+269) (* a (* (* z t) (- b))) (* (* z a) (* y1 y3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (a <= -620000.0) {
		tmp = a * ((x * y) * b);
	} else if (a <= 2.35e-82) {
		tmp = x * (y2 * (c * y0));
	} else if (a <= 1.65e+152) {
		tmp = x * (y2 * (y1 * -a));
	} else if (a <= 1.12e+269) {
		tmp = a * ((z * t) * -b);
	} else {
		tmp = (z * a) * (y1 * y3);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (a <= (-620000.0d0)) then
        tmp = a * ((x * y) * b)
    else if (a <= 2.35d-82) then
        tmp = x * (y2 * (c * y0))
    else if (a <= 1.65d+152) then
        tmp = x * (y2 * (y1 * -a))
    else if (a <= 1.12d+269) then
        tmp = a * ((z * t) * -b)
    else
        tmp = (z * a) * (y1 * y3)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (a <= -620000.0) {
		tmp = a * ((x * y) * b);
	} else if (a <= 2.35e-82) {
		tmp = x * (y2 * (c * y0));
	} else if (a <= 1.65e+152) {
		tmp = x * (y2 * (y1 * -a));
	} else if (a <= 1.12e+269) {
		tmp = a * ((z * t) * -b);
	} else {
		tmp = (z * a) * (y1 * y3);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if a <= -620000.0:
		tmp = a * ((x * y) * b)
	elif a <= 2.35e-82:
		tmp = x * (y2 * (c * y0))
	elif a <= 1.65e+152:
		tmp = x * (y2 * (y1 * -a))
	elif a <= 1.12e+269:
		tmp = a * ((z * t) * -b)
	else:
		tmp = (z * a) * (y1 * y3)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (a <= -620000.0)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	elseif (a <= 2.35e-82)
		tmp = Float64(x * Float64(y2 * Float64(c * y0)));
	elseif (a <= 1.65e+152)
		tmp = Float64(x * Float64(y2 * Float64(y1 * Float64(-a))));
	elseif (a <= 1.12e+269)
		tmp = Float64(a * Float64(Float64(z * t) * Float64(-b)));
	else
		tmp = Float64(Float64(z * a) * Float64(y1 * y3));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (a <= -620000.0)
		tmp = a * ((x * y) * b);
	elseif (a <= 2.35e-82)
		tmp = x * (y2 * (c * y0));
	elseif (a <= 1.65e+152)
		tmp = x * (y2 * (y1 * -a));
	elseif (a <= 1.12e+269)
		tmp = a * ((z * t) * -b);
	else
		tmp = (z * a) * (y1 * y3);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[a, -620000.0], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.35e-82], N[(x * N[(y2 * N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.65e+152], N[(x * N[(y2 * N[(y1 * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.12e+269], N[(a * N[(N[(z * t), $MachinePrecision] * (-b)), $MachinePrecision]), $MachinePrecision], N[(N[(z * a), $MachinePrecision] * N[(y1 * y3), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -6.2e5

   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 32.5%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 40.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 36.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. neg-mul-1 36.8%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + x \cdot y\right)\right) \]

      2. +-commutative 36.8%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y + \left(-t \cdot z\right)\right)}\right) \]

      3. unsub-neg 36.8%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y - t \cdot z\right)}\right) \]

      4. *-commutative 36.8%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) \]

   8. Simplified 36.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   9. Taylor expanded in y around inf 33.1%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 33.1%

          \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot b\right)} \]

   11. Simplified 33.1%

       \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot b\right)} \]

   if -6.2e5 < a < 2.35e-82

   1. Initial program 35.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 36.7%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 24.6%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   5. Taylor expanded in c around inf 23.0%

      \[\leadsto x \cdot \left(y2 \cdot \color{blue}{\left(c \cdot y0\right)}\right) \]

   if 2.35e-82 < a < 1.6500000000000001e152

   1. Initial program 25.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 33.6%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 41.4%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   5. Taylor expanded in c around 0 31.7%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot \left(y1 \cdot y2\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 31.7%

         \[\leadsto x \cdot \color{blue}{\left(-a \cdot \left(y1 \cdot y2\right)\right)} \]

      2. associate-*r* 36.1%

         \[\leadsto x \cdot \left(-\color{blue}{\left(a \cdot y1\right) \cdot y2}\right) \]

      3. distribute-rgt-neg-in 36.1%

         \[\leadsto x \cdot \color{blue}{\left(\left(a \cdot y1\right) \cdot \left(-y2\right)\right)} \]

   7. Simplified 36.1%

      \[\leadsto x \cdot \color{blue}{\left(\left(a \cdot y1\right) \cdot \left(-y2\right)\right)} \]

   if 1.6500000000000001e152 < a < 1.12e269

   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 23.1%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 49.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 40.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. neg-mul-1 40.0%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + x \cdot y\right)\right) \]

      2. +-commutative 40.0%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y + \left(-t \cdot z\right)\right)}\right) \]

      3. unsub-neg 40.0%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y - t \cdot z\right)}\right) \]

      4. *-commutative 40.0%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) \]

   8. Simplified 40.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   9. Taylor expanded in y around 0 38.4%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 38.4%

          \[\leadsto a \cdot \color{blue}{\left(-b \cdot \left(t \cdot z\right)\right)} \]

       2. *-commutative 38.4%

          \[\leadsto a \cdot \left(-\color{blue}{\left(t \cdot z\right) \cdot b}\right) \]

       3. distribute-rgt-neg-in 38.4%

          \[\leadsto a \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot \left(-b\right)\right)} \]

       4. *-commutative 38.4%

          \[\leadsto a \cdot \left(\color{blue}{\left(z \cdot t\right)} \cdot \left(-b\right)\right) \]

   11. Simplified 38.4%

       \[\leadsto a \cdot \color{blue}{\left(\left(z \cdot t\right) \cdot \left(-b\right)\right)} \]

   if 1.12e269 < a

   1. Initial program 6.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 6.7%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 67.2%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in z around inf 47.3%

      \[\leadsto \color{blue}{a \cdot \left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 47.3%

         \[\leadsto \color{blue}{\left(a \cdot z\right) \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)} \]

      2. *-commutative 47.3%

         \[\leadsto \color{blue}{\left(z \cdot a\right)} \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right) \]

      3. +-commutative 47.3%

         \[\leadsto \left(z \cdot a\right) \cdot \color{blue}{\left(y1 \cdot y3 + -1 \cdot \left(b \cdot t\right)\right)} \]

      4. mul-1-neg 47.3%

         \[\leadsto \left(z \cdot a\right) \cdot \left(y1 \cdot y3 + \color{blue}{\left(-b \cdot t\right)}\right) \]

      5. unsub-neg 47.3%

         \[\leadsto \left(z \cdot a\right) \cdot \color{blue}{\left(y1 \cdot y3 - b \cdot t\right)} \]

   8. Simplified 47.3%

      \[\leadsto \color{blue}{\left(z \cdot a\right) \cdot \left(y1 \cdot y3 - b \cdot t\right)} \]

   9. Taylor expanded in y1 around inf 53.8%

      \[\leadsto \left(z \cdot a\right) \cdot \color{blue}{\left(y1 \cdot y3\right)} \]
   10. Step-by-step derivation

       1. *-commutative 53.8%

          \[\leadsto \left(z \cdot a\right) \cdot \color{blue}{\left(y3 \cdot y1\right)} \]

   11. Simplified 53.8%

       \[\leadsto \left(z \cdot a\right) \cdot \color{blue}{\left(y3 \cdot y1\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 30.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -620000:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-82}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+152}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(y1 \cdot \left(-a\right)\right)\right)\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{+269}:\\ \;\;\;\;a \cdot \left(\left(z \cdot t\right) \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot a\right) \cdot \left(y1 \cdot y3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 35: 26.4% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+24}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{-299}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+84}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+271}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(z \cdot t\right) \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= t -2.6e+24)
   (* a (* b (- (* x y) (* z t))))
   (if (<= t 2.15e-299)
     (* b (* k (* z y0)))
     (if (<= t 3.5e+84)
       (* a (* y (- (* x b) (* y3 y5))))
       (if (<= t 1.2e+271) (* c (* (* z t) i)) (* a (* (* z 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 tmp;
	if (t <= -2.6e+24) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (t <= 2.15e-299) {
		tmp = b * (k * (z * y0));
	} else if (t <= 3.5e+84) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (t <= 1.2e+271) {
		tmp = c * ((z * t) * i);
	} else {
		tmp = a * ((z * 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) :: tmp
    if (t <= (-2.6d+24)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (t <= 2.15d-299) then
        tmp = b * (k * (z * y0))
    else if (t <= 3.5d+84) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (t <= 1.2d+271) then
        tmp = c * ((z * t) * i)
    else
        tmp = a * ((z * 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 tmp;
	if (t <= -2.6e+24) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (t <= 2.15e-299) {
		tmp = b * (k * (z * y0));
	} else if (t <= 3.5e+84) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (t <= 1.2e+271) {
		tmp = c * ((z * t) * i);
	} else {
		tmp = a * ((z * t) * -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 t <= -2.6e+24:
		tmp = a * (b * ((x * y) - (z * t)))
	elif t <= 2.15e-299:
		tmp = b * (k * (z * y0))
	elif t <= 3.5e+84:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif t <= 1.2e+271:
		tmp = c * ((z * t) * i)
	else:
		tmp = a * ((z * t) * -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 (t <= -2.6e+24)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (t <= 2.15e-299)
		tmp = Float64(b * Float64(k * Float64(z * y0)));
	elseif (t <= 3.5e+84)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (t <= 1.2e+271)
		tmp = Float64(c * Float64(Float64(z * t) * i));
	else
		tmp = Float64(a * Float64(Float64(z * t) * Float64(-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 (t <= -2.6e+24)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (t <= 2.15e-299)
		tmp = b * (k * (z * y0));
	elseif (t <= 3.5e+84)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (t <= 1.2e+271)
		tmp = c * ((z * t) * i);
	else
		tmp = a * ((z * 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_] := If[LessEqual[t, -2.6e+24], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.15e-299], N[(b * N[(k * N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e+84], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e+271], N[(c * N[(N[(z * t), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(z * t), $MachinePrecision] * (-b)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.5999999999999998e24

   1. Initial program 26.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 26.7%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 36.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 37.4%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. neg-mul-1 37.4%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + x \cdot y\right)\right) \]

      2. +-commutative 37.4%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y + \left(-t \cdot z\right)\right)}\right) \]

      3. unsub-neg 37.4%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y - t \cdot z\right)}\right) \]

      4. *-commutative 37.4%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) \]

   8. Simplified 37.4%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   if -2.5999999999999998e24 < t < 2.1499999999999999e-299

   1. Initial program 33.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 33.7%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around -inf 33.4%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   6. Taylor expanded in k around inf 39.3%

      \[\leadsto -1 \cdot \color{blue}{\left(k \cdot \left(z \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)} \]

   7. Taylor expanded in i around 0 37.7%

      \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot \left(b \cdot \left(k \cdot \left(y0 \cdot z\right)\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 37.7%

         \[\leadsto -1 \cdot \color{blue}{\left(-b \cdot \left(k \cdot \left(y0 \cdot z\right)\right)\right)} \]

      2. *-commutative 37.7%

         \[\leadsto -1 \cdot \left(-\color{blue}{\left(k \cdot \left(y0 \cdot z\right)\right) \cdot b}\right) \]

      3. distribute-rgt-neg-in 37.7%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(k \cdot \left(y0 \cdot z\right)\right) \cdot \left(-b\right)\right)} \]

      4. *-commutative 37.7%

         \[\leadsto -1 \cdot \left(\left(k \cdot \color{blue}{\left(z \cdot y0\right)}\right) \cdot \left(-b\right)\right) \]

   9. Simplified 37.7%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(k \cdot \left(z \cdot y0\right)\right) \cdot \left(-b\right)\right)} \]

   if 2.1499999999999999e-299 < t < 3.4999999999999999e84

   1. Initial program 35.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 35.9%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 32.4%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in y around inf 27.9%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]

   if 3.4999999999999999e84 < t < 1.20000000000000006e271

   1. Initial program 17.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 20.2%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around -inf 47.7%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   6. Taylor expanded in t around inf 51.2%

      \[\leadsto -1 \cdot \color{blue}{\left(t \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 51.2%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

      2. *-commutative 51.2%

         \[\leadsto -1 \cdot \left(\left(t \cdot z\right) \cdot \left(\color{blue}{b \cdot a} - c \cdot i\right)\right) \]

   8. Simplified 51.2%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot \left(b \cdot a - c \cdot i\right)\right)} \]

   9. Taylor expanded in b around 0 45.8%

      \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(i \cdot \left(t \cdot z\right)\right)\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 45.8%

          \[\leadsto -1 \cdot \color{blue}{\left(\left(-1 \cdot c\right) \cdot \left(i \cdot \left(t \cdot z\right)\right)\right)} \]

       2. neg-mul-1 45.8%

          \[\leadsto -1 \cdot \left(\color{blue}{\left(-c\right)} \cdot \left(i \cdot \left(t \cdot z\right)\right)\right) \]

       3. *-commutative 45.8%

          \[\leadsto -1 \cdot \left(\left(-c\right) \cdot \left(i \cdot \color{blue}{\left(z \cdot t\right)}\right)\right) \]

   11. Simplified 45.8%

       \[\leadsto -1 \cdot \color{blue}{\left(\left(-c\right) \cdot \left(i \cdot \left(z \cdot t\right)\right)\right)} \]

   if 1.20000000000000006e271 < t

   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%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 59.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 70.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. neg-mul-1 70.0%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + x \cdot y\right)\right) \]

      2. +-commutative 70.0%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y + \left(-t \cdot z\right)\right)}\right) \]

      3. unsub-neg 70.0%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y - t \cdot z\right)}\right) \]

      4. *-commutative 70.0%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) \]

   8. Simplified 70.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   9. Taylor expanded in y around 0 80.0%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 80.0%

          \[\leadsto a \cdot \color{blue}{\left(-b \cdot \left(t \cdot z\right)\right)} \]

       2. *-commutative 80.0%

          \[\leadsto a \cdot \left(-\color{blue}{\left(t \cdot z\right) \cdot b}\right) \]

       3. distribute-rgt-neg-in 80.0%

          \[\leadsto a \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot \left(-b\right)\right)} \]

       4. *-commutative 80.0%

          \[\leadsto a \cdot \left(\color{blue}{\left(z \cdot t\right)} \cdot \left(-b\right)\right) \]

   11. Simplified 80.0%

       \[\leadsto a \cdot \color{blue}{\left(\left(z \cdot t\right) \cdot \left(-b\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+24}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{-299}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+84}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+271}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(z \cdot t\right) \cdot \left(-b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 36: 22.5% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ t_2 := a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{if}\;y3 \leq -1.95 \cdot 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y3 \leq 2.9 \cdot 10^{-221}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y3 \leq 6 \cdot 10^{-168}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 4.4 \cdot 10^{-16}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y1 (* z y3)))) (t_2 (* a (* (* x y) b))))
   (if (<= y3 -1.95e+95)
     t_1
     (if (<= y3 2.9e-221)
       t_2
       (if (<= y3 6e-168)
         (* b (* j (* t y4)))
         (if (<= y3 4.4e-16) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y1 * (z * y3));
	double t_2 = a * ((x * y) * b);
	double tmp;
	if (y3 <= -1.95e+95) {
		tmp = t_1;
	} else if (y3 <= 2.9e-221) {
		tmp = t_2;
	} else if (y3 <= 6e-168) {
		tmp = b * (j * (t * y4));
	} else if (y3 <= 4.4e-16) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (y1 * (z * y3))
    t_2 = a * ((x * y) * b)
    if (y3 <= (-1.95d+95)) then
        tmp = t_1
    else if (y3 <= 2.9d-221) then
        tmp = t_2
    else if (y3 <= 6d-168) then
        tmp = b * (j * (t * y4))
    else if (y3 <= 4.4d-16) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y1 * (z * y3));
	double t_2 = a * ((x * y) * b);
	double tmp;
	if (y3 <= -1.95e+95) {
		tmp = t_1;
	} else if (y3 <= 2.9e-221) {
		tmp = t_2;
	} else if (y3 <= 6e-168) {
		tmp = b * (j * (t * y4));
	} else if (y3 <= 4.4e-16) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y1 * (z * y3))
	t_2 = a * ((x * y) * b)
	tmp = 0
	if y3 <= -1.95e+95:
		tmp = t_1
	elif y3 <= 2.9e-221:
		tmp = t_2
	elif y3 <= 6e-168:
		tmp = b * (j * (t * y4))
	elif y3 <= 4.4e-16:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y1 * Float64(z * y3)))
	t_2 = Float64(a * Float64(Float64(x * y) * b))
	tmp = 0.0
	if (y3 <= -1.95e+95)
		tmp = t_1;
	elseif (y3 <= 2.9e-221)
		tmp = t_2;
	elseif (y3 <= 6e-168)
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	elseif (y3 <= 4.4e-16)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y1 * (z * y3));
	t_2 = a * ((x * y) * b);
	tmp = 0.0;
	if (y3 <= -1.95e+95)
		tmp = t_1;
	elseif (y3 <= 2.9e-221)
		tmp = t_2;
	elseif (y3 <= 6e-168)
		tmp = b * (j * (t * y4));
	elseif (y3 <= 4.4e-16)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y1 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -1.95e+95], t$95$1, If[LessEqual[y3, 2.9e-221], t$95$2, If[LessEqual[y3, 6e-168], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 4.4e-16], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y3 < -1.9499999999999999e95 or 4.40000000000000001e-16 < y3

   1. Initial program 25.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.1%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 31.7%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in z around inf 33.2%

      \[\leadsto \color{blue}{a \cdot \left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 28.7%

         \[\leadsto \color{blue}{\left(a \cdot z\right) \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)} \]

      2. *-commutative 28.7%

         \[\leadsto \color{blue}{\left(z \cdot a\right)} \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right) \]

      3. +-commutative 28.7%

         \[\leadsto \left(z \cdot a\right) \cdot \color{blue}{\left(y1 \cdot y3 + -1 \cdot \left(b \cdot t\right)\right)} \]

      4. mul-1-neg 28.7%

         \[\leadsto \left(z \cdot a\right) \cdot \left(y1 \cdot y3 + \color{blue}{\left(-b \cdot t\right)}\right) \]

      5. unsub-neg 28.7%

         \[\leadsto \left(z \cdot a\right) \cdot \color{blue}{\left(y1 \cdot y3 - b \cdot t\right)} \]

   8. Simplified 28.7%

      \[\leadsto \color{blue}{\left(z \cdot a\right) \cdot \left(y1 \cdot y3 - b \cdot t\right)} \]

   9. Taylor expanded in y1 around inf 26.8%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]

   if -1.9499999999999999e95 < y3 < 2.89999999999999994e-221 or 5.99999999999999983e-168 < y3 < 4.40000000000000001e-16

   1. Initial program 34.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 35.0%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 42.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 29.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. neg-mul-1 29.3%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + x \cdot y\right)\right) \]

      2. +-commutative 29.3%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y + \left(-t \cdot z\right)\right)}\right) \]

      3. unsub-neg 29.3%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y - t \cdot z\right)}\right) \]

      4. *-commutative 29.3%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) \]

   8. Simplified 29.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   9. Taylor expanded in y around inf 25.9%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 25.9%

          \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot b\right)} \]

   11. Simplified 25.9%

       \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot b\right)} \]

   if 2.89999999999999994e-221 < y3 < 5.99999999999999983e-168

   1. Initial program 33.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 33.3%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 42.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in t around inf 42.2%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 33.8%

         \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)} \]

      2. +-commutative 33.8%

         \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{\left(j \cdot y4 + -1 \cdot \left(a \cdot z\right)\right)} \]

      3. mul-1-neg 33.8%

         \[\leadsto \left(b \cdot t\right) \cdot \left(j \cdot y4 + \color{blue}{\left(-a \cdot z\right)}\right) \]

      4. unsub-neg 33.8%

         \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{\left(j \cdot y4 - a \cdot z\right)} \]

      5. *-commutative 33.8%

         \[\leadsto \left(b \cdot t\right) \cdot \left(\color{blue}{y4 \cdot j} - a \cdot z\right) \]

      6. *-commutative 33.8%

         \[\leadsto \left(b \cdot t\right) \cdot \left(y4 \cdot j - \color{blue}{z \cdot a}\right) \]

   8. Simplified 33.8%

      \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \left(y4 \cdot j - z \cdot a\right)} \]

   9. Taylor expanded in y4 around inf 42.8%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 42.8%

          \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   11. Simplified 42.8%

       \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 27.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -1.95 \cdot 10^{+95}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{elif}\;y3 \leq 2.9 \cdot 10^{-221}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y3 \leq 6 \cdot 10^{-168}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 4.4 \cdot 10^{-16}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 37: 20.6% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8200000:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;a \leq 2.75 \cdot 10^{-53}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+159}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot a\right) \cdot \left(y1 \cdot y3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= a -8200000.0)
   (* a (* (* x y) b))
   (if (<= a 2.75e-53)
     (* x (* y2 (* c y0)))
     (if (<= a 2e+159) (* (* x y) (* a b)) (* (* z a) (* y1 y3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (a <= -8200000.0) {
		tmp = a * ((x * y) * b);
	} else if (a <= 2.75e-53) {
		tmp = x * (y2 * (c * y0));
	} else if (a <= 2e+159) {
		tmp = (x * y) * (a * b);
	} else {
		tmp = (z * a) * (y1 * y3);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (a <= (-8200000.0d0)) then
        tmp = a * ((x * y) * b)
    else if (a <= 2.75d-53) then
        tmp = x * (y2 * (c * y0))
    else if (a <= 2d+159) then
        tmp = (x * y) * (a * b)
    else
        tmp = (z * a) * (y1 * y3)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (a <= -8200000.0) {
		tmp = a * ((x * y) * b);
	} else if (a <= 2.75e-53) {
		tmp = x * (y2 * (c * y0));
	} else if (a <= 2e+159) {
		tmp = (x * y) * (a * b);
	} else {
		tmp = (z * a) * (y1 * y3);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if a <= -8200000.0:
		tmp = a * ((x * y) * b)
	elif a <= 2.75e-53:
		tmp = x * (y2 * (c * y0))
	elif a <= 2e+159:
		tmp = (x * y) * (a * b)
	else:
		tmp = (z * a) * (y1 * y3)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (a <= -8200000.0)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	elseif (a <= 2.75e-53)
		tmp = Float64(x * Float64(y2 * Float64(c * y0)));
	elseif (a <= 2e+159)
		tmp = Float64(Float64(x * y) * Float64(a * b));
	else
		tmp = Float64(Float64(z * a) * Float64(y1 * y3));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (a <= -8200000.0)
		tmp = a * ((x * y) * b);
	elseif (a <= 2.75e-53)
		tmp = x * (y2 * (c * y0));
	elseif (a <= 2e+159)
		tmp = (x * y) * (a * b);
	else
		tmp = (z * a) * (y1 * y3);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[a, -8200000.0], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.75e-53], N[(x * N[(y2 * N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2e+159], N[(N[(x * y), $MachinePrecision] * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(N[(z * a), $MachinePrecision] * N[(y1 * y3), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -8.2e6

   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 32.5%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 40.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 36.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. neg-mul-1 36.8%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + x \cdot y\right)\right) \]

      2. +-commutative 36.8%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y + \left(-t \cdot z\right)\right)}\right) \]

      3. unsub-neg 36.8%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y - t \cdot z\right)}\right) \]

      4. *-commutative 36.8%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) \]

   8. Simplified 36.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   9. Taylor expanded in y around inf 33.1%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 33.1%

          \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot b\right)} \]

   11. Simplified 33.1%

       \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot b\right)} \]

   if -8.2e6 < a < 2.75000000000000011e-53

   1. Initial program 35.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 36.7%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 25.6%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   5. Taylor expanded in c around inf 23.3%

      \[\leadsto x \cdot \left(y2 \cdot \color{blue}{\left(c \cdot y0\right)}\right) \]

   if 2.75000000000000011e-53 < a < 1.9999999999999999e159

   1. Initial program 23.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 23.5%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 27.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 30.7%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. neg-mul-1 30.7%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + x \cdot y\right)\right) \]

      2. +-commutative 30.7%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y + \left(-t \cdot z\right)\right)}\right) \]

      3. unsub-neg 30.7%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y - t \cdot z\right)}\right) \]

      4. *-commutative 30.7%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) \]

   8. Simplified 30.7%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   9. Taylor expanded in y around inf 25.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 27.3%

          \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot \left(x \cdot y\right)} \]

   11. Simplified 27.3%

       \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot \left(x \cdot y\right)} \]

   if 1.9999999999999999e159 < a

   1. Initial program 15.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 15.0%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 56.7%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in z around inf 45.3%

      \[\leadsto \color{blue}{a \cdot \left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 45.3%

         \[\leadsto \color{blue}{\left(a \cdot z\right) \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)} \]

      2. *-commutative 45.3%

         \[\leadsto \color{blue}{\left(z \cdot a\right)} \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right) \]

      3. +-commutative 45.3%

         \[\leadsto \left(z \cdot a\right) \cdot \color{blue}{\left(y1 \cdot y3 + -1 \cdot \left(b \cdot t\right)\right)} \]

      4. mul-1-neg 45.3%

         \[\leadsto \left(z \cdot a\right) \cdot \left(y1 \cdot y3 + \color{blue}{\left(-b \cdot t\right)}\right) \]

      5. unsub-neg 45.3%

         \[\leadsto \left(z \cdot a\right) \cdot \color{blue}{\left(y1 \cdot y3 - b \cdot t\right)} \]

   8. Simplified 45.3%

      \[\leadsto \color{blue}{\left(z \cdot a\right) \cdot \left(y1 \cdot y3 - b \cdot t\right)} \]

   9. Taylor expanded in y1 around inf 33.3%

      \[\leadsto \left(z \cdot a\right) \cdot \color{blue}{\left(y1 \cdot y3\right)} \]
   10. Step-by-step derivation

       1. *-commutative 33.3%

          \[\leadsto \left(z \cdot a\right) \cdot \color{blue}{\left(y3 \cdot y1\right)} \]

   11. Simplified 33.3%

       \[\leadsto \left(z \cdot a\right) \cdot \color{blue}{\left(y3 \cdot y1\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 27.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8200000:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;a \leq 2.75 \cdot 10^{-53}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+159}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot a\right) \cdot \left(y1 \cdot y3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 38: 19.9% accurate, 5.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1300000000:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;a \leq 3.75:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(z \cdot t\right) \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= a -1300000000.0)
   (* a (* (* x y) b))
   (if (<= a 3.75) (* x (* y2 (* c y0))) (* a (* (* z 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 tmp;
	if (a <= -1300000000.0) {
		tmp = a * ((x * y) * b);
	} else if (a <= 3.75) {
		tmp = x * (y2 * (c * y0));
	} else {
		tmp = a * ((z * 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) :: tmp
    if (a <= (-1300000000.0d0)) then
        tmp = a * ((x * y) * b)
    else if (a <= 3.75d0) then
        tmp = x * (y2 * (c * y0))
    else
        tmp = a * ((z * 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 tmp;
	if (a <= -1300000000.0) {
		tmp = a * ((x * y) * b);
	} else if (a <= 3.75) {
		tmp = x * (y2 * (c * y0));
	} else {
		tmp = a * ((z * t) * -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 a <= -1300000000.0:
		tmp = a * ((x * y) * b)
	elif a <= 3.75:
		tmp = x * (y2 * (c * y0))
	else:
		tmp = a * ((z * t) * -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 (a <= -1300000000.0)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	elseif (a <= 3.75)
		tmp = Float64(x * Float64(y2 * Float64(c * y0)));
	else
		tmp = Float64(a * Float64(Float64(z * t) * Float64(-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 (a <= -1300000000.0)
		tmp = a * ((x * y) * b);
	elseif (a <= 3.75)
		tmp = x * (y2 * (c * y0));
	else
		tmp = a * ((z * 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_] := If[LessEqual[a, -1300000000.0], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.75], N[(x * N[(y2 * N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(z * t), $MachinePrecision] * (-b)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.3e9

   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 32.5%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 40.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 36.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. neg-mul-1 36.8%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + x \cdot y\right)\right) \]

      2. +-commutative 36.8%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y + \left(-t \cdot z\right)\right)}\right) \]

      3. unsub-neg 36.8%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y - t \cdot z\right)}\right) \]

      4. *-commutative 36.8%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) \]

   8. Simplified 36.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   9. Taylor expanded in y around inf 33.1%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 33.1%

          \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot b\right)} \]

   11. Simplified 33.1%

       \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot b\right)} \]

   if -1.3e9 < a < 3.75

   1. Initial program 35.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 36.1%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 25.8%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   5. Taylor expanded in c around inf 22.1%

      \[\leadsto x \cdot \left(y2 \cdot \color{blue}{\left(c \cdot y0\right)}\right) \]

   if 3.75 < a

   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 19.1%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 37.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 37.1%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. neg-mul-1 37.1%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + x \cdot y\right)\right) \]

      2. +-commutative 37.1%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y + \left(-t \cdot z\right)\right)}\right) \]

      3. unsub-neg 37.1%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y - t \cdot z\right)}\right) \]

      4. *-commutative 37.1%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) \]

   8. Simplified 37.1%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   9. Taylor expanded in y around 0 27.8%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 27.8%

          \[\leadsto a \cdot \color{blue}{\left(-b \cdot \left(t \cdot z\right)\right)} \]

       2. *-commutative 27.8%

          \[\leadsto a \cdot \left(-\color{blue}{\left(t \cdot z\right) \cdot b}\right) \]

       3. distribute-rgt-neg-in 27.8%

          \[\leadsto a \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot \left(-b\right)\right)} \]

       4. *-commutative 27.8%

          \[\leadsto a \cdot \left(\color{blue}{\left(z \cdot t\right)} \cdot \left(-b\right)\right) \]

   11. Simplified 27.8%

       \[\leadsto a \cdot \color{blue}{\left(\left(z \cdot t\right) \cdot \left(-b\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 26.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1300000000:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;a \leq 3.75:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(z \cdot t\right) \cdot \left(-b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 39: 22.4% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y3 \leq -1.15 \cdot 10^{+97} \lor \neg \left(y3 \leq 2.4 \cdot 10^{-17}\right):\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= y3 -1.15e+97) (not (<= y3 2.4e-17)))
   (* a (* y1 (* z y3)))
   (* 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 ((y3 <= -1.15e+97) || !(y3 <= 2.4e-17)) {
		tmp = a * (y1 * (z * y3));
	} 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 ((y3 <= (-1.15d+97)) .or. (.not. (y3 <= 2.4d-17))) then
        tmp = a * (y1 * (z * y3))
    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 ((y3 <= -1.15e+97) || !(y3 <= 2.4e-17)) {
		tmp = a * (y1 * (z * y3));
	} 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 (y3 <= -1.15e+97) or not (y3 <= 2.4e-17):
		tmp = a * (y1 * (z * y3))
	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 ((y3 <= -1.15e+97) || !(y3 <= 2.4e-17))
		tmp = Float64(a * Float64(y1 * Float64(z * y3)));
	else
		tmp = Float64(a * Float64(Float64(x * y) * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((y3 <= -1.15e+97) || ~((y3 <= 2.4e-17)))
		tmp = a * (y1 * (z * y3));
	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[y3, -1.15e+97], N[Not[LessEqual[y3, 2.4e-17]], $MachinePrecision]], N[(a * N[(y1 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y3 < -1.15000000000000003e97 or 2.39999999999999986e-17 < y3

   1. Initial program 25.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.1%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 31.7%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in z around inf 33.2%

      \[\leadsto \color{blue}{a \cdot \left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 28.7%

         \[\leadsto \color{blue}{\left(a \cdot z\right) \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)} \]

      2. *-commutative 28.7%

         \[\leadsto \color{blue}{\left(z \cdot a\right)} \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right) \]

      3. +-commutative 28.7%

         \[\leadsto \left(z \cdot a\right) \cdot \color{blue}{\left(y1 \cdot y3 + -1 \cdot \left(b \cdot t\right)\right)} \]

      4. mul-1-neg 28.7%

         \[\leadsto \left(z \cdot a\right) \cdot \left(y1 \cdot y3 + \color{blue}{\left(-b \cdot t\right)}\right) \]

      5. unsub-neg 28.7%

         \[\leadsto \left(z \cdot a\right) \cdot \color{blue}{\left(y1 \cdot y3 - b \cdot t\right)} \]

   8. Simplified 28.7%

      \[\leadsto \color{blue}{\left(z \cdot a\right) \cdot \left(y1 \cdot y3 - b \cdot t\right)} \]

   9. Taylor expanded in y1 around inf 26.8%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]

   if -1.15000000000000003e97 < y3 < 2.39999999999999986e-17

   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 34.9%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 42.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 27.6%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. neg-mul-1 27.6%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + x \cdot y\right)\right) \]

      2. +-commutative 27.6%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y + \left(-t \cdot z\right)\right)}\right) \]

      3. unsub-neg 27.6%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y - t \cdot z\right)}\right) \]

      4. *-commutative 27.6%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) \]

   8. Simplified 27.6%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   9. Taylor expanded in y around inf 23.9%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 23.9%

          \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot b\right)} \]

   11. Simplified 23.9%

       \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 25.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -1.15 \cdot 10^{+97} \lor \neg \left(y3 \leq 2.4 \cdot 10^{-17}\right):\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 40: 22.3% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -0.0023 \lor \neg \left(y2 \leq 1.65 \cdot 10^{-28}\right):\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= y2 -0.0023) (not (<= y2 1.65e-28)))
   (* c (* x (* y0 y2)))
   (* a (* (* x y) b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y2 <= -0.0023) || !(y2 <= 1.65e-28)) {
		tmp = c * (x * (y0 * y2));
	} else {
		tmp = a * ((x * y) * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((y2 <= (-0.0023d0)) .or. (.not. (y2 <= 1.65d-28))) then
        tmp = c * (x * (y0 * y2))
    else
        tmp = a * ((x * y) * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y2 <= -0.0023) || !(y2 <= 1.65e-28)) {
		tmp = c * (x * (y0 * y2));
	} else {
		tmp = a * ((x * y) * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (y2 <= -0.0023) or not (y2 <= 1.65e-28):
		tmp = c * (x * (y0 * y2))
	else:
		tmp = a * ((x * y) * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((y2 <= -0.0023) || !(y2 <= 1.65e-28))
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	else
		tmp = Float64(a * Float64(Float64(x * y) * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((y2 <= -0.0023) || ~((y2 <= 1.65e-28)))
		tmp = c * (x * (y0 * y2));
	else
		tmp = a * ((x * y) * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[y2, -0.0023], N[Not[LessEqual[y2, 1.65e-28]], $MachinePrecision]], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y2 < -0.0023 or 1.6500000000000001e-28 < y2

   1. Initial program 29.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 44.6%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 36.2%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   5. Taylor expanded in c around inf 26.2%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]

   if -0.0023 < y2 < 1.6500000000000001e-28

   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 32.3%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 41.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 30.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. neg-mul-1 30.8%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + x \cdot y\right)\right) \]

      2. +-commutative 30.8%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y + \left(-t \cdot z\right)\right)}\right) \]

      3. unsub-neg 30.8%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y - t \cdot z\right)}\right) \]

      4. *-commutative 30.8%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) \]

   8. Simplified 30.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   9. Taylor expanded in y around inf 24.2%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 24.2%

          \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot b\right)} \]

   11. Simplified 24.2%

       \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 25.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -0.0023 \lor \neg \left(y2 \leq 1.65 \cdot 10^{-28}\right):\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 41: 20.6% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -17000000:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-53}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= a -17000000.0)
   (* a (* (* x y) b))
   (if (<= a 3.3e-53) (* x (* y2 (* c y0))) (* (* x y) (* a 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 (a <= -17000000.0) {
		tmp = a * ((x * y) * b);
	} else if (a <= 3.3e-53) {
		tmp = x * (y2 * (c * y0));
	} else {
		tmp = (x * y) * (a * 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 (a <= (-17000000.0d0)) then
        tmp = a * ((x * y) * b)
    else if (a <= 3.3d-53) then
        tmp = x * (y2 * (c * y0))
    else
        tmp = (x * y) * (a * 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 (a <= -17000000.0) {
		tmp = a * ((x * y) * b);
	} else if (a <= 3.3e-53) {
		tmp = x * (y2 * (c * y0));
	} else {
		tmp = (x * y) * (a * 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 a <= -17000000.0:
		tmp = a * ((x * y) * b)
	elif a <= 3.3e-53:
		tmp = x * (y2 * (c * y0))
	else:
		tmp = (x * y) * (a * 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 (a <= -17000000.0)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	elseif (a <= 3.3e-53)
		tmp = Float64(x * Float64(y2 * Float64(c * y0)));
	else
		tmp = Float64(Float64(x * y) * Float64(a * 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 (a <= -17000000.0)
		tmp = a * ((x * y) * b);
	elseif (a <= 3.3e-53)
		tmp = x * (y2 * (c * y0));
	else
		tmp = (x * y) * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[a, -17000000.0], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.3e-53], N[(x * N[(y2 * N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] * N[(a * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.7e7

   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 32.5%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 40.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 36.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. neg-mul-1 36.8%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + x \cdot y\right)\right) \]

      2. +-commutative 36.8%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y + \left(-t \cdot z\right)\right)}\right) \]

      3. unsub-neg 36.8%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y - t \cdot z\right)}\right) \]

      4. *-commutative 36.8%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) \]

   8. Simplified 36.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   9. Taylor expanded in y around inf 33.1%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 33.1%

          \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot b\right)} \]

   11. Simplified 33.1%

       \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot b\right)} \]

   if -1.7e7 < a < 3.30000000000000004e-53

   1. Initial program 35.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 36.7%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 25.6%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   5. Taylor expanded in c around inf 23.3%

      \[\leadsto x \cdot \left(y2 \cdot \color{blue}{\left(c \cdot y0\right)}\right) \]

   if 3.30000000000000004e-53 < a

   1. Initial program 19.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 19.7%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 39.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 34.7%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. neg-mul-1 34.7%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + x \cdot y\right)\right) \]

      2. +-commutative 34.7%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y + \left(-t \cdot z\right)\right)}\right) \]

      3. unsub-neg 34.7%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y - t \cdot z\right)}\right) \]

      4. *-commutative 34.7%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) \]

   8. Simplified 34.7%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   9. Taylor expanded in y around inf 19.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 23.5%

          \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot \left(x \cdot y\right)} \]

   11. Simplified 23.5%

       \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot \left(x \cdot y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 25.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -17000000:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-53}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 42: 17.1% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* y1 (* z 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) {
	return a * (y1 * (z * y3));
}

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 * (y1 * (z * y3))
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 * (y1 * (z * y3));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * (y1 * (z * y3))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(y1 * Float64(z * y3)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * (y1 * (z * y3));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(y1 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 30.3%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

3. Simplified 30.7%

   \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
4. Add Preprocessing

5. Taylor expanded in a around inf 33.5%

   \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

6. Taylor expanded in z around inf 24.1%

   \[\leadsto \color{blue}{a \cdot \left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right)} \]
7. Step-by-step derivation

   1. associate-*r* 21.5%

      \[\leadsto \color{blue}{\left(a \cdot z\right) \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)} \]

   2. *-commutative 21.5%

      \[\leadsto \color{blue}{\left(z \cdot a\right)} \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right) \]

   3. +-commutative 21.5%

      \[\leadsto \left(z \cdot a\right) \cdot \color{blue}{\left(y1 \cdot y3 + -1 \cdot \left(b \cdot t\right)\right)} \]

   4. mul-1-neg 21.5%

      \[\leadsto \left(z \cdot a\right) \cdot \left(y1 \cdot y3 + \color{blue}{\left(-b \cdot t\right)}\right) \]

   5. unsub-neg 21.5%

      \[\leadsto \left(z \cdot a\right) \cdot \color{blue}{\left(y1 \cdot y3 - b \cdot t\right)} \]

8. Simplified 21.5%

   \[\leadsto \color{blue}{\left(z \cdot a\right) \cdot \left(y1 \cdot y3 - b \cdot t\right)} \]

9. Taylor expanded in y1 around inf 13.6%

   \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]

10. Final simplification 13.6%

    \[\leadsto a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right) \]
11. Add Preprocessing

Developer target: 27.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot c - y5 \cdot a\\ t_2 := x \cdot y2 - z \cdot y3\\ t_3 := y2 \cdot t - y3 \cdot y\\ t_4 := k \cdot y2 - j \cdot y3\\ t_5 := y4 \cdot b - y5 \cdot i\\ t_6 := \left(j \cdot t - k \cdot y\right) \cdot t\_5\\ t_7 := b \cdot a - i \cdot c\\ t_8 := t\_7 \cdot \left(y \cdot x - t \cdot z\right)\\ t_9 := j \cdot x - k \cdot z\\ t_10 := \left(b \cdot y0 - i \cdot y1\right) \cdot t\_9\\ t_11 := t\_9 \cdot \left(y0 \cdot b - i \cdot y1\right)\\ t_12 := y4 \cdot y1 - y5 \cdot y0\\ t_13 := t\_4 \cdot t\_12\\ t_14 := \left(y2 \cdot k - y3 \cdot j\right) \cdot t\_12\\ t_15 := \left(\left(\left(\left(k \cdot y\right) \cdot \left(y5 \cdot i\right) - \left(y \cdot b\right) \cdot \left(y4 \cdot k\right)\right) - \left(y5 \cdot t\right) \cdot \left(i \cdot j\right)\right) - \left(t\_3 \cdot t\_1 - t\_14\right)\right) + \left(t\_8 - \left(t\_11 - \left(y2 \cdot x - y3 \cdot z\right) \cdot \left(c \cdot y0 - y1 \cdot a\right)\right)\right)\\ t_16 := \left(\left(t\_6 - \left(y3 \cdot y\right) \cdot \left(y5 \cdot a - y4 \cdot c\right)\right) + \left(\left(y5 \cdot a\right) \cdot \left(t \cdot y2\right) + t\_13\right)\right) + \left(t\_2 \cdot \left(c \cdot y0 - a \cdot y1\right) - \left(t\_10 - \left(y \cdot x - z \cdot t\right) \cdot t\_7\right)\right)\\ t_17 := t \cdot y2 - y \cdot y3\\ \mathbf{if}\;y4 < -7.206256231996481 \cdot 10^{+60}:\\ \;\;\;\;\left(t\_8 - \left(t\_11 - t\_6\right)\right) - \left(\frac{t\_3}{\frac{1}{t\_1}} - t\_14\right)\\ \mathbf{elif}\;y4 < -3.364603505246317 \cdot 10^{-66}:\\ \;\;\;\;\left(\left(\left(\left(t \cdot c\right) \cdot \left(i \cdot z\right) - \left(a \cdot t\right) \cdot \left(b \cdot z\right)\right) - \left(y \cdot c\right) \cdot \left(i \cdot x\right)\right) - t\_10\right) + \left(\left(y0 \cdot c - a \cdot y1\right) \cdot t\_2 - \left(t\_17 \cdot \left(y4 \cdot c - a \cdot y5\right) - \left(y1 \cdot y4 - y5 \cdot y0\right) \cdot t\_4\right)\right)\\ \mathbf{elif}\;y4 < -1.2000065055686116 \cdot 10^{-105}:\\ \;\;\;\;t\_16\\ \mathbf{elif}\;y4 < 6.718963124057495 \cdot 10^{-279}:\\ \;\;\;\;t\_15\\ \mathbf{elif}\;y4 < 4.77962681403792 \cdot 10^{-222}:\\ \;\;\;\;t\_16\\ \mathbf{elif}\;y4 < 2.2852241541266835 \cdot 10^{-175}:\\ \;\;\;\;t\_15\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(k \cdot \left(i \cdot \left(z \cdot y1\right)\right) - \left(j \cdot \left(i \cdot \left(x \cdot y1\right)\right) + y0 \cdot \left(k \cdot \left(z \cdot b\right)\right)\right)\right)\right) + \left(z \cdot \left(y3 \cdot \left(a \cdot y1\right)\right) - \left(y2 \cdot \left(x \cdot \left(a \cdot y1\right)\right) + y0 \cdot \left(z \cdot \left(c \cdot y3\right)\right)\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot t\_5\right) - t\_17 \cdot t\_1\right) + t\_13\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y4 c) (* y5 a)))
        (t_2 (- (* x y2) (* z y3)))
        (t_3 (- (* y2 t) (* y3 y)))
        (t_4 (- (* k y2) (* j y3)))
        (t_5 (- (* y4 b) (* y5 i)))
        (t_6 (* (- (* j t) (* k y)) t_5))
        (t_7 (- (* b a) (* i c)))
        (t_8 (* t_7 (- (* y x) (* t z))))
        (t_9 (- (* j x) (* k z)))
        (t_10 (* (- (* b y0) (* i y1)) t_9))
        (t_11 (* t_9 (- (* y0 b) (* i y1))))
        (t_12 (- (* y4 y1) (* y5 y0)))
        (t_13 (* t_4 t_12))
        (t_14 (* (- (* y2 k) (* y3 j)) t_12))
        (t_15
         (+
          (-
           (-
            (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k)))
            (* (* y5 t) (* i j)))
           (- (* t_3 t_1) t_14))
          (- t_8 (- t_11 (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))))
        (t_16
         (+
          (+
           (- t_6 (* (* y3 y) (- (* y5 a) (* y4 c))))
           (+ (* (* y5 a) (* t y2)) t_13))
          (-
           (* t_2 (- (* c y0) (* a y1)))
           (- t_10 (* (- (* y x) (* z t)) t_7)))))
        (t_17 (- (* t y2) (* y y3))))
   (if (< y4 -7.206256231996481e+60)
     (- (- t_8 (- t_11 t_6)) (- (/ t_3 (/ 1.0 t_1)) t_14))
     (if (< y4 -3.364603505246317e-66)
       (+
        (-
         (- (- (* (* t c) (* i z)) (* (* a t) (* b z))) (* (* y c) (* i x)))
         t_10)
        (-
         (* (- (* y0 c) (* a y1)) t_2)
         (- (* t_17 (- (* y4 c) (* a y5))) (* (- (* y1 y4) (* y5 y0)) t_4))))
       (if (< y4 -1.2000065055686116e-105)
         t_16
         (if (< y4 6.718963124057495e-279)
           t_15
           (if (< y4 4.77962681403792e-222)
             t_16
             (if (< y4 2.2852241541266835e-175)
               t_15
               (+
                (-
                 (+
                  (+
                   (-
                    (* (- (* x y) (* z t)) (- (* a b) (* c i)))
                    (-
                     (* k (* i (* z y1)))
                     (+ (* j (* i (* x y1))) (* y0 (* k (* z b))))))
                   (-
                    (* z (* y3 (* a y1)))
                    (+ (* y2 (* x (* a y1))) (* y0 (* z (* c y3))))))
                  (* (- (* t j) (* y k)) t_5))
                 (* t_17 t_1))
                t_13)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y4 * c) - (y5 * a);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (y2 * t) - (y3 * y);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = (y4 * b) - (y5 * i);
	double t_6 = ((j * t) - (k * y)) * t_5;
	double t_7 = (b * a) - (i * c);
	double t_8 = t_7 * ((y * x) - (t * z));
	double t_9 = (j * x) - (k * z);
	double t_10 = ((b * y0) - (i * y1)) * t_9;
	double t_11 = t_9 * ((y0 * b) - (i * y1));
	double t_12 = (y4 * y1) - (y5 * y0);
	double t_13 = t_4 * t_12;
	double t_14 = ((y2 * k) - (y3 * j)) * t_12;
	double t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	double t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	double t_17 = (t * y2) - (y * y3);
	double tmp;
	if (y4 < -7.206256231996481e+60) {
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	} else if (y4 < -3.364603505246317e-66) {
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	} else if (y4 < -1.2000065055686116e-105) {
		tmp = t_16;
	} else if (y4 < 6.718963124057495e-279) {
		tmp = t_15;
	} else if (y4 < 4.77962681403792e-222) {
		tmp = t_16;
	} else if (y4 < 2.2852241541266835e-175) {
		tmp = t_15;
	} else {
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_10
    real(8) :: t_11
    real(8) :: t_12
    real(8) :: t_13
    real(8) :: t_14
    real(8) :: t_15
    real(8) :: t_16
    real(8) :: t_17
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = (y4 * c) - (y5 * a)
    t_2 = (x * y2) - (z * y3)
    t_3 = (y2 * t) - (y3 * y)
    t_4 = (k * y2) - (j * y3)
    t_5 = (y4 * b) - (y5 * i)
    t_6 = ((j * t) - (k * y)) * t_5
    t_7 = (b * a) - (i * c)
    t_8 = t_7 * ((y * x) - (t * z))
    t_9 = (j * x) - (k * z)
    t_10 = ((b * y0) - (i * y1)) * t_9
    t_11 = t_9 * ((y0 * b) - (i * y1))
    t_12 = (y4 * y1) - (y5 * y0)
    t_13 = t_4 * t_12
    t_14 = ((y2 * k) - (y3 * j)) * t_12
    t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))))
    t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)))
    t_17 = (t * y2) - (y * y3)
    if (y4 < (-7.206256231996481d+60)) then
        tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0d0 / t_1)) - t_14)
    else if (y4 < (-3.364603505246317d-66)) then
        tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)))
    else if (y4 < (-1.2000065055686116d-105)) then
        tmp = t_16
    else if (y4 < 6.718963124057495d-279) then
        tmp = t_15
    else if (y4 < 4.77962681403792d-222) then
        tmp = t_16
    else if (y4 < 2.2852241541266835d-175) then
        tmp = t_15
    else
        tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y4 * c) - (y5 * a);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (y2 * t) - (y3 * y);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = (y4 * b) - (y5 * i);
	double t_6 = ((j * t) - (k * y)) * t_5;
	double t_7 = (b * a) - (i * c);
	double t_8 = t_7 * ((y * x) - (t * z));
	double t_9 = (j * x) - (k * z);
	double t_10 = ((b * y0) - (i * y1)) * t_9;
	double t_11 = t_9 * ((y0 * b) - (i * y1));
	double t_12 = (y4 * y1) - (y5 * y0);
	double t_13 = t_4 * t_12;
	double t_14 = ((y2 * k) - (y3 * j)) * t_12;
	double t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	double t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	double t_17 = (t * y2) - (y * y3);
	double tmp;
	if (y4 < -7.206256231996481e+60) {
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	} else if (y4 < -3.364603505246317e-66) {
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	} else if (y4 < -1.2000065055686116e-105) {
		tmp = t_16;
	} else if (y4 < 6.718963124057495e-279) {
		tmp = t_15;
	} else if (y4 < 4.77962681403792e-222) {
		tmp = t_16;
	} else if (y4 < 2.2852241541266835e-175) {
		tmp = t_15;
	} else {
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y4 * c) - (y5 * a)
	t_2 = (x * y2) - (z * y3)
	t_3 = (y2 * t) - (y3 * y)
	t_4 = (k * y2) - (j * y3)
	t_5 = (y4 * b) - (y5 * i)
	t_6 = ((j * t) - (k * y)) * t_5
	t_7 = (b * a) - (i * c)
	t_8 = t_7 * ((y * x) - (t * z))
	t_9 = (j * x) - (k * z)
	t_10 = ((b * y0) - (i * y1)) * t_9
	t_11 = t_9 * ((y0 * b) - (i * y1))
	t_12 = (y4 * y1) - (y5 * y0)
	t_13 = t_4 * t_12
	t_14 = ((y2 * k) - (y3 * j)) * t_12
	t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))))
	t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)))
	t_17 = (t * y2) - (y * y3)
	tmp = 0
	if y4 < -7.206256231996481e+60:
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14)
	elif y4 < -3.364603505246317e-66:
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)))
	elif y4 < -1.2000065055686116e-105:
		tmp = t_16
	elif y4 < 6.718963124057495e-279:
		tmp = t_15
	elif y4 < 4.77962681403792e-222:
		tmp = t_16
	elif y4 < 2.2852241541266835e-175:
		tmp = t_15
	else:
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y4 * c) - Float64(y5 * a))
	t_2 = Float64(Float64(x * y2) - Float64(z * y3))
	t_3 = Float64(Float64(y2 * t) - Float64(y3 * y))
	t_4 = Float64(Float64(k * y2) - Float64(j * y3))
	t_5 = Float64(Float64(y4 * b) - Float64(y5 * i))
	t_6 = Float64(Float64(Float64(j * t) - Float64(k * y)) * t_5)
	t_7 = Float64(Float64(b * a) - Float64(i * c))
	t_8 = Float64(t_7 * Float64(Float64(y * x) - Float64(t * z)))
	t_9 = Float64(Float64(j * x) - Float64(k * z))
	t_10 = Float64(Float64(Float64(b * y0) - Float64(i * y1)) * t_9)
	t_11 = Float64(t_9 * Float64(Float64(y0 * b) - Float64(i * y1)))
	t_12 = Float64(Float64(y4 * y1) - Float64(y5 * y0))
	t_13 = Float64(t_4 * t_12)
	t_14 = Float64(Float64(Float64(y2 * k) - Float64(y3 * j)) * t_12)
	t_15 = Float64(Float64(Float64(Float64(Float64(Float64(k * y) * Float64(y5 * i)) - Float64(Float64(y * b) * Float64(y4 * k))) - Float64(Float64(y5 * t) * Float64(i * j))) - Float64(Float64(t_3 * t_1) - t_14)) + Float64(t_8 - Float64(t_11 - Float64(Float64(Float64(y2 * x) - Float64(y3 * z)) * Float64(Float64(c * y0) - Float64(y1 * a))))))
	t_16 = Float64(Float64(Float64(t_6 - Float64(Float64(y3 * y) * Float64(Float64(y5 * a) - Float64(y4 * c)))) + Float64(Float64(Float64(y5 * a) * Float64(t * y2)) + t_13)) + Float64(Float64(t_2 * Float64(Float64(c * y0) - Float64(a * y1))) - Float64(t_10 - Float64(Float64(Float64(y * x) - Float64(z * t)) * t_7))))
	t_17 = Float64(Float64(t * y2) - Float64(y * y3))
	tmp = 0.0
	if (y4 < -7.206256231996481e+60)
		tmp = Float64(Float64(t_8 - Float64(t_11 - t_6)) - Float64(Float64(t_3 / Float64(1.0 / t_1)) - t_14));
	elseif (y4 < -3.364603505246317e-66)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(t * c) * Float64(i * z)) - Float64(Float64(a * t) * Float64(b * z))) - Float64(Float64(y * c) * Float64(i * x))) - t_10) + Float64(Float64(Float64(Float64(y0 * c) - Float64(a * y1)) * t_2) - Float64(Float64(t_17 * Float64(Float64(y4 * c) - Float64(a * y5))) - Float64(Float64(Float64(y1 * y4) - Float64(y5 * y0)) * t_4))));
	elseif (y4 < -1.2000065055686116e-105)
		tmp = t_16;
	elseif (y4 < 6.718963124057495e-279)
		tmp = t_15;
	elseif (y4 < 4.77962681403792e-222)
		tmp = t_16;
	elseif (y4 < 2.2852241541266835e-175)
		tmp = t_15;
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) - Float64(z * t)) * Float64(Float64(a * b) - Float64(c * i))) - Float64(Float64(k * Float64(i * Float64(z * y1))) - Float64(Float64(j * Float64(i * Float64(x * y1))) + Float64(y0 * Float64(k * Float64(z * b)))))) + Float64(Float64(z * Float64(y3 * Float64(a * y1))) - Float64(Float64(y2 * Float64(x * Float64(a * y1))) + Float64(y0 * Float64(z * Float64(c * y3)))))) + Float64(Float64(Float64(t * j) - Float64(y * k)) * t_5)) - Float64(t_17 * t_1)) + t_13);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y4 * c) - (y5 * a);
	t_2 = (x * y2) - (z * y3);
	t_3 = (y2 * t) - (y3 * y);
	t_4 = (k * y2) - (j * y3);
	t_5 = (y4 * b) - (y5 * i);
	t_6 = ((j * t) - (k * y)) * t_5;
	t_7 = (b * a) - (i * c);
	t_8 = t_7 * ((y * x) - (t * z));
	t_9 = (j * x) - (k * z);
	t_10 = ((b * y0) - (i * y1)) * t_9;
	t_11 = t_9 * ((y0 * b) - (i * y1));
	t_12 = (y4 * y1) - (y5 * y0);
	t_13 = t_4 * t_12;
	t_14 = ((y2 * k) - (y3 * j)) * t_12;
	t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	t_17 = (t * y2) - (y * y3);
	tmp = 0.0;
	if (y4 < -7.206256231996481e+60)
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	elseif (y4 < -3.364603505246317e-66)
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	elseif (y4 < -1.2000065055686116e-105)
		tmp = t_16;
	elseif (y4 < 6.718963124057495e-279)
		tmp = t_15;
	elseif (y4 < 4.77962681403792e-222)
		tmp = t_16;
	elseif (y4 < 2.2852241541266835e-175)
		tmp = t_15;
	else
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y4 * c), $MachinePrecision] - N[(y5 * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y2 * t), $MachinePrecision] - N[(y3 * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(y4 * b), $MachinePrecision] - N[(y5 * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision] * t$95$5), $MachinePrecision]}, Block[{t$95$7 = N[(N[(b * a), $MachinePrecision] - N[(i * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(t$95$7 * N[(N[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$10 = N[(N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision] * t$95$9), $MachinePrecision]}, Block[{t$95$11 = N[(t$95$9 * N[(N[(y0 * b), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$12 = N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$13 = N[(t$95$4 * t$95$12), $MachinePrecision]}, Block[{t$95$14 = N[(N[(N[(y2 * k), $MachinePrecision] - N[(y3 * j), $MachinePrecision]), $MachinePrecision] * t$95$12), $MachinePrecision]}, Block[{t$95$15 = N[(N[(N[(N[(N[(N[(k * y), $MachinePrecision] * N[(y5 * i), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] * N[(y4 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y5 * t), $MachinePrecision] * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$3 * t$95$1), $MachinePrecision] - t$95$14), $MachinePrecision]), $MachinePrecision] + N[(t$95$8 - N[(t$95$11 - N[(N[(N[(y2 * x), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision] * N[(N[(c * y0), $MachinePrecision] - N[(y1 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$16 = N[(N[(N[(t$95$6 - N[(N[(y3 * y), $MachinePrecision] * N[(N[(y5 * a), $MachinePrecision] - N[(y4 * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y5 * a), $MachinePrecision] * N[(t * y2), $MachinePrecision]), $MachinePrecision] + t$95$13), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$10 - N[(N[(N[(y * x), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$17 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, If[Less[y4, -7.206256231996481e+60], N[(N[(t$95$8 - N[(t$95$11 - t$95$6), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$3 / N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision] - t$95$14), $MachinePrecision]), $MachinePrecision], If[Less[y4, -3.364603505246317e-66], N[(N[(N[(N[(N[(N[(t * c), $MachinePrecision] * N[(i * z), $MachinePrecision]), $MachinePrecision] - N[(N[(a * t), $MachinePrecision] * N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * c), $MachinePrecision] * N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$10), $MachinePrecision] + N[(N[(N[(N[(y0 * c), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision] - N[(N[(t$95$17 * N[(N[(y4 * c), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(y1 * y4), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision] * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[y4, -1.2000065055686116e-105], t$95$16, If[Less[y4, 6.718963124057495e-279], t$95$15, If[Less[y4, 4.77962681403792e-222], t$95$16, If[Less[y4, 2.2852241541266835e-175], t$95$15, N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(k * N[(i * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * N[(i * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(k * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(y3 * N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y2 * N[(x * N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(z * N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * t$95$5), $MachinePrecision]), $MachinePrecision] - N[(t$95$17 * t$95$1), $MachinePrecision]), $MachinePrecision] + t$95$13), $MachinePrecision]]]]]]]]]]]]]]]]]]]]]]]]

Reproduce

herbie shell --seed 2024077 
(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :name "Linear.Matrix:det44 from linear-1.19.1.3"
  :precision binary64

  :alt
  (if (< y4 -7.206256231996481e+60) (- (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))))) (- (/ (- (* y2 t) (* y3 y)) (/ 1.0 (- (* y4 c) (* y5 a)))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (if (< y4 -3.364603505246317e-66) (+ (- (- (- (* (* t c) (* i z)) (* (* a t) (* b z))) (* (* y c) (* i x))) (* (- (* b y0) (* i y1)) (- (* j x) (* k z)))) (- (* (- (* y0 c) (* a y1)) (- (* x y2) (* z y3))) (- (* (- (* t y2) (* y y3)) (- (* y4 c) (* a y5))) (* (- (* y1 y4) (* y5 y0)) (- (* k y2) (* j y3)))))) (if (< y4 -1.2000065055686116e-105) (+ (+ (- (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))) (* (* y3 y) (- (* y5 a) (* y4 c)))) (+ (* (* y5 a) (* t y2)) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* x y2) (* z y3)) (- (* c y0) (* a y1))) (- (* (- (* b y0) (* i y1)) (- (* j x) (* k z))) (* (- (* y x) (* z t)) (- (* b a) (* i c)))))) (if (< y4 6.718963124057495e-279) (+ (- (- (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k))) (* (* y5 t) (* i j))) (- (* (- (* y2 t) (* y3 y)) (- (* y4 c) (* y5 a))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))) (if (< y4 4.77962681403792e-222) (+ (+ (- (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))) (* (* y3 y) (- (* y5 a) (* y4 c)))) (+ (* (* y5 a) (* t y2)) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* x y2) (* z y3)) (- (* c y0) (* a y1))) (- (* (- (* b y0) (* i y1)) (- (* j x) (* k z))) (* (- (* y x) (* z t)) (- (* b a) (* i c)))))) (if (< y4 2.2852241541266835e-175) (+ (- (- (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k))) (* (* y5 t) (* i j))) (- (* (- (* y2 t) (* y3 y)) (- (* y4 c) (* y5 a))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))) (+ (- (+ (+ (- (* (- (* x y) (* z t)) (- (* a b) (* c i))) (- (* k (* i (* z y1))) (+ (* j (* i (* x y1))) (* y0 (* k (* z b)))))) (- (* z (* y3 (* a y1))) (+ (* y2 (* x (* a y1))) (* y0 (* z (* c y3)))))) (* (- (* t j) (* y k)) (- (* y4 b) (* y5 i)))) (* (- (* t y2) (* y y3)) (- (* y4 c) (* y5 a)))) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))))))))

  (+ (- (+ (+ (- (* (- (* x y) (* z t)) (- (* a b) (* c i))) (* (- (* x j) (* z k)) (- (* y0 b) (* y1 i)))) (* (- (* x y2) (* z y3)) (- (* y0 c) (* y1 a)))) (* (- (* t j) (* y k)) (- (* y4 b) (* y5 i)))) (* (- (* t y2) (* y y3)) (- (* y4 c) (* y5 a)))) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0)))))