Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 30.3% → 43.2%

Time: 1.5min

Alternatives: 45

Speedup: 3.1×

• 88.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 30.3% 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: 43.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot t - k \cdot y\\ t_2 := y2 \cdot t - y3 \cdot y\\ t_3 := y3 \cdot z - y2 \cdot x\\ t_4 := \mathsf{fma}\left(t\_3, y1, \mathsf{fma}\left(y \cdot x - t \cdot z, b, t\_2 \cdot y5\right)\right) \cdot a\\ t_5 := j \cdot x - k \cdot z\\ t_6 := y2 \cdot k - y3 \cdot j\\ t_7 := \mathsf{fma}\left(t \cdot z - y \cdot x, c, \mathsf{fma}\left(-y5, t\_1, t\_5 \cdot y1\right)\right) \cdot i\\ \mathbf{if}\;i \leq -2.3 \cdot 10^{+249}:\\ \;\;\;\;\mathsf{fma}\left(t\_3, a, \mathsf{fma}\left(t\_6, y4, t\_5 \cdot i\right)\right) \cdot y1\\ \mathbf{elif}\;i \leq -1.6 \cdot 10^{+204}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot y - j \cdot t, i, \mathsf{fma}\left(-y0, t\_6, t\_2 \cdot a\right)\right) \cdot y5\\ \mathbf{elif}\;i \leq -5.8 \cdot 10^{+90}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;i \leq -8 \cdot 10^{-221}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;i \leq -4.3 \cdot 10^{-252}:\\ \;\;\;\;\left(\mathsf{fma}\left(y1 \cdot k, y4, \mathsf{fma}\left(x, \mathsf{fma}\left(c, y0, \left(-a\right) \cdot y1\right), \mathsf{fma}\left(a, t, \left(-y0\right) \cdot k\right) \cdot y5\right)\right) - \left(y4 \cdot t\right) \cdot c\right) \cdot y2\\ \mathbf{elif}\;i \leq 6.6 \cdot 10^{-253}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;i \leq 2.8 \cdot 10^{-135}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot j - y2 \cdot k, y5, \mathsf{fma}\left(c, y2 \cdot x - y3 \cdot z, \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \cdot y0\\ \mathbf{elif}\;i \leq 1.4 \cdot 10^{-45}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, b, \mathsf{fma}\left(t\_6, y1, \left(y3 \cdot y - y2 \cdot t\right) \cdot c\right)\right) \cdot y4\\ \mathbf{elif}\;i \leq 3.7 \cdot 10^{+24}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;i \leq 1.75 \cdot 10^{+109}:\\ \;\;\;\;\mathsf{fma}\left(y5 \cdot i - y4 \cdot b, k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y\\ \mathbf{elif}\;i \leq 6.2 \cdot 10^{+177}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, z, y4 \cdot y2\right) \cdot y1\right) \cdot k\\ \mathbf{elif}\;i \leq 4.3 \cdot 10^{+207}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot x, \mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right), \mathsf{fma}\left(y3, \mathsf{fma}\left(c, y4, \left(-y5\right) \cdot a\right), \mathsf{fma}\left(-b, y4, y5 \cdot i\right) \cdot k\right) \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_7\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* j t) (* k y)))
        (t_2 (- (* y2 t) (* y3 y)))
        (t_3 (- (* y3 z) (* y2 x)))
        (t_4 (* (fma t_3 y1 (fma (- (* y x) (* t z)) b (* t_2 y5))) a))
        (t_5 (- (* j x) (* k z)))
        (t_6 (- (* y2 k) (* y3 j)))
        (t_7 (* (fma (- (* t z) (* y x)) c (fma (- y5) t_1 (* t_5 y1))) i)))
   (if (<= i -2.3e+249)
     (* (fma t_3 a (fma t_6 y4 (* t_5 i))) y1)
     (if (<= i -1.6e+204)
       (* (fma (- (* k y) (* j t)) i (fma (- y0) t_6 (* t_2 a))) y5)
       (if (<= i -5.8e+90)
         t_7
         (if (<= i -8e-221)
           t_4
           (if (<= i -4.3e-252)
             (*
              (-
               (fma
                (* y1 k)
                y4
                (fma x (fma c y0 (* (- a) y1)) (* (fma a t (* (- y0) k)) y5)))
               (* (* y4 t) c))
              y2)
             (if (<= i 6.6e-253)
               t_4
               (if (<= i 2.8e-135)
                 (*
                  (fma
                   (- (* y3 j) (* y2 k))
                   y5
                   (fma c (- (* y2 x) (* y3 z)) (* (- (* k z) (* j x)) b)))
                  y0)
                 (if (<= i 1.4e-45)
                   (* (fma t_1 b (fma t_6 y1 (* (- (* y3 y) (* y2 t)) c))) y4)
                   (if (<= i 3.7e+24)
                     t_7
                     (if (<= i 1.75e+109)
                       (*
                        (fma
                         (- (* y5 i) (* y4 b))
                         k
                         (fma
                          (- (* b a) (* i c))
                          x
                          (* (- (* y4 c) (* y5 a)) y3)))
                        y)
                       (if (<= i 6.2e+177)
                         (* (* (fma (- i) z (* y4 y2)) y1) k)
                         (if (<= i 4.3e+207)
                           (fma
                            (* y x)
                            (fma a b (* (- c) i))
                            (*
                             (fma
                              y3
                              (fma c y4 (* (- y5) a))
                              (* (fma (- b) y4 (* y5 i)) k))
                             y))
                           t_7))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (j * t) - (k * y);
	double t_2 = (y2 * t) - (y3 * y);
	double t_3 = (y3 * z) - (y2 * x);
	double t_4 = fma(t_3, y1, fma(((y * x) - (t * z)), b, (t_2 * y5))) * a;
	double t_5 = (j * x) - (k * z);
	double t_6 = (y2 * k) - (y3 * j);
	double t_7 = fma(((t * z) - (y * x)), c, fma(-y5, t_1, (t_5 * y1))) * i;
	double tmp;
	if (i <= -2.3e+249) {
		tmp = fma(t_3, a, fma(t_6, y4, (t_5 * i))) * y1;
	} else if (i <= -1.6e+204) {
		tmp = fma(((k * y) - (j * t)), i, fma(-y0, t_6, (t_2 * a))) * y5;
	} else if (i <= -5.8e+90) {
		tmp = t_7;
	} else if (i <= -8e-221) {
		tmp = t_4;
	} else if (i <= -4.3e-252) {
		tmp = (fma((y1 * k), y4, fma(x, fma(c, y0, (-a * y1)), (fma(a, t, (-y0 * k)) * y5))) - ((y4 * t) * c)) * y2;
	} else if (i <= 6.6e-253) {
		tmp = t_4;
	} else if (i <= 2.8e-135) {
		tmp = fma(((y3 * j) - (y2 * k)), y5, fma(c, ((y2 * x) - (y3 * z)), (((k * z) - (j * x)) * b))) * y0;
	} else if (i <= 1.4e-45) {
		tmp = fma(t_1, b, fma(t_6, y1, (((y3 * y) - (y2 * t)) * c))) * y4;
	} else if (i <= 3.7e+24) {
		tmp = t_7;
	} else if (i <= 1.75e+109) {
		tmp = fma(((y5 * i) - (y4 * b)), k, fma(((b * a) - (i * c)), x, (((y4 * c) - (y5 * a)) * y3))) * y;
	} else if (i <= 6.2e+177) {
		tmp = (fma(-i, z, (y4 * y2)) * y1) * k;
	} else if (i <= 4.3e+207) {
		tmp = fma((y * x), fma(a, b, (-c * i)), (fma(y3, fma(c, y4, (-y5 * a)), (fma(-b, y4, (y5 * i)) * k)) * y));
	} else {
		tmp = t_7;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(j * t) - Float64(k * y))
	t_2 = Float64(Float64(y2 * t) - Float64(y3 * y))
	t_3 = Float64(Float64(y3 * z) - Float64(y2 * x))
	t_4 = Float64(fma(t_3, y1, fma(Float64(Float64(y * x) - Float64(t * z)), b, Float64(t_2 * y5))) * a)
	t_5 = Float64(Float64(j * x) - Float64(k * z))
	t_6 = Float64(Float64(y2 * k) - Float64(y3 * j))
	t_7 = Float64(fma(Float64(Float64(t * z) - Float64(y * x)), c, fma(Float64(-y5), t_1, Float64(t_5 * y1))) * i)
	tmp = 0.0
	if (i <= -2.3e+249)
		tmp = Float64(fma(t_3, a, fma(t_6, y4, Float64(t_5 * i))) * y1);
	elseif (i <= -1.6e+204)
		tmp = Float64(fma(Float64(Float64(k * y) - Float64(j * t)), i, fma(Float64(-y0), t_6, Float64(t_2 * a))) * y5);
	elseif (i <= -5.8e+90)
		tmp = t_7;
	elseif (i <= -8e-221)
		tmp = t_4;
	elseif (i <= -4.3e-252)
		tmp = Float64(Float64(fma(Float64(y1 * k), y4, fma(x, fma(c, y0, Float64(Float64(-a) * y1)), Float64(fma(a, t, Float64(Float64(-y0) * k)) * y5))) - Float64(Float64(y4 * t) * c)) * y2);
	elseif (i <= 6.6e-253)
		tmp = t_4;
	elseif (i <= 2.8e-135)
		tmp = Float64(fma(Float64(Float64(y3 * j) - Float64(y2 * k)), y5, fma(c, Float64(Float64(y2 * x) - Float64(y3 * z)), Float64(Float64(Float64(k * z) - Float64(j * x)) * b))) * y0);
	elseif (i <= 1.4e-45)
		tmp = Float64(fma(t_1, b, fma(t_6, y1, Float64(Float64(Float64(y3 * y) - Float64(y2 * t)) * c))) * y4);
	elseif (i <= 3.7e+24)
		tmp = t_7;
	elseif (i <= 1.75e+109)
		tmp = Float64(fma(Float64(Float64(y5 * i) - Float64(y4 * b)), k, fma(Float64(Float64(b * a) - Float64(i * c)), x, Float64(Float64(Float64(y4 * c) - Float64(y5 * a)) * y3))) * y);
	elseif (i <= 6.2e+177)
		tmp = Float64(Float64(fma(Float64(-i), z, Float64(y4 * y2)) * y1) * k);
	elseif (i <= 4.3e+207)
		tmp = fma(Float64(y * x), fma(a, b, Float64(Float64(-c) * i)), Float64(fma(y3, fma(c, y4, Float64(Float64(-y5) * a)), Float64(fma(Float64(-b), y4, Float64(y5 * i)) * k)) * y));
	else
		tmp = t_7;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y2 * t), $MachinePrecision] - N[(y3 * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y3 * z), $MachinePrecision] - N[(y2 * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 * y1 + N[(N[(N[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision] * b + N[(t$95$2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$5 = N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(y2 * k), $MachinePrecision] - N[(y3 * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(N[(N[(t * z), $MachinePrecision] - N[(y * x), $MachinePrecision]), $MachinePrecision] * c + N[((-y5) * t$95$1 + N[(t$95$5 * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[i, -2.3e+249], N[(N[(t$95$3 * a + N[(t$95$6 * y4 + N[(t$95$5 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision], If[LessEqual[i, -1.6e+204], N[(N[(N[(N[(k * y), $MachinePrecision] - N[(j * t), $MachinePrecision]), $MachinePrecision] * i + N[((-y0) * t$95$6 + N[(t$95$2 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y5), $MachinePrecision], If[LessEqual[i, -5.8e+90], t$95$7, If[LessEqual[i, -8e-221], t$95$4, If[LessEqual[i, -4.3e-252], N[(N[(N[(N[(y1 * k), $MachinePrecision] * y4 + N[(x * N[(c * y0 + N[((-a) * y1), $MachinePrecision]), $MachinePrecision] + N[(N[(a * t + N[((-y0) * k), $MachinePrecision]), $MachinePrecision] * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y4 * t), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision] * y2), $MachinePrecision], If[LessEqual[i, 6.6e-253], t$95$4, If[LessEqual[i, 2.8e-135], N[(N[(N[(N[(y3 * j), $MachinePrecision] - N[(y2 * k), $MachinePrecision]), $MachinePrecision] * y5 + N[(c * N[(N[(y2 * x), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(k * z), $MachinePrecision] - N[(j * x), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y0), $MachinePrecision], If[LessEqual[i, 1.4e-45], N[(N[(t$95$1 * b + N[(t$95$6 * y1 + N[(N[(N[(y3 * y), $MachinePrecision] - N[(y2 * t), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision], If[LessEqual[i, 3.7e+24], t$95$7, If[LessEqual[i, 1.75e+109], N[(N[(N[(N[(y5 * i), $MachinePrecision] - N[(y4 * b), $MachinePrecision]), $MachinePrecision] * k + N[(N[(N[(b * a), $MachinePrecision] - N[(i * c), $MachinePrecision]), $MachinePrecision] * x + N[(N[(N[(y4 * c), $MachinePrecision] - N[(y5 * a), $MachinePrecision]), $MachinePrecision] * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[i, 6.2e+177], N[(N[(N[((-i) * z + N[(y4 * y2), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision] * k), $MachinePrecision], If[LessEqual[i, 4.3e+207], N[(N[(y * x), $MachinePrecision] * N[(a * b + N[((-c) * i), $MachinePrecision]), $MachinePrecision] + N[(N[(y3 * N[(c * y4 + N[((-y5) * a), $MachinePrecision]), $MachinePrecision] + N[(N[((-b) * y4 + N[(y5 * i), $MachinePrecision]), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], t$95$7]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if i < -2.2999999999999998e249

   1. Initial program 33.3%

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

   3. Taylor expanded in y1 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 71.5%

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

   if -2.2999999999999998e249 < i < -1.6e204

   1. Initial program 16.5%

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

   3. Taylor expanded in y5 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 67.6%

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

   if -1.6e204 < i < -5.8000000000000003e90 or 1.4000000000000001e-45 < i < 3.69999999999999999e24 or 4.2999999999999997e207 < i

   1. Initial program 23.6%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 69.9%

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

   if -5.8000000000000003e90 < i < -8.00000000000000014e-221 or -4.29999999999999991e-252 < i < 6.6000000000000002e-253

   1. Initial program 40.3%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 61.8%

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

   if -8.00000000000000014e-221 < i < -4.29999999999999991e-252

   1. Initial program 33.2%

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

   3. Taylor expanded in y2 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 56.0%

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

   6. Taylor expanded in y5 around 0

      \[\leadsto \left(-1 \cdot \left(c \cdot \left(t \cdot y4\right)\right) + \left(k \cdot \left(y1 \cdot y4\right) + \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + y5 \cdot \left(-1 \cdot \left(k \cdot y0\right) + a \cdot t\right)\right)\right)\right) \cdot y2 \]
   7. Step-by-step derivation

   8. Applied rewrites 77.6%

      \[\leadsto \left(\mathsf{fma}\left(k \cdot y1, y4, \mathsf{fma}\left(x, \mathsf{fma}\left(c, y0, \left(-a\right) \cdot y1\right), y5 \cdot \mathsf{fma}\left(a, t, -k \cdot y0\right)\right)\right) - c \cdot \left(t \cdot y4\right)\right) \cdot y2 \]

   if 6.6000000000000002e-253 < i < 2.80000000000000023e-135

   1. Initial program 15.0%

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

   3. Taylor expanded in y0 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 59.7%

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

   if 2.80000000000000023e-135 < i < 1.4000000000000001e-45

   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 y4 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 66.2%

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

   if 3.69999999999999999e24 < i < 1.74999999999999992e109

   1. Initial program 17.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 78.5%

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

   if 1.74999999999999992e109 < i < 6.1999999999999998e177

   1. Initial program 25.6%

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

   3. Taylor expanded in y1 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 50.0%

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

   6. Taylor expanded in j around inf

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

   8. Applied rewrites 50.3%

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

   9. Taylor expanded in k around inf

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

   11. Applied rewrites 75.5%

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

   if 6.1999999999999998e177 < i < 4.2999999999999997e207

   1. Initial program 42.9%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 85.7%

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

   6. Taylor expanded in i around inf

      \[\leadsto \left(i \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 43.8%

      \[\leadsto \left(i \cdot \mathsf{fma}\left(k, y5, -c \cdot x\right)\right) \cdot y \]

   9. Taylor expanded in x around 0

      \[\leadsto x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right) + \color{blue}{y \cdot \left(k \cdot \left(i \cdot y5 - b \cdot y4\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 100.0%

       \[\leadsto \mathsf{fma}\left(x \cdot y, \color{blue}{\mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right)}, y \cdot \mathsf{fma}\left(y3, \mathsf{fma}\left(c, y4, \left(-a\right) \cdot y5\right), k \cdot \mathsf{fma}\left(-b, y4, i \cdot y5\right)\right)\right) \]
3. Recombined 10 regimes into one program.

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.3 \cdot 10^{+249}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot z - y2 \cdot x, a, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1\\ \mathbf{elif}\;i \leq -1.6 \cdot 10^{+204}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot y - j \cdot t, i, \mathsf{fma}\left(-y0, y2 \cdot k - y3 \cdot j, \left(y2 \cdot t - y3 \cdot y\right) \cdot a\right)\right) \cdot y5\\ \mathbf{elif}\;i \leq -5.8 \cdot 10^{+90}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot z - y \cdot x, c, \mathsf{fma}\left(-y5, j \cdot t - k \cdot y, \left(j \cdot x - k \cdot z\right) \cdot y1\right)\right) \cdot i\\ \mathbf{elif}\;i \leq -8 \cdot 10^{-221}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot z - y2 \cdot x, y1, \mathsf{fma}\left(y \cdot x - t \cdot z, b, \left(y2 \cdot t - y3 \cdot y\right) \cdot y5\right)\right) \cdot a\\ \mathbf{elif}\;i \leq -4.3 \cdot 10^{-252}:\\ \;\;\;\;\left(\mathsf{fma}\left(y1 \cdot k, y4, \mathsf{fma}\left(x, \mathsf{fma}\left(c, y0, \left(-a\right) \cdot y1\right), \mathsf{fma}\left(a, t, \left(-y0\right) \cdot k\right) \cdot y5\right)\right) - \left(y4 \cdot t\right) \cdot c\right) \cdot y2\\ \mathbf{elif}\;i \leq 6.6 \cdot 10^{-253}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot z - y2 \cdot x, y1, \mathsf{fma}\left(y \cdot x - t \cdot z, b, \left(y2 \cdot t - y3 \cdot y\right) \cdot y5\right)\right) \cdot a\\ \mathbf{elif}\;i \leq 2.8 \cdot 10^{-135}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot j - y2 \cdot k, y5, \mathsf{fma}\left(c, y2 \cdot x - y3 \cdot z, \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \cdot y0\\ \mathbf{elif}\;i \leq 1.4 \cdot 10^{-45}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot t - k \cdot y, b, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y1, \left(y3 \cdot y - y2 \cdot t\right) \cdot c\right)\right) \cdot y4\\ \mathbf{elif}\;i \leq 3.7 \cdot 10^{+24}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot z - y \cdot x, c, \mathsf{fma}\left(-y5, j \cdot t - k \cdot y, \left(j \cdot x - k \cdot z\right) \cdot y1\right)\right) \cdot i\\ \mathbf{elif}\;i \leq 1.75 \cdot 10^{+109}:\\ \;\;\;\;\mathsf{fma}\left(y5 \cdot i - y4 \cdot b, k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y\\ \mathbf{elif}\;i \leq 6.2 \cdot 10^{+177}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, z, y4 \cdot y2\right) \cdot y1\right) \cdot k\\ \mathbf{elif}\;i \leq 4.3 \cdot 10^{+207}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot x, \mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right), \mathsf{fma}\left(y3, \mathsf{fma}\left(c, y4, \left(-y5\right) \cdot a\right), \mathsf{fma}\left(-b, y4, y5 \cdot i\right) \cdot k\right) \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot z - y \cdot x, c, \mathsf{fma}\left(-y5, j \cdot t - k \cdot y, \left(j \cdot x - k \cdot z\right) \cdot y1\right)\right) \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 48.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b, y4, \left(-i\right) \cdot y5\right)\\ t_2 := \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right) \cdot \mathsf{fma}\left(c, y4, \left(-y5\right) \cdot a\right)\\ t_3 := \mathsf{fma}\left(j, t, \left(-k\right) \cdot y\right)\\ t_4 := \mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right)\\ t_5 := \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right)\\ t_6 := j \cdot x - k \cdot z\\ t_7 := y2 \cdot k - y3 \cdot j\\ t_8 := \left(\left(\left(\left(y2 \cdot x - y3 \cdot z\right) \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(\left(y1 \cdot i - y0 \cdot b\right) \cdot t\_6 - \left(i \cdot c - b \cdot a\right) \cdot \left(y \cdot x - t \cdot z\right)\right)\right) - \left(j \cdot t - k \cdot y\right) \cdot \left(y5 \cdot i - y4 \cdot b\right)\right) - \left(y5 \cdot a - y4 \cdot c\right) \cdot \left(y3 \cdot y - y2 \cdot t\right)\right) - \left(y5 \cdot y0 - y4 \cdot y1\right) \cdot t\_7\\ \mathbf{if}\;t\_8 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(-1, \mathsf{fma}\left(t, t\_4 \cdot z, \left(\mathsf{fma}\left(c, y0, \left(-a\right) \cdot y1\right) \cdot z\right) \cdot y3\right), \mathsf{fma}\left(t\_1, t\_3, \mathsf{fma}\left(y1, y4, \left(-y0\right) \cdot y5\right) \cdot t\_5\right)\right) - \mathsf{fma}\left(-1, \left(\mathsf{fma}\left(b, y0, \left(-i\right) \cdot y1\right) \cdot z\right) \cdot k, t\_2\right)\\ \mathbf{elif}\;t\_8 \leq \infty:\\ \;\;\;\;\left(\mathsf{fma}\left(y4 \cdot y1, t\_5, \mathsf{fma}\left(t\_4, \mathsf{fma}\left(x, y, \left(-t\right) \cdot z\right), t\_3 \cdot t\_1\right)\right) - \mathsf{fma}\left(x, y2, \left(-y3\right) \cdot z\right) \cdot \left(y1 \cdot a\right)\right) - \mathsf{fma}\left(-i, \mathsf{fma}\left(j, x, \left(-k\right) \cdot z\right) \cdot y1, t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot z - y2 \cdot x, a, \mathsf{fma}\left(t\_7, y4, t\_6 \cdot i\right)\right) \cdot y1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (fma b y4 (* (- i) y5)))
        (t_2 (* (fma t y2 (* (- y) y3)) (fma c y4 (* (- y5) a))))
        (t_3 (fma j t (* (- k) y)))
        (t_4 (fma a b (* (- c) i)))
        (t_5 (fma k y2 (* (- j) y3)))
        (t_6 (- (* j x) (* k z)))
        (t_7 (- (* y2 k) (* y3 j)))
        (t_8
         (-
          (-
           (-
            (+
             (* (- (* y2 x) (* y3 z)) (- (* y0 c) (* y1 a)))
             (-
              (* (- (* y1 i) (* y0 b)) t_6)
              (* (- (* i c) (* b a)) (- (* y x) (* t z)))))
            (* (- (* j t) (* k y)) (- (* y5 i) (* y4 b))))
           (* (- (* y5 a) (* y4 c)) (- (* y3 y) (* y2 t))))
          (* (- (* y5 y0) (* y4 y1)) t_7))))
   (if (<= t_8 (- INFINITY))
     (-
      (fma
       -1.0
       (fma t (* t_4 z) (* (* (fma c y0 (* (- a) y1)) z) y3))
       (fma t_1 t_3 (* (fma y1 y4 (* (- y0) y5)) t_5)))
      (fma -1.0 (* (* (fma b y0 (* (- i) y1)) z) k) t_2))
     (if (<= t_8 INFINITY)
       (-
        (-
         (fma (* y4 y1) t_5 (fma t_4 (fma x y (* (- t) z)) (* t_3 t_1)))
         (* (fma x y2 (* (- y3) z)) (* y1 a)))
        (fma (- i) (* (fma j x (* (- k) z)) y1) t_2))
       (* (fma (- (* y3 z) (* y2 x)) a (fma t_7 y4 (* t_6 i))) y1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = fma(b, y4, (-i * y5));
	double t_2 = fma(t, y2, (-y * y3)) * fma(c, y4, (-y5 * a));
	double t_3 = fma(j, t, (-k * y));
	double t_4 = fma(a, b, (-c * i));
	double t_5 = fma(k, y2, (-j * y3));
	double t_6 = (j * x) - (k * z);
	double t_7 = (y2 * k) - (y3 * j);
	double t_8 = ((((((y2 * x) - (y3 * z)) * ((y0 * c) - (y1 * a))) + ((((y1 * i) - (y0 * b)) * t_6) - (((i * c) - (b * a)) * ((y * x) - (t * z))))) - (((j * t) - (k * y)) * ((y5 * i) - (y4 * b)))) - (((y5 * a) - (y4 * c)) * ((y3 * y) - (y2 * t)))) - (((y5 * y0) - (y4 * y1)) * t_7);
	double tmp;
	if (t_8 <= -((double) INFINITY)) {
		tmp = fma(-1.0, fma(t, (t_4 * z), ((fma(c, y0, (-a * y1)) * z) * y3)), fma(t_1, t_3, (fma(y1, y4, (-y0 * y5)) * t_5))) - fma(-1.0, ((fma(b, y0, (-i * y1)) * z) * k), t_2);
	} else if (t_8 <= ((double) INFINITY)) {
		tmp = (fma((y4 * y1), t_5, fma(t_4, fma(x, y, (-t * z)), (t_3 * t_1))) - (fma(x, y2, (-y3 * z)) * (y1 * a))) - fma(-i, (fma(j, x, (-k * z)) * y1), t_2);
	} else {
		tmp = fma(((y3 * z) - (y2 * x)), a, fma(t_7, y4, (t_6 * i))) * y1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = fma(b, y4, Float64(Float64(-i) * y5))
	t_2 = Float64(fma(t, y2, Float64(Float64(-y) * y3)) * fma(c, y4, Float64(Float64(-y5) * a)))
	t_3 = fma(j, t, Float64(Float64(-k) * y))
	t_4 = fma(a, b, Float64(Float64(-c) * i))
	t_5 = fma(k, y2, Float64(Float64(-j) * y3))
	t_6 = Float64(Float64(j * x) - Float64(k * z))
	t_7 = Float64(Float64(y2 * k) - Float64(y3 * j))
	t_8 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(y2 * x) - Float64(y3 * z)) * Float64(Float64(y0 * c) - Float64(y1 * a))) + Float64(Float64(Float64(Float64(y1 * i) - Float64(y0 * b)) * t_6) - Float64(Float64(Float64(i * c) - Float64(b * a)) * Float64(Float64(y * x) - Float64(t * z))))) - Float64(Float64(Float64(j * t) - Float64(k * y)) * Float64(Float64(y5 * i) - Float64(y4 * b)))) - Float64(Float64(Float64(y5 * a) - Float64(y4 * c)) * Float64(Float64(y3 * y) - Float64(y2 * t)))) - Float64(Float64(Float64(y5 * y0) - Float64(y4 * y1)) * t_7))
	tmp = 0.0
	if (t_8 <= Float64(-Inf))
		tmp = Float64(fma(-1.0, fma(t, Float64(t_4 * z), Float64(Float64(fma(c, y0, Float64(Float64(-a) * y1)) * z) * y3)), fma(t_1, t_3, Float64(fma(y1, y4, Float64(Float64(-y0) * y5)) * t_5))) - fma(-1.0, Float64(Float64(fma(b, y0, Float64(Float64(-i) * y1)) * z) * k), t_2));
	elseif (t_8 <= Inf)
		tmp = Float64(Float64(fma(Float64(y4 * y1), t_5, fma(t_4, fma(x, y, Float64(Float64(-t) * z)), Float64(t_3 * t_1))) - Float64(fma(x, y2, Float64(Float64(-y3) * z)) * Float64(y1 * a))) - fma(Float64(-i), Float64(fma(j, x, Float64(Float64(-k) * z)) * y1), t_2));
	else
		tmp = Float64(fma(Float64(Float64(y3 * z) - Float64(y2 * x)), a, fma(t_7, y4, Float64(t_6 * i))) * y1);
	end
	return 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 * y4 + N[((-i) * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * y2 + N[((-y) * y3), $MachinePrecision]), $MachinePrecision] * N[(c * y4 + N[((-y5) * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * t + N[((-k) * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(a * b + N[((-c) * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(k * y2 + N[((-j) * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(y2 * k), $MachinePrecision] - N[(y3 * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(N[(N[(N[(N[(N[(N[(y2 * x), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision] * N[(N[(y0 * c), $MachinePrecision] - N[(y1 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(y1 * i), $MachinePrecision] - N[(y0 * b), $MachinePrecision]), $MachinePrecision] * t$95$6), $MachinePrecision] - N[(N[(N[(i * c), $MachinePrecision] - N[(b * a), $MachinePrecision]), $MachinePrecision] * N[(N[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision] * N[(N[(y5 * i), $MachinePrecision] - N[(y4 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(y5 * a), $MachinePrecision] - N[(y4 * c), $MachinePrecision]), $MachinePrecision] * N[(N[(y3 * y), $MachinePrecision] - N[(y2 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(y5 * y0), $MachinePrecision] - N[(y4 * y1), $MachinePrecision]), $MachinePrecision] * t$95$7), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$8, (-Infinity)], N[(N[(-1.0 * N[(t * N[(t$95$4 * z), $MachinePrecision] + N[(N[(N[(c * y0 + N[((-a) * y1), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] * y3), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * t$95$3 + N[(N[(y1 * y4 + N[((-y0) * y5), $MachinePrecision]), $MachinePrecision] * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(-1.0 * N[(N[(N[(b * y0 + N[((-i) * y1), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] * k), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$8, Infinity], N[(N[(N[(N[(y4 * y1), $MachinePrecision] * t$95$5 + N[(t$95$4 * N[(x * y + N[((-t) * z), $MachinePrecision]), $MachinePrecision] + N[(t$95$3 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * y2 + N[((-y3) * z), $MachinePrecision]), $MachinePrecision] * N[(y1 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[((-i) * N[(N[(j * x + N[((-k) * z), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(y3 * z), $MachinePrecision] - N[(y2 * x), $MachinePrecision]), $MachinePrecision] * a + N[(t$95$7 * y4 + N[(t$95$6 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 3 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 82.3%

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

   3. Taylor expanded in y5 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 48.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 72.8%

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

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

   1. Initial program 93.2%

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

   3. Taylor expanded in y2 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 51.9%

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

   6. Taylor expanded in y0 around 0

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

   8. Applied rewrites 79.8%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y1 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 43.5%

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

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(y2 \cdot x - y3 \cdot z\right) \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(\left(y1 \cdot i - y0 \cdot b\right) \cdot \left(j \cdot x - k \cdot z\right) - \left(i \cdot c - b \cdot a\right) \cdot \left(y \cdot x - t \cdot z\right)\right)\right) - \left(j \cdot t - k \cdot y\right) \cdot \left(y5 \cdot i - y4 \cdot b\right)\right) - \left(y5 \cdot a - y4 \cdot c\right) \cdot \left(y3 \cdot y - y2 \cdot t\right)\right) - \left(y5 \cdot y0 - y4 \cdot y1\right) \cdot \left(y2 \cdot k - y3 \cdot j\right) \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(-1, \mathsf{fma}\left(t, \mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right) \cdot z, \left(\mathsf{fma}\left(c, y0, \left(-a\right) \cdot y1\right) \cdot z\right) \cdot y3\right), \mathsf{fma}\left(\mathsf{fma}\left(b, y4, \left(-i\right) \cdot y5\right), \mathsf{fma}\left(j, t, \left(-k\right) \cdot y\right), \mathsf{fma}\left(y1, y4, \left(-y0\right) \cdot y5\right) \cdot \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right)\right)\right) - \mathsf{fma}\left(-1, \left(\mathsf{fma}\left(b, y0, \left(-i\right) \cdot y1\right) \cdot z\right) \cdot k, \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right) \cdot \mathsf{fma}\left(c, y4, \left(-y5\right) \cdot a\right)\right)\\ \mathbf{elif}\;\left(\left(\left(\left(y2 \cdot x - y3 \cdot z\right) \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(\left(y1 \cdot i - y0 \cdot b\right) \cdot \left(j \cdot x - k \cdot z\right) - \left(i \cdot c - b \cdot a\right) \cdot \left(y \cdot x - t \cdot z\right)\right)\right) - \left(j \cdot t - k \cdot y\right) \cdot \left(y5 \cdot i - y4 \cdot b\right)\right) - \left(y5 \cdot a - y4 \cdot c\right) \cdot \left(y3 \cdot y - y2 \cdot t\right)\right) - \left(y5 \cdot y0 - y4 \cdot y1\right) \cdot \left(y2 \cdot k - y3 \cdot j\right) \leq \infty:\\ \;\;\;\;\left(\mathsf{fma}\left(y4 \cdot y1, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \mathsf{fma}\left(\mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right), \mathsf{fma}\left(x, y, \left(-t\right) \cdot z\right), \mathsf{fma}\left(j, t, \left(-k\right) \cdot y\right) \cdot \mathsf{fma}\left(b, y4, \left(-i\right) \cdot y5\right)\right)\right) - \mathsf{fma}\left(x, y2, \left(-y3\right) \cdot z\right) \cdot \left(y1 \cdot a\right)\right) - \mathsf{fma}\left(-i, \mathsf{fma}\left(j, x, \left(-k\right) \cdot z\right) \cdot y1, \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right) \cdot \mathsf{fma}\left(c, y4, \left(-y5\right) \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot z - y2 \cdot x, a, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 49.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y5 \cdot a - y4 \cdot c\right) \cdot \left(y3 \cdot y - y2 \cdot t\right)\\ t_2 := j \cdot x - k \cdot z\\ t_3 := y5 \cdot i - y4 \cdot b\\ t_4 := y2 \cdot k - y3 \cdot j\\ t_5 := \left(y5 \cdot y0 - y4 \cdot y1\right) \cdot t\_4\\ t_6 := \left(\left(\left(\left(y2 \cdot x - y3 \cdot z\right) \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(\left(y1 \cdot i - y0 \cdot b\right) \cdot t\_2 - \left(i \cdot c - b \cdot a\right) \cdot \left(y \cdot x - t \cdot z\right)\right)\right) - \left(j \cdot t - k \cdot y\right) \cdot t\_3\right) - t\_1\right) - t\_5\\ \mathbf{if}\;t\_6 \leq -\infty:\\ \;\;\;\;\left(\left(\left(\mathsf{fma}\left(b, y0, \left(-i\right) \cdot y1\right) \cdot z\right) \cdot k + \left(k \cdot y - j \cdot t\right) \cdot t\_3\right) - t\_1\right) - t\_5\\ \mathbf{elif}\;t\_6 \leq \infty:\\ \;\;\;\;\left(\mathsf{fma}\left(y4 \cdot y1, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \mathsf{fma}\left(\mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right), \mathsf{fma}\left(x, y, \left(-t\right) \cdot z\right), \mathsf{fma}\left(j, t, \left(-k\right) \cdot y\right) \cdot \mathsf{fma}\left(b, y4, \left(-i\right) \cdot y5\right)\right)\right) - \mathsf{fma}\left(x, y2, \left(-y3\right) \cdot z\right) \cdot \left(y1 \cdot a\right)\right) - \mathsf{fma}\left(-i, \mathsf{fma}\left(j, x, \left(-k\right) \cdot z\right) \cdot y1, \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right) \cdot \mathsf{fma}\left(c, y4, \left(-y5\right) \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot z - y2 \cdot x, a, \mathsf{fma}\left(t\_4, y4, t\_2 \cdot i\right)\right) \cdot y1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (- (* y5 a) (* y4 c)) (- (* y3 y) (* y2 t))))
        (t_2 (- (* j x) (* k z)))
        (t_3 (- (* y5 i) (* y4 b)))
        (t_4 (- (* y2 k) (* y3 j)))
        (t_5 (* (- (* y5 y0) (* y4 y1)) t_4))
        (t_6
         (-
          (-
           (-
            (+
             (* (- (* y2 x) (* y3 z)) (- (* y0 c) (* y1 a)))
             (-
              (* (- (* y1 i) (* y0 b)) t_2)
              (* (- (* i c) (* b a)) (- (* y x) (* t z)))))
            (* (- (* j t) (* k y)) t_3))
           t_1)
          t_5)))
   (if (<= t_6 (- INFINITY))
     (-
      (-
       (+ (* (* (fma b y0 (* (- i) y1)) z) k) (* (- (* k y) (* j t)) t_3))
       t_1)
      t_5)
     (if (<= t_6 INFINITY)
       (-
        (-
         (fma
          (* y4 y1)
          (fma k y2 (* (- j) y3))
          (fma
           (fma a b (* (- c) i))
           (fma x y (* (- t) z))
           (* (fma j t (* (- k) y)) (fma b y4 (* (- i) y5)))))
         (* (fma x y2 (* (- y3) z)) (* y1 a)))
        (fma
         (- i)
         (* (fma j x (* (- k) z)) y1)
         (* (fma t y2 (* (- y) y3)) (fma c y4 (* (- y5) a)))))
       (* (fma (- (* y3 z) (* y2 x)) a (fma t_4 y4 (* t_2 i))) y1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = ((y5 * a) - (y4 * c)) * ((y3 * y) - (y2 * t));
	double t_2 = (j * x) - (k * z);
	double t_3 = (y5 * i) - (y4 * b);
	double t_4 = (y2 * k) - (y3 * j);
	double t_5 = ((y5 * y0) - (y4 * y1)) * t_4;
	double t_6 = ((((((y2 * x) - (y3 * z)) * ((y0 * c) - (y1 * a))) + ((((y1 * i) - (y0 * b)) * t_2) - (((i * c) - (b * a)) * ((y * x) - (t * z))))) - (((j * t) - (k * y)) * t_3)) - t_1) - t_5;
	double tmp;
	if (t_6 <= -((double) INFINITY)) {
		tmp = ((((fma(b, y0, (-i * y1)) * z) * k) + (((k * y) - (j * t)) * t_3)) - t_1) - t_5;
	} else if (t_6 <= ((double) INFINITY)) {
		tmp = (fma((y4 * y1), fma(k, y2, (-j * y3)), fma(fma(a, b, (-c * i)), fma(x, y, (-t * z)), (fma(j, t, (-k * y)) * fma(b, y4, (-i * y5))))) - (fma(x, y2, (-y3 * z)) * (y1 * a))) - fma(-i, (fma(j, x, (-k * z)) * y1), (fma(t, y2, (-y * y3)) * fma(c, y4, (-y5 * a))));
	} else {
		tmp = fma(((y3 * z) - (y2 * x)), a, fma(t_4, y4, (t_2 * i))) * y1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(Float64(y5 * a) - Float64(y4 * c)) * Float64(Float64(y3 * y) - Float64(y2 * t)))
	t_2 = Float64(Float64(j * x) - Float64(k * z))
	t_3 = Float64(Float64(y5 * i) - Float64(y4 * b))
	t_4 = Float64(Float64(y2 * k) - Float64(y3 * j))
	t_5 = Float64(Float64(Float64(y5 * y0) - Float64(y4 * y1)) * t_4)
	t_6 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(y2 * x) - Float64(y3 * z)) * Float64(Float64(y0 * c) - Float64(y1 * a))) + Float64(Float64(Float64(Float64(y1 * i) - Float64(y0 * b)) * t_2) - Float64(Float64(Float64(i * c) - Float64(b * a)) * Float64(Float64(y * x) - Float64(t * z))))) - Float64(Float64(Float64(j * t) - Float64(k * y)) * t_3)) - t_1) - t_5)
	tmp = 0.0
	if (t_6 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(Float64(Float64(fma(b, y0, Float64(Float64(-i) * y1)) * z) * k) + Float64(Float64(Float64(k * y) - Float64(j * t)) * t_3)) - t_1) - t_5);
	elseif (t_6 <= Inf)
		tmp = Float64(Float64(fma(Float64(y4 * y1), fma(k, y2, Float64(Float64(-j) * y3)), fma(fma(a, b, Float64(Float64(-c) * i)), fma(x, y, Float64(Float64(-t) * z)), Float64(fma(j, t, Float64(Float64(-k) * y)) * fma(b, y4, Float64(Float64(-i) * y5))))) - Float64(fma(x, y2, Float64(Float64(-y3) * z)) * Float64(y1 * a))) - fma(Float64(-i), Float64(fma(j, x, Float64(Float64(-k) * z)) * y1), Float64(fma(t, y2, Float64(Float64(-y) * y3)) * fma(c, y4, Float64(Float64(-y5) * a)))));
	else
		tmp = Float64(fma(Float64(Float64(y3 * z) - Float64(y2 * x)), a, fma(t_4, y4, Float64(t_2 * i))) * y1);
	end
	return 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[(N[(y5 * a), $MachinePrecision] - N[(y4 * c), $MachinePrecision]), $MachinePrecision] * N[(N[(y3 * y), $MachinePrecision] - N[(y2 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y5 * i), $MachinePrecision] - N[(y4 * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(y2 * k), $MachinePrecision] - N[(y3 * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(y5 * y0), $MachinePrecision] - N[(y4 * y1), $MachinePrecision]), $MachinePrecision] * t$95$4), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(N[(N[(N[(N[(y2 * x), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision] * N[(N[(y0 * c), $MachinePrecision] - N[(y1 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(y1 * i), $MachinePrecision] - N[(y0 * b), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision] - N[(N[(N[(i * c), $MachinePrecision] - N[(b * a), $MachinePrecision]), $MachinePrecision] * N[(N[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision] * t$95$3), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - t$95$5), $MachinePrecision]}, If[LessEqual[t$95$6, (-Infinity)], N[(N[(N[(N[(N[(N[(b * y0 + N[((-i) * y1), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] * k), $MachinePrecision] + N[(N[(N[(k * y), $MachinePrecision] - N[(j * t), $MachinePrecision]), $MachinePrecision] * t$95$3), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - t$95$5), $MachinePrecision], If[LessEqual[t$95$6, Infinity], N[(N[(N[(N[(y4 * y1), $MachinePrecision] * N[(k * y2 + N[((-j) * y3), $MachinePrecision]), $MachinePrecision] + N[(N[(a * b + N[((-c) * i), $MachinePrecision]), $MachinePrecision] * N[(x * y + N[((-t) * z), $MachinePrecision]), $MachinePrecision] + N[(N[(j * t + N[((-k) * y), $MachinePrecision]), $MachinePrecision] * N[(b * y4 + N[((-i) * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * y2 + N[((-y3) * z), $MachinePrecision]), $MachinePrecision] * N[(y1 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[((-i) * N[(N[(j * x + N[((-k) * z), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision] + N[(N[(t * y2 + N[((-y) * y3), $MachinePrecision]), $MachinePrecision] * N[(c * y4 + N[((-y5) * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(y3 * z), $MachinePrecision] - N[(y2 * x), $MachinePrecision]), $MachinePrecision] * a + N[(t$95$4 * y4 + N[(t$95$2 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 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 82.3%

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

   3. Taylor expanded in k around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 69.9

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

   5. Applied rewrites 69.9%

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

   6. Taylor expanded in k around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. cancel-sign-sub-inv N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-neg.f64 72.7

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

   8. Applied rewrites 72.7%

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

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

   1. Initial program 93.2%

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

   3. Taylor expanded in y2 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 51.9%

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

   6. Taylor expanded in y0 around 0

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

   8. Applied rewrites 79.8%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y1 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 43.5%

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

4. Final simplification 55.3%

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

Alternative 4: 55.5% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y2 * k), $MachinePrecision] - N[(y3 * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(N[(N[(N[(y2 * x), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision] * N[(N[(y0 * c), $MachinePrecision] - N[(y1 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(y1 * i), $MachinePrecision] - N[(y0 * b), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision] - N[(N[(N[(i * c), $MachinePrecision] - N[(b * a), $MachinePrecision]), $MachinePrecision] * N[(N[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision] * N[(N[(y5 * i), $MachinePrecision] - N[(y4 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(y5 * a), $MachinePrecision] - N[(y4 * c), $MachinePrecision]), $MachinePrecision] * N[(N[(y3 * y), $MachinePrecision] - N[(y2 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(y5 * y0), $MachinePrecision] - N[(y4 * y1), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, Infinity], t$95$3, N[(N[(N[(N[(y3 * z), $MachinePrecision] - N[(y2 * x), $MachinePrecision]), $MachinePrecision] * a + N[(t$95$2 * y4 + N[(t$95$1 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y1), $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 89.3%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y1 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 43.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.4%

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

Alternative 5: 48.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y5 \cdot a - y4 \cdot c\right) \cdot \left(y3 \cdot y - y2 \cdot t\right)\\ t_2 := y \cdot x - t \cdot z\\ t_3 := j \cdot x - k \cdot z\\ t_4 := y2 \cdot k - y3 \cdot j\\ t_5 := \left(j \cdot t - k \cdot y\right) \cdot \left(y5 \cdot i - y4 \cdot b\right)\\ t_6 := \left(y5 \cdot y0 - y4 \cdot y1\right) \cdot t\_4\\ \mathbf{if}\;\left(\left(\left(\left(y2 \cdot x - y3 \cdot z\right) \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(\left(y1 \cdot i - y0 \cdot b\right) \cdot t\_3 - \left(i \cdot c - b \cdot a\right) \cdot t\_2\right)\right) - t\_5\right) - t\_1\right) - t\_6 \leq \infty:\\ \;\;\;\;\left(\left(\mathsf{fma}\left(-c, t\_2, t\_3 \cdot y1\right) \cdot i - t\_5\right) - t\_1\right) - t\_6\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot z - y2 \cdot x, a, \mathsf{fma}\left(t\_4, y4, t\_3 \cdot i\right)\right) \cdot y1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (- (* y5 a) (* y4 c)) (- (* y3 y) (* y2 t))))
        (t_2 (- (* y x) (* t z)))
        (t_3 (- (* j x) (* k z)))
        (t_4 (- (* y2 k) (* y3 j)))
        (t_5 (* (- (* j t) (* k y)) (- (* y5 i) (* y4 b))))
        (t_6 (* (- (* y5 y0) (* y4 y1)) t_4)))
   (if (<=
        (-
         (-
          (-
           (+
            (* (- (* y2 x) (* y3 z)) (- (* y0 c) (* y1 a)))
            (- (* (- (* y1 i) (* y0 b)) t_3) (* (- (* i c) (* b a)) t_2)))
           t_5)
          t_1)
         t_6)
        INFINITY)
     (- (- (- (* (fma (- c) t_2 (* t_3 y1)) i) t_5) t_1) t_6)
     (* (fma (- (* y3 z) (* y2 x)) a (fma t_4 y4 (* t_3 i))) y1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = ((y5 * a) - (y4 * c)) * ((y3 * y) - (y2 * t));
	double t_2 = (y * x) - (t * z);
	double t_3 = (j * x) - (k * z);
	double t_4 = (y2 * k) - (y3 * j);
	double t_5 = ((j * t) - (k * y)) * ((y5 * i) - (y4 * b));
	double t_6 = ((y5 * y0) - (y4 * y1)) * t_4;
	double tmp;
	if ((((((((y2 * x) - (y3 * z)) * ((y0 * c) - (y1 * a))) + ((((y1 * i) - (y0 * b)) * t_3) - (((i * c) - (b * a)) * t_2))) - t_5) - t_1) - t_6) <= ((double) INFINITY)) {
		tmp = (((fma(-c, t_2, (t_3 * y1)) * i) - t_5) - t_1) - t_6;
	} else {
		tmp = fma(((y3 * z) - (y2 * x)), a, fma(t_4, y4, (t_3 * i))) * y1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(Float64(y5 * a) - Float64(y4 * c)) * Float64(Float64(y3 * y) - Float64(y2 * t)))
	t_2 = Float64(Float64(y * x) - Float64(t * z))
	t_3 = Float64(Float64(j * x) - Float64(k * z))
	t_4 = Float64(Float64(y2 * k) - Float64(y3 * j))
	t_5 = Float64(Float64(Float64(j * t) - Float64(k * y)) * Float64(Float64(y5 * i) - Float64(y4 * b)))
	t_6 = Float64(Float64(Float64(y5 * y0) - Float64(y4 * y1)) * t_4)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(y2 * x) - Float64(y3 * z)) * Float64(Float64(y0 * c) - Float64(y1 * a))) + Float64(Float64(Float64(Float64(y1 * i) - Float64(y0 * b)) * t_3) - Float64(Float64(Float64(i * c) - Float64(b * a)) * t_2))) - t_5) - t_1) - t_6) <= Inf)
		tmp = Float64(Float64(Float64(Float64(fma(Float64(-c), t_2, Float64(t_3 * y1)) * i) - t_5) - t_1) - t_6);
	else
		tmp = Float64(fma(Float64(Float64(y3 * z) - Float64(y2 * x)), a, fma(t_4, y4, Float64(t_3 * i))) * y1);
	end
	return 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[(N[(y5 * a), $MachinePrecision] - N[(y4 * c), $MachinePrecision]), $MachinePrecision] * N[(N[(y3 * y), $MachinePrecision] - N[(y2 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(y2 * k), $MachinePrecision] - N[(y3 * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision] * N[(N[(y5 * i), $MachinePrecision] - N[(y4 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(y5 * y0), $MachinePrecision] - N[(y4 * y1), $MachinePrecision]), $MachinePrecision] * t$95$4), $MachinePrecision]}, If[LessEqual[N[(N[(N[(N[(N[(N[(N[(y2 * x), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision] * N[(N[(y0 * c), $MachinePrecision] - N[(y1 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(y1 * i), $MachinePrecision] - N[(y0 * b), $MachinePrecision]), $MachinePrecision] * t$95$3), $MachinePrecision] - N[(N[(N[(i * c), $MachinePrecision] - N[(b * a), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$5), $MachinePrecision] - t$95$1), $MachinePrecision] - t$95$6), $MachinePrecision], Infinity], N[(N[(N[(N[(N[((-c) * t$95$2 + N[(t$95$3 * y1), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision] - t$95$5), $MachinePrecision] - t$95$1), $MachinePrecision] - t$95$6), $MachinePrecision], N[(N[(N[(N[(y3 * z), $MachinePrecision] - N[(y2 * x), $MachinePrecision]), $MachinePrecision] * a + N[(t$95$4 * y4 + N[(t$95$3 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y1), $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 89.3%

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

   3. Taylor expanded in i around inf

      \[\leadsto \left(\left(\color{blue}{i \cdot \left(-1 \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 72.6%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y1 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 43.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 53.6%

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

Alternative 6: 48.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y5 \cdot a - y4 \cdot c\right) \cdot \left(y3 \cdot y - y2 \cdot t\right)\\ t_2 := j \cdot x - k \cdot z\\ t_3 := y5 \cdot i - y4 \cdot b\\ t_4 := y2 \cdot k - y3 \cdot j\\ t_5 := \left(y5 \cdot y0 - y4 \cdot y1\right) \cdot t\_4\\ \mathbf{if}\;\left(\left(\left(\left(y2 \cdot x - y3 \cdot z\right) \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(\left(y1 \cdot i - y0 \cdot b\right) \cdot t\_2 - \left(i \cdot c - b \cdot a\right) \cdot \left(y \cdot x - t \cdot z\right)\right)\right) - \left(j \cdot t - k \cdot y\right) \cdot t\_3\right) - t\_1\right) - t\_5 \leq \infty:\\ \;\;\;\;\left(\left(\left(\mathsf{fma}\left(b, y0, \left(-i\right) \cdot y1\right) \cdot z\right) \cdot k + \left(k \cdot y - j \cdot t\right) \cdot t\_3\right) - t\_1\right) - t\_5\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot z - y2 \cdot x, a, \mathsf{fma}\left(t\_4, y4, t\_2 \cdot i\right)\right) \cdot y1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (- (* y5 a) (* y4 c)) (- (* y3 y) (* y2 t))))
        (t_2 (- (* j x) (* k z)))
        (t_3 (- (* y5 i) (* y4 b)))
        (t_4 (- (* y2 k) (* y3 j)))
        (t_5 (* (- (* y5 y0) (* y4 y1)) t_4)))
   (if (<=
        (-
         (-
          (-
           (+
            (* (- (* y2 x) (* y3 z)) (- (* y0 c) (* y1 a)))
            (-
             (* (- (* y1 i) (* y0 b)) t_2)
             (* (- (* i c) (* b a)) (- (* y x) (* t z)))))
           (* (- (* j t) (* k y)) t_3))
          t_1)
         t_5)
        INFINITY)
     (-
      (-
       (+ (* (* (fma b y0 (* (- i) y1)) z) k) (* (- (* k y) (* j t)) t_3))
       t_1)
      t_5)
     (* (fma (- (* y3 z) (* y2 x)) a (fma t_4 y4 (* t_2 i))) y1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = ((y5 * a) - (y4 * c)) * ((y3 * y) - (y2 * t));
	double t_2 = (j * x) - (k * z);
	double t_3 = (y5 * i) - (y4 * b);
	double t_4 = (y2 * k) - (y3 * j);
	double t_5 = ((y5 * y0) - (y4 * y1)) * t_4;
	double tmp;
	if ((((((((y2 * x) - (y3 * z)) * ((y0 * c) - (y1 * a))) + ((((y1 * i) - (y0 * b)) * t_2) - (((i * c) - (b * a)) * ((y * x) - (t * z))))) - (((j * t) - (k * y)) * t_3)) - t_1) - t_5) <= ((double) INFINITY)) {
		tmp = ((((fma(b, y0, (-i * y1)) * z) * k) + (((k * y) - (j * t)) * t_3)) - t_1) - t_5;
	} else {
		tmp = fma(((y3 * z) - (y2 * x)), a, fma(t_4, y4, (t_2 * i))) * y1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(Float64(y5 * a) - Float64(y4 * c)) * Float64(Float64(y3 * y) - Float64(y2 * t)))
	t_2 = Float64(Float64(j * x) - Float64(k * z))
	t_3 = Float64(Float64(y5 * i) - Float64(y4 * b))
	t_4 = Float64(Float64(y2 * k) - Float64(y3 * j))
	t_5 = Float64(Float64(Float64(y5 * y0) - Float64(y4 * y1)) * t_4)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(y2 * x) - Float64(y3 * z)) * Float64(Float64(y0 * c) - Float64(y1 * a))) + Float64(Float64(Float64(Float64(y1 * i) - Float64(y0 * b)) * t_2) - Float64(Float64(Float64(i * c) - Float64(b * a)) * Float64(Float64(y * x) - Float64(t * z))))) - Float64(Float64(Float64(j * t) - Float64(k * y)) * t_3)) - t_1) - t_5) <= Inf)
		tmp = Float64(Float64(Float64(Float64(Float64(fma(b, y0, Float64(Float64(-i) * y1)) * z) * k) + Float64(Float64(Float64(k * y) - Float64(j * t)) * t_3)) - t_1) - t_5);
	else
		tmp = Float64(fma(Float64(Float64(y3 * z) - Float64(y2 * x)), a, fma(t_4, y4, Float64(t_2 * i))) * y1);
	end
	return 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[(N[(y5 * a), $MachinePrecision] - N[(y4 * c), $MachinePrecision]), $MachinePrecision] * N[(N[(y3 * y), $MachinePrecision] - N[(y2 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y5 * i), $MachinePrecision] - N[(y4 * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(y2 * k), $MachinePrecision] - N[(y3 * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(y5 * y0), $MachinePrecision] - N[(y4 * y1), $MachinePrecision]), $MachinePrecision] * t$95$4), $MachinePrecision]}, If[LessEqual[N[(N[(N[(N[(N[(N[(N[(y2 * x), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision] * N[(N[(y0 * c), $MachinePrecision] - N[(y1 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(y1 * i), $MachinePrecision] - N[(y0 * b), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision] - N[(N[(N[(i * c), $MachinePrecision] - N[(b * a), $MachinePrecision]), $MachinePrecision] * N[(N[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision] * t$95$3), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - t$95$5), $MachinePrecision], Infinity], N[(N[(N[(N[(N[(N[(b * y0 + N[((-i) * y1), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] * k), $MachinePrecision] + N[(N[(N[(k * y), $MachinePrecision] - N[(j * t), $MachinePrecision]), $MachinePrecision] * t$95$3), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - t$95$5), $MachinePrecision], N[(N[(N[(N[(y3 * z), $MachinePrecision] - N[(y2 * x), $MachinePrecision]), $MachinePrecision] * a + N[(t$95$4 * y4 + N[(t$95$2 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y1), $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 89.3%

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

   3. Taylor expanded in k around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 68.2

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

   5. Applied rewrites 68.2%

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

   6. Taylor expanded in k around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. cancel-sign-sub-inv N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-neg.f64 69.2

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

   8. Applied rewrites 69.2%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y1 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 43.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 52.4%

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

Alternative 7: 47.9% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y2 * k), $MachinePrecision] - N[(y3 * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(N[(N[(N[(N[(y2 * x), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision] * N[(N[(y0 * c), $MachinePrecision] - N[(y1 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(y1 * i), $MachinePrecision] - N[(y0 * b), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision] - N[(N[(N[(i * c), $MachinePrecision] - N[(b * a), $MachinePrecision]), $MachinePrecision] * N[(N[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision] * N[(N[(y5 * i), $MachinePrecision] - N[(y4 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(y5 * a), $MachinePrecision] - N[(y4 * c), $MachinePrecision]), $MachinePrecision] * N[(N[(y3 * y), $MachinePrecision] - N[(y2 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(y5 * y0), $MachinePrecision] - N[(y4 * y1), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[((-y3) * j + N[(y2 * k), $MachinePrecision]), $MachinePrecision] * N[(y5 * (-y0) + N[(y4 * y1), $MachinePrecision]), $MachinePrecision] + N[((-N[((-a) * y5 + N[(y4 * c), $MachinePrecision]), $MachinePrecision]) * N[((-y3) * y + N[(y2 * t), $MachinePrecision]), $MachinePrecision] + N[(N[((-i) * y5 + N[(y4 * b), $MachinePrecision]), $MachinePrecision] * N[((-k) * y + N[(j * t), $MachinePrecision]), $MachinePrecision] + N[(N[((-i) * y1 + N[(y0 * b), $MachinePrecision]), $MachinePrecision] * N[(k * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(y3 * z), $MachinePrecision] - N[(y2 * x), $MachinePrecision]), $MachinePrecision] * a + N[(t$95$2 * y4 + N[(t$95$1 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y1), $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 89.3%

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

   3. Taylor expanded in k around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 68.2

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

   5. Applied rewrites 68.2%

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

   7. Applied rewrites 68.2%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y1 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 43.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 52.1%

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

Alternative 8: 39.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y3 \cdot z - y2 \cdot x\\ t_2 := y2 \cdot t - y3 \cdot y\\ t_3 := y2 \cdot k - y3 \cdot j\\ t_4 := \mathsf{fma}\left(j \cdot t - k \cdot y, b, \mathsf{fma}\left(t\_3, y1, \left(y3 \cdot y - y2 \cdot t\right) \cdot c\right)\right) \cdot y4\\ t_5 := b \cdot a - i \cdot c\\ t_6 := y5 \cdot i - y4 \cdot b\\ \mathbf{if}\;i \leq -2.3 \cdot 10^{+249}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, a, \mathsf{fma}\left(t\_3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1\\ \mathbf{elif}\;i \leq -9.2 \cdot 10^{+203}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot y - j \cdot t, i, \mathsf{fma}\left(-y0, t\_3, t\_2 \cdot a\right)\right) \cdot y5\\ \mathbf{elif}\;i \leq -2.6 \cdot 10^{+131}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, k, y3 \cdot a\right) \cdot z\right) \cdot y1\\ \mathbf{elif}\;i \leq -20000000000000:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{-295}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, y1, \mathsf{fma}\left(y \cdot x - t \cdot z, b, t\_2 \cdot y5\right)\right) \cdot a\\ \mathbf{elif}\;i \leq 2.8 \cdot 10^{-135}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot j - y2 \cdot k, y5, \left(\left(-x\right) \cdot j\right) \cdot b\right) \cdot y0\\ \mathbf{elif}\;i \leq 2.3 \cdot 10^{-79}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;i \leq 2.8 \cdot 10^{-11}:\\ \;\;\;\;\mathsf{fma}\left(t\_5, y, \mathsf{fma}\left(y0 \cdot c - y1 \cdot a, y2, \left(y1 \cdot i - y0 \cdot b\right) \cdot j\right)\right) \cdot x\\ \mathbf{elif}\;i \leq 1.75 \cdot 10^{+109}:\\ \;\;\;\;\mathsf{fma}\left(t\_6, k, \mathsf{fma}\left(t\_5, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y\\ \mathbf{elif}\;i \leq 5.6 \cdot 10^{+177}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, z, y4 \cdot y2\right) \cdot y1\right) \cdot k\\ \mathbf{elif}\;i \leq 8 \cdot 10^{+267}:\\ \;\;\;\;\mathsf{fma}\left(t\_6, y, \mathsf{fma}\left(y4 \cdot y1 - y5 \cdot y0, y2, \left(y0 \cdot b - y1 \cdot i\right) \cdot z\right)\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y5, \left(-c\right) \cdot x\right) \cdot i\right) \cdot y\\ \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 (- (* y3 z) (* y2 x)))
        (t_2 (- (* y2 t) (* y3 y)))
        (t_3 (- (* y2 k) (* y3 j)))
        (t_4
         (*
          (fma (- (* j t) (* k y)) b (fma t_3 y1 (* (- (* y3 y) (* y2 t)) c)))
          y4))
        (t_5 (- (* b a) (* i c)))
        (t_6 (- (* y5 i) (* y4 b))))
   (if (<= i -2.3e+249)
     (* (fma t_1 a (fma t_3 y4 (* (- (* j x) (* k z)) i))) y1)
     (if (<= i -9.2e+203)
       (* (fma (- (* k y) (* j t)) i (fma (- y0) t_3 (* t_2 a))) y5)
       (if (<= i -2.6e+131)
         (* (* (fma (- i) k (* y3 a)) z) y1)
         (if (<= i -20000000000000.0)
           t_4
           (if (<= i 4.8e-295)
             (* (fma t_1 y1 (fma (- (* y x) (* t z)) b (* t_2 y5))) a)
             (if (<= i 2.8e-135)
               (* (fma (- (* y3 j) (* y2 k)) y5 (* (* (- x) j) b)) y0)
               (if (<= i 2.3e-79)
                 t_4
                 (if (<= i 2.8e-11)
                   (*
                    (fma
                     t_5
                     y
                     (fma
                      (- (* y0 c) (* y1 a))
                      y2
                      (* (- (* y1 i) (* y0 b)) j)))
                    x)
                   (if (<= i 1.75e+109)
                     (* (fma t_6 k (fma t_5 x (* (- (* y4 c) (* y5 a)) y3))) y)
                     (if (<= i 5.6e+177)
                       (* (* (fma (- i) z (* y4 y2)) y1) k)
                       (if (<= i 8e+267)
                         (*
                          (fma
                           t_6
                           y
                           (fma
                            (- (* y4 y1) (* y5 y0))
                            y2
                            (* (- (* y0 b) (* y1 i)) z)))
                          k)
                         (* (* (fma k y5 (* (- c) x)) i) y))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y3 * z) - (y2 * x);
	double t_2 = (y2 * t) - (y3 * y);
	double t_3 = (y2 * k) - (y3 * j);
	double t_4 = fma(((j * t) - (k * y)), b, fma(t_3, y1, (((y3 * y) - (y2 * t)) * c))) * y4;
	double t_5 = (b * a) - (i * c);
	double t_6 = (y5 * i) - (y4 * b);
	double tmp;
	if (i <= -2.3e+249) {
		tmp = fma(t_1, a, fma(t_3, y4, (((j * x) - (k * z)) * i))) * y1;
	} else if (i <= -9.2e+203) {
		tmp = fma(((k * y) - (j * t)), i, fma(-y0, t_3, (t_2 * a))) * y5;
	} else if (i <= -2.6e+131) {
		tmp = (fma(-i, k, (y3 * a)) * z) * y1;
	} else if (i <= -20000000000000.0) {
		tmp = t_4;
	} else if (i <= 4.8e-295) {
		tmp = fma(t_1, y1, fma(((y * x) - (t * z)), b, (t_2 * y5))) * a;
	} else if (i <= 2.8e-135) {
		tmp = fma(((y3 * j) - (y2 * k)), y5, ((-x * j) * b)) * y0;
	} else if (i <= 2.3e-79) {
		tmp = t_4;
	} else if (i <= 2.8e-11) {
		tmp = fma(t_5, y, fma(((y0 * c) - (y1 * a)), y2, (((y1 * i) - (y0 * b)) * j))) * x;
	} else if (i <= 1.75e+109) {
		tmp = fma(t_6, k, fma(t_5, x, (((y4 * c) - (y5 * a)) * y3))) * y;
	} else if (i <= 5.6e+177) {
		tmp = (fma(-i, z, (y4 * y2)) * y1) * k;
	} else if (i <= 8e+267) {
		tmp = fma(t_6, y, fma(((y4 * y1) - (y5 * y0)), y2, (((y0 * b) - (y1 * i)) * z))) * k;
	} else {
		tmp = (fma(k, y5, (-c * x)) * i) * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y3 * z) - Float64(y2 * x))
	t_2 = Float64(Float64(y2 * t) - Float64(y3 * y))
	t_3 = Float64(Float64(y2 * k) - Float64(y3 * j))
	t_4 = Float64(fma(Float64(Float64(j * t) - Float64(k * y)), b, fma(t_3, y1, Float64(Float64(Float64(y3 * y) - Float64(y2 * t)) * c))) * y4)
	t_5 = Float64(Float64(b * a) - Float64(i * c))
	t_6 = Float64(Float64(y5 * i) - Float64(y4 * b))
	tmp = 0.0
	if (i <= -2.3e+249)
		tmp = Float64(fma(t_1, a, fma(t_3, y4, Float64(Float64(Float64(j * x) - Float64(k * z)) * i))) * y1);
	elseif (i <= -9.2e+203)
		tmp = Float64(fma(Float64(Float64(k * y) - Float64(j * t)), i, fma(Float64(-y0), t_3, Float64(t_2 * a))) * y5);
	elseif (i <= -2.6e+131)
		tmp = Float64(Float64(fma(Float64(-i), k, Float64(y3 * a)) * z) * y1);
	elseif (i <= -20000000000000.0)
		tmp = t_4;
	elseif (i <= 4.8e-295)
		tmp = Float64(fma(t_1, y1, fma(Float64(Float64(y * x) - Float64(t * z)), b, Float64(t_2 * y5))) * a);
	elseif (i <= 2.8e-135)
		tmp = Float64(fma(Float64(Float64(y3 * j) - Float64(y2 * k)), y5, Float64(Float64(Float64(-x) * j) * b)) * y0);
	elseif (i <= 2.3e-79)
		tmp = t_4;
	elseif (i <= 2.8e-11)
		tmp = Float64(fma(t_5, y, fma(Float64(Float64(y0 * c) - Float64(y1 * a)), y2, Float64(Float64(Float64(y1 * i) - Float64(y0 * b)) * j))) * x);
	elseif (i <= 1.75e+109)
		tmp = Float64(fma(t_6, k, fma(t_5, x, Float64(Float64(Float64(y4 * c) - Float64(y5 * a)) * y3))) * y);
	elseif (i <= 5.6e+177)
		tmp = Float64(Float64(fma(Float64(-i), z, Float64(y4 * y2)) * y1) * k);
	elseif (i <= 8e+267)
		tmp = Float64(fma(t_6, y, fma(Float64(Float64(y4 * y1) - Float64(y5 * y0)), y2, Float64(Float64(Float64(y0 * b) - Float64(y1 * i)) * z))) * k);
	else
		tmp = Float64(Float64(fma(k, y5, Float64(Float64(-c) * x)) * i) * y);
	end
	return 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[(y3 * z), $MachinePrecision] - N[(y2 * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y2 * t), $MachinePrecision] - N[(y3 * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y2 * k), $MachinePrecision] - N[(y3 * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision] * b + N[(t$95$3 * y1 + N[(N[(N[(y3 * y), $MachinePrecision] - N[(y2 * t), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision]}, Block[{t$95$5 = N[(N[(b * a), $MachinePrecision] - N[(i * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(y5 * i), $MachinePrecision] - N[(y4 * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.3e+249], N[(N[(t$95$1 * a + N[(t$95$3 * y4 + N[(N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision], If[LessEqual[i, -9.2e+203], N[(N[(N[(N[(k * y), $MachinePrecision] - N[(j * t), $MachinePrecision]), $MachinePrecision] * i + N[((-y0) * t$95$3 + N[(t$95$2 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y5), $MachinePrecision], If[LessEqual[i, -2.6e+131], N[(N[(N[((-i) * k + N[(y3 * a), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] * y1), $MachinePrecision], If[LessEqual[i, -20000000000000.0], t$95$4, If[LessEqual[i, 4.8e-295], N[(N[(t$95$1 * y1 + N[(N[(N[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision] * b + N[(t$95$2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[i, 2.8e-135], N[(N[(N[(N[(y3 * j), $MachinePrecision] - N[(y2 * k), $MachinePrecision]), $MachinePrecision] * y5 + N[(N[((-x) * j), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] * y0), $MachinePrecision], If[LessEqual[i, 2.3e-79], t$95$4, If[LessEqual[i, 2.8e-11], N[(N[(t$95$5 * y + N[(N[(N[(y0 * c), $MachinePrecision] - N[(y1 * a), $MachinePrecision]), $MachinePrecision] * y2 + N[(N[(N[(y1 * i), $MachinePrecision] - N[(y0 * b), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[i, 1.75e+109], N[(N[(t$95$6 * k + N[(t$95$5 * x + N[(N[(N[(y4 * c), $MachinePrecision] - N[(y5 * a), $MachinePrecision]), $MachinePrecision] * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[i, 5.6e+177], N[(N[(N[((-i) * z + N[(y4 * y2), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision] * k), $MachinePrecision], If[LessEqual[i, 8e+267], N[(N[(t$95$6 * y + N[(N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision] * y2 + N[(N[(N[(y0 * b), $MachinePrecision] - N[(y1 * i), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * k), $MachinePrecision], N[(N[(N[(k * y5 + N[((-c) * x), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision] * y), $MachinePrecision]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 11 regimes

2. if i < -2.2999999999999998e249

   1. Initial program 33.3%

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

   3. Taylor expanded in y1 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 71.5%

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

   if -2.2999999999999998e249 < i < -9.1999999999999996e203

   1. Initial program 16.5%

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

   3. Taylor expanded in y5 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 67.6%

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

   if -9.1999999999999996e203 < i < -2.6e131

   1. Initial program 27.0%

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

   3. Taylor expanded in y1 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 76.9%

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

   6. Taylor expanded in j around inf

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

   8. Applied rewrites 36.8%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 77.1%

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

   if -2.6e131 < i < -2e13 or 2.80000000000000023e-135 < i < 2.30000000000000012e-79

   1. Initial program 42.2%

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

   3. Taylor expanded in y4 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 71.4%

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

   if -2e13 < i < 4.7999999999999996e-295

   1. Initial program 41.3%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 59.4%

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

   if 4.7999999999999996e-295 < i < 2.80000000000000023e-135

   1. Initial program 17.8%

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

   3. Taylor expanded in y0 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 56.2%

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

   6. Taylor expanded in j around inf

      \[\leadsto \mathsf{fma}\left(-\left(k \cdot y2 - j \cdot y3\right), y5, -1 \cdot \left(b \cdot \left(j \cdot x\right)\right)\right) \cdot y0 \]
   7. Step-by-step derivation

   8. Applied rewrites 53.6%

      \[\leadsto \mathsf{fma}\left(-\left(k \cdot y2 - j \cdot y3\right), y5, -b \cdot \left(j \cdot x\right)\right) \cdot y0 \]

   if 2.30000000000000012e-79 < i < 2.8e-11

   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 x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 66.1%

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

   if 2.8e-11 < i < 1.74999999999999992e109

   1. Initial program 18.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 78.8%

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

   if 1.74999999999999992e109 < i < 5.60000000000000004e177

   1. Initial program 25.6%

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

   3. Taylor expanded in y1 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 50.0%

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

   6. Taylor expanded in j around inf

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

   8. Applied rewrites 50.3%

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

   9. Taylor expanded in k around inf

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

   11. Applied rewrites 75.5%

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

   if 5.60000000000000004e177 < i < 7.9999999999999998e267

   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 k around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 82.4%

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

   if 7.9999999999999998e267 < i

   1. Initial program 8.3%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 8.3%

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

   6. Taylor expanded in i around inf

      \[\leadsto \left(i \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 66.7%

      \[\leadsto \left(i \cdot \mathsf{fma}\left(k, y5, -c \cdot x\right)\right) \cdot y \]
3. Recombined 11 regimes into one program.

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.3 \cdot 10^{+249}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot z - y2 \cdot x, a, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1\\ \mathbf{elif}\;i \leq -9.2 \cdot 10^{+203}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot y - j \cdot t, i, \mathsf{fma}\left(-y0, y2 \cdot k - y3 \cdot j, \left(y2 \cdot t - y3 \cdot y\right) \cdot a\right)\right) \cdot y5\\ \mathbf{elif}\;i \leq -2.6 \cdot 10^{+131}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, k, y3 \cdot a\right) \cdot z\right) \cdot y1\\ \mathbf{elif}\;i \leq -20000000000000:\\ \;\;\;\;\mathsf{fma}\left(j \cdot t - k \cdot y, b, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y1, \left(y3 \cdot y - y2 \cdot t\right) \cdot c\right)\right) \cdot y4\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{-295}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot z - y2 \cdot x, y1, \mathsf{fma}\left(y \cdot x - t \cdot z, b, \left(y2 \cdot t - y3 \cdot y\right) \cdot y5\right)\right) \cdot a\\ \mathbf{elif}\;i \leq 2.8 \cdot 10^{-135}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot j - y2 \cdot k, y5, \left(\left(-x\right) \cdot j\right) \cdot b\right) \cdot y0\\ \mathbf{elif}\;i \leq 2.3 \cdot 10^{-79}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot t - k \cdot y, b, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y1, \left(y3 \cdot y - y2 \cdot t\right) \cdot c\right)\right) \cdot y4\\ \mathbf{elif}\;i \leq 2.8 \cdot 10^{-11}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot a - i \cdot c, y, \mathsf{fma}\left(y0 \cdot c - y1 \cdot a, y2, \left(y1 \cdot i - y0 \cdot b\right) \cdot j\right)\right) \cdot x\\ \mathbf{elif}\;i \leq 1.75 \cdot 10^{+109}:\\ \;\;\;\;\mathsf{fma}\left(y5 \cdot i - y4 \cdot b, k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y\\ \mathbf{elif}\;i \leq 5.6 \cdot 10^{+177}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, z, y4 \cdot y2\right) \cdot y1\right) \cdot k\\ \mathbf{elif}\;i \leq 8 \cdot 10^{+267}:\\ \;\;\;\;\mathsf{fma}\left(y5 \cdot i - y4 \cdot b, y, \mathsf{fma}\left(y4 \cdot y1 - y5 \cdot y0, y2, \left(y0 \cdot b - y1 \cdot i\right) \cdot z\right)\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y5, \left(-c\right) \cdot x\right) \cdot i\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 43.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot t - k \cdot y\\ t_2 := y2 \cdot t - y3 \cdot y\\ t_3 := y3 \cdot z - y2 \cdot x\\ t_4 := j \cdot x - k \cdot z\\ t_5 := y2 \cdot k - y3 \cdot j\\ t_6 := \mathsf{fma}\left(t \cdot z - y \cdot x, c, \mathsf{fma}\left(-y5, t\_1, t\_4 \cdot y1\right)\right) \cdot i\\ \mathbf{if}\;i \leq -2.3 \cdot 10^{+249}:\\ \;\;\;\;\mathsf{fma}\left(t\_3, a, \mathsf{fma}\left(t\_5, y4, t\_4 \cdot i\right)\right) \cdot y1\\ \mathbf{elif}\;i \leq -1.6 \cdot 10^{+204}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot y - j \cdot t, i, \mathsf{fma}\left(-y0, t\_5, t\_2 \cdot a\right)\right) \cdot y5\\ \mathbf{elif}\;i \leq -5.8 \cdot 10^{+90}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;i \leq 6.6 \cdot 10^{-253}:\\ \;\;\;\;\mathsf{fma}\left(t\_3, y1, \mathsf{fma}\left(y \cdot x - t \cdot z, b, t\_2 \cdot y5\right)\right) \cdot a\\ \mathbf{elif}\;i \leq 2.8 \cdot 10^{-135}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot j - y2 \cdot k, y5, \mathsf{fma}\left(c, y2 \cdot x - y3 \cdot z, \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \cdot y0\\ \mathbf{elif}\;i \leq 1.4 \cdot 10^{-45}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, b, \mathsf{fma}\left(t\_5, y1, \left(y3 \cdot y - y2 \cdot t\right) \cdot c\right)\right) \cdot y4\\ \mathbf{elif}\;i \leq 3.7 \cdot 10^{+24}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;i \leq 1.75 \cdot 10^{+109}:\\ \;\;\;\;\mathsf{fma}\left(y5 \cdot i - y4 \cdot b, k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y\\ \mathbf{elif}\;i \leq 6.2 \cdot 10^{+177}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, z, y4 \cdot y2\right) \cdot y1\right) \cdot k\\ \mathbf{elif}\;i \leq 4.3 \cdot 10^{+207}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot x, \mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right), \mathsf{fma}\left(y3, \mathsf{fma}\left(c, y4, \left(-y5\right) \cdot a\right), \mathsf{fma}\left(-b, y4, y5 \cdot i\right) \cdot k\right) \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_6\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* j t) (* k y)))
        (t_2 (- (* y2 t) (* y3 y)))
        (t_3 (- (* y3 z) (* y2 x)))
        (t_4 (- (* j x) (* k z)))
        (t_5 (- (* y2 k) (* y3 j)))
        (t_6 (* (fma (- (* t z) (* y x)) c (fma (- y5) t_1 (* t_4 y1))) i)))
   (if (<= i -2.3e+249)
     (* (fma t_3 a (fma t_5 y4 (* t_4 i))) y1)
     (if (<= i -1.6e+204)
       (* (fma (- (* k y) (* j t)) i (fma (- y0) t_5 (* t_2 a))) y5)
       (if (<= i -5.8e+90)
         t_6
         (if (<= i 6.6e-253)
           (* (fma t_3 y1 (fma (- (* y x) (* t z)) b (* t_2 y5))) a)
           (if (<= i 2.8e-135)
             (*
              (fma
               (- (* y3 j) (* y2 k))
               y5
               (fma c (- (* y2 x) (* y3 z)) (* (- (* k z) (* j x)) b)))
              y0)
             (if (<= i 1.4e-45)
               (* (fma t_1 b (fma t_5 y1 (* (- (* y3 y) (* y2 t)) c))) y4)
               (if (<= i 3.7e+24)
                 t_6
                 (if (<= i 1.75e+109)
                   (*
                    (fma
                     (- (* y5 i) (* y4 b))
                     k
                     (fma (- (* b a) (* i c)) x (* (- (* y4 c) (* y5 a)) y3)))
                    y)
                   (if (<= i 6.2e+177)
                     (* (* (fma (- i) z (* y4 y2)) y1) k)
                     (if (<= i 4.3e+207)
                       (fma
                        (* y x)
                        (fma a b (* (- c) i))
                        (*
                         (fma
                          y3
                          (fma c y4 (* (- y5) a))
                          (* (fma (- b) y4 (* y5 i)) k))
                         y))
                       t_6))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (j * t) - (k * y);
	double t_2 = (y2 * t) - (y3 * y);
	double t_3 = (y3 * z) - (y2 * x);
	double t_4 = (j * x) - (k * z);
	double t_5 = (y2 * k) - (y3 * j);
	double t_6 = fma(((t * z) - (y * x)), c, fma(-y5, t_1, (t_4 * y1))) * i;
	double tmp;
	if (i <= -2.3e+249) {
		tmp = fma(t_3, a, fma(t_5, y4, (t_4 * i))) * y1;
	} else if (i <= -1.6e+204) {
		tmp = fma(((k * y) - (j * t)), i, fma(-y0, t_5, (t_2 * a))) * y5;
	} else if (i <= -5.8e+90) {
		tmp = t_6;
	} else if (i <= 6.6e-253) {
		tmp = fma(t_3, y1, fma(((y * x) - (t * z)), b, (t_2 * y5))) * a;
	} else if (i <= 2.8e-135) {
		tmp = fma(((y3 * j) - (y2 * k)), y5, fma(c, ((y2 * x) - (y3 * z)), (((k * z) - (j * x)) * b))) * y0;
	} else if (i <= 1.4e-45) {
		tmp = fma(t_1, b, fma(t_5, y1, (((y3 * y) - (y2 * t)) * c))) * y4;
	} else if (i <= 3.7e+24) {
		tmp = t_6;
	} else if (i <= 1.75e+109) {
		tmp = fma(((y5 * i) - (y4 * b)), k, fma(((b * a) - (i * c)), x, (((y4 * c) - (y5 * a)) * y3))) * y;
	} else if (i <= 6.2e+177) {
		tmp = (fma(-i, z, (y4 * y2)) * y1) * k;
	} else if (i <= 4.3e+207) {
		tmp = fma((y * x), fma(a, b, (-c * i)), (fma(y3, fma(c, y4, (-y5 * a)), (fma(-b, y4, (y5 * i)) * k)) * y));
	} else {
		tmp = t_6;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(j * t) - Float64(k * y))
	t_2 = Float64(Float64(y2 * t) - Float64(y3 * y))
	t_3 = Float64(Float64(y3 * z) - Float64(y2 * x))
	t_4 = Float64(Float64(j * x) - Float64(k * z))
	t_5 = Float64(Float64(y2 * k) - Float64(y3 * j))
	t_6 = Float64(fma(Float64(Float64(t * z) - Float64(y * x)), c, fma(Float64(-y5), t_1, Float64(t_4 * y1))) * i)
	tmp = 0.0
	if (i <= -2.3e+249)
		tmp = Float64(fma(t_3, a, fma(t_5, y4, Float64(t_4 * i))) * y1);
	elseif (i <= -1.6e+204)
		tmp = Float64(fma(Float64(Float64(k * y) - Float64(j * t)), i, fma(Float64(-y0), t_5, Float64(t_2 * a))) * y5);
	elseif (i <= -5.8e+90)
		tmp = t_6;
	elseif (i <= 6.6e-253)
		tmp = Float64(fma(t_3, y1, fma(Float64(Float64(y * x) - Float64(t * z)), b, Float64(t_2 * y5))) * a);
	elseif (i <= 2.8e-135)
		tmp = Float64(fma(Float64(Float64(y3 * j) - Float64(y2 * k)), y5, fma(c, Float64(Float64(y2 * x) - Float64(y3 * z)), Float64(Float64(Float64(k * z) - Float64(j * x)) * b))) * y0);
	elseif (i <= 1.4e-45)
		tmp = Float64(fma(t_1, b, fma(t_5, y1, Float64(Float64(Float64(y3 * y) - Float64(y2 * t)) * c))) * y4);
	elseif (i <= 3.7e+24)
		tmp = t_6;
	elseif (i <= 1.75e+109)
		tmp = Float64(fma(Float64(Float64(y5 * i) - Float64(y4 * b)), k, fma(Float64(Float64(b * a) - Float64(i * c)), x, Float64(Float64(Float64(y4 * c) - Float64(y5 * a)) * y3))) * y);
	elseif (i <= 6.2e+177)
		tmp = Float64(Float64(fma(Float64(-i), z, Float64(y4 * y2)) * y1) * k);
	elseif (i <= 4.3e+207)
		tmp = fma(Float64(y * x), fma(a, b, Float64(Float64(-c) * i)), Float64(fma(y3, fma(c, y4, Float64(Float64(-y5) * a)), Float64(fma(Float64(-b), y4, Float64(y5 * i)) * k)) * y));
	else
		tmp = t_6;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y2 * t), $MachinePrecision] - N[(y3 * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y3 * z), $MachinePrecision] - N[(y2 * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(y2 * k), $MachinePrecision] - N[(y3 * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(N[(t * z), $MachinePrecision] - N[(y * x), $MachinePrecision]), $MachinePrecision] * c + N[((-y5) * t$95$1 + N[(t$95$4 * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[i, -2.3e+249], N[(N[(t$95$3 * a + N[(t$95$5 * y4 + N[(t$95$4 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision], If[LessEqual[i, -1.6e+204], N[(N[(N[(N[(k * y), $MachinePrecision] - N[(j * t), $MachinePrecision]), $MachinePrecision] * i + N[((-y0) * t$95$5 + N[(t$95$2 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y5), $MachinePrecision], If[LessEqual[i, -5.8e+90], t$95$6, If[LessEqual[i, 6.6e-253], N[(N[(t$95$3 * y1 + N[(N[(N[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision] * b + N[(t$95$2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[i, 2.8e-135], N[(N[(N[(N[(y3 * j), $MachinePrecision] - N[(y2 * k), $MachinePrecision]), $MachinePrecision] * y5 + N[(c * N[(N[(y2 * x), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(k * z), $MachinePrecision] - N[(j * x), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y0), $MachinePrecision], If[LessEqual[i, 1.4e-45], N[(N[(t$95$1 * b + N[(t$95$5 * y1 + N[(N[(N[(y3 * y), $MachinePrecision] - N[(y2 * t), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision], If[LessEqual[i, 3.7e+24], t$95$6, If[LessEqual[i, 1.75e+109], N[(N[(N[(N[(y5 * i), $MachinePrecision] - N[(y4 * b), $MachinePrecision]), $MachinePrecision] * k + N[(N[(N[(b * a), $MachinePrecision] - N[(i * c), $MachinePrecision]), $MachinePrecision] * x + N[(N[(N[(y4 * c), $MachinePrecision] - N[(y5 * a), $MachinePrecision]), $MachinePrecision] * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[i, 6.2e+177], N[(N[(N[((-i) * z + N[(y4 * y2), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision] * k), $MachinePrecision], If[LessEqual[i, 4.3e+207], N[(N[(y * x), $MachinePrecision] * N[(a * b + N[((-c) * i), $MachinePrecision]), $MachinePrecision] + N[(N[(y3 * N[(c * y4 + N[((-y5) * a), $MachinePrecision]), $MachinePrecision] + N[(N[((-b) * y4 + N[(y5 * i), $MachinePrecision]), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], t$95$6]]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if i < -2.2999999999999998e249

   1. Initial program 33.3%

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

   3. Taylor expanded in y1 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 71.5%

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

   if -2.2999999999999998e249 < i < -1.6e204

   1. Initial program 16.5%

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

   3. Taylor expanded in y5 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 67.6%

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

   if -1.6e204 < i < -5.8000000000000003e90 or 1.4000000000000001e-45 < i < 3.69999999999999999e24 or 4.2999999999999997e207 < i

   1. Initial program 23.6%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 69.9%

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

   if -5.8000000000000003e90 < i < 6.6000000000000002e-253

   1. Initial program 39.6%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 57.9%

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

   if 6.6000000000000002e-253 < i < 2.80000000000000023e-135

   1. Initial program 15.0%

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

   3. Taylor expanded in y0 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 59.7%

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

   if 2.80000000000000023e-135 < i < 1.4000000000000001e-45

   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 y4 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 66.2%

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

   if 3.69999999999999999e24 < i < 1.74999999999999992e109

   1. Initial program 17.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 78.5%

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

   if 1.74999999999999992e109 < i < 6.1999999999999998e177

   1. Initial program 25.6%

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

   3. Taylor expanded in y1 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 50.0%

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

   6. Taylor expanded in j around inf

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

   8. Applied rewrites 50.3%

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

   9. Taylor expanded in k around inf

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

   11. Applied rewrites 75.5%

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

   if 6.1999999999999998e177 < i < 4.2999999999999997e207

   1. Initial program 42.9%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 85.7%

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

   6. Taylor expanded in i around inf

      \[\leadsto \left(i \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 43.8%

      \[\leadsto \left(i \cdot \mathsf{fma}\left(k, y5, -c \cdot x\right)\right) \cdot y \]

   9. Taylor expanded in x around 0

      \[\leadsto x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right) + \color{blue}{y \cdot \left(k \cdot \left(i \cdot y5 - b \cdot y4\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 100.0%

       \[\leadsto \mathsf{fma}\left(x \cdot y, \color{blue}{\mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right)}, y \cdot \mathsf{fma}\left(y3, \mathsf{fma}\left(c, y4, \left(-a\right) \cdot y5\right), k \cdot \mathsf{fma}\left(-b, y4, i \cdot y5\right)\right)\right) \]
3. Recombined 9 regimes into one program.

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.3 \cdot 10^{+249}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot z - y2 \cdot x, a, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1\\ \mathbf{elif}\;i \leq -1.6 \cdot 10^{+204}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot y - j \cdot t, i, \mathsf{fma}\left(-y0, y2 \cdot k - y3 \cdot j, \left(y2 \cdot t - y3 \cdot y\right) \cdot a\right)\right) \cdot y5\\ \mathbf{elif}\;i \leq -5.8 \cdot 10^{+90}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot z - y \cdot x, c, \mathsf{fma}\left(-y5, j \cdot t - k \cdot y, \left(j \cdot x - k \cdot z\right) \cdot y1\right)\right) \cdot i\\ \mathbf{elif}\;i \leq 6.6 \cdot 10^{-253}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot z - y2 \cdot x, y1, \mathsf{fma}\left(y \cdot x - t \cdot z, b, \left(y2 \cdot t - y3 \cdot y\right) \cdot y5\right)\right) \cdot a\\ \mathbf{elif}\;i \leq 2.8 \cdot 10^{-135}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot j - y2 \cdot k, y5, \mathsf{fma}\left(c, y2 \cdot x - y3 \cdot z, \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \cdot y0\\ \mathbf{elif}\;i \leq 1.4 \cdot 10^{-45}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot t - k \cdot y, b, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y1, \left(y3 \cdot y - y2 \cdot t\right) \cdot c\right)\right) \cdot y4\\ \mathbf{elif}\;i \leq 3.7 \cdot 10^{+24}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot z - y \cdot x, c, \mathsf{fma}\left(-y5, j \cdot t - k \cdot y, \left(j \cdot x - k \cdot z\right) \cdot y1\right)\right) \cdot i\\ \mathbf{elif}\;i \leq 1.75 \cdot 10^{+109}:\\ \;\;\;\;\mathsf{fma}\left(y5 \cdot i - y4 \cdot b, k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y\\ \mathbf{elif}\;i \leq 6.2 \cdot 10^{+177}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, z, y4 \cdot y2\right) \cdot y1\right) \cdot k\\ \mathbf{elif}\;i \leq 4.3 \cdot 10^{+207}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot x, \mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right), \mathsf{fma}\left(y3, \mathsf{fma}\left(c, y4, \left(-y5\right) \cdot a\right), \mathsf{fma}\left(-b, y4, y5 \cdot i\right) \cdot k\right) \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot z - y \cdot x, c, \mathsf{fma}\left(-y5, j \cdot t - k \cdot y, \left(j \cdot x - k \cdot z\right) \cdot y1\right)\right) \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 42.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot t - k \cdot y\\ t_2 := y2 \cdot t - y3 \cdot y\\ t_3 := y5 \cdot i - y4 \cdot b\\ t_4 := y3 \cdot z - y2 \cdot x\\ t_5 := j \cdot x - k \cdot z\\ t_6 := y2 \cdot k - y3 \cdot j\\ t_7 := \mathsf{fma}\left(t \cdot z - y \cdot x, c, \mathsf{fma}\left(-y5, t\_1, t\_5 \cdot y1\right)\right) \cdot i\\ \mathbf{if}\;i \leq -2.3 \cdot 10^{+249}:\\ \;\;\;\;\mathsf{fma}\left(t\_4, a, \mathsf{fma}\left(t\_6, y4, t\_5 \cdot i\right)\right) \cdot y1\\ \mathbf{elif}\;i \leq -1.6 \cdot 10^{+204}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot y - j \cdot t, i, \mathsf{fma}\left(-y0, t\_6, t\_2 \cdot a\right)\right) \cdot y5\\ \mathbf{elif}\;i \leq -5.8 \cdot 10^{+90}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;i \leq 6.6 \cdot 10^{-253}:\\ \;\;\;\;\mathsf{fma}\left(t\_4, y1, \mathsf{fma}\left(y \cdot x - t \cdot z, b, t\_2 \cdot y5\right)\right) \cdot a\\ \mathbf{elif}\;i \leq 2.8 \cdot 10^{-135}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot j - y2 \cdot k, y5, \mathsf{fma}\left(c, y2 \cdot x - y3 \cdot z, \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \cdot y0\\ \mathbf{elif}\;i \leq 1.4 \cdot 10^{-45}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, b, \mathsf{fma}\left(t\_6, y1, \left(y3 \cdot y - y2 \cdot t\right) \cdot c\right)\right) \cdot y4\\ \mathbf{elif}\;i \leq 3.7 \cdot 10^{+24}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;i \leq 1.75 \cdot 10^{+109}:\\ \;\;\;\;\mathsf{fma}\left(t\_3, k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y\\ \mathbf{elif}\;i \leq 5.6 \cdot 10^{+177}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, z, y4 \cdot y2\right) \cdot y1\right) \cdot k\\ \mathbf{elif}\;i \leq 4.5 \cdot 10^{+249}:\\ \;\;\;\;\mathsf{fma}\left(t\_3, y, \mathsf{fma}\left(y4 \cdot y1 - y5 \cdot y0, y2, \left(y0 \cdot b - y1 \cdot i\right) \cdot z\right)\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t\_7\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* j t) (* k y)))
        (t_2 (- (* y2 t) (* y3 y)))
        (t_3 (- (* y5 i) (* y4 b)))
        (t_4 (- (* y3 z) (* y2 x)))
        (t_5 (- (* j x) (* k z)))
        (t_6 (- (* y2 k) (* y3 j)))
        (t_7 (* (fma (- (* t z) (* y x)) c (fma (- y5) t_1 (* t_5 y1))) i)))
   (if (<= i -2.3e+249)
     (* (fma t_4 a (fma t_6 y4 (* t_5 i))) y1)
     (if (<= i -1.6e+204)
       (* (fma (- (* k y) (* j t)) i (fma (- y0) t_6 (* t_2 a))) y5)
       (if (<= i -5.8e+90)
         t_7
         (if (<= i 6.6e-253)
           (* (fma t_4 y1 (fma (- (* y x) (* t z)) b (* t_2 y5))) a)
           (if (<= i 2.8e-135)
             (*
              (fma
               (- (* y3 j) (* y2 k))
               y5
               (fma c (- (* y2 x) (* y3 z)) (* (- (* k z) (* j x)) b)))
              y0)
             (if (<= i 1.4e-45)
               (* (fma t_1 b (fma t_6 y1 (* (- (* y3 y) (* y2 t)) c))) y4)
               (if (<= i 3.7e+24)
                 t_7
                 (if (<= i 1.75e+109)
                   (*
                    (fma
                     t_3
                     k
                     (fma (- (* b a) (* i c)) x (* (- (* y4 c) (* y5 a)) y3)))
                    y)
                   (if (<= i 5.6e+177)
                     (* (* (fma (- i) z (* y4 y2)) y1) k)
                     (if (<= i 4.5e+249)
                       (*
                        (fma
                         t_3
                         y
                         (fma
                          (- (* y4 y1) (* y5 y0))
                          y2
                          (* (- (* y0 b) (* y1 i)) z)))
                        k)
                       t_7))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (j * t) - (k * y);
	double t_2 = (y2 * t) - (y3 * y);
	double t_3 = (y5 * i) - (y4 * b);
	double t_4 = (y3 * z) - (y2 * x);
	double t_5 = (j * x) - (k * z);
	double t_6 = (y2 * k) - (y3 * j);
	double t_7 = fma(((t * z) - (y * x)), c, fma(-y5, t_1, (t_5 * y1))) * i;
	double tmp;
	if (i <= -2.3e+249) {
		tmp = fma(t_4, a, fma(t_6, y4, (t_5 * i))) * y1;
	} else if (i <= -1.6e+204) {
		tmp = fma(((k * y) - (j * t)), i, fma(-y0, t_6, (t_2 * a))) * y5;
	} else if (i <= -5.8e+90) {
		tmp = t_7;
	} else if (i <= 6.6e-253) {
		tmp = fma(t_4, y1, fma(((y * x) - (t * z)), b, (t_2 * y5))) * a;
	} else if (i <= 2.8e-135) {
		tmp = fma(((y3 * j) - (y2 * k)), y5, fma(c, ((y2 * x) - (y3 * z)), (((k * z) - (j * x)) * b))) * y0;
	} else if (i <= 1.4e-45) {
		tmp = fma(t_1, b, fma(t_6, y1, (((y3 * y) - (y2 * t)) * c))) * y4;
	} else if (i <= 3.7e+24) {
		tmp = t_7;
	} else if (i <= 1.75e+109) {
		tmp = fma(t_3, k, fma(((b * a) - (i * c)), x, (((y4 * c) - (y5 * a)) * y3))) * y;
	} else if (i <= 5.6e+177) {
		tmp = (fma(-i, z, (y4 * y2)) * y1) * k;
	} else if (i <= 4.5e+249) {
		tmp = fma(t_3, y, fma(((y4 * y1) - (y5 * y0)), y2, (((y0 * b) - (y1 * i)) * z))) * k;
	} else {
		tmp = t_7;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(j * t) - Float64(k * y))
	t_2 = Float64(Float64(y2 * t) - Float64(y3 * y))
	t_3 = Float64(Float64(y5 * i) - Float64(y4 * b))
	t_4 = Float64(Float64(y3 * z) - Float64(y2 * x))
	t_5 = Float64(Float64(j * x) - Float64(k * z))
	t_6 = Float64(Float64(y2 * k) - Float64(y3 * j))
	t_7 = Float64(fma(Float64(Float64(t * z) - Float64(y * x)), c, fma(Float64(-y5), t_1, Float64(t_5 * y1))) * i)
	tmp = 0.0
	if (i <= -2.3e+249)
		tmp = Float64(fma(t_4, a, fma(t_6, y4, Float64(t_5 * i))) * y1);
	elseif (i <= -1.6e+204)
		tmp = Float64(fma(Float64(Float64(k * y) - Float64(j * t)), i, fma(Float64(-y0), t_6, Float64(t_2 * a))) * y5);
	elseif (i <= -5.8e+90)
		tmp = t_7;
	elseif (i <= 6.6e-253)
		tmp = Float64(fma(t_4, y1, fma(Float64(Float64(y * x) - Float64(t * z)), b, Float64(t_2 * y5))) * a);
	elseif (i <= 2.8e-135)
		tmp = Float64(fma(Float64(Float64(y3 * j) - Float64(y2 * k)), y5, fma(c, Float64(Float64(y2 * x) - Float64(y3 * z)), Float64(Float64(Float64(k * z) - Float64(j * x)) * b))) * y0);
	elseif (i <= 1.4e-45)
		tmp = Float64(fma(t_1, b, fma(t_6, y1, Float64(Float64(Float64(y3 * y) - Float64(y2 * t)) * c))) * y4);
	elseif (i <= 3.7e+24)
		tmp = t_7;
	elseif (i <= 1.75e+109)
		tmp = Float64(fma(t_3, k, fma(Float64(Float64(b * a) - Float64(i * c)), x, Float64(Float64(Float64(y4 * c) - Float64(y5 * a)) * y3))) * y);
	elseif (i <= 5.6e+177)
		tmp = Float64(Float64(fma(Float64(-i), z, Float64(y4 * y2)) * y1) * k);
	elseif (i <= 4.5e+249)
		tmp = Float64(fma(t_3, y, fma(Float64(Float64(y4 * y1) - Float64(y5 * y0)), y2, Float64(Float64(Float64(y0 * b) - Float64(y1 * i)) * z))) * k);
	else
		tmp = t_7;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y2 * t), $MachinePrecision] - N[(y3 * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y5 * i), $MachinePrecision] - N[(y4 * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(y3 * z), $MachinePrecision] - N[(y2 * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(y2 * k), $MachinePrecision] - N[(y3 * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(N[(N[(t * z), $MachinePrecision] - N[(y * x), $MachinePrecision]), $MachinePrecision] * c + N[((-y5) * t$95$1 + N[(t$95$5 * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[i, -2.3e+249], N[(N[(t$95$4 * a + N[(t$95$6 * y4 + N[(t$95$5 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision], If[LessEqual[i, -1.6e+204], N[(N[(N[(N[(k * y), $MachinePrecision] - N[(j * t), $MachinePrecision]), $MachinePrecision] * i + N[((-y0) * t$95$6 + N[(t$95$2 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y5), $MachinePrecision], If[LessEqual[i, -5.8e+90], t$95$7, If[LessEqual[i, 6.6e-253], N[(N[(t$95$4 * y1 + N[(N[(N[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision] * b + N[(t$95$2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[i, 2.8e-135], N[(N[(N[(N[(y3 * j), $MachinePrecision] - N[(y2 * k), $MachinePrecision]), $MachinePrecision] * y5 + N[(c * N[(N[(y2 * x), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(k * z), $MachinePrecision] - N[(j * x), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y0), $MachinePrecision], If[LessEqual[i, 1.4e-45], N[(N[(t$95$1 * b + N[(t$95$6 * y1 + N[(N[(N[(y3 * y), $MachinePrecision] - N[(y2 * t), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision], If[LessEqual[i, 3.7e+24], t$95$7, If[LessEqual[i, 1.75e+109], N[(N[(t$95$3 * k + N[(N[(N[(b * a), $MachinePrecision] - N[(i * c), $MachinePrecision]), $MachinePrecision] * x + N[(N[(N[(y4 * c), $MachinePrecision] - N[(y5 * a), $MachinePrecision]), $MachinePrecision] * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[i, 5.6e+177], N[(N[(N[((-i) * z + N[(y4 * y2), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision] * k), $MachinePrecision], If[LessEqual[i, 4.5e+249], N[(N[(t$95$3 * y + N[(N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision] * y2 + N[(N[(N[(y0 * b), $MachinePrecision] - N[(y1 * i), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * k), $MachinePrecision], t$95$7]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if i < -2.2999999999999998e249

   1. Initial program 33.3%

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

   3. Taylor expanded in y1 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 71.5%

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

   if -2.2999999999999998e249 < i < -1.6e204

   1. Initial program 16.5%

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

   3. Taylor expanded in y5 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 67.6%

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

   if -1.6e204 < i < -5.8000000000000003e90 or 1.4000000000000001e-45 < i < 3.69999999999999999e24 or 4.4999999999999996e249 < i

   1. Initial program 22.9%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 69.7%

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

   if -5.8000000000000003e90 < i < 6.6000000000000002e-253

   1. Initial program 39.6%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 57.9%

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

   if 6.6000000000000002e-253 < i < 2.80000000000000023e-135

   1. Initial program 15.0%

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

   3. Taylor expanded in y0 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 59.7%

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

   if 2.80000000000000023e-135 < i < 1.4000000000000001e-45

   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 y4 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 66.2%

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

   if 3.69999999999999999e24 < i < 1.74999999999999992e109

   1. Initial program 17.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 78.5%

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

   if 1.74999999999999992e109 < i < 5.60000000000000004e177

   1. Initial program 25.6%

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

   3. Taylor expanded in y1 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 50.0%

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

   6. Taylor expanded in j around inf

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

   8. Applied rewrites 50.3%

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

   9. Taylor expanded in k around inf

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

   11. Applied rewrites 75.5%

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

   if 5.60000000000000004e177 < i < 4.4999999999999996e249

   1. Initial program 35.7%

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

   3. Taylor expanded in k around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 85.7%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.3 \cdot 10^{+249}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot z - y2 \cdot x, a, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1\\ \mathbf{elif}\;i \leq -1.6 \cdot 10^{+204}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot y - j \cdot t, i, \mathsf{fma}\left(-y0, y2 \cdot k - y3 \cdot j, \left(y2 \cdot t - y3 \cdot y\right) \cdot a\right)\right) \cdot y5\\ \mathbf{elif}\;i \leq -5.8 \cdot 10^{+90}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot z - y \cdot x, c, \mathsf{fma}\left(-y5, j \cdot t - k \cdot y, \left(j \cdot x - k \cdot z\right) \cdot y1\right)\right) \cdot i\\ \mathbf{elif}\;i \leq 6.6 \cdot 10^{-253}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot z - y2 \cdot x, y1, \mathsf{fma}\left(y \cdot x - t \cdot z, b, \left(y2 \cdot t - y3 \cdot y\right) \cdot y5\right)\right) \cdot a\\ \mathbf{elif}\;i \leq 2.8 \cdot 10^{-135}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot j - y2 \cdot k, y5, \mathsf{fma}\left(c, y2 \cdot x - y3 \cdot z, \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \cdot y0\\ \mathbf{elif}\;i \leq 1.4 \cdot 10^{-45}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot t - k \cdot y, b, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y1, \left(y3 \cdot y - y2 \cdot t\right) \cdot c\right)\right) \cdot y4\\ \mathbf{elif}\;i \leq 3.7 \cdot 10^{+24}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot z - y \cdot x, c, \mathsf{fma}\left(-y5, j \cdot t - k \cdot y, \left(j \cdot x - k \cdot z\right) \cdot y1\right)\right) \cdot i\\ \mathbf{elif}\;i \leq 1.75 \cdot 10^{+109}:\\ \;\;\;\;\mathsf{fma}\left(y5 \cdot i - y4 \cdot b, k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y\\ \mathbf{elif}\;i \leq 5.6 \cdot 10^{+177}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, z, y4 \cdot y2\right) \cdot y1\right) \cdot k\\ \mathbf{elif}\;i \leq 4.5 \cdot 10^{+249}:\\ \;\;\;\;\mathsf{fma}\left(y5 \cdot i - y4 \cdot b, y, \mathsf{fma}\left(y4 \cdot y1 - y5 \cdot y0, y2, \left(y0 \cdot b - y1 \cdot i\right) \cdot z\right)\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot z - y \cdot x, c, \mathsf{fma}\left(-y5, j \cdot t - k \cdot y, \left(j \cdot x - k \cdot z\right) \cdot y1\right)\right) \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 38.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y3 \cdot z - y2 \cdot x\\ t_2 := y2 \cdot k - y3 \cdot j\\ t_3 := b \cdot a - i \cdot c\\ t_4 := y5 \cdot i - y4 \cdot b\\ \mathbf{if}\;i \leq -9.5 \cdot 10^{+232}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, a, \mathsf{fma}\left(t\_2, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1\\ \mathbf{elif}\;i \leq -1 \cdot 10^{+192}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y1, \left(-t\right) \cdot c\right) \cdot y4\right) \cdot y2\\ \mathbf{elif}\;i \leq -7.5 \cdot 10^{+90}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y, \left(-t\right) \cdot j\right) \cdot i\right) \cdot y5\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{-295}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, y1, \mathsf{fma}\left(y \cdot x - t \cdot z, b, \left(y2 \cdot t - y3 \cdot y\right) \cdot y5\right)\right) \cdot a\\ \mathbf{elif}\;i \leq 2.8 \cdot 10^{-135}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot j - y2 \cdot k, y5, \left(\left(-x\right) \cdot j\right) \cdot b\right) \cdot y0\\ \mathbf{elif}\;i \leq 2.3 \cdot 10^{-79}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot t - k \cdot y, b, \mathsf{fma}\left(t\_2, y1, \left(y3 \cdot y - y2 \cdot t\right) \cdot c\right)\right) \cdot y4\\ \mathbf{elif}\;i \leq 2.8 \cdot 10^{-11}:\\ \;\;\;\;\mathsf{fma}\left(t\_3, y, \mathsf{fma}\left(y0 \cdot c - y1 \cdot a, y2, \left(y1 \cdot i - y0 \cdot b\right) \cdot j\right)\right) \cdot x\\ \mathbf{elif}\;i \leq 1.75 \cdot 10^{+109}:\\ \;\;\;\;\mathsf{fma}\left(t\_4, k, \mathsf{fma}\left(t\_3, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y\\ \mathbf{elif}\;i \leq 5.6 \cdot 10^{+177}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, z, y4 \cdot y2\right) \cdot y1\right) \cdot k\\ \mathbf{elif}\;i \leq 8 \cdot 10^{+267}:\\ \;\;\;\;\mathsf{fma}\left(t\_4, y, \mathsf{fma}\left(y4 \cdot y1 - y5 \cdot y0, y2, \left(y0 \cdot b - y1 \cdot i\right) \cdot z\right)\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y5, \left(-c\right) \cdot x\right) \cdot i\right) \cdot y\\ \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 (- (* y3 z) (* y2 x)))
        (t_2 (- (* y2 k) (* y3 j)))
        (t_3 (- (* b a) (* i c)))
        (t_4 (- (* y5 i) (* y4 b))))
   (if (<= i -9.5e+232)
     (* (fma t_1 a (fma t_2 y4 (* (- (* j x) (* k z)) i))) y1)
     (if (<= i -1e+192)
       (* (* (fma k y1 (* (- t) c)) y4) y2)
       (if (<= i -7.5e+90)
         (* (* (fma k y (* (- t) j)) i) y5)
         (if (<= i 4.8e-295)
           (*
            (fma
             t_1
             y1
             (fma (- (* y x) (* t z)) b (* (- (* y2 t) (* y3 y)) y5)))
            a)
           (if (<= i 2.8e-135)
             (* (fma (- (* y3 j) (* y2 k)) y5 (* (* (- x) j) b)) y0)
             (if (<= i 2.3e-79)
               (*
                (fma
                 (- (* j t) (* k y))
                 b
                 (fma t_2 y1 (* (- (* y3 y) (* y2 t)) c)))
                y4)
               (if (<= i 2.8e-11)
                 (*
                  (fma
                   t_3
                   y
                   (fma (- (* y0 c) (* y1 a)) y2 (* (- (* y1 i) (* y0 b)) j)))
                  x)
                 (if (<= i 1.75e+109)
                   (* (fma t_4 k (fma t_3 x (* (- (* y4 c) (* y5 a)) y3))) y)
                   (if (<= i 5.6e+177)
                     (* (* (fma (- i) z (* y4 y2)) y1) k)
                     (if (<= i 8e+267)
                       (*
                        (fma
                         t_4
                         y
                         (fma
                          (- (* y4 y1) (* y5 y0))
                          y2
                          (* (- (* y0 b) (* y1 i)) z)))
                        k)
                       (* (* (fma k y5 (* (- c) x)) i) y)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y3 * z) - (y2 * x);
	double t_2 = (y2 * k) - (y3 * j);
	double t_3 = (b * a) - (i * c);
	double t_4 = (y5 * i) - (y4 * b);
	double tmp;
	if (i <= -9.5e+232) {
		tmp = fma(t_1, a, fma(t_2, y4, (((j * x) - (k * z)) * i))) * y1;
	} else if (i <= -1e+192) {
		tmp = (fma(k, y1, (-t * c)) * y4) * y2;
	} else if (i <= -7.5e+90) {
		tmp = (fma(k, y, (-t * j)) * i) * y5;
	} else if (i <= 4.8e-295) {
		tmp = fma(t_1, y1, fma(((y * x) - (t * z)), b, (((y2 * t) - (y3 * y)) * y5))) * a;
	} else if (i <= 2.8e-135) {
		tmp = fma(((y3 * j) - (y2 * k)), y5, ((-x * j) * b)) * y0;
	} else if (i <= 2.3e-79) {
		tmp = fma(((j * t) - (k * y)), b, fma(t_2, y1, (((y3 * y) - (y2 * t)) * c))) * y4;
	} else if (i <= 2.8e-11) {
		tmp = fma(t_3, y, fma(((y0 * c) - (y1 * a)), y2, (((y1 * i) - (y0 * b)) * j))) * x;
	} else if (i <= 1.75e+109) {
		tmp = fma(t_4, k, fma(t_3, x, (((y4 * c) - (y5 * a)) * y3))) * y;
	} else if (i <= 5.6e+177) {
		tmp = (fma(-i, z, (y4 * y2)) * y1) * k;
	} else if (i <= 8e+267) {
		tmp = fma(t_4, y, fma(((y4 * y1) - (y5 * y0)), y2, (((y0 * b) - (y1 * i)) * z))) * k;
	} else {
		tmp = (fma(k, y5, (-c * x)) * i) * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y3 * z) - Float64(y2 * x))
	t_2 = Float64(Float64(y2 * k) - Float64(y3 * j))
	t_3 = Float64(Float64(b * a) - Float64(i * c))
	t_4 = Float64(Float64(y5 * i) - Float64(y4 * b))
	tmp = 0.0
	if (i <= -9.5e+232)
		tmp = Float64(fma(t_1, a, fma(t_2, y4, Float64(Float64(Float64(j * x) - Float64(k * z)) * i))) * y1);
	elseif (i <= -1e+192)
		tmp = Float64(Float64(fma(k, y1, Float64(Float64(-t) * c)) * y4) * y2);
	elseif (i <= -7.5e+90)
		tmp = Float64(Float64(fma(k, y, Float64(Float64(-t) * j)) * i) * y5);
	elseif (i <= 4.8e-295)
		tmp = Float64(fma(t_1, y1, fma(Float64(Float64(y * x) - Float64(t * z)), b, Float64(Float64(Float64(y2 * t) - Float64(y3 * y)) * y5))) * a);
	elseif (i <= 2.8e-135)
		tmp = Float64(fma(Float64(Float64(y3 * j) - Float64(y2 * k)), y5, Float64(Float64(Float64(-x) * j) * b)) * y0);
	elseif (i <= 2.3e-79)
		tmp = Float64(fma(Float64(Float64(j * t) - Float64(k * y)), b, fma(t_2, y1, Float64(Float64(Float64(y3 * y) - Float64(y2 * t)) * c))) * y4);
	elseif (i <= 2.8e-11)
		tmp = Float64(fma(t_3, y, fma(Float64(Float64(y0 * c) - Float64(y1 * a)), y2, Float64(Float64(Float64(y1 * i) - Float64(y0 * b)) * j))) * x);
	elseif (i <= 1.75e+109)
		tmp = Float64(fma(t_4, k, fma(t_3, x, Float64(Float64(Float64(y4 * c) - Float64(y5 * a)) * y3))) * y);
	elseif (i <= 5.6e+177)
		tmp = Float64(Float64(fma(Float64(-i), z, Float64(y4 * y2)) * y1) * k);
	elseif (i <= 8e+267)
		tmp = Float64(fma(t_4, y, fma(Float64(Float64(y4 * y1) - Float64(y5 * y0)), y2, Float64(Float64(Float64(y0 * b) - Float64(y1 * i)) * z))) * k);
	else
		tmp = Float64(Float64(fma(k, y5, Float64(Float64(-c) * x)) * i) * y);
	end
	return 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[(y3 * z), $MachinePrecision] - N[(y2 * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y2 * k), $MachinePrecision] - N[(y3 * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * a), $MachinePrecision] - N[(i * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(y5 * i), $MachinePrecision] - N[(y4 * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -9.5e+232], N[(N[(t$95$1 * a + N[(t$95$2 * y4 + N[(N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision], If[LessEqual[i, -1e+192], N[(N[(N[(k * y1 + N[((-t) * c), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision] * y2), $MachinePrecision], If[LessEqual[i, -7.5e+90], N[(N[(N[(k * y + N[((-t) * j), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision] * y5), $MachinePrecision], If[LessEqual[i, 4.8e-295], N[(N[(t$95$1 * y1 + N[(N[(N[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision] * b + N[(N[(N[(y2 * t), $MachinePrecision] - N[(y3 * y), $MachinePrecision]), $MachinePrecision] * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[i, 2.8e-135], N[(N[(N[(N[(y3 * j), $MachinePrecision] - N[(y2 * k), $MachinePrecision]), $MachinePrecision] * y5 + N[(N[((-x) * j), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] * y0), $MachinePrecision], If[LessEqual[i, 2.3e-79], N[(N[(N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision] * b + N[(t$95$2 * y1 + N[(N[(N[(y3 * y), $MachinePrecision] - N[(y2 * t), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision], If[LessEqual[i, 2.8e-11], N[(N[(t$95$3 * y + N[(N[(N[(y0 * c), $MachinePrecision] - N[(y1 * a), $MachinePrecision]), $MachinePrecision] * y2 + N[(N[(N[(y1 * i), $MachinePrecision] - N[(y0 * b), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[i, 1.75e+109], N[(N[(t$95$4 * k + N[(t$95$3 * x + N[(N[(N[(y4 * c), $MachinePrecision] - N[(y5 * a), $MachinePrecision]), $MachinePrecision] * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[i, 5.6e+177], N[(N[(N[((-i) * z + N[(y4 * y2), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision] * k), $MachinePrecision], If[LessEqual[i, 8e+267], N[(N[(t$95$4 * y + N[(N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision] * y2 + N[(N[(N[(y0 * b), $MachinePrecision] - N[(y1 * i), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * k), $MachinePrecision], N[(N[(N[(k * y5 + N[((-c) * x), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision] * y), $MachinePrecision]]]]]]]]]]]]]]]

Derivation

1. Split input into 11 regimes

2. if i < -9.4999999999999996e232

   1. Initial program 28.6%

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

   3. Taylor expanded in y1 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 64.5%

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

   if -9.4999999999999996e232 < i < -1.00000000000000004e192

   1. Initial program 24.4%

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

   3. Taylor expanded in y2 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 63.0%

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

   6. Taylor expanded in y4 around inf

      \[\leadsto \left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right) \cdot y2 \]
   7. Step-by-step derivation

   8. Applied rewrites 75.5%

      \[\leadsto \left(y4 \cdot \mathsf{fma}\left(k, y1, -c \cdot t\right)\right) \cdot y2 \]

   if -1.00000000000000004e192 < i < -7.50000000000000014e90

   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 y5 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 64.3%

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

   6. Taylor expanded in i around inf

      \[\leadsto \left(i \cdot \left(k \cdot y - j \cdot t\right)\right) \cdot y5 \]
   7. Step-by-step derivation

   8. Applied rewrites 71.9%

      \[\leadsto \left(i \cdot \mathsf{fma}\left(k, y, \left(-j\right) \cdot t\right)\right) \cdot y5 \]

   if -7.50000000000000014e90 < i < 4.7999999999999996e-295

   1. Initial program 40.5%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 59.0%

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

   if 4.7999999999999996e-295 < i < 2.80000000000000023e-135

   1. Initial program 17.8%

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

   3. Taylor expanded in y0 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 56.2%

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

   6. Taylor expanded in j around inf

      \[\leadsto \mathsf{fma}\left(-\left(k \cdot y2 - j \cdot y3\right), y5, -1 \cdot \left(b \cdot \left(j \cdot x\right)\right)\right) \cdot y0 \]
   7. Step-by-step derivation

   8. Applied rewrites 53.6%

      \[\leadsto \mathsf{fma}\left(-\left(k \cdot y2 - j \cdot y3\right), y5, -b \cdot \left(j \cdot x\right)\right) \cdot y0 \]

   if 2.80000000000000023e-135 < i < 2.30000000000000012e-79

   1. Initial program 49.9%

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

   3. Taylor expanded in y4 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 69.3%

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

   if 2.30000000000000012e-79 < i < 2.8e-11

   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 x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 66.1%

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

   if 2.8e-11 < i < 1.74999999999999992e109

   1. Initial program 18.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 78.8%

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

   if 1.74999999999999992e109 < i < 5.60000000000000004e177

   1. Initial program 25.6%

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

   3. Taylor expanded in y1 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 50.0%

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

   6. Taylor expanded in j around inf

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

   8. Applied rewrites 50.3%

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

   9. Taylor expanded in k around inf

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

   11. Applied rewrites 75.5%

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

   if 5.60000000000000004e177 < i < 7.9999999999999998e267

   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 k around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 82.4%

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

   if 7.9999999999999998e267 < i

   1. Initial program 8.3%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 8.3%

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

   6. Taylor expanded in i around inf

      \[\leadsto \left(i \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 66.7%

      \[\leadsto \left(i \cdot \mathsf{fma}\left(k, y5, -c \cdot x\right)\right) \cdot y \]
3. Recombined 11 regimes into one program.

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -9.5 \cdot 10^{+232}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot z - y2 \cdot x, a, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1\\ \mathbf{elif}\;i \leq -1 \cdot 10^{+192}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y1, \left(-t\right) \cdot c\right) \cdot y4\right) \cdot y2\\ \mathbf{elif}\;i \leq -7.5 \cdot 10^{+90}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y, \left(-t\right) \cdot j\right) \cdot i\right) \cdot y5\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{-295}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot z - y2 \cdot x, y1, \mathsf{fma}\left(y \cdot x - t \cdot z, b, \left(y2 \cdot t - y3 \cdot y\right) \cdot y5\right)\right) \cdot a\\ \mathbf{elif}\;i \leq 2.8 \cdot 10^{-135}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot j - y2 \cdot k, y5, \left(\left(-x\right) \cdot j\right) \cdot b\right) \cdot y0\\ \mathbf{elif}\;i \leq 2.3 \cdot 10^{-79}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot t - k \cdot y, b, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y1, \left(y3 \cdot y - y2 \cdot t\right) \cdot c\right)\right) \cdot y4\\ \mathbf{elif}\;i \leq 2.8 \cdot 10^{-11}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot a - i \cdot c, y, \mathsf{fma}\left(y0 \cdot c - y1 \cdot a, y2, \left(y1 \cdot i - y0 \cdot b\right) \cdot j\right)\right) \cdot x\\ \mathbf{elif}\;i \leq 1.75 \cdot 10^{+109}:\\ \;\;\;\;\mathsf{fma}\left(y5 \cdot i - y4 \cdot b, k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y\\ \mathbf{elif}\;i \leq 5.6 \cdot 10^{+177}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, z, y4 \cdot y2\right) \cdot y1\right) \cdot k\\ \mathbf{elif}\;i \leq 8 \cdot 10^{+267}:\\ \;\;\;\;\mathsf{fma}\left(y5 \cdot i - y4 \cdot b, y, \mathsf{fma}\left(y4 \cdot y1 - y5 \cdot y0, y2, \left(y0 \cdot b - y1 \cdot i\right) \cdot z\right)\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y5, \left(-c\right) \cdot x\right) \cdot i\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 38.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y5 \cdot i - y4 \cdot b\\ t_2 := y3 \cdot z - y2 \cdot x\\ t_3 := b \cdot a - i \cdot c\\ \mathbf{if}\;i \leq -9.5 \cdot 10^{+232}:\\ \;\;\;\;\mathsf{fma}\left(t\_2, a, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1\\ \mathbf{elif}\;i \leq -1 \cdot 10^{+192}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y1, \left(-t\right) \cdot c\right) \cdot y4\right) \cdot y2\\ \mathbf{elif}\;i \leq -7.5 \cdot 10^{+90}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y, \left(-t\right) \cdot j\right) \cdot i\right) \cdot y5\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{-295}:\\ \;\;\;\;\mathsf{fma}\left(t\_2, y1, \mathsf{fma}\left(y \cdot x - t \cdot z, b, \left(y2 \cdot t - y3 \cdot y\right) \cdot y5\right)\right) \cdot a\\ \mathbf{elif}\;i \leq 1.35 \cdot 10^{-176}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot j - y2 \cdot k, y5, \left(\left(-x\right) \cdot j\right) \cdot b\right) \cdot y0\\ \mathbf{elif}\;i \leq 3.15 \cdot 10^{-40}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, k, \mathsf{fma}\left(-y3, y5, b \cdot x\right) \cdot a\right) \cdot y\\ \mathbf{elif}\;i \leq 2.8 \cdot 10^{-11}:\\ \;\;\;\;\mathsf{fma}\left(t\_3, y, \mathsf{fma}\left(y0 \cdot c - y1 \cdot a, y2, \left(y1 \cdot i - y0 \cdot b\right) \cdot j\right)\right) \cdot x\\ \mathbf{elif}\;i \leq 1.75 \cdot 10^{+109}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, k, \mathsf{fma}\left(t\_3, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y\\ \mathbf{elif}\;i \leq 5.6 \cdot 10^{+177}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, z, y4 \cdot y2\right) \cdot y1\right) \cdot k\\ \mathbf{elif}\;i \leq 8 \cdot 10^{+267}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, y, \mathsf{fma}\left(y4 \cdot y1 - y5 \cdot y0, y2, \left(y0 \cdot b - y1 \cdot i\right) \cdot z\right)\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y5, \left(-c\right) \cdot x\right) \cdot i\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y5 i) (* y4 b)))
        (t_2 (- (* y3 z) (* y2 x)))
        (t_3 (- (* b a) (* i c))))
   (if (<= i -9.5e+232)
     (*
      (fma t_2 a (fma (- (* y2 k) (* y3 j)) y4 (* (- (* j x) (* k z)) i)))
      y1)
     (if (<= i -1e+192)
       (* (* (fma k y1 (* (- t) c)) y4) y2)
       (if (<= i -7.5e+90)
         (* (* (fma k y (* (- t) j)) i) y5)
         (if (<= i 4.8e-295)
           (*
            (fma
             t_2
             y1
             (fma (- (* y x) (* t z)) b (* (- (* y2 t) (* y3 y)) y5)))
            a)
           (if (<= i 1.35e-176)
             (* (fma (- (* y3 j) (* y2 k)) y5 (* (* (- x) j) b)) y0)
             (if (<= i 3.15e-40)
               (* (fma t_1 k (* (fma (- y3) y5 (* b x)) a)) y)
               (if (<= i 2.8e-11)
                 (*
                  (fma
                   t_3
                   y
                   (fma (- (* y0 c) (* y1 a)) y2 (* (- (* y1 i) (* y0 b)) j)))
                  x)
                 (if (<= i 1.75e+109)
                   (* (fma t_1 k (fma t_3 x (* (- (* y4 c) (* y5 a)) y3))) y)
                   (if (<= i 5.6e+177)
                     (* (* (fma (- i) z (* y4 y2)) y1) k)
                     (if (<= i 8e+267)
                       (*
                        (fma
                         t_1
                         y
                         (fma
                          (- (* y4 y1) (* y5 y0))
                          y2
                          (* (- (* y0 b) (* y1 i)) z)))
                        k)
                       (* (* (fma k y5 (* (- c) x)) i) y)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y5 * i) - (y4 * b);
	double t_2 = (y3 * z) - (y2 * x);
	double t_3 = (b * a) - (i * c);
	double tmp;
	if (i <= -9.5e+232) {
		tmp = fma(t_2, a, fma(((y2 * k) - (y3 * j)), y4, (((j * x) - (k * z)) * i))) * y1;
	} else if (i <= -1e+192) {
		tmp = (fma(k, y1, (-t * c)) * y4) * y2;
	} else if (i <= -7.5e+90) {
		tmp = (fma(k, y, (-t * j)) * i) * y5;
	} else if (i <= 4.8e-295) {
		tmp = fma(t_2, y1, fma(((y * x) - (t * z)), b, (((y2 * t) - (y3 * y)) * y5))) * a;
	} else if (i <= 1.35e-176) {
		tmp = fma(((y3 * j) - (y2 * k)), y5, ((-x * j) * b)) * y0;
	} else if (i <= 3.15e-40) {
		tmp = fma(t_1, k, (fma(-y3, y5, (b * x)) * a)) * y;
	} else if (i <= 2.8e-11) {
		tmp = fma(t_3, y, fma(((y0 * c) - (y1 * a)), y2, (((y1 * i) - (y0 * b)) * j))) * x;
	} else if (i <= 1.75e+109) {
		tmp = fma(t_1, k, fma(t_3, x, (((y4 * c) - (y5 * a)) * y3))) * y;
	} else if (i <= 5.6e+177) {
		tmp = (fma(-i, z, (y4 * y2)) * y1) * k;
	} else if (i <= 8e+267) {
		tmp = fma(t_1, y, fma(((y4 * y1) - (y5 * y0)), y2, (((y0 * b) - (y1 * i)) * z))) * k;
	} else {
		tmp = (fma(k, y5, (-c * x)) * i) * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y5 * i) - Float64(y4 * b))
	t_2 = Float64(Float64(y3 * z) - Float64(y2 * x))
	t_3 = Float64(Float64(b * a) - Float64(i * c))
	tmp = 0.0
	if (i <= -9.5e+232)
		tmp = Float64(fma(t_2, a, fma(Float64(Float64(y2 * k) - Float64(y3 * j)), y4, Float64(Float64(Float64(j * x) - Float64(k * z)) * i))) * y1);
	elseif (i <= -1e+192)
		tmp = Float64(Float64(fma(k, y1, Float64(Float64(-t) * c)) * y4) * y2);
	elseif (i <= -7.5e+90)
		tmp = Float64(Float64(fma(k, y, Float64(Float64(-t) * j)) * i) * y5);
	elseif (i <= 4.8e-295)
		tmp = Float64(fma(t_2, y1, fma(Float64(Float64(y * x) - Float64(t * z)), b, Float64(Float64(Float64(y2 * t) - Float64(y3 * y)) * y5))) * a);
	elseif (i <= 1.35e-176)
		tmp = Float64(fma(Float64(Float64(y3 * j) - Float64(y2 * k)), y5, Float64(Float64(Float64(-x) * j) * b)) * y0);
	elseif (i <= 3.15e-40)
		tmp = Float64(fma(t_1, k, Float64(fma(Float64(-y3), y5, Float64(b * x)) * a)) * y);
	elseif (i <= 2.8e-11)
		tmp = Float64(fma(t_3, y, fma(Float64(Float64(y0 * c) - Float64(y1 * a)), y2, Float64(Float64(Float64(y1 * i) - Float64(y0 * b)) * j))) * x);
	elseif (i <= 1.75e+109)
		tmp = Float64(fma(t_1, k, fma(t_3, x, Float64(Float64(Float64(y4 * c) - Float64(y5 * a)) * y3))) * y);
	elseif (i <= 5.6e+177)
		tmp = Float64(Float64(fma(Float64(-i), z, Float64(y4 * y2)) * y1) * k);
	elseif (i <= 8e+267)
		tmp = Float64(fma(t_1, y, fma(Float64(Float64(y4 * y1) - Float64(y5 * y0)), y2, Float64(Float64(Float64(y0 * b) - Float64(y1 * i)) * z))) * k);
	else
		tmp = Float64(Float64(fma(k, y5, Float64(Float64(-c) * x)) * i) * y);
	end
	return 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[(y5 * i), $MachinePrecision] - N[(y4 * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y3 * z), $MachinePrecision] - N[(y2 * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * a), $MachinePrecision] - N[(i * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -9.5e+232], N[(N[(t$95$2 * a + N[(N[(N[(y2 * k), $MachinePrecision] - N[(y3 * j), $MachinePrecision]), $MachinePrecision] * y4 + N[(N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision], If[LessEqual[i, -1e+192], N[(N[(N[(k * y1 + N[((-t) * c), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision] * y2), $MachinePrecision], If[LessEqual[i, -7.5e+90], N[(N[(N[(k * y + N[((-t) * j), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision] * y5), $MachinePrecision], If[LessEqual[i, 4.8e-295], N[(N[(t$95$2 * y1 + N[(N[(N[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision] * b + N[(N[(N[(y2 * t), $MachinePrecision] - N[(y3 * y), $MachinePrecision]), $MachinePrecision] * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[i, 1.35e-176], N[(N[(N[(N[(y3 * j), $MachinePrecision] - N[(y2 * k), $MachinePrecision]), $MachinePrecision] * y5 + N[(N[((-x) * j), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] * y0), $MachinePrecision], If[LessEqual[i, 3.15e-40], N[(N[(t$95$1 * k + N[(N[((-y3) * y5 + N[(b * x), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[i, 2.8e-11], N[(N[(t$95$3 * y + N[(N[(N[(y0 * c), $MachinePrecision] - N[(y1 * a), $MachinePrecision]), $MachinePrecision] * y2 + N[(N[(N[(y1 * i), $MachinePrecision] - N[(y0 * b), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[i, 1.75e+109], N[(N[(t$95$1 * k + N[(t$95$3 * x + N[(N[(N[(y4 * c), $MachinePrecision] - N[(y5 * a), $MachinePrecision]), $MachinePrecision] * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[i, 5.6e+177], N[(N[(N[((-i) * z + N[(y4 * y2), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision] * k), $MachinePrecision], If[LessEqual[i, 8e+267], N[(N[(t$95$1 * y + N[(N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision] * y2 + N[(N[(N[(y0 * b), $MachinePrecision] - N[(y1 * i), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * k), $MachinePrecision], N[(N[(N[(k * y5 + N[((-c) * x), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision] * y), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 11 regimes

2. if i < -9.4999999999999996e232

   1. Initial program 28.6%

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

   3. Taylor expanded in y1 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 64.5%

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

   if -9.4999999999999996e232 < i < -1.00000000000000004e192

   1. Initial program 24.4%

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

   3. Taylor expanded in y2 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 63.0%

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

   6. Taylor expanded in y4 around inf

      \[\leadsto \left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right) \cdot y2 \]
   7. Step-by-step derivation

   8. Applied rewrites 75.5%

      \[\leadsto \left(y4 \cdot \mathsf{fma}\left(k, y1, -c \cdot t\right)\right) \cdot y2 \]

   if -1.00000000000000004e192 < i < -7.50000000000000014e90

   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 y5 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 64.3%

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

   6. Taylor expanded in i around inf

      \[\leadsto \left(i \cdot \left(k \cdot y - j \cdot t\right)\right) \cdot y5 \]
   7. Step-by-step derivation

   8. Applied rewrites 71.9%

      \[\leadsto \left(i \cdot \mathsf{fma}\left(k, y, \left(-j\right) \cdot t\right)\right) \cdot y5 \]

   if -7.50000000000000014e90 < i < 4.7999999999999996e-295

   1. Initial program 40.5%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 59.0%

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

   if 4.7999999999999996e-295 < i < 1.3499999999999999e-176

   1. Initial program 22.4%

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

   3. Taylor expanded in y0 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 55.6%

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

   6. Taylor expanded in j around inf

      \[\leadsto \mathsf{fma}\left(-\left(k \cdot y2 - j \cdot y3\right), y5, -1 \cdot \left(b \cdot \left(j \cdot x\right)\right)\right) \cdot y0 \]
   7. Step-by-step derivation

   8. Applied rewrites 55.9%

      \[\leadsto \mathsf{fma}\left(-\left(k \cdot y2 - j \cdot y3\right), y5, -b \cdot \left(j \cdot x\right)\right) \cdot y0 \]

   if 1.3499999999999999e-176 < i < 3.1500000000000001e-40

   1. Initial program 35.7%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 48.7%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, a \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 58.5%

      \[\leadsto \mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, a \cdot \mathsf{fma}\left(-y3, y5, b \cdot x\right)\right) \cdot y \]

   if 3.1500000000000001e-40 < i < 2.8e-11

   1. Initial program 33.3%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 84.4%

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

   if 2.8e-11 < i < 1.74999999999999992e109

   1. Initial program 18.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 78.8%

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

   if 1.74999999999999992e109 < i < 5.60000000000000004e177

   1. Initial program 25.6%

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

   3. Taylor expanded in y1 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 50.0%

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

   6. Taylor expanded in j around inf

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

   8. Applied rewrites 50.3%

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

   9. Taylor expanded in k around inf

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

   11. Applied rewrites 75.5%

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

   if 5.60000000000000004e177 < i < 7.9999999999999998e267

   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 k around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 82.4%

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

   if 7.9999999999999998e267 < i

   1. Initial program 8.3%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 8.3%

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

   6. Taylor expanded in i around inf

      \[\leadsto \left(i \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 66.7%

      \[\leadsto \left(i \cdot \mathsf{fma}\left(k, y5, -c \cdot x\right)\right) \cdot y \]
3. Recombined 11 regimes into one program.

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -9.5 \cdot 10^{+232}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot z - y2 \cdot x, a, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1\\ \mathbf{elif}\;i \leq -1 \cdot 10^{+192}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y1, \left(-t\right) \cdot c\right) \cdot y4\right) \cdot y2\\ \mathbf{elif}\;i \leq -7.5 \cdot 10^{+90}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y, \left(-t\right) \cdot j\right) \cdot i\right) \cdot y5\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{-295}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot z - y2 \cdot x, y1, \mathsf{fma}\left(y \cdot x - t \cdot z, b, \left(y2 \cdot t - y3 \cdot y\right) \cdot y5\right)\right) \cdot a\\ \mathbf{elif}\;i \leq 1.35 \cdot 10^{-176}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot j - y2 \cdot k, y5, \left(\left(-x\right) \cdot j\right) \cdot b\right) \cdot y0\\ \mathbf{elif}\;i \leq 3.15 \cdot 10^{-40}:\\ \;\;\;\;\mathsf{fma}\left(y5 \cdot i - y4 \cdot b, k, \mathsf{fma}\left(-y3, y5, b \cdot x\right) \cdot a\right) \cdot y\\ \mathbf{elif}\;i \leq 2.8 \cdot 10^{-11}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot a - i \cdot c, y, \mathsf{fma}\left(y0 \cdot c - y1 \cdot a, y2, \left(y1 \cdot i - y0 \cdot b\right) \cdot j\right)\right) \cdot x\\ \mathbf{elif}\;i \leq 1.75 \cdot 10^{+109}:\\ \;\;\;\;\mathsf{fma}\left(y5 \cdot i - y4 \cdot b, k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y\\ \mathbf{elif}\;i \leq 5.6 \cdot 10^{+177}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, z, y4 \cdot y2\right) \cdot y1\right) \cdot k\\ \mathbf{elif}\;i \leq 8 \cdot 10^{+267}:\\ \;\;\;\;\mathsf{fma}\left(y5 \cdot i - y4 \cdot b, y, \mathsf{fma}\left(y4 \cdot y1 - y5 \cdot y0, y2, \left(y0 \cdot b - y1 \cdot i\right) \cdot z\right)\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y5, \left(-c\right) \cdot x\right) \cdot i\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 40.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y3 \cdot z - y2 \cdot x\\ t_2 := y2 \cdot k - y3 \cdot j\\ t_3 := y2 \cdot t - y3 \cdot y\\ t_4 := y5 \cdot i - y4 \cdot b\\ \mathbf{if}\;i \leq -2.3 \cdot 10^{+249}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, a, \mathsf{fma}\left(t\_2, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1\\ \mathbf{elif}\;i \leq -9.2 \cdot 10^{+203}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot y - j \cdot t, i, \mathsf{fma}\left(-y0, t\_2, t\_3 \cdot a\right)\right) \cdot y5\\ \mathbf{elif}\;i \leq -2.6 \cdot 10^{+131}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, k, y3 \cdot a\right) \cdot z\right) \cdot y1\\ \mathbf{elif}\;i \leq -20000000000000:\\ \;\;\;\;\mathsf{fma}\left(j \cdot t - k \cdot y, b, \mathsf{fma}\left(t\_2, y1, \left(y3 \cdot y - y2 \cdot t\right) \cdot c\right)\right) \cdot y4\\ \mathbf{elif}\;i \leq 6.6 \cdot 10^{-253}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, y1, \mathsf{fma}\left(y \cdot x - t \cdot z, b, t\_3 \cdot y5\right)\right) \cdot a\\ \mathbf{elif}\;i \leq 1.15 \cdot 10^{-190}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot j - y2 \cdot k, y5, \mathsf{fma}\left(c, y2 \cdot x - y3 \cdot z, \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \cdot y0\\ \mathbf{elif}\;i \leq 1.75 \cdot 10^{+109}:\\ \;\;\;\;\mathsf{fma}\left(t\_4, k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y\\ \mathbf{elif}\;i \leq 5.6 \cdot 10^{+177}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, z, y4 \cdot y2\right) \cdot y1\right) \cdot k\\ \mathbf{elif}\;i \leq 8 \cdot 10^{+267}:\\ \;\;\;\;\mathsf{fma}\left(t\_4, y, \mathsf{fma}\left(y4 \cdot y1 - y5 \cdot y0, y2, \left(y0 \cdot b - y1 \cdot i\right) \cdot z\right)\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y5, \left(-c\right) \cdot x\right) \cdot i\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y3 z) (* y2 x)))
        (t_2 (- (* y2 k) (* y3 j)))
        (t_3 (- (* y2 t) (* y3 y)))
        (t_4 (- (* y5 i) (* y4 b))))
   (if (<= i -2.3e+249)
     (* (fma t_1 a (fma t_2 y4 (* (- (* j x) (* k z)) i))) y1)
     (if (<= i -9.2e+203)
       (* (fma (- (* k y) (* j t)) i (fma (- y0) t_2 (* t_3 a))) y5)
       (if (<= i -2.6e+131)
         (* (* (fma (- i) k (* y3 a)) z) y1)
         (if (<= i -20000000000000.0)
           (*
            (fma
             (- (* j t) (* k y))
             b
             (fma t_2 y1 (* (- (* y3 y) (* y2 t)) c)))
            y4)
           (if (<= i 6.6e-253)
             (* (fma t_1 y1 (fma (- (* y x) (* t z)) b (* t_3 y5))) a)
             (if (<= i 1.15e-190)
               (*
                (fma
                 (- (* y3 j) (* y2 k))
                 y5
                 (fma c (- (* y2 x) (* y3 z)) (* (- (* k z) (* j x)) b)))
                y0)
               (if (<= i 1.75e+109)
                 (*
                  (fma
                   t_4
                   k
                   (fma (- (* b a) (* i c)) x (* (- (* y4 c) (* y5 a)) y3)))
                  y)
                 (if (<= i 5.6e+177)
                   (* (* (fma (- i) z (* y4 y2)) y1) k)
                   (if (<= i 8e+267)
                     (*
                      (fma
                       t_4
                       y
                       (fma
                        (- (* y4 y1) (* y5 y0))
                        y2
                        (* (- (* y0 b) (* y1 i)) z)))
                      k)
                     (* (* (fma k y5 (* (- c) x)) i) y))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y3 * z) - (y2 * x);
	double t_2 = (y2 * k) - (y3 * j);
	double t_3 = (y2 * t) - (y3 * y);
	double t_4 = (y5 * i) - (y4 * b);
	double tmp;
	if (i <= -2.3e+249) {
		tmp = fma(t_1, a, fma(t_2, y4, (((j * x) - (k * z)) * i))) * y1;
	} else if (i <= -9.2e+203) {
		tmp = fma(((k * y) - (j * t)), i, fma(-y0, t_2, (t_3 * a))) * y5;
	} else if (i <= -2.6e+131) {
		tmp = (fma(-i, k, (y3 * a)) * z) * y1;
	} else if (i <= -20000000000000.0) {
		tmp = fma(((j * t) - (k * y)), b, fma(t_2, y1, (((y3 * y) - (y2 * t)) * c))) * y4;
	} else if (i <= 6.6e-253) {
		tmp = fma(t_1, y1, fma(((y * x) - (t * z)), b, (t_3 * y5))) * a;
	} else if (i <= 1.15e-190) {
		tmp = fma(((y3 * j) - (y2 * k)), y5, fma(c, ((y2 * x) - (y3 * z)), (((k * z) - (j * x)) * b))) * y0;
	} else if (i <= 1.75e+109) {
		tmp = fma(t_4, k, fma(((b * a) - (i * c)), x, (((y4 * c) - (y5 * a)) * y3))) * y;
	} else if (i <= 5.6e+177) {
		tmp = (fma(-i, z, (y4 * y2)) * y1) * k;
	} else if (i <= 8e+267) {
		tmp = fma(t_4, y, fma(((y4 * y1) - (y5 * y0)), y2, (((y0 * b) - (y1 * i)) * z))) * k;
	} else {
		tmp = (fma(k, y5, (-c * x)) * i) * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y3 * z) - Float64(y2 * x))
	t_2 = Float64(Float64(y2 * k) - Float64(y3 * j))
	t_3 = Float64(Float64(y2 * t) - Float64(y3 * y))
	t_4 = Float64(Float64(y5 * i) - Float64(y4 * b))
	tmp = 0.0
	if (i <= -2.3e+249)
		tmp = Float64(fma(t_1, a, fma(t_2, y4, Float64(Float64(Float64(j * x) - Float64(k * z)) * i))) * y1);
	elseif (i <= -9.2e+203)
		tmp = Float64(fma(Float64(Float64(k * y) - Float64(j * t)), i, fma(Float64(-y0), t_2, Float64(t_3 * a))) * y5);
	elseif (i <= -2.6e+131)
		tmp = Float64(Float64(fma(Float64(-i), k, Float64(y3 * a)) * z) * y1);
	elseif (i <= -20000000000000.0)
		tmp = Float64(fma(Float64(Float64(j * t) - Float64(k * y)), b, fma(t_2, y1, Float64(Float64(Float64(y3 * y) - Float64(y2 * t)) * c))) * y4);
	elseif (i <= 6.6e-253)
		tmp = Float64(fma(t_1, y1, fma(Float64(Float64(y * x) - Float64(t * z)), b, Float64(t_3 * y5))) * a);
	elseif (i <= 1.15e-190)
		tmp = Float64(fma(Float64(Float64(y3 * j) - Float64(y2 * k)), y5, fma(c, Float64(Float64(y2 * x) - Float64(y3 * z)), Float64(Float64(Float64(k * z) - Float64(j * x)) * b))) * y0);
	elseif (i <= 1.75e+109)
		tmp = Float64(fma(t_4, k, fma(Float64(Float64(b * a) - Float64(i * c)), x, Float64(Float64(Float64(y4 * c) - Float64(y5 * a)) * y3))) * y);
	elseif (i <= 5.6e+177)
		tmp = Float64(Float64(fma(Float64(-i), z, Float64(y4 * y2)) * y1) * k);
	elseif (i <= 8e+267)
		tmp = Float64(fma(t_4, y, fma(Float64(Float64(y4 * y1) - Float64(y5 * y0)), y2, Float64(Float64(Float64(y0 * b) - Float64(y1 * i)) * z))) * k);
	else
		tmp = Float64(Float64(fma(k, y5, Float64(Float64(-c) * x)) * i) * y);
	end
	return 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[(y3 * z), $MachinePrecision] - N[(y2 * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y2 * k), $MachinePrecision] - N[(y3 * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y2 * t), $MachinePrecision] - N[(y3 * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(y5 * i), $MachinePrecision] - N[(y4 * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.3e+249], N[(N[(t$95$1 * a + N[(t$95$2 * y4 + N[(N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision], If[LessEqual[i, -9.2e+203], N[(N[(N[(N[(k * y), $MachinePrecision] - N[(j * t), $MachinePrecision]), $MachinePrecision] * i + N[((-y0) * t$95$2 + N[(t$95$3 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y5), $MachinePrecision], If[LessEqual[i, -2.6e+131], N[(N[(N[((-i) * k + N[(y3 * a), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] * y1), $MachinePrecision], If[LessEqual[i, -20000000000000.0], N[(N[(N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision] * b + N[(t$95$2 * y1 + N[(N[(N[(y3 * y), $MachinePrecision] - N[(y2 * t), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision], If[LessEqual[i, 6.6e-253], N[(N[(t$95$1 * y1 + N[(N[(N[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision] * b + N[(t$95$3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[i, 1.15e-190], N[(N[(N[(N[(y3 * j), $MachinePrecision] - N[(y2 * k), $MachinePrecision]), $MachinePrecision] * y5 + N[(c * N[(N[(y2 * x), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(k * z), $MachinePrecision] - N[(j * x), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y0), $MachinePrecision], If[LessEqual[i, 1.75e+109], N[(N[(t$95$4 * k + N[(N[(N[(b * a), $MachinePrecision] - N[(i * c), $MachinePrecision]), $MachinePrecision] * x + N[(N[(N[(y4 * c), $MachinePrecision] - N[(y5 * a), $MachinePrecision]), $MachinePrecision] * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[i, 5.6e+177], N[(N[(N[((-i) * z + N[(y4 * y2), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision] * k), $MachinePrecision], If[LessEqual[i, 8e+267], N[(N[(t$95$4 * y + N[(N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision] * y2 + N[(N[(N[(y0 * b), $MachinePrecision] - N[(y1 * i), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * k), $MachinePrecision], N[(N[(N[(k * y5 + N[((-c) * x), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision] * y), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if i < -2.2999999999999998e249

   1. Initial program 33.3%

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

   3. Taylor expanded in y1 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 71.5%

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

   if -2.2999999999999998e249 < i < -9.1999999999999996e203

   1. Initial program 16.5%

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

   3. Taylor expanded in y5 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 67.6%

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

   if -9.1999999999999996e203 < i < -2.6e131

   1. Initial program 27.0%

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

   3. Taylor expanded in y1 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 76.9%

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

   6. Taylor expanded in j around inf

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

   8. Applied rewrites 36.8%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 77.1%

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

   if -2.6e131 < i < -2e13

   1. Initial program 33.9%

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

   3. Taylor expanded in y4 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 73.7%

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

   if -2e13 < i < 6.6000000000000002e-253

   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 a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 58.0%

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

   if 6.6000000000000002e-253 < i < 1.14999999999999996e-190

   1. Initial program 23.8%

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

   3. Taylor expanded in y0 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 64.8%

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

   if 1.14999999999999996e-190 < i < 1.74999999999999992e109

   1. Initial program 27.3%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 59.2%

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

   if 1.74999999999999992e109 < i < 5.60000000000000004e177

   1. Initial program 25.6%

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

   3. Taylor expanded in y1 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 50.0%

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

   6. Taylor expanded in j around inf

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

   8. Applied rewrites 50.3%

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

   9. Taylor expanded in k around inf

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

   11. Applied rewrites 75.5%

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

   if 5.60000000000000004e177 < i < 7.9999999999999998e267

   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 k around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 82.4%

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

   if 7.9999999999999998e267 < i

   1. Initial program 8.3%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 8.3%

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

   6. Taylor expanded in i around inf

      \[\leadsto \left(i \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 66.7%

      \[\leadsto \left(i \cdot \mathsf{fma}\left(k, y5, -c \cdot x\right)\right) \cdot y \]
3. Recombined 10 regimes into one program.

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.3 \cdot 10^{+249}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot z - y2 \cdot x, a, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1\\ \mathbf{elif}\;i \leq -9.2 \cdot 10^{+203}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot y - j \cdot t, i, \mathsf{fma}\left(-y0, y2 \cdot k - y3 \cdot j, \left(y2 \cdot t - y3 \cdot y\right) \cdot a\right)\right) \cdot y5\\ \mathbf{elif}\;i \leq -2.6 \cdot 10^{+131}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, k, y3 \cdot a\right) \cdot z\right) \cdot y1\\ \mathbf{elif}\;i \leq -20000000000000:\\ \;\;\;\;\mathsf{fma}\left(j \cdot t - k \cdot y, b, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y1, \left(y3 \cdot y - y2 \cdot t\right) \cdot c\right)\right) \cdot y4\\ \mathbf{elif}\;i \leq 6.6 \cdot 10^{-253}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot z - y2 \cdot x, y1, \mathsf{fma}\left(y \cdot x - t \cdot z, b, \left(y2 \cdot t - y3 \cdot y\right) \cdot y5\right)\right) \cdot a\\ \mathbf{elif}\;i \leq 1.15 \cdot 10^{-190}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot j - y2 \cdot k, y5, \mathsf{fma}\left(c, y2 \cdot x - y3 \cdot z, \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \cdot y0\\ \mathbf{elif}\;i \leq 1.75 \cdot 10^{+109}:\\ \;\;\;\;\mathsf{fma}\left(y5 \cdot i - y4 \cdot b, k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y\\ \mathbf{elif}\;i \leq 5.6 \cdot 10^{+177}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, z, y4 \cdot y2\right) \cdot y1\right) \cdot k\\ \mathbf{elif}\;i \leq 8 \cdot 10^{+267}:\\ \;\;\;\;\mathsf{fma}\left(y5 \cdot i - y4 \cdot b, y, \mathsf{fma}\left(y4 \cdot y1 - y5 \cdot y0, y2, \left(y0 \cdot b - y1 \cdot i\right) \cdot z\right)\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y5, \left(-c\right) \cdot x\right) \cdot i\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 39.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y3 \cdot z - y2 \cdot x\\ t_2 := y5 \cdot i - y4 \cdot b\\ \mathbf{if}\;i \leq -9.5 \cdot 10^{+232}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, a, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1\\ \mathbf{elif}\;i \leq -1 \cdot 10^{+192}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y1, \left(-t\right) \cdot c\right) \cdot y4\right) \cdot y2\\ \mathbf{elif}\;i \leq -7.5 \cdot 10^{+90}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y, \left(-t\right) \cdot j\right) \cdot i\right) \cdot y5\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{-295}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, y1, \mathsf{fma}\left(y \cdot x - t \cdot z, b, \left(y2 \cdot t - y3 \cdot y\right) \cdot y5\right)\right) \cdot a\\ \mathbf{elif}\;i \leq 5 \cdot 10^{-182}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot j - y2 \cdot k, y5, \left(\left(-x\right) \cdot j\right) \cdot b\right) \cdot y0\\ \mathbf{elif}\;i \leq 1.75 \cdot 10^{+109}:\\ \;\;\;\;\mathsf{fma}\left(t\_2, k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y\\ \mathbf{elif}\;i \leq 5.6 \cdot 10^{+177}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, z, y4 \cdot y2\right) \cdot y1\right) \cdot k\\ \mathbf{elif}\;i \leq 8 \cdot 10^{+267}:\\ \;\;\;\;\mathsf{fma}\left(t\_2, y, \mathsf{fma}\left(y4 \cdot y1 - y5 \cdot y0, y2, \left(y0 \cdot b - y1 \cdot i\right) \cdot z\right)\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y5, \left(-c\right) \cdot x\right) \cdot i\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y3 z) (* y2 x))) (t_2 (- (* y5 i) (* y4 b))))
   (if (<= i -9.5e+232)
     (*
      (fma t_1 a (fma (- (* y2 k) (* y3 j)) y4 (* (- (* j x) (* k z)) i)))
      y1)
     (if (<= i -1e+192)
       (* (* (fma k y1 (* (- t) c)) y4) y2)
       (if (<= i -7.5e+90)
         (* (* (fma k y (* (- t) j)) i) y5)
         (if (<= i 4.8e-295)
           (*
            (fma
             t_1
             y1
             (fma (- (* y x) (* t z)) b (* (- (* y2 t) (* y3 y)) y5)))
            a)
           (if (<= i 5e-182)
             (* (fma (- (* y3 j) (* y2 k)) y5 (* (* (- x) j) b)) y0)
             (if (<= i 1.75e+109)
               (*
                (fma
                 t_2
                 k
                 (fma (- (* b a) (* i c)) x (* (- (* y4 c) (* y5 a)) y3)))
                y)
               (if (<= i 5.6e+177)
                 (* (* (fma (- i) z (* y4 y2)) y1) k)
                 (if (<= i 8e+267)
                   (*
                    (fma
                     t_2
                     y
                     (fma
                      (- (* y4 y1) (* y5 y0))
                      y2
                      (* (- (* y0 b) (* y1 i)) z)))
                    k)
                   (* (* (fma k y5 (* (- c) x)) i) y)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y3 * z) - (y2 * x);
	double t_2 = (y5 * i) - (y4 * b);
	double tmp;
	if (i <= -9.5e+232) {
		tmp = fma(t_1, a, fma(((y2 * k) - (y3 * j)), y4, (((j * x) - (k * z)) * i))) * y1;
	} else if (i <= -1e+192) {
		tmp = (fma(k, y1, (-t * c)) * y4) * y2;
	} else if (i <= -7.5e+90) {
		tmp = (fma(k, y, (-t * j)) * i) * y5;
	} else if (i <= 4.8e-295) {
		tmp = fma(t_1, y1, fma(((y * x) - (t * z)), b, (((y2 * t) - (y3 * y)) * y5))) * a;
	} else if (i <= 5e-182) {
		tmp = fma(((y3 * j) - (y2 * k)), y5, ((-x * j) * b)) * y0;
	} else if (i <= 1.75e+109) {
		tmp = fma(t_2, k, fma(((b * a) - (i * c)), x, (((y4 * c) - (y5 * a)) * y3))) * y;
	} else if (i <= 5.6e+177) {
		tmp = (fma(-i, z, (y4 * y2)) * y1) * k;
	} else if (i <= 8e+267) {
		tmp = fma(t_2, y, fma(((y4 * y1) - (y5 * y0)), y2, (((y0 * b) - (y1 * i)) * z))) * k;
	} else {
		tmp = (fma(k, y5, (-c * x)) * i) * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y3 * z) - Float64(y2 * x))
	t_2 = Float64(Float64(y5 * i) - Float64(y4 * b))
	tmp = 0.0
	if (i <= -9.5e+232)
		tmp = Float64(fma(t_1, a, fma(Float64(Float64(y2 * k) - Float64(y3 * j)), y4, Float64(Float64(Float64(j * x) - Float64(k * z)) * i))) * y1);
	elseif (i <= -1e+192)
		tmp = Float64(Float64(fma(k, y1, Float64(Float64(-t) * c)) * y4) * y2);
	elseif (i <= -7.5e+90)
		tmp = Float64(Float64(fma(k, y, Float64(Float64(-t) * j)) * i) * y5);
	elseif (i <= 4.8e-295)
		tmp = Float64(fma(t_1, y1, fma(Float64(Float64(y * x) - Float64(t * z)), b, Float64(Float64(Float64(y2 * t) - Float64(y3 * y)) * y5))) * a);
	elseif (i <= 5e-182)
		tmp = Float64(fma(Float64(Float64(y3 * j) - Float64(y2 * k)), y5, Float64(Float64(Float64(-x) * j) * b)) * y0);
	elseif (i <= 1.75e+109)
		tmp = Float64(fma(t_2, k, fma(Float64(Float64(b * a) - Float64(i * c)), x, Float64(Float64(Float64(y4 * c) - Float64(y5 * a)) * y3))) * y);
	elseif (i <= 5.6e+177)
		tmp = Float64(Float64(fma(Float64(-i), z, Float64(y4 * y2)) * y1) * k);
	elseif (i <= 8e+267)
		tmp = Float64(fma(t_2, y, fma(Float64(Float64(y4 * y1) - Float64(y5 * y0)), y2, Float64(Float64(Float64(y0 * b) - Float64(y1 * i)) * z))) * k);
	else
		tmp = Float64(Float64(fma(k, y5, Float64(Float64(-c) * x)) * i) * y);
	end
	return 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[(y3 * z), $MachinePrecision] - N[(y2 * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y5 * i), $MachinePrecision] - N[(y4 * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -9.5e+232], N[(N[(t$95$1 * a + N[(N[(N[(y2 * k), $MachinePrecision] - N[(y3 * j), $MachinePrecision]), $MachinePrecision] * y4 + N[(N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision], If[LessEqual[i, -1e+192], N[(N[(N[(k * y1 + N[((-t) * c), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision] * y2), $MachinePrecision], If[LessEqual[i, -7.5e+90], N[(N[(N[(k * y + N[((-t) * j), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision] * y5), $MachinePrecision], If[LessEqual[i, 4.8e-295], N[(N[(t$95$1 * y1 + N[(N[(N[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision] * b + N[(N[(N[(y2 * t), $MachinePrecision] - N[(y3 * y), $MachinePrecision]), $MachinePrecision] * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[i, 5e-182], N[(N[(N[(N[(y3 * j), $MachinePrecision] - N[(y2 * k), $MachinePrecision]), $MachinePrecision] * y5 + N[(N[((-x) * j), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] * y0), $MachinePrecision], If[LessEqual[i, 1.75e+109], N[(N[(t$95$2 * k + N[(N[(N[(b * a), $MachinePrecision] - N[(i * c), $MachinePrecision]), $MachinePrecision] * x + N[(N[(N[(y4 * c), $MachinePrecision] - N[(y5 * a), $MachinePrecision]), $MachinePrecision] * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[i, 5.6e+177], N[(N[(N[((-i) * z + N[(y4 * y2), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision] * k), $MachinePrecision], If[LessEqual[i, 8e+267], N[(N[(t$95$2 * y + N[(N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision] * y2 + N[(N[(N[(y0 * b), $MachinePrecision] - N[(y1 * i), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * k), $MachinePrecision], N[(N[(N[(k * y5 + N[((-c) * x), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision] * y), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if i < -9.4999999999999996e232

   1. Initial program 28.6%

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

   3. Taylor expanded in y1 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 64.5%

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

   if -9.4999999999999996e232 < i < -1.00000000000000004e192

   1. Initial program 24.4%

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

   3. Taylor expanded in y2 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 63.0%

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

   6. Taylor expanded in y4 around inf

      \[\leadsto \left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right) \cdot y2 \]
   7. Step-by-step derivation

   8. Applied rewrites 75.5%

      \[\leadsto \left(y4 \cdot \mathsf{fma}\left(k, y1, -c \cdot t\right)\right) \cdot y2 \]

   if -1.00000000000000004e192 < i < -7.50000000000000014e90

   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 y5 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 64.3%

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

   6. Taylor expanded in i around inf

      \[\leadsto \left(i \cdot \left(k \cdot y - j \cdot t\right)\right) \cdot y5 \]
   7. Step-by-step derivation

   8. Applied rewrites 71.9%

      \[\leadsto \left(i \cdot \mathsf{fma}\left(k, y, \left(-j\right) \cdot t\right)\right) \cdot y5 \]

   if -7.50000000000000014e90 < i < 4.7999999999999996e-295

   1. Initial program 40.5%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 59.0%

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

   if 4.7999999999999996e-295 < i < 5.00000000000000024e-182

   1. Initial program 23.3%

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

   3. Taylor expanded in y0 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 53.8%

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

   6. Taylor expanded in j around inf

      \[\leadsto \mathsf{fma}\left(-\left(k \cdot y2 - j \cdot y3\right), y5, -1 \cdot \left(b \cdot \left(j \cdot x\right)\right)\right) \cdot y0 \]
   7. Step-by-step derivation

   8. Applied rewrites 54.2%

      \[\leadsto \mathsf{fma}\left(-\left(k \cdot y2 - j \cdot y3\right), y5, -b \cdot \left(j \cdot x\right)\right) \cdot y0 \]

   if 5.00000000000000024e-182 < i < 1.74999999999999992e109

   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 y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 59.5%

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

   if 1.74999999999999992e109 < i < 5.60000000000000004e177

   1. Initial program 25.6%

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

   3. Taylor expanded in y1 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 50.0%

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

   6. Taylor expanded in j around inf

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

   8. Applied rewrites 50.3%

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

   9. Taylor expanded in k around inf

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

   11. Applied rewrites 75.5%

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

   if 5.60000000000000004e177 < i < 7.9999999999999998e267

   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 k around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 82.4%

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

   if 7.9999999999999998e267 < i

   1. Initial program 8.3%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 8.3%

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

   6. Taylor expanded in i around inf

      \[\leadsto \left(i \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 66.7%

      \[\leadsto \left(i \cdot \mathsf{fma}\left(k, y5, -c \cdot x\right)\right) \cdot y \]
3. Recombined 9 regimes into one program.

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -9.5 \cdot 10^{+232}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot z - y2 \cdot x, a, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1\\ \mathbf{elif}\;i \leq -1 \cdot 10^{+192}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y1, \left(-t\right) \cdot c\right) \cdot y4\right) \cdot y2\\ \mathbf{elif}\;i \leq -7.5 \cdot 10^{+90}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y, \left(-t\right) \cdot j\right) \cdot i\right) \cdot y5\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{-295}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot z - y2 \cdot x, y1, \mathsf{fma}\left(y \cdot x - t \cdot z, b, \left(y2 \cdot t - y3 \cdot y\right) \cdot y5\right)\right) \cdot a\\ \mathbf{elif}\;i \leq 5 \cdot 10^{-182}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot j - y2 \cdot k, y5, \left(\left(-x\right) \cdot j\right) \cdot b\right) \cdot y0\\ \mathbf{elif}\;i \leq 1.75 \cdot 10^{+109}:\\ \;\;\;\;\mathsf{fma}\left(y5 \cdot i - y4 \cdot b, k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y\\ \mathbf{elif}\;i \leq 5.6 \cdot 10^{+177}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, z, y4 \cdot y2\right) \cdot y1\right) \cdot k\\ \mathbf{elif}\;i \leq 8 \cdot 10^{+267}:\\ \;\;\;\;\mathsf{fma}\left(y5 \cdot i - y4 \cdot b, y, \mathsf{fma}\left(y4 \cdot y1 - y5 \cdot y0, y2, \left(y0 \cdot b - y1 \cdot i\right) \cdot z\right)\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y5, \left(-c\right) \cdot x\right) \cdot i\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 39.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y3 \cdot z - y2 \cdot x\\ t_2 := \mathsf{fma}\left(y5 \cdot i - y4 \cdot b, k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y\\ \mathbf{if}\;i \leq -9.5 \cdot 10^{+232}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, a, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1\\ \mathbf{elif}\;i \leq -1 \cdot 10^{+192}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y1, \left(-t\right) \cdot c\right) \cdot y4\right) \cdot y2\\ \mathbf{elif}\;i \leq -7.5 \cdot 10^{+90}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y, \left(-t\right) \cdot j\right) \cdot i\right) \cdot y5\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{-295}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, y1, \mathsf{fma}\left(y \cdot x - t \cdot z, b, \left(y2 \cdot t - y3 \cdot y\right) \cdot y5\right)\right) \cdot a\\ \mathbf{elif}\;i \leq 5 \cdot 10^{-182}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot j - y2 \cdot k, y5, \left(\left(-x\right) \cdot j\right) \cdot b\right) \cdot y0\\ \mathbf{elif}\;i \leq 1.75 \cdot 10^{+109}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 5.8 \cdot 10^{+177}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, z, y4 \cdot y2\right) \cdot y1\right) \cdot k\\ \mathbf{elif}\;i \leq 8 \cdot 10^{+267}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y5, \left(-c\right) \cdot x\right) \cdot i\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y3 z) (* y2 x)))
        (t_2
         (*
          (fma
           (- (* y5 i) (* y4 b))
           k
           (fma (- (* b a) (* i c)) x (* (- (* y4 c) (* y5 a)) y3)))
          y)))
   (if (<= i -9.5e+232)
     (*
      (fma t_1 a (fma (- (* y2 k) (* y3 j)) y4 (* (- (* j x) (* k z)) i)))
      y1)
     (if (<= i -1e+192)
       (* (* (fma k y1 (* (- t) c)) y4) y2)
       (if (<= i -7.5e+90)
         (* (* (fma k y (* (- t) j)) i) y5)
         (if (<= i 4.8e-295)
           (*
            (fma
             t_1
             y1
             (fma (- (* y x) (* t z)) b (* (- (* y2 t) (* y3 y)) y5)))
            a)
           (if (<= i 5e-182)
             (* (fma (- (* y3 j) (* y2 k)) y5 (* (* (- x) j) b)) y0)
             (if (<= i 1.75e+109)
               t_2
               (if (<= i 5.8e+177)
                 (* (* (fma (- i) z (* y4 y2)) y1) k)
                 (if (<= i 8e+267)
                   t_2
                   (* (* (fma k y5 (* (- c) x)) i) y)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y3 * z) - (y2 * x);
	double t_2 = fma(((y5 * i) - (y4 * b)), k, fma(((b * a) - (i * c)), x, (((y4 * c) - (y5 * a)) * y3))) * y;
	double tmp;
	if (i <= -9.5e+232) {
		tmp = fma(t_1, a, fma(((y2 * k) - (y3 * j)), y4, (((j * x) - (k * z)) * i))) * y1;
	} else if (i <= -1e+192) {
		tmp = (fma(k, y1, (-t * c)) * y4) * y2;
	} else if (i <= -7.5e+90) {
		tmp = (fma(k, y, (-t * j)) * i) * y5;
	} else if (i <= 4.8e-295) {
		tmp = fma(t_1, y1, fma(((y * x) - (t * z)), b, (((y2 * t) - (y3 * y)) * y5))) * a;
	} else if (i <= 5e-182) {
		tmp = fma(((y3 * j) - (y2 * k)), y5, ((-x * j) * b)) * y0;
	} else if (i <= 1.75e+109) {
		tmp = t_2;
	} else if (i <= 5.8e+177) {
		tmp = (fma(-i, z, (y4 * y2)) * y1) * k;
	} else if (i <= 8e+267) {
		tmp = t_2;
	} else {
		tmp = (fma(k, y5, (-c * x)) * i) * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y3 * z) - Float64(y2 * x))
	t_2 = Float64(fma(Float64(Float64(y5 * i) - Float64(y4 * b)), k, fma(Float64(Float64(b * a) - Float64(i * c)), x, Float64(Float64(Float64(y4 * c) - Float64(y5 * a)) * y3))) * y)
	tmp = 0.0
	if (i <= -9.5e+232)
		tmp = Float64(fma(t_1, a, fma(Float64(Float64(y2 * k) - Float64(y3 * j)), y4, Float64(Float64(Float64(j * x) - Float64(k * z)) * i))) * y1);
	elseif (i <= -1e+192)
		tmp = Float64(Float64(fma(k, y1, Float64(Float64(-t) * c)) * y4) * y2);
	elseif (i <= -7.5e+90)
		tmp = Float64(Float64(fma(k, y, Float64(Float64(-t) * j)) * i) * y5);
	elseif (i <= 4.8e-295)
		tmp = Float64(fma(t_1, y1, fma(Float64(Float64(y * x) - Float64(t * z)), b, Float64(Float64(Float64(y2 * t) - Float64(y3 * y)) * y5))) * a);
	elseif (i <= 5e-182)
		tmp = Float64(fma(Float64(Float64(y3 * j) - Float64(y2 * k)), y5, Float64(Float64(Float64(-x) * j) * b)) * y0);
	elseif (i <= 1.75e+109)
		tmp = t_2;
	elseif (i <= 5.8e+177)
		tmp = Float64(Float64(fma(Float64(-i), z, Float64(y4 * y2)) * y1) * k);
	elseif (i <= 8e+267)
		tmp = t_2;
	else
		tmp = Float64(Float64(fma(k, y5, Float64(Float64(-c) * x)) * i) * y);
	end
	return 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[(y3 * z), $MachinePrecision] - N[(y2 * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(y5 * i), $MachinePrecision] - N[(y4 * b), $MachinePrecision]), $MachinePrecision] * k + N[(N[(N[(b * a), $MachinePrecision] - N[(i * c), $MachinePrecision]), $MachinePrecision] * x + N[(N[(N[(y4 * c), $MachinePrecision] - N[(y5 * a), $MachinePrecision]), $MachinePrecision] * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[i, -9.5e+232], N[(N[(t$95$1 * a + N[(N[(N[(y2 * k), $MachinePrecision] - N[(y3 * j), $MachinePrecision]), $MachinePrecision] * y4 + N[(N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision], If[LessEqual[i, -1e+192], N[(N[(N[(k * y1 + N[((-t) * c), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision] * y2), $MachinePrecision], If[LessEqual[i, -7.5e+90], N[(N[(N[(k * y + N[((-t) * j), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision] * y5), $MachinePrecision], If[LessEqual[i, 4.8e-295], N[(N[(t$95$1 * y1 + N[(N[(N[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision] * b + N[(N[(N[(y2 * t), $MachinePrecision] - N[(y3 * y), $MachinePrecision]), $MachinePrecision] * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[i, 5e-182], N[(N[(N[(N[(y3 * j), $MachinePrecision] - N[(y2 * k), $MachinePrecision]), $MachinePrecision] * y5 + N[(N[((-x) * j), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] * y0), $MachinePrecision], If[LessEqual[i, 1.75e+109], t$95$2, If[LessEqual[i, 5.8e+177], N[(N[(N[((-i) * z + N[(y4 * y2), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision] * k), $MachinePrecision], If[LessEqual[i, 8e+267], t$95$2, N[(N[(N[(k * y5 + N[((-c) * x), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision] * y), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if i < -9.4999999999999996e232

   1. Initial program 28.6%

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

   3. Taylor expanded in y1 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 64.5%

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

   if -9.4999999999999996e232 < i < -1.00000000000000004e192

   1. Initial program 24.4%

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

   3. Taylor expanded in y2 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 63.0%

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

   6. Taylor expanded in y4 around inf

      \[\leadsto \left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right) \cdot y2 \]
   7. Step-by-step derivation

   8. Applied rewrites 75.5%

      \[\leadsto \left(y4 \cdot \mathsf{fma}\left(k, y1, -c \cdot t\right)\right) \cdot y2 \]

   if -1.00000000000000004e192 < i < -7.50000000000000014e90

   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 y5 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 64.3%

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

   6. Taylor expanded in i around inf

      \[\leadsto \left(i \cdot \left(k \cdot y - j \cdot t\right)\right) \cdot y5 \]
   7. Step-by-step derivation

   8. Applied rewrites 71.9%

      \[\leadsto \left(i \cdot \mathsf{fma}\left(k, y, \left(-j\right) \cdot t\right)\right) \cdot y5 \]

   if -7.50000000000000014e90 < i < 4.7999999999999996e-295

   1. Initial program 40.5%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 59.0%

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

   if 4.7999999999999996e-295 < i < 5.00000000000000024e-182

   1. Initial program 23.3%

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

   3. Taylor expanded in y0 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 53.8%

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

   6. Taylor expanded in j around inf

      \[\leadsto \mathsf{fma}\left(-\left(k \cdot y2 - j \cdot y3\right), y5, -1 \cdot \left(b \cdot \left(j \cdot x\right)\right)\right) \cdot y0 \]
   7. Step-by-step derivation

   8. Applied rewrites 54.2%

      \[\leadsto \mathsf{fma}\left(-\left(k \cdot y2 - j \cdot y3\right), y5, -b \cdot \left(j \cdot x\right)\right) \cdot y0 \]

   if 5.00000000000000024e-182 < i < 1.74999999999999992e109 or 5.80000000000000027e177 < i < 7.9999999999999998e267

   1. Initial program 29.8%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 63.2%

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

   if 1.74999999999999992e109 < i < 5.80000000000000027e177

   1. Initial program 25.6%

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

   3. Taylor expanded in y1 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 50.0%

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

   6. Taylor expanded in j around inf

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

   8. Applied rewrites 50.3%

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

   9. Taylor expanded in k around inf

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

   11. Applied rewrites 75.5%

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

   if 7.9999999999999998e267 < i

   1. Initial program 8.3%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 8.3%

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

   6. Taylor expanded in i around inf

      \[\leadsto \left(i \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 66.7%

      \[\leadsto \left(i \cdot \mathsf{fma}\left(k, y5, -c \cdot x\right)\right) \cdot y \]
3. Recombined 8 regimes into one program.

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -9.5 \cdot 10^{+232}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot z - y2 \cdot x, a, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1\\ \mathbf{elif}\;i \leq -1 \cdot 10^{+192}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y1, \left(-t\right) \cdot c\right) \cdot y4\right) \cdot y2\\ \mathbf{elif}\;i \leq -7.5 \cdot 10^{+90}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y, \left(-t\right) \cdot j\right) \cdot i\right) \cdot y5\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{-295}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot z - y2 \cdot x, y1, \mathsf{fma}\left(y \cdot x - t \cdot z, b, \left(y2 \cdot t - y3 \cdot y\right) \cdot y5\right)\right) \cdot a\\ \mathbf{elif}\;i \leq 5 \cdot 10^{-182}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot j - y2 \cdot k, y5, \left(\left(-x\right) \cdot j\right) \cdot b\right) \cdot y0\\ \mathbf{elif}\;i \leq 1.75 \cdot 10^{+109}:\\ \;\;\;\;\mathsf{fma}\left(y5 \cdot i - y4 \cdot b, k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y\\ \mathbf{elif}\;i \leq 5.8 \cdot 10^{+177}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, z, y4 \cdot y2\right) \cdot y1\right) \cdot k\\ \mathbf{elif}\;i \leq 8 \cdot 10^{+267}:\\ \;\;\;\;\mathsf{fma}\left(y5 \cdot i - y4 \cdot b, k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y5, \left(-c\right) \cdot x\right) \cdot i\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 34.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\mathsf{fma}\left(-b, z, y5 \cdot y2\right) \cdot t\right) \cdot a\\ t_2 := \left(\mathsf{fma}\left(-x, y1, y5 \cdot t\right) \cdot y2\right) \cdot a\\ t_3 := \left(\mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right) \cdot y1\right) \cdot a\\ \mathbf{if}\;i \leq -1.3 \cdot 10^{+141}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, k, y3 \cdot a\right) \cdot z\right) \cdot y1\\ \mathbf{elif}\;i \leq -2 \cdot 10^{-23}:\\ \;\;\;\;\left(\mathsf{fma}\left(b \cdot a, x, \mathsf{fma}\left(-b, y4, y5 \cdot i\right) \cdot k\right) - \left(y5 \cdot y3\right) \cdot a\right) \cdot y\\ \mathbf{elif}\;i \leq -1.52 \cdot 10^{-69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -3.7 \cdot 10^{-140}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;i \leq -1.35 \cdot 10^{-194}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -2.1 \cdot 10^{-211}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y1, \left(-t\right) \cdot c\right) \cdot y4\right) \cdot y2\\ \mathbf{elif}\;i \leq -4.8 \cdot 10^{-215}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;i \leq -2.7 \cdot 10^{-227}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 2 \cdot 10^{-298}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 1.35 \cdot 10^{-176}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot j - y2 \cdot k, y5, \left(\left(-x\right) \cdot j\right) \cdot b\right) \cdot y0\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{+251}:\\ \;\;\;\;\mathsf{fma}\left(y5 \cdot i - y4 \cdot b, k, \mathsf{fma}\left(-y3, y5, b \cdot x\right) \cdot a\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y5, \left(-c\right) \cdot x\right) \cdot i\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* (fma (- b) z (* y5 y2)) t) a))
        (t_2 (* (* (fma (- x) y1 (* y5 t)) y2) a))
        (t_3 (* (* (fma y3 z (* (- x) y2)) y1) a)))
   (if (<= i -1.3e+141)
     (* (* (fma (- i) k (* y3 a)) z) y1)
     (if (<= i -2e-23)
       (* (- (fma (* b a) x (* (fma (- b) y4 (* y5 i)) k)) (* (* y5 y3) a)) y)
       (if (<= i -1.52e-69)
         t_1
         (if (<= i -3.7e-140)
           t_3
           (if (<= i -1.35e-194)
             t_2
             (if (<= i -2.1e-211)
               (* (* (fma k y1 (* (- t) c)) y4) y2)
               (if (<= i -4.8e-215)
                 t_3
                 (if (<= i -2.7e-227)
                   t_1
                   (if (<= i 2e-298)
                     t_2
                     (if (<= i 1.35e-176)
                       (* (fma (- (* y3 j) (* y2 k)) y5 (* (* (- x) j) b)) y0)
                       (if (<= i 1.1e+251)
                         (*
                          (fma
                           (- (* y5 i) (* y4 b))
                           k
                           (* (fma (- y3) y5 (* b x)) a))
                          y)
                         (* (* (fma k y5 (* (- c) x)) i) y))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (fma(-b, z, (y5 * y2)) * t) * a;
	double t_2 = (fma(-x, y1, (y5 * t)) * y2) * a;
	double t_3 = (fma(y3, z, (-x * y2)) * y1) * a;
	double tmp;
	if (i <= -1.3e+141) {
		tmp = (fma(-i, k, (y3 * a)) * z) * y1;
	} else if (i <= -2e-23) {
		tmp = (fma((b * a), x, (fma(-b, y4, (y5 * i)) * k)) - ((y5 * y3) * a)) * y;
	} else if (i <= -1.52e-69) {
		tmp = t_1;
	} else if (i <= -3.7e-140) {
		tmp = t_3;
	} else if (i <= -1.35e-194) {
		tmp = t_2;
	} else if (i <= -2.1e-211) {
		tmp = (fma(k, y1, (-t * c)) * y4) * y2;
	} else if (i <= -4.8e-215) {
		tmp = t_3;
	} else if (i <= -2.7e-227) {
		tmp = t_1;
	} else if (i <= 2e-298) {
		tmp = t_2;
	} else if (i <= 1.35e-176) {
		tmp = fma(((y3 * j) - (y2 * k)), y5, ((-x * j) * b)) * y0;
	} else if (i <= 1.1e+251) {
		tmp = fma(((y5 * i) - (y4 * b)), k, (fma(-y3, y5, (b * x)) * a)) * y;
	} else {
		tmp = (fma(k, y5, (-c * x)) * i) * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(fma(Float64(-b), z, Float64(y5 * y2)) * t) * a)
	t_2 = Float64(Float64(fma(Float64(-x), y1, Float64(y5 * t)) * y2) * a)
	t_3 = Float64(Float64(fma(y3, z, Float64(Float64(-x) * y2)) * y1) * a)
	tmp = 0.0
	if (i <= -1.3e+141)
		tmp = Float64(Float64(fma(Float64(-i), k, Float64(y3 * a)) * z) * y1);
	elseif (i <= -2e-23)
		tmp = Float64(Float64(fma(Float64(b * a), x, Float64(fma(Float64(-b), y4, Float64(y5 * i)) * k)) - Float64(Float64(y5 * y3) * a)) * y);
	elseif (i <= -1.52e-69)
		tmp = t_1;
	elseif (i <= -3.7e-140)
		tmp = t_3;
	elseif (i <= -1.35e-194)
		tmp = t_2;
	elseif (i <= -2.1e-211)
		tmp = Float64(Float64(fma(k, y1, Float64(Float64(-t) * c)) * y4) * y2);
	elseif (i <= -4.8e-215)
		tmp = t_3;
	elseif (i <= -2.7e-227)
		tmp = t_1;
	elseif (i <= 2e-298)
		tmp = t_2;
	elseif (i <= 1.35e-176)
		tmp = Float64(fma(Float64(Float64(y3 * j) - Float64(y2 * k)), y5, Float64(Float64(Float64(-x) * j) * b)) * y0);
	elseif (i <= 1.1e+251)
		tmp = Float64(fma(Float64(Float64(y5 * i) - Float64(y4 * b)), k, Float64(fma(Float64(-y3), y5, Float64(b * x)) * a)) * y);
	else
		tmp = Float64(Float64(fma(k, y5, Float64(Float64(-c) * x)) * i) * y);
	end
	return 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[(N[((-b) * z + N[(y5 * y2), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[((-x) * y1 + N[(y5 * t), $MachinePrecision]), $MachinePrecision] * y2), $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(y3 * z + N[((-x) * y2), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[i, -1.3e+141], N[(N[(N[((-i) * k + N[(y3 * a), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] * y1), $MachinePrecision], If[LessEqual[i, -2e-23], N[(N[(N[(N[(b * a), $MachinePrecision] * x + N[(N[((-b) * y4 + N[(y5 * i), $MachinePrecision]), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision] - N[(N[(y5 * y3), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[i, -1.52e-69], t$95$1, If[LessEqual[i, -3.7e-140], t$95$3, If[LessEqual[i, -1.35e-194], t$95$2, If[LessEqual[i, -2.1e-211], N[(N[(N[(k * y1 + N[((-t) * c), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision] * y2), $MachinePrecision], If[LessEqual[i, -4.8e-215], t$95$3, If[LessEqual[i, -2.7e-227], t$95$1, If[LessEqual[i, 2e-298], t$95$2, If[LessEqual[i, 1.35e-176], N[(N[(N[(N[(y3 * j), $MachinePrecision] - N[(y2 * k), $MachinePrecision]), $MachinePrecision] * y5 + N[(N[((-x) * j), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] * y0), $MachinePrecision], If[LessEqual[i, 1.1e+251], N[(N[(N[(N[(y5 * i), $MachinePrecision] - N[(y4 * b), $MachinePrecision]), $MachinePrecision] * k + N[(N[((-y3) * y5 + N[(b * x), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], N[(N[(N[(k * y5 + N[((-c) * x), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision] * y), $MachinePrecision]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if i < -1.3e141

   1. Initial program 25.5%

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

   3. Taylor expanded in y1 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 59.4%

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

   6. Taylor expanded in j around inf

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

   8. Applied rewrites 37.9%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 57.3%

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

   if -1.3e141 < i < -1.99999999999999992e-23

   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 y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 60.1%

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

   6. Taylor expanded in i around inf

      \[\leadsto \left(i \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 33.3%

      \[\leadsto \left(i \cdot \mathsf{fma}\left(k, y5, -c \cdot x\right)\right) \cdot y \]

   9. Taylor expanded in c around 0

      \[\leadsto \left(-1 \cdot \left(a \cdot \left(y3 \cdot y5\right)\right) + \left(a \cdot \left(b \cdot x\right) + k \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right) \cdot y \]
   10. Step-by-step derivation

   11. Applied rewrites 68.7%

       \[\leadsto \left(\mathsf{fma}\left(a \cdot b, x, k \cdot \mathsf{fma}\left(-b, y4, i \cdot y5\right)\right) - a \cdot \left(y3 \cdot y5\right)\right) \cdot y \]

   if -1.99999999999999992e-23 < i < -1.5199999999999999e-69 or -4.8000000000000002e-215 < i < -2.7e-227

   1. Initial program 46.7%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 73.3%

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

   6. Taylor expanded in t around inf

      \[\leadsto \left(t \cdot \left(-1 \cdot \left(b \cdot z\right) + y2 \cdot y5\right)\right) \cdot a \]
   7. Step-by-step derivation

   8. Applied rewrites 73.4%

      \[\leadsto \left(t \cdot \mathsf{fma}\left(-b, z, y2 \cdot y5\right)\right) \cdot a \]

   if -1.5199999999999999e-69 < i < -3.69999999999999977e-140 or -2.10000000000000008e-211 < i < -4.8000000000000002e-215

   1. Initial program 50.0%

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

   3. Taylor expanded in y1 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 42.3%

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

   6. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 67.0%

      \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right)\right)} \]

   if -3.69999999999999977e-140 < i < -1.35e-194 or -2.7e-227 < i < 1.99999999999999982e-298

   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 a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 59.9%

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

   6. Taylor expanded in y2 around inf

      \[\leadsto \left(y2 \cdot \left(-1 \cdot \left(x \cdot y1\right) + t \cdot y5\right)\right) \cdot a \]
   7. Step-by-step derivation

   8. Applied rewrites 54.9%

      \[\leadsto \left(y2 \cdot \mathsf{fma}\left(-x, y1, t \cdot y5\right)\right) \cdot a \]

   if -1.35e-194 < i < -2.10000000000000008e-211

   1. Initial program 33.3%

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

   3. Taylor expanded in y2 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in y4 around inf

      \[\leadsto \left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right) \cdot y2 \]
   7. Step-by-step derivation

   8. Applied rewrites 100.0%

      \[\leadsto \left(y4 \cdot \mathsf{fma}\left(k, y1, -c \cdot t\right)\right) \cdot y2 \]

   if 1.99999999999999982e-298 < i < 1.3499999999999999e-176

   1. Initial program 22.4%

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

   3. Taylor expanded in y0 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 55.6%

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

   6. Taylor expanded in j around inf

      \[\leadsto \mathsf{fma}\left(-\left(k \cdot y2 - j \cdot y3\right), y5, -1 \cdot \left(b \cdot \left(j \cdot x\right)\right)\right) \cdot y0 \]
   7. Step-by-step derivation

   8. Applied rewrites 55.9%

      \[\leadsto \mathsf{fma}\left(-\left(k \cdot y2 - j \cdot y3\right), y5, -b \cdot \left(j \cdot x\right)\right) \cdot y0 \]

   if 1.3499999999999999e-176 < i < 1.1e251

   1. Initial program 30.5%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 57.1%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, a \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 56.2%

      \[\leadsto \mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, a \cdot \mathsf{fma}\left(-y3, y5, b \cdot x\right)\right) \cdot y \]

   if 1.1e251 < i

   1. Initial program 7.1%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 21.4%

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

   6. Taylor expanded in i around inf

      \[\leadsto \left(i \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 64.5%

      \[\leadsto \left(i \cdot \mathsf{fma}\left(k, y5, -c \cdot x\right)\right) \cdot y \]
3. Recombined 9 regimes into one program.

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.3 \cdot 10^{+141}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, k, y3 \cdot a\right) \cdot z\right) \cdot y1\\ \mathbf{elif}\;i \leq -2 \cdot 10^{-23}:\\ \;\;\;\;\left(\mathsf{fma}\left(b \cdot a, x, \mathsf{fma}\left(-b, y4, y5 \cdot i\right) \cdot k\right) - \left(y5 \cdot y3\right) \cdot a\right) \cdot y\\ \mathbf{elif}\;i \leq -1.52 \cdot 10^{-69}:\\ \;\;\;\;\left(\mathsf{fma}\left(-b, z, y5 \cdot y2\right) \cdot t\right) \cdot a\\ \mathbf{elif}\;i \leq -3.7 \cdot 10^{-140}:\\ \;\;\;\;\left(\mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right) \cdot y1\right) \cdot a\\ \mathbf{elif}\;i \leq -1.35 \cdot 10^{-194}:\\ \;\;\;\;\left(\mathsf{fma}\left(-x, y1, y5 \cdot t\right) \cdot y2\right) \cdot a\\ \mathbf{elif}\;i \leq -2.1 \cdot 10^{-211}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y1, \left(-t\right) \cdot c\right) \cdot y4\right) \cdot y2\\ \mathbf{elif}\;i \leq -4.8 \cdot 10^{-215}:\\ \;\;\;\;\left(\mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right) \cdot y1\right) \cdot a\\ \mathbf{elif}\;i \leq -2.7 \cdot 10^{-227}:\\ \;\;\;\;\left(\mathsf{fma}\left(-b, z, y5 \cdot y2\right) \cdot t\right) \cdot a\\ \mathbf{elif}\;i \leq 2 \cdot 10^{-298}:\\ \;\;\;\;\left(\mathsf{fma}\left(-x, y1, y5 \cdot t\right) \cdot y2\right) \cdot a\\ \mathbf{elif}\;i \leq 1.35 \cdot 10^{-176}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot j - y2 \cdot k, y5, \left(\left(-x\right) \cdot j\right) \cdot b\right) \cdot y0\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{+251}:\\ \;\;\;\;\mathsf{fma}\left(y5 \cdot i - y4 \cdot b, k, \mathsf{fma}\left(-y3, y5, b \cdot x\right) \cdot a\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y5, \left(-c\right) \cdot x\right) \cdot i\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 30.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+92}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y, \left(-t\right) \cdot j\right) \cdot i\right) \cdot y5\\ \mathbf{elif}\;t \leq -4.05 \cdot 10^{+18}:\\ \;\;\;\;\left(\mathsf{fma}\left(-b, j, y2 \cdot c\right) \cdot y0\right) \cdot x\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-60}:\\ \;\;\;\;\left(y1 \cdot z\right) \cdot \mathsf{fma}\left(-i, k, y3 \cdot a\right)\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-147}:\\ \;\;\;\;\left(\mathsf{fma}\left(y1, y4, \left(-y0\right) \cdot y5\right) \cdot k\right) \cdot y2\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-155}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, z, y4 \cdot y2\right) \cdot y1\right) \cdot k\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-255}:\\ \;\;\;\;\left(\mathsf{fma}\left(a, x, \left(-k\right) \cdot y4\right) \cdot b\right) \cdot y\\ \mathbf{elif}\;t \leq 1.42 \cdot 10^{-277}:\\ \;\;\;\;\left(\mathsf{fma}\left(-1, y5 \cdot y2, b \cdot z\right) \cdot y0\right) \cdot k\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-233}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right) \cdot y4\right) \cdot y1\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-104}:\\ \;\;\;\;\left(\mathsf{fma}\left(-y3, y5, b \cdot x\right) \cdot a\right) \cdot y\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-38}:\\ \;\;\;\;\left(\mathsf{fma}\left(-1, y0 \cdot j, a \cdot y\right) \cdot b\right) \cdot x\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+107}:\\ \;\;\;\;\left(\mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right) \cdot y1\right) \cdot a\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+194}:\\ \;\;\;\;\left(\mathsf{fma}\left(-1, y0 \cdot k, a \cdot t\right) \cdot y5\right) \cdot y2\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(x, y, \left(-t\right) \cdot z\right) \cdot b\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= t -1.7e+92)
   (* (* (fma k y (* (- t) j)) i) y5)
   (if (<= t -4.05e+18)
     (* (* (fma (- b) j (* y2 c)) y0) x)
     (if (<= t -4.5e-60)
       (* (* y1 z) (fma (- i) k (* y3 a)))
       (if (<= t -2e-147)
         (* (* (fma y1 y4 (* (- y0) y5)) k) y2)
         (if (<= t -3e-155)
           (* (* (fma (- i) z (* y4 y2)) y1) k)
           (if (<= t -6e-255)
             (* (* (fma a x (* (- k) y4)) b) y)
             (if (<= t 1.42e-277)
               (* (* (fma -1.0 (* y5 y2) (* b z)) y0) k)
               (if (<= t 6e-233)
                 (* (* (fma k y2 (* (- j) y3)) y4) y1)
                 (if (<= t 2.3e-104)
                   (* (* (fma (- y3) y5 (* b x)) a) y)
                   (if (<= t 2.2e-38)
                     (* (* (fma -1.0 (* y0 j) (* a y)) b) x)
                     (if (<= t 8.5e+107)
                       (* (* (fma y3 z (* (- x) y2)) y1) a)
                       (if (<= t 3.3e+194)
                         (* (* (fma -1.0 (* y0 k) (* a t)) y5) y2)
                         (* (* (fma x y (* (- t) z)) b) a))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (t <= -1.7e+92) {
		tmp = (fma(k, y, (-t * j)) * i) * y5;
	} else if (t <= -4.05e+18) {
		tmp = (fma(-b, j, (y2 * c)) * y0) * x;
	} else if (t <= -4.5e-60) {
		tmp = (y1 * z) * fma(-i, k, (y3 * a));
	} else if (t <= -2e-147) {
		tmp = (fma(y1, y4, (-y0 * y5)) * k) * y2;
	} else if (t <= -3e-155) {
		tmp = (fma(-i, z, (y4 * y2)) * y1) * k;
	} else if (t <= -6e-255) {
		tmp = (fma(a, x, (-k * y4)) * b) * y;
	} else if (t <= 1.42e-277) {
		tmp = (fma(-1.0, (y5 * y2), (b * z)) * y0) * k;
	} else if (t <= 6e-233) {
		tmp = (fma(k, y2, (-j * y3)) * y4) * y1;
	} else if (t <= 2.3e-104) {
		tmp = (fma(-y3, y5, (b * x)) * a) * y;
	} else if (t <= 2.2e-38) {
		tmp = (fma(-1.0, (y0 * j), (a * y)) * b) * x;
	} else if (t <= 8.5e+107) {
		tmp = (fma(y3, z, (-x * y2)) * y1) * a;
	} else if (t <= 3.3e+194) {
		tmp = (fma(-1.0, (y0 * k), (a * t)) * y5) * y2;
	} else {
		tmp = (fma(x, y, (-t * z)) * b) * a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (t <= -1.7e+92)
		tmp = Float64(Float64(fma(k, y, Float64(Float64(-t) * j)) * i) * y5);
	elseif (t <= -4.05e+18)
		tmp = Float64(Float64(fma(Float64(-b), j, Float64(y2 * c)) * y0) * x);
	elseif (t <= -4.5e-60)
		tmp = Float64(Float64(y1 * z) * fma(Float64(-i), k, Float64(y3 * a)));
	elseif (t <= -2e-147)
		tmp = Float64(Float64(fma(y1, y4, Float64(Float64(-y0) * y5)) * k) * y2);
	elseif (t <= -3e-155)
		tmp = Float64(Float64(fma(Float64(-i), z, Float64(y4 * y2)) * y1) * k);
	elseif (t <= -6e-255)
		tmp = Float64(Float64(fma(a, x, Float64(Float64(-k) * y4)) * b) * y);
	elseif (t <= 1.42e-277)
		tmp = Float64(Float64(fma(-1.0, Float64(y5 * y2), Float64(b * z)) * y0) * k);
	elseif (t <= 6e-233)
		tmp = Float64(Float64(fma(k, y2, Float64(Float64(-j) * y3)) * y4) * y1);
	elseif (t <= 2.3e-104)
		tmp = Float64(Float64(fma(Float64(-y3), y5, Float64(b * x)) * a) * y);
	elseif (t <= 2.2e-38)
		tmp = Float64(Float64(fma(-1.0, Float64(y0 * j), Float64(a * y)) * b) * x);
	elseif (t <= 8.5e+107)
		tmp = Float64(Float64(fma(y3, z, Float64(Float64(-x) * y2)) * y1) * a);
	elseif (t <= 3.3e+194)
		tmp = Float64(Float64(fma(-1.0, Float64(y0 * k), Float64(a * t)) * y5) * y2);
	else
		tmp = Float64(Float64(fma(x, y, Float64(Float64(-t) * z)) * b) * a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[t, -1.7e+92], N[(N[(N[(k * y + N[((-t) * j), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision] * y5), $MachinePrecision], If[LessEqual[t, -4.05e+18], N[(N[(N[((-b) * j + N[(y2 * c), $MachinePrecision]), $MachinePrecision] * y0), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t, -4.5e-60], N[(N[(y1 * z), $MachinePrecision] * N[((-i) * k + N[(y3 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2e-147], N[(N[(N[(y1 * y4 + N[((-y0) * y5), $MachinePrecision]), $MachinePrecision] * k), $MachinePrecision] * y2), $MachinePrecision], If[LessEqual[t, -3e-155], N[(N[(N[((-i) * z + N[(y4 * y2), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision] * k), $MachinePrecision], If[LessEqual[t, -6e-255], N[(N[(N[(a * x + N[((-k) * y4), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 1.42e-277], N[(N[(N[(-1.0 * N[(y5 * y2), $MachinePrecision] + N[(b * z), $MachinePrecision]), $MachinePrecision] * y0), $MachinePrecision] * k), $MachinePrecision], If[LessEqual[t, 6e-233], N[(N[(N[(k * y2 + N[((-j) * y3), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision] * y1), $MachinePrecision], If[LessEqual[t, 2.3e-104], N[(N[(N[((-y3) * y5 + N[(b * x), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 2.2e-38], N[(N[(N[(-1.0 * N[(y0 * j), $MachinePrecision] + N[(a * y), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t, 8.5e+107], N[(N[(N[(y3 * z + N[((-x) * y2), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[t, 3.3e+194], N[(N[(N[(-1.0 * N[(y0 * k), $MachinePrecision] + N[(a * t), $MachinePrecision]), $MachinePrecision] * y5), $MachinePrecision] * y2), $MachinePrecision], N[(N[(N[(x * y + N[((-t) * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision] * a), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 13 regimes

2. if t < -1.6999999999999999e92

   1. Initial program 21.9%

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

   3. Taylor expanded in y5 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 62.3%

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

   6. Taylor expanded in i around inf

      \[\leadsto \left(i \cdot \left(k \cdot y - j \cdot t\right)\right) \cdot y5 \]
   7. Step-by-step derivation

   8. Applied rewrites 54.1%

      \[\leadsto \left(i \cdot \mathsf{fma}\left(k, y, \left(-j\right) \cdot t\right)\right) \cdot y5 \]

   if -1.6999999999999999e92 < t < -4.05e18

   1. Initial program 53.2%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 60.5%

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

   6. Taylor expanded in y around inf

      \[\leadsto \left(y \cdot \left(a \cdot b - c \cdot i\right)\right) \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 16.1%

      \[\leadsto \left(y \cdot \mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right)\right) \cdot x \]

   9. Taylor expanded in y0 around inf

      \[\leadsto \left(y0 \cdot \left(-1 \cdot \left(b \cdot j\right) + c \cdot y2\right)\right) \cdot x \]
   10. Step-by-step derivation

   11. Applied rewrites 61.0%

       \[\leadsto \left(y0 \cdot \mathsf{fma}\left(-b, j, c \cdot y2\right)\right) \cdot x \]

   if -4.05e18 < t < -4.50000000000000001e-60

   1. Initial program 29.3%

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

   3. Taylor expanded in y1 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 55.9%

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

   6. Taylor expanded in j around inf

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

   8. Applied rewrites 36.2%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 73.7%

       \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \mathsf{fma}\left(-i, k, a \cdot y3\right)\right)} \]
   12. Step-by-step derivation

   13. Applied rewrites 73.7%

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

   if -4.50000000000000001e-60 < t < -1.9999999999999999e-147

   1. Initial program 32.6%

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

   3. Taylor expanded in y2 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 48.2%

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

   6. Taylor expanded in k around inf

      \[\leadsto \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) \cdot y2 \]
   7. Step-by-step derivation

   8. Applied rewrites 53.6%

      \[\leadsto \left(k \cdot \mathsf{fma}\left(y1, y4, \left(-y0\right) \cdot y5\right)\right) \cdot y2 \]

   if -1.9999999999999999e-147 < t < -2.99999999999999984e-155

   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

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 76.4%

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

   6. Taylor expanded in j around inf

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

   8. Applied rewrites 26.0%

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

   9. Taylor expanded in k around inf

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

   11. Applied rewrites 88.0%

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

   if -2.99999999999999984e-155 < t < -6.00000000000000004e-255

   1. Initial program 31.7%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 63.8%

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

   6. Taylor expanded in b around inf

      \[\leadsto \left(b \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 63.4%

      \[\leadsto \left(b \cdot \mathsf{fma}\left(a, x, -k \cdot y4\right)\right) \cdot y \]

   if -6.00000000000000004e-255 < t < 1.4199999999999999e-277

   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 y0 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 50.9%

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

   6. Taylor expanded in k around inf

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

   8. Applied rewrites 62.3%

      \[\leadsto k \cdot \color{blue}{\left(y0 \cdot \mathsf{fma}\left(-1, y2 \cdot y5, b \cdot z\right)\right)} \]

   if 1.4199999999999999e-277 < t < 5.99999999999999997e-233

   1. Initial program 13.3%

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

   3. Taylor expanded in y1 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 50.2%

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

   6. Taylor expanded in y4 around inf

      \[\leadsto \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \cdot y1 \]
   7. Step-by-step derivation

   8. Applied rewrites 63.2%

      \[\leadsto \left(y4 \cdot \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right)\right) \cdot y1 \]

   if 5.99999999999999997e-233 < t < 2.2999999999999999e-104

   1. Initial program 36.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 61.9%

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

   6. Taylor expanded in a around inf

      \[\leadsto \left(a \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 62.8%

      \[\leadsto \left(a \cdot \mathsf{fma}\left(-y3, y5, b \cdot x\right)\right) \cdot y \]

   if 2.2999999999999999e-104 < t < 2.20000000000000007e-38

   1. Initial program 47.5%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 57.4%

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

   6. Taylor expanded in b around inf

      \[\leadsto \left(b \cdot \left(-1 \cdot \left(j \cdot y0\right) + a \cdot y\right)\right) \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 53.6%

      \[\leadsto \left(b \cdot \mathsf{fma}\left(-1, j \cdot y0, a \cdot y\right)\right) \cdot x \]

   if 2.20000000000000007e-38 < t < 8.4999999999999999e107

   1. Initial program 28.1%

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

   3. Taylor expanded in y1 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 59.6%

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

   6. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 60.0%

      \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right)\right)} \]

   if 8.4999999999999999e107 < t < 3.29999999999999983e194

   1. Initial program 22.2%

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

   3. Taylor expanded in y5 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 38.9%

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

   6. Taylor expanded in y2 around inf

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

   8. Applied rewrites 56.3%

      \[\leadsto y2 \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(-1, k \cdot y0, a \cdot t\right)\right)} \]

   if 3.29999999999999983e194 < t

   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 a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 40.6%

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

   6. Taylor expanded in b around inf

      \[\leadsto \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) \cdot a \]
   7. Step-by-step derivation

   8. Applied rewrites 70.8%

      \[\leadsto \left(b \cdot \mathsf{fma}\left(x, y, \left(-t\right) \cdot z\right)\right) \cdot a \]
3. Recombined 13 regimes into one program.

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+92}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y, \left(-t\right) \cdot j\right) \cdot i\right) \cdot y5\\ \mathbf{elif}\;t \leq -4.05 \cdot 10^{+18}:\\ \;\;\;\;\left(\mathsf{fma}\left(-b, j, y2 \cdot c\right) \cdot y0\right) \cdot x\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-60}:\\ \;\;\;\;\left(y1 \cdot z\right) \cdot \mathsf{fma}\left(-i, k, y3 \cdot a\right)\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-147}:\\ \;\;\;\;\left(\mathsf{fma}\left(y1, y4, \left(-y0\right) \cdot y5\right) \cdot k\right) \cdot y2\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-155}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, z, y4 \cdot y2\right) \cdot y1\right) \cdot k\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-255}:\\ \;\;\;\;\left(\mathsf{fma}\left(a, x, \left(-k\right) \cdot y4\right) \cdot b\right) \cdot y\\ \mathbf{elif}\;t \leq 1.42 \cdot 10^{-277}:\\ \;\;\;\;\left(\mathsf{fma}\left(-1, y5 \cdot y2, b \cdot z\right) \cdot y0\right) \cdot k\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-233}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right) \cdot y4\right) \cdot y1\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-104}:\\ \;\;\;\;\left(\mathsf{fma}\left(-y3, y5, b \cdot x\right) \cdot a\right) \cdot y\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-38}:\\ \;\;\;\;\left(\mathsf{fma}\left(-1, y0 \cdot j, a \cdot y\right) \cdot b\right) \cdot x\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+107}:\\ \;\;\;\;\left(\mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right) \cdot y1\right) \cdot a\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+194}:\\ \;\;\;\;\left(\mathsf{fma}\left(-1, y0 \cdot k, a \cdot t\right) \cdot y5\right) \cdot y2\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(x, y, \left(-t\right) \cdot z\right) \cdot b\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 30.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+92}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y, \left(-t\right) \cdot j\right) \cdot i\right) \cdot y5\\ \mathbf{elif}\;t \leq -4.05 \cdot 10^{+18}:\\ \;\;\;\;\left(\mathsf{fma}\left(-b, j, y2 \cdot c\right) \cdot y0\right) \cdot x\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-60}:\\ \;\;\;\;\left(y1 \cdot z\right) \cdot \mathsf{fma}\left(-i, k, y3 \cdot a\right)\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-147}:\\ \;\;\;\;\left(\mathsf{fma}\left(y1, y4, \left(-y0\right) \cdot y5\right) \cdot k\right) \cdot y2\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-155}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, z, y4 \cdot y2\right) \cdot y1\right) \cdot k\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-255}:\\ \;\;\;\;\left(\mathsf{fma}\left(a, x, \left(-k\right) \cdot y4\right) \cdot b\right) \cdot y\\ \mathbf{elif}\;t \leq 1.42 \cdot 10^{-277}:\\ \;\;\;\;\left(\mathsf{fma}\left(-1, y5 \cdot y2, b \cdot z\right) \cdot y0\right) \cdot k\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-233}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right) \cdot y4\right) \cdot y1\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-92}:\\ \;\;\;\;\left(\mathsf{fma}\left(-y3, y5, b \cdot x\right) \cdot a\right) \cdot y\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-42}:\\ \;\;\;\;\left(\mathsf{fma}\left(b, y0, \left(-i\right) \cdot y1\right) \cdot \left(-j\right)\right) \cdot x\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+107}:\\ \;\;\;\;\left(\mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right) \cdot y1\right) \cdot a\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+194}:\\ \;\;\;\;\left(\mathsf{fma}\left(-1, y0 \cdot k, a \cdot t\right) \cdot y5\right) \cdot y2\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(x, y, \left(-t\right) \cdot z\right) \cdot b\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= t -1.7e+92)
   (* (* (fma k y (* (- t) j)) i) y5)
   (if (<= t -4.05e+18)
     (* (* (fma (- b) j (* y2 c)) y0) x)
     (if (<= t -4.5e-60)
       (* (* y1 z) (fma (- i) k (* y3 a)))
       (if (<= t -2e-147)
         (* (* (fma y1 y4 (* (- y0) y5)) k) y2)
         (if (<= t -3e-155)
           (* (* (fma (- i) z (* y4 y2)) y1) k)
           (if (<= t -6e-255)
             (* (* (fma a x (* (- k) y4)) b) y)
             (if (<= t 1.42e-277)
               (* (* (fma -1.0 (* y5 y2) (* b z)) y0) k)
               (if (<= t 6e-233)
                 (* (* (fma k y2 (* (- j) y3)) y4) y1)
                 (if (<= t 7.8e-92)
                   (* (* (fma (- y3) y5 (* b x)) a) y)
                   (if (<= t 8.8e-42)
                     (* (* (fma b y0 (* (- i) y1)) (- j)) x)
                     (if (<= t 8.5e+107)
                       (* (* (fma y3 z (* (- x) y2)) y1) a)
                       (if (<= t 3.3e+194)
                         (* (* (fma -1.0 (* y0 k) (* a t)) y5) y2)
                         (* (* (fma x y (* (- t) z)) b) a))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (t <= -1.7e+92) {
		tmp = (fma(k, y, (-t * j)) * i) * y5;
	} else if (t <= -4.05e+18) {
		tmp = (fma(-b, j, (y2 * c)) * y0) * x;
	} else if (t <= -4.5e-60) {
		tmp = (y1 * z) * fma(-i, k, (y3 * a));
	} else if (t <= -2e-147) {
		tmp = (fma(y1, y4, (-y0 * y5)) * k) * y2;
	} else if (t <= -3e-155) {
		tmp = (fma(-i, z, (y4 * y2)) * y1) * k;
	} else if (t <= -6e-255) {
		tmp = (fma(a, x, (-k * y4)) * b) * y;
	} else if (t <= 1.42e-277) {
		tmp = (fma(-1.0, (y5 * y2), (b * z)) * y0) * k;
	} else if (t <= 6e-233) {
		tmp = (fma(k, y2, (-j * y3)) * y4) * y1;
	} else if (t <= 7.8e-92) {
		tmp = (fma(-y3, y5, (b * x)) * a) * y;
	} else if (t <= 8.8e-42) {
		tmp = (fma(b, y0, (-i * y1)) * -j) * x;
	} else if (t <= 8.5e+107) {
		tmp = (fma(y3, z, (-x * y2)) * y1) * a;
	} else if (t <= 3.3e+194) {
		tmp = (fma(-1.0, (y0 * k), (a * t)) * y5) * y2;
	} else {
		tmp = (fma(x, y, (-t * z)) * b) * a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (t <= -1.7e+92)
		tmp = Float64(Float64(fma(k, y, Float64(Float64(-t) * j)) * i) * y5);
	elseif (t <= -4.05e+18)
		tmp = Float64(Float64(fma(Float64(-b), j, Float64(y2 * c)) * y0) * x);
	elseif (t <= -4.5e-60)
		tmp = Float64(Float64(y1 * z) * fma(Float64(-i), k, Float64(y3 * a)));
	elseif (t <= -2e-147)
		tmp = Float64(Float64(fma(y1, y4, Float64(Float64(-y0) * y5)) * k) * y2);
	elseif (t <= -3e-155)
		tmp = Float64(Float64(fma(Float64(-i), z, Float64(y4 * y2)) * y1) * k);
	elseif (t <= -6e-255)
		tmp = Float64(Float64(fma(a, x, Float64(Float64(-k) * y4)) * b) * y);
	elseif (t <= 1.42e-277)
		tmp = Float64(Float64(fma(-1.0, Float64(y5 * y2), Float64(b * z)) * y0) * k);
	elseif (t <= 6e-233)
		tmp = Float64(Float64(fma(k, y2, Float64(Float64(-j) * y3)) * y4) * y1);
	elseif (t <= 7.8e-92)
		tmp = Float64(Float64(fma(Float64(-y3), y5, Float64(b * x)) * a) * y);
	elseif (t <= 8.8e-42)
		tmp = Float64(Float64(fma(b, y0, Float64(Float64(-i) * y1)) * Float64(-j)) * x);
	elseif (t <= 8.5e+107)
		tmp = Float64(Float64(fma(y3, z, Float64(Float64(-x) * y2)) * y1) * a);
	elseif (t <= 3.3e+194)
		tmp = Float64(Float64(fma(-1.0, Float64(y0 * k), Float64(a * t)) * y5) * y2);
	else
		tmp = Float64(Float64(fma(x, y, Float64(Float64(-t) * z)) * b) * a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[t, -1.7e+92], N[(N[(N[(k * y + N[((-t) * j), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision] * y5), $MachinePrecision], If[LessEqual[t, -4.05e+18], N[(N[(N[((-b) * j + N[(y2 * c), $MachinePrecision]), $MachinePrecision] * y0), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t, -4.5e-60], N[(N[(y1 * z), $MachinePrecision] * N[((-i) * k + N[(y3 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2e-147], N[(N[(N[(y1 * y4 + N[((-y0) * y5), $MachinePrecision]), $MachinePrecision] * k), $MachinePrecision] * y2), $MachinePrecision], If[LessEqual[t, -3e-155], N[(N[(N[((-i) * z + N[(y4 * y2), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision] * k), $MachinePrecision], If[LessEqual[t, -6e-255], N[(N[(N[(a * x + N[((-k) * y4), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 1.42e-277], N[(N[(N[(-1.0 * N[(y5 * y2), $MachinePrecision] + N[(b * z), $MachinePrecision]), $MachinePrecision] * y0), $MachinePrecision] * k), $MachinePrecision], If[LessEqual[t, 6e-233], N[(N[(N[(k * y2 + N[((-j) * y3), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision] * y1), $MachinePrecision], If[LessEqual[t, 7.8e-92], N[(N[(N[((-y3) * y5 + N[(b * x), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 8.8e-42], N[(N[(N[(b * y0 + N[((-i) * y1), $MachinePrecision]), $MachinePrecision] * (-j)), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t, 8.5e+107], N[(N[(N[(y3 * z + N[((-x) * y2), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[t, 3.3e+194], N[(N[(N[(-1.0 * N[(y0 * k), $MachinePrecision] + N[(a * t), $MachinePrecision]), $MachinePrecision] * y5), $MachinePrecision] * y2), $MachinePrecision], N[(N[(N[(x * y + N[((-t) * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision] * a), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 13 regimes

2. if t < -1.6999999999999999e92

   1. Initial program 21.9%

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

   3. Taylor expanded in y5 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 62.3%

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

   6. Taylor expanded in i around inf

      \[\leadsto \left(i \cdot \left(k \cdot y - j \cdot t\right)\right) \cdot y5 \]
   7. Step-by-step derivation

   8. Applied rewrites 54.1%

      \[\leadsto \left(i \cdot \mathsf{fma}\left(k, y, \left(-j\right) \cdot t\right)\right) \cdot y5 \]

   if -1.6999999999999999e92 < t < -4.05e18

   1. Initial program 53.2%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 60.5%

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

   6. Taylor expanded in y around inf

      \[\leadsto \left(y \cdot \left(a \cdot b - c \cdot i\right)\right) \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 16.1%

      \[\leadsto \left(y \cdot \mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right)\right) \cdot x \]

   9. Taylor expanded in y0 around inf

      \[\leadsto \left(y0 \cdot \left(-1 \cdot \left(b \cdot j\right) + c \cdot y2\right)\right) \cdot x \]
   10. Step-by-step derivation

   11. Applied rewrites 61.0%

       \[\leadsto \left(y0 \cdot \mathsf{fma}\left(-b, j, c \cdot y2\right)\right) \cdot x \]

   if -4.05e18 < t < -4.50000000000000001e-60

   1. Initial program 29.3%

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

   3. Taylor expanded in y1 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 55.9%

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

   6. Taylor expanded in j around inf

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

   8. Applied rewrites 36.2%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 73.7%

       \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \mathsf{fma}\left(-i, k, a \cdot y3\right)\right)} \]
   12. Step-by-step derivation

   13. Applied rewrites 73.7%

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

   if -4.50000000000000001e-60 < t < -1.9999999999999999e-147

   1. Initial program 32.6%

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

   3. Taylor expanded in y2 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 48.2%

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

   6. Taylor expanded in k around inf

      \[\leadsto \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) \cdot y2 \]
   7. Step-by-step derivation

   8. Applied rewrites 53.6%

      \[\leadsto \left(k \cdot \mathsf{fma}\left(y1, y4, \left(-y0\right) \cdot y5\right)\right) \cdot y2 \]

   if -1.9999999999999999e-147 < t < -2.99999999999999984e-155

   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

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 76.4%

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

   6. Taylor expanded in j around inf

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

   8. Applied rewrites 26.0%

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

   9. Taylor expanded in k around inf

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

   11. Applied rewrites 88.0%

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

   if -2.99999999999999984e-155 < t < -6.00000000000000004e-255

   1. Initial program 31.7%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 63.8%

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

   6. Taylor expanded in b around inf

      \[\leadsto \left(b \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 63.4%

      \[\leadsto \left(b \cdot \mathsf{fma}\left(a, x, -k \cdot y4\right)\right) \cdot y \]

   if -6.00000000000000004e-255 < t < 1.4199999999999999e-277

   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 y0 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 50.9%

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

   6. Taylor expanded in k around inf

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

   8. Applied rewrites 62.3%

      \[\leadsto k \cdot \color{blue}{\left(y0 \cdot \mathsf{fma}\left(-1, y2 \cdot y5, b \cdot z\right)\right)} \]

   if 1.4199999999999999e-277 < t < 5.99999999999999997e-233

   1. Initial program 13.3%

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

   3. Taylor expanded in y1 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 50.2%

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

   6. Taylor expanded in y4 around inf

      \[\leadsto \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \cdot y1 \]
   7. Step-by-step derivation

   8. Applied rewrites 63.2%

      \[\leadsto \left(y4 \cdot \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right)\right) \cdot y1 \]

   if 5.99999999999999997e-233 < t < 7.7999999999999993e-92

   1. Initial program 37.6%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 54.9%

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

   6. Taylor expanded in a around inf

      \[\leadsto \left(a \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 58.7%

      \[\leadsto \left(a \cdot \mathsf{fma}\left(-y3, y5, b \cdot x\right)\right) \cdot y \]

   if 7.7999999999999993e-92 < t < 8.8000000000000002e-42

   1. Initial program 47.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 59.1%

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

   6. Taylor expanded in j around inf

      \[\leadsto \left(-1 \cdot \left(j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 54.0%

      \[\leadsto \left(-j \cdot \mathsf{fma}\left(b, y0, \left(-i\right) \cdot y1\right)\right) \cdot x \]

   if 8.8000000000000002e-42 < t < 8.4999999999999999e107

   1. Initial program 28.1%

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

   3. Taylor expanded in y1 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 59.6%

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

   6. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 60.0%

      \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right)\right)} \]

   if 8.4999999999999999e107 < t < 3.29999999999999983e194

   1. Initial program 22.2%

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

   3. Taylor expanded in y5 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 38.9%

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

   6. Taylor expanded in y2 around inf

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

   8. Applied rewrites 56.3%

      \[\leadsto y2 \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(-1, k \cdot y0, a \cdot t\right)\right)} \]

   if 3.29999999999999983e194 < t

   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 a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 40.6%

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

   6. Taylor expanded in b around inf

      \[\leadsto \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) \cdot a \]
   7. Step-by-step derivation

   8. Applied rewrites 70.8%

      \[\leadsto \left(b \cdot \mathsf{fma}\left(x, y, \left(-t\right) \cdot z\right)\right) \cdot a \]
3. Recombined 13 regimes into one program.

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+92}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y, \left(-t\right) \cdot j\right) \cdot i\right) \cdot y5\\ \mathbf{elif}\;t \leq -4.05 \cdot 10^{+18}:\\ \;\;\;\;\left(\mathsf{fma}\left(-b, j, y2 \cdot c\right) \cdot y0\right) \cdot x\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-60}:\\ \;\;\;\;\left(y1 \cdot z\right) \cdot \mathsf{fma}\left(-i, k, y3 \cdot a\right)\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-147}:\\ \;\;\;\;\left(\mathsf{fma}\left(y1, y4, \left(-y0\right) \cdot y5\right) \cdot k\right) \cdot y2\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-155}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, z, y4 \cdot y2\right) \cdot y1\right) \cdot k\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-255}:\\ \;\;\;\;\left(\mathsf{fma}\left(a, x, \left(-k\right) \cdot y4\right) \cdot b\right) \cdot y\\ \mathbf{elif}\;t \leq 1.42 \cdot 10^{-277}:\\ \;\;\;\;\left(\mathsf{fma}\left(-1, y5 \cdot y2, b \cdot z\right) \cdot y0\right) \cdot k\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-233}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right) \cdot y4\right) \cdot y1\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-92}:\\ \;\;\;\;\left(\mathsf{fma}\left(-y3, y5, b \cdot x\right) \cdot a\right) \cdot y\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-42}:\\ \;\;\;\;\left(\mathsf{fma}\left(b, y0, \left(-i\right) \cdot y1\right) \cdot \left(-j\right)\right) \cdot x\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+107}:\\ \;\;\;\;\left(\mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right) \cdot y1\right) \cdot a\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+194}:\\ \;\;\;\;\left(\mathsf{fma}\left(-1, y0 \cdot k, a \cdot t\right) \cdot y5\right) \cdot y2\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(x, y, \left(-t\right) \cdot z\right) \cdot b\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 30.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+92}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y, \left(-t\right) \cdot j\right) \cdot i\right) \cdot y5\\ \mathbf{elif}\;t \leq -4.05 \cdot 10^{+18}:\\ \;\;\;\;\left(\mathsf{fma}\left(-b, j, y2 \cdot c\right) \cdot y0\right) \cdot x\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-60}:\\ \;\;\;\;\left(y1 \cdot z\right) \cdot \mathsf{fma}\left(-i, k, y3 \cdot a\right)\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-147}:\\ \;\;\;\;\left(\mathsf{fma}\left(y1, y4, \left(-y0\right) \cdot y5\right) \cdot k\right) \cdot y2\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-155}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, z, y4 \cdot y2\right) \cdot y1\right) \cdot k\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-254}:\\ \;\;\;\;\left(\mathsf{fma}\left(a, x, \left(-k\right) \cdot y4\right) \cdot b\right) \cdot y\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-306}:\\ \;\;\;\;\mathsf{fma}\left(c, x, \left(-y5\right) \cdot k\right) \cdot \left(y2 \cdot y0\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-233}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right) \cdot y4\right) \cdot y1\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-92}:\\ \;\;\;\;\left(\mathsf{fma}\left(-y3, y5, b \cdot x\right) \cdot a\right) \cdot y\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-42}:\\ \;\;\;\;\left(\mathsf{fma}\left(b, y0, \left(-i\right) \cdot y1\right) \cdot \left(-j\right)\right) \cdot x\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+107}:\\ \;\;\;\;\left(\mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right) \cdot y1\right) \cdot a\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+194}:\\ \;\;\;\;\left(\mathsf{fma}\left(-1, y0 \cdot k, a \cdot t\right) \cdot y5\right) \cdot y2\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(x, y, \left(-t\right) \cdot z\right) \cdot b\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= t -1.7e+92)
   (* (* (fma k y (* (- t) j)) i) y5)
   (if (<= t -4.05e+18)
     (* (* (fma (- b) j (* y2 c)) y0) x)
     (if (<= t -4.5e-60)
       (* (* y1 z) (fma (- i) k (* y3 a)))
       (if (<= t -2e-147)
         (* (* (fma y1 y4 (* (- y0) y5)) k) y2)
         (if (<= t -3e-155)
           (* (* (fma (- i) z (* y4 y2)) y1) k)
           (if (<= t -1.1e-254)
             (* (* (fma a x (* (- k) y4)) b) y)
             (if (<= t -1.45e-306)
               (* (fma c x (* (- y5) k)) (* y2 y0))
               (if (<= t 6e-233)
                 (* (* (fma k y2 (* (- j) y3)) y4) y1)
                 (if (<= t 7.8e-92)
                   (* (* (fma (- y3) y5 (* b x)) a) y)
                   (if (<= t 8.8e-42)
                     (* (* (fma b y0 (* (- i) y1)) (- j)) x)
                     (if (<= t 8.5e+107)
                       (* (* (fma y3 z (* (- x) y2)) y1) a)
                       (if (<= t 3.3e+194)
                         (* (* (fma -1.0 (* y0 k) (* a t)) y5) y2)
                         (* (* (fma x y (* (- t) z)) b) a))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (t <= -1.7e+92) {
		tmp = (fma(k, y, (-t * j)) * i) * y5;
	} else if (t <= -4.05e+18) {
		tmp = (fma(-b, j, (y2 * c)) * y0) * x;
	} else if (t <= -4.5e-60) {
		tmp = (y1 * z) * fma(-i, k, (y3 * a));
	} else if (t <= -2e-147) {
		tmp = (fma(y1, y4, (-y0 * y5)) * k) * y2;
	} else if (t <= -3e-155) {
		tmp = (fma(-i, z, (y4 * y2)) * y1) * k;
	} else if (t <= -1.1e-254) {
		tmp = (fma(a, x, (-k * y4)) * b) * y;
	} else if (t <= -1.45e-306) {
		tmp = fma(c, x, (-y5 * k)) * (y2 * y0);
	} else if (t <= 6e-233) {
		tmp = (fma(k, y2, (-j * y3)) * y4) * y1;
	} else if (t <= 7.8e-92) {
		tmp = (fma(-y3, y5, (b * x)) * a) * y;
	} else if (t <= 8.8e-42) {
		tmp = (fma(b, y0, (-i * y1)) * -j) * x;
	} else if (t <= 8.5e+107) {
		tmp = (fma(y3, z, (-x * y2)) * y1) * a;
	} else if (t <= 3.3e+194) {
		tmp = (fma(-1.0, (y0 * k), (a * t)) * y5) * y2;
	} else {
		tmp = (fma(x, y, (-t * z)) * b) * a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (t <= -1.7e+92)
		tmp = Float64(Float64(fma(k, y, Float64(Float64(-t) * j)) * i) * y5);
	elseif (t <= -4.05e+18)
		tmp = Float64(Float64(fma(Float64(-b), j, Float64(y2 * c)) * y0) * x);
	elseif (t <= -4.5e-60)
		tmp = Float64(Float64(y1 * z) * fma(Float64(-i), k, Float64(y3 * a)));
	elseif (t <= -2e-147)
		tmp = Float64(Float64(fma(y1, y4, Float64(Float64(-y0) * y5)) * k) * y2);
	elseif (t <= -3e-155)
		tmp = Float64(Float64(fma(Float64(-i), z, Float64(y4 * y2)) * y1) * k);
	elseif (t <= -1.1e-254)
		tmp = Float64(Float64(fma(a, x, Float64(Float64(-k) * y4)) * b) * y);
	elseif (t <= -1.45e-306)
		tmp = Float64(fma(c, x, Float64(Float64(-y5) * k)) * Float64(y2 * y0));
	elseif (t <= 6e-233)
		tmp = Float64(Float64(fma(k, y2, Float64(Float64(-j) * y3)) * y4) * y1);
	elseif (t <= 7.8e-92)
		tmp = Float64(Float64(fma(Float64(-y3), y5, Float64(b * x)) * a) * y);
	elseif (t <= 8.8e-42)
		tmp = Float64(Float64(fma(b, y0, Float64(Float64(-i) * y1)) * Float64(-j)) * x);
	elseif (t <= 8.5e+107)
		tmp = Float64(Float64(fma(y3, z, Float64(Float64(-x) * y2)) * y1) * a);
	elseif (t <= 3.3e+194)
		tmp = Float64(Float64(fma(-1.0, Float64(y0 * k), Float64(a * t)) * y5) * y2);
	else
		tmp = Float64(Float64(fma(x, y, Float64(Float64(-t) * z)) * b) * a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[t, -1.7e+92], N[(N[(N[(k * y + N[((-t) * j), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision] * y5), $MachinePrecision], If[LessEqual[t, -4.05e+18], N[(N[(N[((-b) * j + N[(y2 * c), $MachinePrecision]), $MachinePrecision] * y0), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t, -4.5e-60], N[(N[(y1 * z), $MachinePrecision] * N[((-i) * k + N[(y3 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2e-147], N[(N[(N[(y1 * y4 + N[((-y0) * y5), $MachinePrecision]), $MachinePrecision] * k), $MachinePrecision] * y2), $MachinePrecision], If[LessEqual[t, -3e-155], N[(N[(N[((-i) * z + N[(y4 * y2), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision] * k), $MachinePrecision], If[LessEqual[t, -1.1e-254], N[(N[(N[(a * x + N[((-k) * y4), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, -1.45e-306], N[(N[(c * x + N[((-y5) * k), $MachinePrecision]), $MachinePrecision] * N[(y2 * y0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e-233], N[(N[(N[(k * y2 + N[((-j) * y3), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision] * y1), $MachinePrecision], If[LessEqual[t, 7.8e-92], N[(N[(N[((-y3) * y5 + N[(b * x), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 8.8e-42], N[(N[(N[(b * y0 + N[((-i) * y1), $MachinePrecision]), $MachinePrecision] * (-j)), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t, 8.5e+107], N[(N[(N[(y3 * z + N[((-x) * y2), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[t, 3.3e+194], N[(N[(N[(-1.0 * N[(y0 * k), $MachinePrecision] + N[(a * t), $MachinePrecision]), $MachinePrecision] * y5), $MachinePrecision] * y2), $MachinePrecision], N[(N[(N[(x * y + N[((-t) * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision] * a), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 13 regimes

2. if t < -1.6999999999999999e92

   1. Initial program 21.9%

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

   3. Taylor expanded in y5 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 62.3%

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

   6. Taylor expanded in i around inf

      \[\leadsto \left(i \cdot \left(k \cdot y - j \cdot t\right)\right) \cdot y5 \]
   7. Step-by-step derivation

   8. Applied rewrites 54.1%

      \[\leadsto \left(i \cdot \mathsf{fma}\left(k, y, \left(-j\right) \cdot t\right)\right) \cdot y5 \]

   if -1.6999999999999999e92 < t < -4.05e18

   1. Initial program 53.2%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 60.5%

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

   6. Taylor expanded in y around inf

      \[\leadsto \left(y \cdot \left(a \cdot b - c \cdot i\right)\right) \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 16.1%

      \[\leadsto \left(y \cdot \mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right)\right) \cdot x \]

   9. Taylor expanded in y0 around inf

      \[\leadsto \left(y0 \cdot \left(-1 \cdot \left(b \cdot j\right) + c \cdot y2\right)\right) \cdot x \]
   10. Step-by-step derivation

   11. Applied rewrites 61.0%

       \[\leadsto \left(y0 \cdot \mathsf{fma}\left(-b, j, c \cdot y2\right)\right) \cdot x \]

   if -4.05e18 < t < -4.50000000000000001e-60

   1. Initial program 29.3%

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

   3. Taylor expanded in y1 around inf

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 55.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 36.2%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-1, y3 \cdot y4, i \cdot x\right)\right)} \]

   9. Taylor expanded in z around inf

      \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(i \cdot k\right) + a \cdot y3\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 73.7%

       \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \mathsf{fma}\left(-i, k, a \cdot y3\right)\right)} \]
   12. Step-by-step derivation

   13. Applied rewrites 73.7%

       \[\leadsto \mathsf{fma}\left(-i, k, y3 \cdot a\right) \cdot \left(y1 \cdot \color{blue}{z}\right) \]

   if -4.50000000000000001e-60 < t < -1.9999999999999999e-147

   1. Initial program 32.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Applied rewrites 48.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y4 \cdot y1 - y0 \cdot y5, k, \mathsf{fma}\left(c \cdot y0 - y1 \cdot a, x, \left(-t\right) \cdot \left(c \cdot y4 - y5 \cdot a\right)\right)\right) \cdot y2} \]

   6. Taylor expanded in k around inf

      \[\leadsto \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) \cdot y2 \]
   7. Step-by-step derivation

   8. Applied rewrites 53.6%

      \[\leadsto \left(k \cdot \mathsf{fma}\left(y1, y4, \left(-y0\right) \cdot y5\right)\right) \cdot y2 \]

   if -1.9999999999999999e-147 < t < -2.99999999999999984e-155

   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

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 76.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 26.0%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-1, y3 \cdot y4, i \cdot x\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto k \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(i \cdot z\right) + y2 \cdot y4\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 88.0%

       \[\leadsto k \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-i, z, y2 \cdot y4\right)\right)} \]

   if -2.99999999999999984e-155 < t < -1.1000000000000001e-254

   1. Initial program 31.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 63.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - c \cdot i, x, \left(c \cdot y4 - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in b around inf

      \[\leadsto \left(b \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 63.4%

      \[\leadsto \left(b \cdot \mathsf{fma}\left(a, x, -k \cdot y4\right)\right) \cdot y \]

   if -1.1000000000000001e-254 < t < -1.4499999999999999e-306

   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

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Applied rewrites 57.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y4 \cdot y1 - y0 \cdot y5, k, \mathsf{fma}\left(c \cdot y0 - y1 \cdot a, x, \left(-t\right) \cdot \left(c \cdot y4 - y5 \cdot a\right)\right)\right) \cdot y2} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto y0 \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(k \cdot y5\right) + c \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 66.5%

      \[\leadsto \left(y0 \cdot y2\right) \cdot \color{blue}{\mathsf{fma}\left(c, x, -k \cdot y5\right)} \]

   if -1.4499999999999999e-306 < t < 5.99999999999999997e-233

   1. Initial program 27.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 54.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in y4 around inf

      \[\leadsto \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \cdot y1 \]
   7. Step-by-step derivation

   8. Applied rewrites 54.2%

      \[\leadsto \left(y4 \cdot \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right)\right) \cdot y1 \]

   if 5.99999999999999997e-233 < t < 7.7999999999999993e-92

   1. Initial program 37.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 54.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - c \cdot i, x, \left(c \cdot y4 - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in a around inf

      \[\leadsto \left(a \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 58.7%

      \[\leadsto \left(a \cdot \mathsf{fma}\left(-y3, y5, b \cdot x\right)\right) \cdot y \]

   if 7.7999999999999993e-92 < t < 8.8000000000000002e-42

   1. Initial program 47.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot x} \]

   5. Applied rewrites 59.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot a - c \cdot i, y, \mathsf{fma}\left(c \cdot y0 - y1 \cdot a, y2, \left(-j\right) \cdot \left(y0 \cdot b - i \cdot y1\right)\right)\right) \cdot x} \]

   6. Taylor expanded in j around inf

      \[\leadsto \left(-1 \cdot \left(j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 54.0%

      \[\leadsto \left(-j \cdot \mathsf{fma}\left(b, y0, \left(-i\right) \cdot y1\right)\right) \cdot x \]

   if 8.8000000000000002e-42 < t < 8.4999999999999999e107

   1. Initial program 28.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 59.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 60.0%

      \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right)\right)} \]

   if 8.4999999999999999e107 < t < 3.29999999999999983e194

   1. Initial program 22.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

   5. Applied rewrites 38.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(j \cdot t - k \cdot y\right), i, \mathsf{fma}\left(-y0, k \cdot y2 - j \cdot y3, \left(t \cdot y2 - y \cdot y3\right) \cdot a\right)\right) \cdot y5} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto y2 \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(k \cdot y0\right) + a \cdot t\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 56.3%

      \[\leadsto y2 \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(-1, k \cdot y0, a \cdot t\right)\right)} \]

   if 3.29999999999999983e194 < t

   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 a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot a} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot a} \]

   5. Applied rewrites 40.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), y1, \mathsf{fma}\left(y \cdot x - t \cdot z, b, \left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]

   6. Taylor expanded in b around inf

      \[\leadsto \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) \cdot a \]
   7. Step-by-step derivation

   8. Applied rewrites 70.8%

      \[\leadsto \left(b \cdot \mathsf{fma}\left(x, y, \left(-t\right) \cdot z\right)\right) \cdot a \]
3. Recombined 13 regimes into one program.

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+92}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y, \left(-t\right) \cdot j\right) \cdot i\right) \cdot y5\\ \mathbf{elif}\;t \leq -4.05 \cdot 10^{+18}:\\ \;\;\;\;\left(\mathsf{fma}\left(-b, j, y2 \cdot c\right) \cdot y0\right) \cdot x\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-60}:\\ \;\;\;\;\left(y1 \cdot z\right) \cdot \mathsf{fma}\left(-i, k, y3 \cdot a\right)\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-147}:\\ \;\;\;\;\left(\mathsf{fma}\left(y1, y4, \left(-y0\right) \cdot y5\right) \cdot k\right) \cdot y2\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-155}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, z, y4 \cdot y2\right) \cdot y1\right) \cdot k\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-254}:\\ \;\;\;\;\left(\mathsf{fma}\left(a, x, \left(-k\right) \cdot y4\right) \cdot b\right) \cdot y\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-306}:\\ \;\;\;\;\mathsf{fma}\left(c, x, \left(-y5\right) \cdot k\right) \cdot \left(y2 \cdot y0\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-233}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right) \cdot y4\right) \cdot y1\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-92}:\\ \;\;\;\;\left(\mathsf{fma}\left(-y3, y5, b \cdot x\right) \cdot a\right) \cdot y\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-42}:\\ \;\;\;\;\left(\mathsf{fma}\left(b, y0, \left(-i\right) \cdot y1\right) \cdot \left(-j\right)\right) \cdot x\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+107}:\\ \;\;\;\;\left(\mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right) \cdot y1\right) \cdot a\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+194}:\\ \;\;\;\;\left(\mathsf{fma}\left(-1, y0 \cdot k, a \cdot t\right) \cdot y5\right) \cdot y2\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(x, y, \left(-t\right) \cdot z\right) \cdot b\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 35.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y5 \cdot i - y4 \cdot b, k, \mathsf{fma}\left(-y3, y5, b \cdot x\right) \cdot a\right) \cdot y\\ t_2 := \mathsf{fma}\left(y3 \cdot z - y2 \cdot x, a, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1\\ \mathbf{if}\;x \leq -1.35 \cdot 10^{+232}:\\ \;\;\;\;\left(\mathsf{fma}\left(-1, i \cdot z, y4 \cdot y2\right) \cdot k\right) \cdot y1\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{+141}:\\ \;\;\;\;\left(\mathsf{fma}\left(b, y0, \left(-i\right) \cdot y1\right) \cdot \left(-j\right)\right) \cdot x\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{+55}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-307}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y, \left(-t\right) \cdot j\right) \cdot i\right) \cdot y5\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-86}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+83}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(-1, j \cdot b, y2 \cdot c\right) \cdot x\right) \cdot y0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (fma (- (* y5 i) (* y4 b)) k (* (fma (- y3) y5 (* b x)) a)) y))
        (t_2
         (*
          (fma
           (- (* y3 z) (* y2 x))
           a
           (fma (- (* y2 k) (* y3 j)) y4 (* (- (* j x) (* k z)) i)))
          y1)))
   (if (<= x -1.35e+232)
     (* (* (fma -1.0 (* i z) (* y4 y2)) k) y1)
     (if (<= x -3.9e+141)
       (* (* (fma b y0 (* (- i) y1)) (- j)) x)
       (if (<= x -5.4e+55)
         t_2
         (if (<= x -7.2e-106)
           t_1
           (if (<= x -3e-307)
             (* (* (fma k y (* (- t) j)) i) y5)
             (if (<= x 3.4e-86)
               t_2
               (if (<= x 3e+83)
                 t_1
                 (* (* (fma -1.0 (* j b) (* y2 c)) x) 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 = fma(((y5 * i) - (y4 * b)), k, (fma(-y3, y5, (b * x)) * a)) * y;
	double t_2 = fma(((y3 * z) - (y2 * x)), a, fma(((y2 * k) - (y3 * j)), y4, (((j * x) - (k * z)) * i))) * y1;
	double tmp;
	if (x <= -1.35e+232) {
		tmp = (fma(-1.0, (i * z), (y4 * y2)) * k) * y1;
	} else if (x <= -3.9e+141) {
		tmp = (fma(b, y0, (-i * y1)) * -j) * x;
	} else if (x <= -5.4e+55) {
		tmp = t_2;
	} else if (x <= -7.2e-106) {
		tmp = t_1;
	} else if (x <= -3e-307) {
		tmp = (fma(k, y, (-t * j)) * i) * y5;
	} else if (x <= 3.4e-86) {
		tmp = t_2;
	} else if (x <= 3e+83) {
		tmp = t_1;
	} else {
		tmp = (fma(-1.0, (j * b), (y2 * c)) * x) * 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(fma(Float64(Float64(y5 * i) - Float64(y4 * b)), k, Float64(fma(Float64(-y3), y5, Float64(b * x)) * a)) * y)
	t_2 = Float64(fma(Float64(Float64(y3 * z) - Float64(y2 * x)), a, fma(Float64(Float64(y2 * k) - Float64(y3 * j)), y4, Float64(Float64(Float64(j * x) - Float64(k * z)) * i))) * y1)
	tmp = 0.0
	if (x <= -1.35e+232)
		tmp = Float64(Float64(fma(-1.0, Float64(i * z), Float64(y4 * y2)) * k) * y1);
	elseif (x <= -3.9e+141)
		tmp = Float64(Float64(fma(b, y0, Float64(Float64(-i) * y1)) * Float64(-j)) * x);
	elseif (x <= -5.4e+55)
		tmp = t_2;
	elseif (x <= -7.2e-106)
		tmp = t_1;
	elseif (x <= -3e-307)
		tmp = Float64(Float64(fma(k, y, Float64(Float64(-t) * j)) * i) * y5);
	elseif (x <= 3.4e-86)
		tmp = t_2;
	elseif (x <= 3e+83)
		tmp = t_1;
	else
		tmp = Float64(Float64(fma(-1.0, Float64(j * b), Float64(y2 * c)) * x) * y0);
	end
	return 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[(N[(N[(y5 * i), $MachinePrecision] - N[(y4 * b), $MachinePrecision]), $MachinePrecision] * k + N[(N[((-y3) * y5 + N[(b * x), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(y3 * z), $MachinePrecision] - N[(y2 * x), $MachinePrecision]), $MachinePrecision] * a + N[(N[(N[(y2 * k), $MachinePrecision] - N[(y3 * j), $MachinePrecision]), $MachinePrecision] * y4 + N[(N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision]}, If[LessEqual[x, -1.35e+232], N[(N[(N[(-1.0 * N[(i * z), $MachinePrecision] + N[(y4 * y2), $MachinePrecision]), $MachinePrecision] * k), $MachinePrecision] * y1), $MachinePrecision], If[LessEqual[x, -3.9e+141], N[(N[(N[(b * y0 + N[((-i) * y1), $MachinePrecision]), $MachinePrecision] * (-j)), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, -5.4e+55], t$95$2, If[LessEqual[x, -7.2e-106], t$95$1, If[LessEqual[x, -3e-307], N[(N[(N[(k * y + N[((-t) * j), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision] * y5), $MachinePrecision], If[LessEqual[x, 3.4e-86], t$95$2, If[LessEqual[x, 3e+83], t$95$1, N[(N[(N[(-1.0 * N[(j * b), $MachinePrecision] + N[(y2 * c), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] * y0), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -1.35e232

   1. Initial program 22.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 39.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in k around inf

      \[\leadsto \left(k \cdot \left(-1 \cdot \left(i \cdot z\right) + y2 \cdot y4\right)\right) \cdot y1 \]
   7. Step-by-step derivation

   8. Applied rewrites 62.0%

      \[\leadsto \left(k \cdot \mathsf{fma}\left(-1, i \cdot z, y2 \cdot y4\right)\right) \cdot y1 \]

   if -1.35e232 < x < -3.89999999999999991e141

   1. Initial program 21.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot x} \]

   5. Applied rewrites 43.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot a - c \cdot i, y, \mathsf{fma}\left(c \cdot y0 - y1 \cdot a, y2, \left(-j\right) \cdot \left(y0 \cdot b - i \cdot y1\right)\right)\right) \cdot x} \]

   6. Taylor expanded in j around inf

      \[\leadsto \left(-1 \cdot \left(j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 57.5%

      \[\leadsto \left(-j \cdot \mathsf{fma}\left(b, y0, \left(-i\right) \cdot y1\right)\right) \cdot x \]

   if -3.89999999999999991e141 < x < -5.39999999999999954e55 or -2.9999999999999999e-307 < x < 3.4e-86

   1. Initial program 37.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 57.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   if -5.39999999999999954e55 < x < -7.20000000000000025e-106 or 3.4e-86 < x < 3e83

   1. Initial program 33.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 53.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - c \cdot i, x, \left(c \cdot y4 - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, a \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 64.4%

      \[\leadsto \mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, a \cdot \mathsf{fma}\left(-y3, y5, b \cdot x\right)\right) \cdot y \]

   if -7.20000000000000025e-106 < x < -2.9999999999999999e-307

   1. Initial program 26.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

   5. Applied rewrites 50.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(j \cdot t - k \cdot y\right), i, \mathsf{fma}\left(-y0, k \cdot y2 - j \cdot y3, \left(t \cdot y2 - y \cdot y3\right) \cdot a\right)\right) \cdot y5} \]

   6. Taylor expanded in i around inf

      \[\leadsto \left(i \cdot \left(k \cdot y - j \cdot t\right)\right) \cdot y5 \]
   7. Step-by-step derivation

   8. Applied rewrites 48.5%

      \[\leadsto \left(i \cdot \mathsf{fma}\left(k, y, \left(-j\right) \cdot t\right)\right) \cdot y5 \]

   if 3e83 < x

   1. Initial program 27.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y0} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y0} \]

   5. Applied rewrites 38.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(k \cdot y2 - j \cdot y3\right), y5, \mathsf{fma}\left(c, y2 \cdot x - z \cdot y3, \left(-b\right) \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y0} \]

   6. Taylor expanded in x around inf

      \[\leadsto \left(x \cdot \left(-1 \cdot \left(b \cdot j\right) + c \cdot y2\right)\right) \cdot y0 \]
   7. Step-by-step derivation

   8. Applied rewrites 48.5%

      \[\leadsto \left(x \cdot \mathsf{fma}\left(-1, b \cdot j, c \cdot y2\right)\right) \cdot y0 \]
3. Recombined 6 regimes into one program.

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+232}:\\ \;\;\;\;\left(\mathsf{fma}\left(-1, i \cdot z, y4 \cdot y2\right) \cdot k\right) \cdot y1\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{+141}:\\ \;\;\;\;\left(\mathsf{fma}\left(b, y0, \left(-i\right) \cdot y1\right) \cdot \left(-j\right)\right) \cdot x\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{+55}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot z - y2 \cdot x, a, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-106}:\\ \;\;\;\;\mathsf{fma}\left(y5 \cdot i - y4 \cdot b, k, \mathsf{fma}\left(-y3, y5, b \cdot x\right) \cdot a\right) \cdot y\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-307}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y, \left(-t\right) \cdot j\right) \cdot i\right) \cdot y5\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-86}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot z - y2 \cdot x, a, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+83}:\\ \;\;\;\;\mathsf{fma}\left(y5 \cdot i - y4 \cdot b, k, \mathsf{fma}\left(-y3, y5, b \cdot x\right) \cdot a\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(-1, j \cdot b, y2 \cdot c\right) \cdot x\right) \cdot y0\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 30.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right) \cdot y1\right) \cdot a\\ t_2 := \left(\mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right) \cdot y5\right) \cdot a\\ t_3 := \left(\mathsf{fma}\left(-i, z, y4 \cdot y2\right) \cdot y1\right) \cdot k\\ \mathbf{if}\;y3 \leq -3.8 \cdot 10^{+230}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, t, y3 \cdot y0\right) \cdot y5\right) \cdot j\\ \mathbf{elif}\;y3 \leq -3.6 \cdot 10^{+130}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y3 \leq -1.15 \cdot 10^{+74}:\\ \;\;\;\;\left(\mathsf{fma}\left(j, y3, \left(-k\right) \cdot y2\right) \cdot y5\right) \cdot y0\\ \mathbf{elif}\;y3 \leq -2.8 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y3 \leq -1.45 \cdot 10^{-46}:\\ \;\;\;\;\left(a \cdot t\right) \cdot \mathsf{fma}\left(-b, z, y5 \cdot y2\right)\\ \mathbf{elif}\;y3 \leq -2.6 \cdot 10^{-59}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y3 \leq -7.2 \cdot 10^{-130}:\\ \;\;\;\;\mathsf{fma}\left(c, x, \left(-y5\right) \cdot k\right) \cdot \left(y2 \cdot y0\right)\\ \mathbf{elif}\;y3 \leq -1.25 \cdot 10^{-168}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y3 \leq -9.5 \cdot 10^{-214}:\\ \;\;\;\;\left(\mathsf{fma}\left(j, x, \left(-k\right) \cdot z\right) \cdot y1\right) \cdot i\\ \mathbf{elif}\;y3 \leq -5.6 \cdot 10^{-290}:\\ \;\;\;\;\mathsf{fma}\left(k, y4, \left(-x\right) \cdot a\right) \cdot \left(y2 \cdot y1\right)\\ \mathbf{elif}\;y3 \leq 50000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y3 \leq 5.4 \cdot 10^{+121}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* (fma y3 z (* (- x) y2)) y1) a))
        (t_2 (* (* (fma t y2 (* (- y) y3)) y5) a))
        (t_3 (* (* (fma (- i) z (* y4 y2)) y1) k)))
   (if (<= y3 -3.8e+230)
     (* (* (fma (- i) t (* y3 y0)) y5) j)
     (if (<= y3 -3.6e+130)
       t_1
       (if (<= y3 -1.15e+74)
         (* (* (fma j y3 (* (- k) y2)) y5) y0)
         (if (<= y3 -2.8e+50)
           t_1
           (if (<= y3 -1.45e-46)
             (* (* a t) (fma (- b) z (* y5 y2)))
             (if (<= y3 -2.6e-59)
               t_2
               (if (<= y3 -7.2e-130)
                 (* (fma c x (* (- y5) k)) (* y2 y0))
                 (if (<= y3 -1.25e-168)
                   t_3
                   (if (<= y3 -9.5e-214)
                     (* (* (fma j x (* (- k) z)) y1) i)
                     (if (<= y3 -5.6e-290)
                       (* (fma k y4 (* (- x) a)) (* y2 y1))
                       (if (<= y3 50000000.0)
                         t_3
                         (if (<= y3 5.4e+121) 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 = (fma(y3, z, (-x * y2)) * y1) * a;
	double t_2 = (fma(t, y2, (-y * y3)) * y5) * a;
	double t_3 = (fma(-i, z, (y4 * y2)) * y1) * k;
	double tmp;
	if (y3 <= -3.8e+230) {
		tmp = (fma(-i, t, (y3 * y0)) * y5) * j;
	} else if (y3 <= -3.6e+130) {
		tmp = t_1;
	} else if (y3 <= -1.15e+74) {
		tmp = (fma(j, y3, (-k * y2)) * y5) * y0;
	} else if (y3 <= -2.8e+50) {
		tmp = t_1;
	} else if (y3 <= -1.45e-46) {
		tmp = (a * t) * fma(-b, z, (y5 * y2));
	} else if (y3 <= -2.6e-59) {
		tmp = t_2;
	} else if (y3 <= -7.2e-130) {
		tmp = fma(c, x, (-y5 * k)) * (y2 * y0);
	} else if (y3 <= -1.25e-168) {
		tmp = t_3;
	} else if (y3 <= -9.5e-214) {
		tmp = (fma(j, x, (-k * z)) * y1) * i;
	} else if (y3 <= -5.6e-290) {
		tmp = fma(k, y4, (-x * a)) * (y2 * y1);
	} else if (y3 <= 50000000.0) {
		tmp = t_3;
	} else if (y3 <= 5.4e+121) {
		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(Float64(fma(y3, z, Float64(Float64(-x) * y2)) * y1) * a)
	t_2 = Float64(Float64(fma(t, y2, Float64(Float64(-y) * y3)) * y5) * a)
	t_3 = Float64(Float64(fma(Float64(-i), z, Float64(y4 * y2)) * y1) * k)
	tmp = 0.0
	if (y3 <= -3.8e+230)
		tmp = Float64(Float64(fma(Float64(-i), t, Float64(y3 * y0)) * y5) * j);
	elseif (y3 <= -3.6e+130)
		tmp = t_1;
	elseif (y3 <= -1.15e+74)
		tmp = Float64(Float64(fma(j, y3, Float64(Float64(-k) * y2)) * y5) * y0);
	elseif (y3 <= -2.8e+50)
		tmp = t_1;
	elseif (y3 <= -1.45e-46)
		tmp = Float64(Float64(a * t) * fma(Float64(-b), z, Float64(y5 * y2)));
	elseif (y3 <= -2.6e-59)
		tmp = t_2;
	elseif (y3 <= -7.2e-130)
		tmp = Float64(fma(c, x, Float64(Float64(-y5) * k)) * Float64(y2 * y0));
	elseif (y3 <= -1.25e-168)
		tmp = t_3;
	elseif (y3 <= -9.5e-214)
		tmp = Float64(Float64(fma(j, x, Float64(Float64(-k) * z)) * y1) * i);
	elseif (y3 <= -5.6e-290)
		tmp = Float64(fma(k, y4, Float64(Float64(-x) * a)) * Float64(y2 * y1));
	elseif (y3 <= 50000000.0)
		tmp = t_3;
	elseif (y3 <= 5.4e+121)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return 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[(N[(y3 * z + N[((-x) * y2), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t * y2 + N[((-y) * y3), $MachinePrecision]), $MachinePrecision] * y5), $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[((-i) * z + N[(y4 * y2), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[y3, -3.8e+230], N[(N[(N[((-i) * t + N[(y3 * y0), $MachinePrecision]), $MachinePrecision] * y5), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[y3, -3.6e+130], t$95$1, If[LessEqual[y3, -1.15e+74], N[(N[(N[(j * y3 + N[((-k) * y2), $MachinePrecision]), $MachinePrecision] * y5), $MachinePrecision] * y0), $MachinePrecision], If[LessEqual[y3, -2.8e+50], t$95$1, If[LessEqual[y3, -1.45e-46], N[(N[(a * t), $MachinePrecision] * N[((-b) * z + N[(y5 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -2.6e-59], t$95$2, If[LessEqual[y3, -7.2e-130], N[(N[(c * x + N[((-y5) * k), $MachinePrecision]), $MachinePrecision] * N[(y2 * y0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -1.25e-168], t$95$3, If[LessEqual[y3, -9.5e-214], N[(N[(N[(j * x + N[((-k) * z), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision] * i), $MachinePrecision], If[LessEqual[y3, -5.6e-290], N[(N[(k * y4 + N[((-x) * a), $MachinePrecision]), $MachinePrecision] * N[(y2 * y1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 50000000.0], t$95$3, If[LessEqual[y3, 5.4e+121], t$95$1, t$95$2]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y3 < -3.8e230

   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 y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

   5. Applied rewrites 47.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(j \cdot t - k \cdot y\right), i, \mathsf{fma}\left(-y0, k \cdot y2 - j \cdot y3, \left(t \cdot y2 - y \cdot y3\right) \cdot a\right)\right) \cdot y5} \]

   6. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 36.0%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right)\right)} \]

   9. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 59.2%

       \[\leadsto j \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(-i, t, y0 \cdot y3\right)\right)} \]

   if -3.8e230 < y3 < -3.6000000000000001e130 or -1.1499999999999999e74 < y3 < -2.7999999999999998e50 or 5e7 < y3 < 5.4000000000000004e121

   1. Initial program 21.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 45.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 54.3%

      \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right)\right)} \]

   if -3.6000000000000001e130 < y3 < -1.1499999999999999e74

   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 y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y0} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y0} \]

   5. Applied rewrites 54.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(k \cdot y2 - j \cdot y3\right), y5, \mathsf{fma}\left(c, y2 \cdot x - z \cdot y3, \left(-b\right) \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y0} \]

   6. Taylor expanded in y5 around inf

      \[\leadsto \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) \cdot y0 \]
   7. Step-by-step derivation

   8. Applied rewrites 72.8%

      \[\leadsto \left(y5 \cdot \mathsf{fma}\left(j, y3, \left(-k\right) \cdot y2\right)\right) \cdot y0 \]

   if -2.7999999999999998e50 < y3 < -1.45000000000000002e-46

   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 a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot a} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot a} \]

   5. Applied rewrites 50.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), y1, \mathsf{fma}\left(y \cdot x - t \cdot z, b, \left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]

   6. Taylor expanded in t around inf

      \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(-1 \cdot \left(b \cdot z\right) + y2 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 75.7%

      \[\leadsto \left(a \cdot t\right) \cdot \color{blue}{\mathsf{fma}\left(-b, z, y2 \cdot y5\right)} \]

   if -1.45000000000000002e-46 < y3 < -2.59999999999999998e-59 or 5.4000000000000004e121 < y3

   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 y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

   5. Applied rewrites 51.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(j \cdot t - k \cdot y\right), i, \mathsf{fma}\left(-y0, k \cdot y2 - j \cdot y3, \left(t \cdot y2 - y \cdot y3\right) \cdot a\right)\right) \cdot y5} \]

   6. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 59.2%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right)\right)} \]

   if -2.59999999999999998e-59 < y3 < -7.2000000000000003e-130

   1. Initial program 21.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Applied rewrites 51.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y4 \cdot y1 - y0 \cdot y5, k, \mathsf{fma}\left(c \cdot y0 - y1 \cdot a, x, \left(-t\right) \cdot \left(c \cdot y4 - y5 \cdot a\right)\right)\right) \cdot y2} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto y0 \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(k \cdot y5\right) + c \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 39.5%

      \[\leadsto \left(y0 \cdot y2\right) \cdot \color{blue}{\mathsf{fma}\left(c, x, -k \cdot y5\right)} \]

   if -7.2000000000000003e-130 < y3 < -1.25e-168 or -5.59999999999999993e-290 < y3 < 5e7

   1. Initial program 33.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 48.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 14.6%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-1, y3 \cdot y4, i \cdot x\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto k \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(i \cdot z\right) + y2 \cdot y4\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 56.7%

       \[\leadsto k \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-i, z, y2 \cdot y4\right)\right)} \]

   if -1.25e-168 < y3 < -9.4999999999999999e-214

   1. Initial program 33.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 57.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in i around inf

      \[\leadsto i \cdot \color{blue}{\left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 78.3%

      \[\leadsto i \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(j, x, \left(-k\right) \cdot z\right)\right)} \]

   if -9.4999999999999999e-214 < y3 < -5.59999999999999993e-290

   1. Initial program 47.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 22.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 10.8%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-1, y3 \cdot y4, i \cdot x\right)\right)} \]

   9. Taylor expanded in y2 around inf

      \[\leadsto y1 \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 38.8%

       \[\leadsto \left(y1 \cdot y2\right) \cdot \color{blue}{\mathsf{fma}\left(k, y4, -a \cdot x\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -3.8 \cdot 10^{+230}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, t, y3 \cdot y0\right) \cdot y5\right) \cdot j\\ \mathbf{elif}\;y3 \leq -3.6 \cdot 10^{+130}:\\ \;\;\;\;\left(\mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right) \cdot y1\right) \cdot a\\ \mathbf{elif}\;y3 \leq -1.15 \cdot 10^{+74}:\\ \;\;\;\;\left(\mathsf{fma}\left(j, y3, \left(-k\right) \cdot y2\right) \cdot y5\right) \cdot y0\\ \mathbf{elif}\;y3 \leq -2.8 \cdot 10^{+50}:\\ \;\;\;\;\left(\mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right) \cdot y1\right) \cdot a\\ \mathbf{elif}\;y3 \leq -1.45 \cdot 10^{-46}:\\ \;\;\;\;\left(a \cdot t\right) \cdot \mathsf{fma}\left(-b, z, y5 \cdot y2\right)\\ \mathbf{elif}\;y3 \leq -2.6 \cdot 10^{-59}:\\ \;\;\;\;\left(\mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right) \cdot y5\right) \cdot a\\ \mathbf{elif}\;y3 \leq -7.2 \cdot 10^{-130}:\\ \;\;\;\;\mathsf{fma}\left(c, x, \left(-y5\right) \cdot k\right) \cdot \left(y2 \cdot y0\right)\\ \mathbf{elif}\;y3 \leq -1.25 \cdot 10^{-168}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, z, y4 \cdot y2\right) \cdot y1\right) \cdot k\\ \mathbf{elif}\;y3 \leq -9.5 \cdot 10^{-214}:\\ \;\;\;\;\left(\mathsf{fma}\left(j, x, \left(-k\right) \cdot z\right) \cdot y1\right) \cdot i\\ \mathbf{elif}\;y3 \leq -5.6 \cdot 10^{-290}:\\ \;\;\;\;\mathsf{fma}\left(k, y4, \left(-x\right) \cdot a\right) \cdot \left(y2 \cdot y1\right)\\ \mathbf{elif}\;y3 \leq 50000000:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, z, y4 \cdot y2\right) \cdot y1\right) \cdot k\\ \mathbf{elif}\;y3 \leq 5.4 \cdot 10^{+121}:\\ \;\;\;\;\left(\mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right) \cdot y1\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right) \cdot y5\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 31.4% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+92}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y, \left(-t\right) \cdot j\right) \cdot i\right) \cdot y5\\ \mathbf{elif}\;t \leq -4.05 \cdot 10^{+18}:\\ \;\;\;\;\left(\mathsf{fma}\left(-b, j, y2 \cdot c\right) \cdot y0\right) \cdot x\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-60}:\\ \;\;\;\;\left(y1 \cdot z\right) \cdot \mathsf{fma}\left(-i, k, y3 \cdot a\right)\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-147}:\\ \;\;\;\;\left(\mathsf{fma}\left(y1, y4, \left(-y0\right) \cdot y5\right) \cdot k\right) \cdot y2\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-155}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, z, y4 \cdot y2\right) \cdot y1\right) \cdot k\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-255}:\\ \;\;\;\;\left(\mathsf{fma}\left(a, x, \left(-k\right) \cdot y4\right) \cdot b\right) \cdot y\\ \mathbf{elif}\;t \leq 1.42 \cdot 10^{-277}:\\ \;\;\;\;\left(\mathsf{fma}\left(-1, y5 \cdot y2, b \cdot z\right) \cdot y0\right) \cdot k\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-238}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right) \cdot y4\right) \cdot y1\\ \mathbf{elif}\;t \leq 820:\\ \;\;\;\;\mathsf{fma}\left(y5 \cdot i, k, \mathsf{fma}\left(-y3, y5, b \cdot x\right) \cdot a\right) \cdot y\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+107}:\\ \;\;\;\;\left(\mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right) \cdot y1\right) \cdot a\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+194}:\\ \;\;\;\;\left(\mathsf{fma}\left(-1, y0 \cdot k, a \cdot t\right) \cdot y5\right) \cdot y2\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(x, y, \left(-t\right) \cdot z\right) \cdot b\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= t -1.7e+92)
   (* (* (fma k y (* (- t) j)) i) y5)
   (if (<= t -4.05e+18)
     (* (* (fma (- b) j (* y2 c)) y0) x)
     (if (<= t -4.5e-60)
       (* (* y1 z) (fma (- i) k (* y3 a)))
       (if (<= t -2e-147)
         (* (* (fma y1 y4 (* (- y0) y5)) k) y2)
         (if (<= t -3e-155)
           (* (* (fma (- i) z (* y4 y2)) y1) k)
           (if (<= t -6e-255)
             (* (* (fma a x (* (- k) y4)) b) y)
             (if (<= t 1.42e-277)
               (* (* (fma -1.0 (* y5 y2) (* b z)) y0) k)
               (if (<= t 5.4e-238)
                 (* (* (fma k y2 (* (- j) y3)) y4) y1)
                 (if (<= t 820.0)
                   (* (fma (* y5 i) k (* (fma (- y3) y5 (* b x)) a)) y)
                   (if (<= t 8.5e+107)
                     (* (* (fma y3 z (* (- x) y2)) y1) a)
                     (if (<= t 3.3e+194)
                       (* (* (fma -1.0 (* y0 k) (* a t)) y5) y2)
                       (* (* (fma x y (* (- t) z)) b) a)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (t <= -1.7e+92) {
		tmp = (fma(k, y, (-t * j)) * i) * y5;
	} else if (t <= -4.05e+18) {
		tmp = (fma(-b, j, (y2 * c)) * y0) * x;
	} else if (t <= -4.5e-60) {
		tmp = (y1 * z) * fma(-i, k, (y3 * a));
	} else if (t <= -2e-147) {
		tmp = (fma(y1, y4, (-y0 * y5)) * k) * y2;
	} else if (t <= -3e-155) {
		tmp = (fma(-i, z, (y4 * y2)) * y1) * k;
	} else if (t <= -6e-255) {
		tmp = (fma(a, x, (-k * y4)) * b) * y;
	} else if (t <= 1.42e-277) {
		tmp = (fma(-1.0, (y5 * y2), (b * z)) * y0) * k;
	} else if (t <= 5.4e-238) {
		tmp = (fma(k, y2, (-j * y3)) * y4) * y1;
	} else if (t <= 820.0) {
		tmp = fma((y5 * i), k, (fma(-y3, y5, (b * x)) * a)) * y;
	} else if (t <= 8.5e+107) {
		tmp = (fma(y3, z, (-x * y2)) * y1) * a;
	} else if (t <= 3.3e+194) {
		tmp = (fma(-1.0, (y0 * k), (a * t)) * y5) * y2;
	} else {
		tmp = (fma(x, y, (-t * z)) * b) * a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (t <= -1.7e+92)
		tmp = Float64(Float64(fma(k, y, Float64(Float64(-t) * j)) * i) * y5);
	elseif (t <= -4.05e+18)
		tmp = Float64(Float64(fma(Float64(-b), j, Float64(y2 * c)) * y0) * x);
	elseif (t <= -4.5e-60)
		tmp = Float64(Float64(y1 * z) * fma(Float64(-i), k, Float64(y3 * a)));
	elseif (t <= -2e-147)
		tmp = Float64(Float64(fma(y1, y4, Float64(Float64(-y0) * y5)) * k) * y2);
	elseif (t <= -3e-155)
		tmp = Float64(Float64(fma(Float64(-i), z, Float64(y4 * y2)) * y1) * k);
	elseif (t <= -6e-255)
		tmp = Float64(Float64(fma(a, x, Float64(Float64(-k) * y4)) * b) * y);
	elseif (t <= 1.42e-277)
		tmp = Float64(Float64(fma(-1.0, Float64(y5 * y2), Float64(b * z)) * y0) * k);
	elseif (t <= 5.4e-238)
		tmp = Float64(Float64(fma(k, y2, Float64(Float64(-j) * y3)) * y4) * y1);
	elseif (t <= 820.0)
		tmp = Float64(fma(Float64(y5 * i), k, Float64(fma(Float64(-y3), y5, Float64(b * x)) * a)) * y);
	elseif (t <= 8.5e+107)
		tmp = Float64(Float64(fma(y3, z, Float64(Float64(-x) * y2)) * y1) * a);
	elseif (t <= 3.3e+194)
		tmp = Float64(Float64(fma(-1.0, Float64(y0 * k), Float64(a * t)) * y5) * y2);
	else
		tmp = Float64(Float64(fma(x, y, Float64(Float64(-t) * z)) * b) * a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[t, -1.7e+92], N[(N[(N[(k * y + N[((-t) * j), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision] * y5), $MachinePrecision], If[LessEqual[t, -4.05e+18], N[(N[(N[((-b) * j + N[(y2 * c), $MachinePrecision]), $MachinePrecision] * y0), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t, -4.5e-60], N[(N[(y1 * z), $MachinePrecision] * N[((-i) * k + N[(y3 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2e-147], N[(N[(N[(y1 * y4 + N[((-y0) * y5), $MachinePrecision]), $MachinePrecision] * k), $MachinePrecision] * y2), $MachinePrecision], If[LessEqual[t, -3e-155], N[(N[(N[((-i) * z + N[(y4 * y2), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision] * k), $MachinePrecision], If[LessEqual[t, -6e-255], N[(N[(N[(a * x + N[((-k) * y4), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 1.42e-277], N[(N[(N[(-1.0 * N[(y5 * y2), $MachinePrecision] + N[(b * z), $MachinePrecision]), $MachinePrecision] * y0), $MachinePrecision] * k), $MachinePrecision], If[LessEqual[t, 5.4e-238], N[(N[(N[(k * y2 + N[((-j) * y3), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision] * y1), $MachinePrecision], If[LessEqual[t, 820.0], N[(N[(N[(y5 * i), $MachinePrecision] * k + N[(N[((-y3) * y5 + N[(b * x), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 8.5e+107], N[(N[(N[(y3 * z + N[((-x) * y2), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[t, 3.3e+194], N[(N[(N[(-1.0 * N[(y0 * k), $MachinePrecision] + N[(a * t), $MachinePrecision]), $MachinePrecision] * y5), $MachinePrecision] * y2), $MachinePrecision], N[(N[(N[(x * y + N[((-t) * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision] * a), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 12 regimes

2. if t < -1.6999999999999999e92

   1. Initial program 21.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

   5. Applied rewrites 62.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(j \cdot t - k \cdot y\right), i, \mathsf{fma}\left(-y0, k \cdot y2 - j \cdot y3, \left(t \cdot y2 - y \cdot y3\right) \cdot a\right)\right) \cdot y5} \]

   6. Taylor expanded in i around inf

      \[\leadsto \left(i \cdot \left(k \cdot y - j \cdot t\right)\right) \cdot y5 \]
   7. Step-by-step derivation

   8. Applied rewrites 54.1%

      \[\leadsto \left(i \cdot \mathsf{fma}\left(k, y, \left(-j\right) \cdot t\right)\right) \cdot y5 \]

   if -1.6999999999999999e92 < t < -4.05e18

   1. Initial program 53.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot x} \]

   5. Applied rewrites 60.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot a - c \cdot i, y, \mathsf{fma}\left(c \cdot y0 - y1 \cdot a, y2, \left(-j\right) \cdot \left(y0 \cdot b - i \cdot y1\right)\right)\right) \cdot x} \]

   6. Taylor expanded in y around inf

      \[\leadsto \left(y \cdot \left(a \cdot b - c \cdot i\right)\right) \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 16.1%

      \[\leadsto \left(y \cdot \mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right)\right) \cdot x \]

   9. Taylor expanded in y0 around inf

      \[\leadsto \left(y0 \cdot \left(-1 \cdot \left(b \cdot j\right) + c \cdot y2\right)\right) \cdot x \]
   10. Step-by-step derivation

   11. Applied rewrites 61.0%

       \[\leadsto \left(y0 \cdot \mathsf{fma}\left(-b, j, c \cdot y2\right)\right) \cdot x \]

   if -4.05e18 < t < -4.50000000000000001e-60

   1. Initial program 29.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 55.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 36.2%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-1, y3 \cdot y4, i \cdot x\right)\right)} \]

   9. Taylor expanded in z around inf

      \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(i \cdot k\right) + a \cdot y3\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 73.7%

       \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \mathsf{fma}\left(-i, k, a \cdot y3\right)\right)} \]
   12. Step-by-step derivation

   13. Applied rewrites 73.7%

       \[\leadsto \mathsf{fma}\left(-i, k, y3 \cdot a\right) \cdot \left(y1 \cdot \color{blue}{z}\right) \]

   if -4.50000000000000001e-60 < t < -1.9999999999999999e-147

   1. Initial program 32.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Applied rewrites 48.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y4 \cdot y1 - y0 \cdot y5, k, \mathsf{fma}\left(c \cdot y0 - y1 \cdot a, x, \left(-t\right) \cdot \left(c \cdot y4 - y5 \cdot a\right)\right)\right) \cdot y2} \]

   6. Taylor expanded in k around inf

      \[\leadsto \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) \cdot y2 \]
   7. Step-by-step derivation

   8. Applied rewrites 53.6%

      \[\leadsto \left(k \cdot \mathsf{fma}\left(y1, y4, \left(-y0\right) \cdot y5\right)\right) \cdot y2 \]

   if -1.9999999999999999e-147 < t < -2.99999999999999984e-155

   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

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 76.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 26.0%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-1, y3 \cdot y4, i \cdot x\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto k \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(i \cdot z\right) + y2 \cdot y4\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 88.0%

       \[\leadsto k \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-i, z, y2 \cdot y4\right)\right)} \]

   if -2.99999999999999984e-155 < t < -6.00000000000000004e-255

   1. Initial program 31.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 63.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - c \cdot i, x, \left(c \cdot y4 - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in b around inf

      \[\leadsto \left(b \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 63.4%

      \[\leadsto \left(b \cdot \mathsf{fma}\left(a, x, -k \cdot y4\right)\right) \cdot y \]

   if -6.00000000000000004e-255 < t < 1.4199999999999999e-277

   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 y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y0} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y0} \]

   5. Applied rewrites 50.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(k \cdot y2 - j \cdot y3\right), y5, \mathsf{fma}\left(c, y2 \cdot x - z \cdot y3, \left(-b\right) \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y0} \]

   6. Taylor expanded in k around inf

      \[\leadsto k \cdot \color{blue}{\left(y0 \cdot \left(-1 \cdot \left(y2 \cdot y5\right) + b \cdot z\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 62.3%

      \[\leadsto k \cdot \color{blue}{\left(y0 \cdot \mathsf{fma}\left(-1, y2 \cdot y5, b \cdot z\right)\right)} \]

   if 1.4199999999999999e-277 < t < 5.39999999999999981e-238

   1. Initial program 13.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 50.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in y4 around inf

      \[\leadsto \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \cdot y1 \]
   7. Step-by-step derivation

   8. Applied rewrites 63.2%

      \[\leadsto \left(y4 \cdot \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right)\right) \cdot y1 \]

   if 5.39999999999999981e-238 < t < 820

   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 y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 52.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - c \cdot i, x, \left(c \cdot y4 - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, a \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 59.3%

      \[\leadsto \mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, a \cdot \mathsf{fma}\left(-y3, y5, b \cdot x\right)\right) \cdot y \]

   9. Taylor expanded in b around 0

      \[\leadsto \mathsf{fma}\left(i \cdot y5, k, a \cdot \mathsf{fma}\left(-y3, y5, b \cdot x\right)\right) \cdot y \]
   10. Step-by-step derivation

   11. Applied rewrites 55.7%

       \[\leadsto \mathsf{fma}\left(i \cdot y5, k, a \cdot \mathsf{fma}\left(-y3, y5, b \cdot x\right)\right) \cdot y \]

   if 820 < t < 8.4999999999999999e107

   1. Initial program 26.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 61.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 65.9%

      \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right)\right)} \]

   if 8.4999999999999999e107 < t < 3.29999999999999983e194

   1. Initial program 22.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

   5. Applied rewrites 38.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(j \cdot t - k \cdot y\right), i, \mathsf{fma}\left(-y0, k \cdot y2 - j \cdot y3, \left(t \cdot y2 - y \cdot y3\right) \cdot a\right)\right) \cdot y5} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto y2 \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(k \cdot y0\right) + a \cdot t\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 56.3%

      \[\leadsto y2 \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(-1, k \cdot y0, a \cdot t\right)\right)} \]

   if 3.29999999999999983e194 < t

   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 a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot a} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot a} \]

   5. Applied rewrites 40.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), y1, \mathsf{fma}\left(y \cdot x - t \cdot z, b, \left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]

   6. Taylor expanded in b around inf

      \[\leadsto \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) \cdot a \]
   7. Step-by-step derivation

   8. Applied rewrites 70.8%

      \[\leadsto \left(b \cdot \mathsf{fma}\left(x, y, \left(-t\right) \cdot z\right)\right) \cdot a \]
3. Recombined 12 regimes into one program.

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+92}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y, \left(-t\right) \cdot j\right) \cdot i\right) \cdot y5\\ \mathbf{elif}\;t \leq -4.05 \cdot 10^{+18}:\\ \;\;\;\;\left(\mathsf{fma}\left(-b, j, y2 \cdot c\right) \cdot y0\right) \cdot x\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-60}:\\ \;\;\;\;\left(y1 \cdot z\right) \cdot \mathsf{fma}\left(-i, k, y3 \cdot a\right)\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-147}:\\ \;\;\;\;\left(\mathsf{fma}\left(y1, y4, \left(-y0\right) \cdot y5\right) \cdot k\right) \cdot y2\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-155}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, z, y4 \cdot y2\right) \cdot y1\right) \cdot k\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-255}:\\ \;\;\;\;\left(\mathsf{fma}\left(a, x, \left(-k\right) \cdot y4\right) \cdot b\right) \cdot y\\ \mathbf{elif}\;t \leq 1.42 \cdot 10^{-277}:\\ \;\;\;\;\left(\mathsf{fma}\left(-1, y5 \cdot y2, b \cdot z\right) \cdot y0\right) \cdot k\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-238}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right) \cdot y4\right) \cdot y1\\ \mathbf{elif}\;t \leq 820:\\ \;\;\;\;\mathsf{fma}\left(y5 \cdot i, k, \mathsf{fma}\left(-y3, y5, b \cdot x\right) \cdot a\right) \cdot y\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+107}:\\ \;\;\;\;\left(\mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right) \cdot y1\right) \cdot a\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+194}:\\ \;\;\;\;\left(\mathsf{fma}\left(-1, y0 \cdot k, a \cdot t\right) \cdot y5\right) \cdot y2\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(x, y, \left(-t\right) \cdot z\right) \cdot b\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 30.2% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+92}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y, \left(-t\right) \cdot j\right) \cdot i\right) \cdot y5\\ \mathbf{elif}\;t \leq -4.05 \cdot 10^{+18}:\\ \;\;\;\;\left(\mathsf{fma}\left(-b, j, y2 \cdot c\right) \cdot y0\right) \cdot x\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-60}:\\ \;\;\;\;\left(y1 \cdot z\right) \cdot \mathsf{fma}\left(-i, k, y3 \cdot a\right)\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-147}:\\ \;\;\;\;\left(\mathsf{fma}\left(y1, y4, \left(-y0\right) \cdot y5\right) \cdot k\right) \cdot y2\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-155}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, z, y4 \cdot y2\right) \cdot y1\right) \cdot k\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-254}:\\ \;\;\;\;\left(\mathsf{fma}\left(a, x, \left(-k\right) \cdot y4\right) \cdot b\right) \cdot y\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-306}:\\ \;\;\;\;\mathsf{fma}\left(c, x, \left(-y5\right) \cdot k\right) \cdot \left(y2 \cdot y0\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-233}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right) \cdot y4\right) \cdot y1\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-92}:\\ \;\;\;\;\left(\mathsf{fma}\left(-y3, y5, b \cdot x\right) \cdot a\right) \cdot y\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-42}:\\ \;\;\;\;\left(\mathsf{fma}\left(b, y0, \left(-i\right) \cdot y1\right) \cdot \left(-j\right)\right) \cdot x\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{+150}:\\ \;\;\;\;\left(\mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right) \cdot y1\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(x, y, \left(-t\right) \cdot z\right) \cdot b\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= t -1.7e+92)
   (* (* (fma k y (* (- t) j)) i) y5)
   (if (<= t -4.05e+18)
     (* (* (fma (- b) j (* y2 c)) y0) x)
     (if (<= t -4.5e-60)
       (* (* y1 z) (fma (- i) k (* y3 a)))
       (if (<= t -2e-147)
         (* (* (fma y1 y4 (* (- y0) y5)) k) y2)
         (if (<= t -3e-155)
           (* (* (fma (- i) z (* y4 y2)) y1) k)
           (if (<= t -1.1e-254)
             (* (* (fma a x (* (- k) y4)) b) y)
             (if (<= t -1.45e-306)
               (* (fma c x (* (- y5) k)) (* y2 y0))
               (if (<= t 6e-233)
                 (* (* (fma k y2 (* (- j) y3)) y4) y1)
                 (if (<= t 7.8e-92)
                   (* (* (fma (- y3) y5 (* b x)) a) y)
                   (if (<= t 8.8e-42)
                     (* (* (fma b y0 (* (- i) y1)) (- j)) x)
                     (if (<= t 1.16e+150)
                       (* (* (fma y3 z (* (- x) y2)) y1) a)
                       (* (* (fma x y (* (- t) z)) b) a)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (t <= -1.7e+92) {
		tmp = (fma(k, y, (-t * j)) * i) * y5;
	} else if (t <= -4.05e+18) {
		tmp = (fma(-b, j, (y2 * c)) * y0) * x;
	} else if (t <= -4.5e-60) {
		tmp = (y1 * z) * fma(-i, k, (y3 * a));
	} else if (t <= -2e-147) {
		tmp = (fma(y1, y4, (-y0 * y5)) * k) * y2;
	} else if (t <= -3e-155) {
		tmp = (fma(-i, z, (y4 * y2)) * y1) * k;
	} else if (t <= -1.1e-254) {
		tmp = (fma(a, x, (-k * y4)) * b) * y;
	} else if (t <= -1.45e-306) {
		tmp = fma(c, x, (-y5 * k)) * (y2 * y0);
	} else if (t <= 6e-233) {
		tmp = (fma(k, y2, (-j * y3)) * y4) * y1;
	} else if (t <= 7.8e-92) {
		tmp = (fma(-y3, y5, (b * x)) * a) * y;
	} else if (t <= 8.8e-42) {
		tmp = (fma(b, y0, (-i * y1)) * -j) * x;
	} else if (t <= 1.16e+150) {
		tmp = (fma(y3, z, (-x * y2)) * y1) * a;
	} else {
		tmp = (fma(x, y, (-t * z)) * b) * a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (t <= -1.7e+92)
		tmp = Float64(Float64(fma(k, y, Float64(Float64(-t) * j)) * i) * y5);
	elseif (t <= -4.05e+18)
		tmp = Float64(Float64(fma(Float64(-b), j, Float64(y2 * c)) * y0) * x);
	elseif (t <= -4.5e-60)
		tmp = Float64(Float64(y1 * z) * fma(Float64(-i), k, Float64(y3 * a)));
	elseif (t <= -2e-147)
		tmp = Float64(Float64(fma(y1, y4, Float64(Float64(-y0) * y5)) * k) * y2);
	elseif (t <= -3e-155)
		tmp = Float64(Float64(fma(Float64(-i), z, Float64(y4 * y2)) * y1) * k);
	elseif (t <= -1.1e-254)
		tmp = Float64(Float64(fma(a, x, Float64(Float64(-k) * y4)) * b) * y);
	elseif (t <= -1.45e-306)
		tmp = Float64(fma(c, x, Float64(Float64(-y5) * k)) * Float64(y2 * y0));
	elseif (t <= 6e-233)
		tmp = Float64(Float64(fma(k, y2, Float64(Float64(-j) * y3)) * y4) * y1);
	elseif (t <= 7.8e-92)
		tmp = Float64(Float64(fma(Float64(-y3), y5, Float64(b * x)) * a) * y);
	elseif (t <= 8.8e-42)
		tmp = Float64(Float64(fma(b, y0, Float64(Float64(-i) * y1)) * Float64(-j)) * x);
	elseif (t <= 1.16e+150)
		tmp = Float64(Float64(fma(y3, z, Float64(Float64(-x) * y2)) * y1) * a);
	else
		tmp = Float64(Float64(fma(x, y, Float64(Float64(-t) * z)) * b) * a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[t, -1.7e+92], N[(N[(N[(k * y + N[((-t) * j), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision] * y5), $MachinePrecision], If[LessEqual[t, -4.05e+18], N[(N[(N[((-b) * j + N[(y2 * c), $MachinePrecision]), $MachinePrecision] * y0), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t, -4.5e-60], N[(N[(y1 * z), $MachinePrecision] * N[((-i) * k + N[(y3 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2e-147], N[(N[(N[(y1 * y4 + N[((-y0) * y5), $MachinePrecision]), $MachinePrecision] * k), $MachinePrecision] * y2), $MachinePrecision], If[LessEqual[t, -3e-155], N[(N[(N[((-i) * z + N[(y4 * y2), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision] * k), $MachinePrecision], If[LessEqual[t, -1.1e-254], N[(N[(N[(a * x + N[((-k) * y4), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, -1.45e-306], N[(N[(c * x + N[((-y5) * k), $MachinePrecision]), $MachinePrecision] * N[(y2 * y0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e-233], N[(N[(N[(k * y2 + N[((-j) * y3), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision] * y1), $MachinePrecision], If[LessEqual[t, 7.8e-92], N[(N[(N[((-y3) * y5 + N[(b * x), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 8.8e-42], N[(N[(N[(b * y0 + N[((-i) * y1), $MachinePrecision]), $MachinePrecision] * (-j)), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t, 1.16e+150], N[(N[(N[(y3 * z + N[((-x) * y2), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision] * a), $MachinePrecision], N[(N[(N[(x * y + N[((-t) * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision] * a), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 12 regimes

2. if t < -1.6999999999999999e92

   1. Initial program 21.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

   5. Applied rewrites 62.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(j \cdot t - k \cdot y\right), i, \mathsf{fma}\left(-y0, k \cdot y2 - j \cdot y3, \left(t \cdot y2 - y \cdot y3\right) \cdot a\right)\right) \cdot y5} \]

   6. Taylor expanded in i around inf

      \[\leadsto \left(i \cdot \left(k \cdot y - j \cdot t\right)\right) \cdot y5 \]
   7. Step-by-step derivation

   8. Applied rewrites 54.1%

      \[\leadsto \left(i \cdot \mathsf{fma}\left(k, y, \left(-j\right) \cdot t\right)\right) \cdot y5 \]

   if -1.6999999999999999e92 < t < -4.05e18

   1. Initial program 53.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot x} \]

   5. Applied rewrites 60.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot a - c \cdot i, y, \mathsf{fma}\left(c \cdot y0 - y1 \cdot a, y2, \left(-j\right) \cdot \left(y0 \cdot b - i \cdot y1\right)\right)\right) \cdot x} \]

   6. Taylor expanded in y around inf

      \[\leadsto \left(y \cdot \left(a \cdot b - c \cdot i\right)\right) \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 16.1%

      \[\leadsto \left(y \cdot \mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right)\right) \cdot x \]

   9. Taylor expanded in y0 around inf

      \[\leadsto \left(y0 \cdot \left(-1 \cdot \left(b \cdot j\right) + c \cdot y2\right)\right) \cdot x \]
   10. Step-by-step derivation

   11. Applied rewrites 61.0%

       \[\leadsto \left(y0 \cdot \mathsf{fma}\left(-b, j, c \cdot y2\right)\right) \cdot x \]

   if -4.05e18 < t < -4.50000000000000001e-60

   1. Initial program 29.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 55.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 36.2%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-1, y3 \cdot y4, i \cdot x\right)\right)} \]

   9. Taylor expanded in z around inf

      \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(i \cdot k\right) + a \cdot y3\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 73.7%

       \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \mathsf{fma}\left(-i, k, a \cdot y3\right)\right)} \]
   12. Step-by-step derivation

   13. Applied rewrites 73.7%

       \[\leadsto \mathsf{fma}\left(-i, k, y3 \cdot a\right) \cdot \left(y1 \cdot \color{blue}{z}\right) \]

   if -4.50000000000000001e-60 < t < -1.9999999999999999e-147

   1. Initial program 32.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Applied rewrites 48.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y4 \cdot y1 - y0 \cdot y5, k, \mathsf{fma}\left(c \cdot y0 - y1 \cdot a, x, \left(-t\right) \cdot \left(c \cdot y4 - y5 \cdot a\right)\right)\right) \cdot y2} \]

   6. Taylor expanded in k around inf

      \[\leadsto \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) \cdot y2 \]
   7. Step-by-step derivation

   8. Applied rewrites 53.6%

      \[\leadsto \left(k \cdot \mathsf{fma}\left(y1, y4, \left(-y0\right) \cdot y5\right)\right) \cdot y2 \]

   if -1.9999999999999999e-147 < t < -2.99999999999999984e-155

   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

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 76.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 26.0%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-1, y3 \cdot y4, i \cdot x\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto k \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(i \cdot z\right) + y2 \cdot y4\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 88.0%

       \[\leadsto k \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-i, z, y2 \cdot y4\right)\right)} \]

   if -2.99999999999999984e-155 < t < -1.1000000000000001e-254

   1. Initial program 31.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 63.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - c \cdot i, x, \left(c \cdot y4 - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in b around inf

      \[\leadsto \left(b \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 63.4%

      \[\leadsto \left(b \cdot \mathsf{fma}\left(a, x, -k \cdot y4\right)\right) \cdot y \]

   if -1.1000000000000001e-254 < t < -1.4499999999999999e-306

   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

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Applied rewrites 57.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y4 \cdot y1 - y0 \cdot y5, k, \mathsf{fma}\left(c \cdot y0 - y1 \cdot a, x, \left(-t\right) \cdot \left(c \cdot y4 - y5 \cdot a\right)\right)\right) \cdot y2} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto y0 \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(k \cdot y5\right) + c \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 66.5%

      \[\leadsto \left(y0 \cdot y2\right) \cdot \color{blue}{\mathsf{fma}\left(c, x, -k \cdot y5\right)} \]

   if -1.4499999999999999e-306 < t < 5.99999999999999997e-233

   1. Initial program 27.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 54.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in y4 around inf

      \[\leadsto \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \cdot y1 \]
   7. Step-by-step derivation

   8. Applied rewrites 54.2%

      \[\leadsto \left(y4 \cdot \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right)\right) \cdot y1 \]

   if 5.99999999999999997e-233 < t < 7.7999999999999993e-92

   1. Initial program 37.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 54.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - c \cdot i, x, \left(c \cdot y4 - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in a around inf

      \[\leadsto \left(a \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 58.7%

      \[\leadsto \left(a \cdot \mathsf{fma}\left(-y3, y5, b \cdot x\right)\right) \cdot y \]

   if 7.7999999999999993e-92 < t < 8.8000000000000002e-42

   1. Initial program 47.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot x} \]

   5. Applied rewrites 59.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot a - c \cdot i, y, \mathsf{fma}\left(c \cdot y0 - y1 \cdot a, y2, \left(-j\right) \cdot \left(y0 \cdot b - i \cdot y1\right)\right)\right) \cdot x} \]

   6. Taylor expanded in j around inf

      \[\leadsto \left(-1 \cdot \left(j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 54.0%

      \[\leadsto \left(-j \cdot \mathsf{fma}\left(b, y0, \left(-i\right) \cdot y1\right)\right) \cdot x \]

   if 8.8000000000000002e-42 < t < 1.16000000000000008e150

   1. Initial program 27.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 57.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 52.8%

      \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right)\right)} \]

   if 1.16000000000000008e150 < t

   1. Initial program 23.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot a} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot a} \]

   5. Applied rewrites 42.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), y1, \mathsf{fma}\left(y \cdot x - t \cdot z, b, \left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]

   6. Taylor expanded in b around inf

      \[\leadsto \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) \cdot a \]
   7. Step-by-step derivation

   8. Applied rewrites 62.4%

      \[\leadsto \left(b \cdot \mathsf{fma}\left(x, y, \left(-t\right) \cdot z\right)\right) \cdot a \]
3. Recombined 12 regimes into one program.

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+92}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y, \left(-t\right) \cdot j\right) \cdot i\right) \cdot y5\\ \mathbf{elif}\;t \leq -4.05 \cdot 10^{+18}:\\ \;\;\;\;\left(\mathsf{fma}\left(-b, j, y2 \cdot c\right) \cdot y0\right) \cdot x\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-60}:\\ \;\;\;\;\left(y1 \cdot z\right) \cdot \mathsf{fma}\left(-i, k, y3 \cdot a\right)\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-147}:\\ \;\;\;\;\left(\mathsf{fma}\left(y1, y4, \left(-y0\right) \cdot y5\right) \cdot k\right) \cdot y2\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-155}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, z, y4 \cdot y2\right) \cdot y1\right) \cdot k\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-254}:\\ \;\;\;\;\left(\mathsf{fma}\left(a, x, \left(-k\right) \cdot y4\right) \cdot b\right) \cdot y\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-306}:\\ \;\;\;\;\mathsf{fma}\left(c, x, \left(-y5\right) \cdot k\right) \cdot \left(y2 \cdot y0\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-233}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right) \cdot y4\right) \cdot y1\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-92}:\\ \;\;\;\;\left(\mathsf{fma}\left(-y3, y5, b \cdot x\right) \cdot a\right) \cdot y\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-42}:\\ \;\;\;\;\left(\mathsf{fma}\left(b, y0, \left(-i\right) \cdot y1\right) \cdot \left(-j\right)\right) \cdot x\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{+150}:\\ \;\;\;\;\left(\mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right) \cdot y1\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(x, y, \left(-t\right) \cdot z\right) \cdot b\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 29.9% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\mathsf{fma}\left(-i, z, y4 \cdot y2\right) \cdot y1\right) \cdot k\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{+92}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y, \left(-t\right) \cdot j\right) \cdot i\right) \cdot y5\\ \mathbf{elif}\;t \leq -4.05 \cdot 10^{+18}:\\ \;\;\;\;\left(\mathsf{fma}\left(-b, j, y2 \cdot c\right) \cdot y0\right) \cdot x\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-60}:\\ \;\;\;\;\left(y1 \cdot z\right) \cdot \mathsf{fma}\left(-i, k, y3 \cdot a\right)\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-147}:\\ \;\;\;\;\left(\mathsf{fma}\left(y1, y4, \left(-y0\right) \cdot y5\right) \cdot k\right) \cdot y2\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-155}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-254}:\\ \;\;\;\;\left(\mathsf{fma}\left(a, x, \left(-k\right) \cdot y4\right) \cdot b\right) \cdot y\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-306}:\\ \;\;\;\;\mathsf{fma}\left(c, x, \left(-y5\right) \cdot k\right) \cdot \left(y2 \cdot y0\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-233}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right) \cdot y4\right) \cdot y1\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-84}:\\ \;\;\;\;\left(\mathsf{fma}\left(-y3, y5, b \cdot x\right) \cdot a\right) \cdot y\\ \mathbf{elif}\;t \leq 185000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{+150}:\\ \;\;\;\;\left(\mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right) \cdot y1\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(x, y, \left(-t\right) \cdot z\right) \cdot b\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* (fma (- i) z (* y4 y2)) y1) k)))
   (if (<= t -1.7e+92)
     (* (* (fma k y (* (- t) j)) i) y5)
     (if (<= t -4.05e+18)
       (* (* (fma (- b) j (* y2 c)) y0) x)
       (if (<= t -4.5e-60)
         (* (* y1 z) (fma (- i) k (* y3 a)))
         (if (<= t -2e-147)
           (* (* (fma y1 y4 (* (- y0) y5)) k) y2)
           (if (<= t -3e-155)
             t_1
             (if (<= t -1.1e-254)
               (* (* (fma a x (* (- k) y4)) b) y)
               (if (<= t -1.45e-306)
                 (* (fma c x (* (- y5) k)) (* y2 y0))
                 (if (<= t 6e-233)
                   (* (* (fma k y2 (* (- j) y3)) y4) y1)
                   (if (<= t 9e-84)
                     (* (* (fma (- y3) y5 (* b x)) a) y)
                     (if (<= t 185000000000.0)
                       t_1
                       (if (<= t 1.16e+150)
                         (* (* (fma y3 z (* (- x) y2)) y1) a)
                         (* (* (fma x y (* (- t) z)) b) 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 = (fma(-i, z, (y4 * y2)) * y1) * k;
	double tmp;
	if (t <= -1.7e+92) {
		tmp = (fma(k, y, (-t * j)) * i) * y5;
	} else if (t <= -4.05e+18) {
		tmp = (fma(-b, j, (y2 * c)) * y0) * x;
	} else if (t <= -4.5e-60) {
		tmp = (y1 * z) * fma(-i, k, (y3 * a));
	} else if (t <= -2e-147) {
		tmp = (fma(y1, y4, (-y0 * y5)) * k) * y2;
	} else if (t <= -3e-155) {
		tmp = t_1;
	} else if (t <= -1.1e-254) {
		tmp = (fma(a, x, (-k * y4)) * b) * y;
	} else if (t <= -1.45e-306) {
		tmp = fma(c, x, (-y5 * k)) * (y2 * y0);
	} else if (t <= 6e-233) {
		tmp = (fma(k, y2, (-j * y3)) * y4) * y1;
	} else if (t <= 9e-84) {
		tmp = (fma(-y3, y5, (b * x)) * a) * y;
	} else if (t <= 185000000000.0) {
		tmp = t_1;
	} else if (t <= 1.16e+150) {
		tmp = (fma(y3, z, (-x * y2)) * y1) * a;
	} else {
		tmp = (fma(x, y, (-t * z)) * b) * 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(fma(Float64(-i), z, Float64(y4 * y2)) * y1) * k)
	tmp = 0.0
	if (t <= -1.7e+92)
		tmp = Float64(Float64(fma(k, y, Float64(Float64(-t) * j)) * i) * y5);
	elseif (t <= -4.05e+18)
		tmp = Float64(Float64(fma(Float64(-b), j, Float64(y2 * c)) * y0) * x);
	elseif (t <= -4.5e-60)
		tmp = Float64(Float64(y1 * z) * fma(Float64(-i), k, Float64(y3 * a)));
	elseif (t <= -2e-147)
		tmp = Float64(Float64(fma(y1, y4, Float64(Float64(-y0) * y5)) * k) * y2);
	elseif (t <= -3e-155)
		tmp = t_1;
	elseif (t <= -1.1e-254)
		tmp = Float64(Float64(fma(a, x, Float64(Float64(-k) * y4)) * b) * y);
	elseif (t <= -1.45e-306)
		tmp = Float64(fma(c, x, Float64(Float64(-y5) * k)) * Float64(y2 * y0));
	elseif (t <= 6e-233)
		tmp = Float64(Float64(fma(k, y2, Float64(Float64(-j) * y3)) * y4) * y1);
	elseif (t <= 9e-84)
		tmp = Float64(Float64(fma(Float64(-y3), y5, Float64(b * x)) * a) * y);
	elseif (t <= 185000000000.0)
		tmp = t_1;
	elseif (t <= 1.16e+150)
		tmp = Float64(Float64(fma(y3, z, Float64(Float64(-x) * y2)) * y1) * a);
	else
		tmp = Float64(Float64(fma(x, y, Float64(Float64(-t) * z)) * b) * a);
	end
	return 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[(N[((-i) * z + N[(y4 * y2), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t, -1.7e+92], N[(N[(N[(k * y + N[((-t) * j), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision] * y5), $MachinePrecision], If[LessEqual[t, -4.05e+18], N[(N[(N[((-b) * j + N[(y2 * c), $MachinePrecision]), $MachinePrecision] * y0), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t, -4.5e-60], N[(N[(y1 * z), $MachinePrecision] * N[((-i) * k + N[(y3 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2e-147], N[(N[(N[(y1 * y4 + N[((-y0) * y5), $MachinePrecision]), $MachinePrecision] * k), $MachinePrecision] * y2), $MachinePrecision], If[LessEqual[t, -3e-155], t$95$1, If[LessEqual[t, -1.1e-254], N[(N[(N[(a * x + N[((-k) * y4), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, -1.45e-306], N[(N[(c * x + N[((-y5) * k), $MachinePrecision]), $MachinePrecision] * N[(y2 * y0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e-233], N[(N[(N[(k * y2 + N[((-j) * y3), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision] * y1), $MachinePrecision], If[LessEqual[t, 9e-84], N[(N[(N[((-y3) * y5 + N[(b * x), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 185000000000.0], t$95$1, If[LessEqual[t, 1.16e+150], N[(N[(N[(y3 * z + N[((-x) * y2), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision] * a), $MachinePrecision], N[(N[(N[(x * y + N[((-t) * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision] * a), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 11 regimes

2. if t < -1.6999999999999999e92

   1. Initial program 21.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

   5. Applied rewrites 62.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(j \cdot t - k \cdot y\right), i, \mathsf{fma}\left(-y0, k \cdot y2 - j \cdot y3, \left(t \cdot y2 - y \cdot y3\right) \cdot a\right)\right) \cdot y5} \]

   6. Taylor expanded in i around inf

      \[\leadsto \left(i \cdot \left(k \cdot y - j \cdot t\right)\right) \cdot y5 \]
   7. Step-by-step derivation

   8. Applied rewrites 54.1%

      \[\leadsto \left(i \cdot \mathsf{fma}\left(k, y, \left(-j\right) \cdot t\right)\right) \cdot y5 \]

   if -1.6999999999999999e92 < t < -4.05e18

   1. Initial program 53.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot x} \]

   5. Applied rewrites 60.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot a - c \cdot i, y, \mathsf{fma}\left(c \cdot y0 - y1 \cdot a, y2, \left(-j\right) \cdot \left(y0 \cdot b - i \cdot y1\right)\right)\right) \cdot x} \]

   6. Taylor expanded in y around inf

      \[\leadsto \left(y \cdot \left(a \cdot b - c \cdot i\right)\right) \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 16.1%

      \[\leadsto \left(y \cdot \mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right)\right) \cdot x \]

   9. Taylor expanded in y0 around inf

      \[\leadsto \left(y0 \cdot \left(-1 \cdot \left(b \cdot j\right) + c \cdot y2\right)\right) \cdot x \]
   10. Step-by-step derivation

   11. Applied rewrites 61.0%

       \[\leadsto \left(y0 \cdot \mathsf{fma}\left(-b, j, c \cdot y2\right)\right) \cdot x \]

   if -4.05e18 < t < -4.50000000000000001e-60

   1. Initial program 29.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 55.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 36.2%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-1, y3 \cdot y4, i \cdot x\right)\right)} \]

   9. Taylor expanded in z around inf

      \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(i \cdot k\right) + a \cdot y3\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 73.7%

       \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \mathsf{fma}\left(-i, k, a \cdot y3\right)\right)} \]
   12. Step-by-step derivation

   13. Applied rewrites 73.7%

       \[\leadsto \mathsf{fma}\left(-i, k, y3 \cdot a\right) \cdot \left(y1 \cdot \color{blue}{z}\right) \]

   if -4.50000000000000001e-60 < t < -1.9999999999999999e-147

   1. Initial program 32.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Applied rewrites 48.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y4 \cdot y1 - y0 \cdot y5, k, \mathsf{fma}\left(c \cdot y0 - y1 \cdot a, x, \left(-t\right) \cdot \left(c \cdot y4 - y5 \cdot a\right)\right)\right) \cdot y2} \]

   6. Taylor expanded in k around inf

      \[\leadsto \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) \cdot y2 \]
   7. Step-by-step derivation

   8. Applied rewrites 53.6%

      \[\leadsto \left(k \cdot \mathsf{fma}\left(y1, y4, \left(-y0\right) \cdot y5\right)\right) \cdot y2 \]

   if -1.9999999999999999e-147 < t < -2.99999999999999984e-155 or 9.00000000000000031e-84 < t < 1.85e11

   1. Initial program 39.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 40.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 19.1%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-1, y3 \cdot y4, i \cdot x\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto k \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(i \cdot z\right) + y2 \cdot y4\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 56.0%

       \[\leadsto k \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-i, z, y2 \cdot y4\right)\right)} \]

   if -2.99999999999999984e-155 < t < -1.1000000000000001e-254

   1. Initial program 31.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 63.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - c \cdot i, x, \left(c \cdot y4 - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in b around inf

      \[\leadsto \left(b \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 63.4%

      \[\leadsto \left(b \cdot \mathsf{fma}\left(a, x, -k \cdot y4\right)\right) \cdot y \]

   if -1.1000000000000001e-254 < t < -1.4499999999999999e-306

   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

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Applied rewrites 57.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y4 \cdot y1 - y0 \cdot y5, k, \mathsf{fma}\left(c \cdot y0 - y1 \cdot a, x, \left(-t\right) \cdot \left(c \cdot y4 - y5 \cdot a\right)\right)\right) \cdot y2} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto y0 \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(k \cdot y5\right) + c \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 66.5%

      \[\leadsto \left(y0 \cdot y2\right) \cdot \color{blue}{\mathsf{fma}\left(c, x, -k \cdot y5\right)} \]

   if -1.4499999999999999e-306 < t < 5.99999999999999997e-233

   1. Initial program 27.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 54.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in y4 around inf

      \[\leadsto \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \cdot y1 \]
   7. Step-by-step derivation

   8. Applied rewrites 54.2%

      \[\leadsto \left(y4 \cdot \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right)\right) \cdot y1 \]

   if 5.99999999999999997e-233 < t < 9.00000000000000031e-84

   1. Initial program 38.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 54.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - c \cdot i, x, \left(c \cdot y4 - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in a around inf

      \[\leadsto \left(a \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 55.7%

      \[\leadsto \left(a \cdot \mathsf{fma}\left(-y3, y5, b \cdot x\right)\right) \cdot y \]

   if 1.85e11 < t < 1.16000000000000008e150

   1. Initial program 25.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 60.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 57.5%

      \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right)\right)} \]

   if 1.16000000000000008e150 < t

   1. Initial program 23.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot a} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot a} \]

   5. Applied rewrites 42.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), y1, \mathsf{fma}\left(y \cdot x - t \cdot z, b, \left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]

   6. Taylor expanded in b around inf

      \[\leadsto \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) \cdot a \]
   7. Step-by-step derivation

   8. Applied rewrites 62.4%

      \[\leadsto \left(b \cdot \mathsf{fma}\left(x, y, \left(-t\right) \cdot z\right)\right) \cdot a \]
3. Recombined 11 regimes into one program.

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+92}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y, \left(-t\right) \cdot j\right) \cdot i\right) \cdot y5\\ \mathbf{elif}\;t \leq -4.05 \cdot 10^{+18}:\\ \;\;\;\;\left(\mathsf{fma}\left(-b, j, y2 \cdot c\right) \cdot y0\right) \cdot x\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-60}:\\ \;\;\;\;\left(y1 \cdot z\right) \cdot \mathsf{fma}\left(-i, k, y3 \cdot a\right)\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-147}:\\ \;\;\;\;\left(\mathsf{fma}\left(y1, y4, \left(-y0\right) \cdot y5\right) \cdot k\right) \cdot y2\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-155}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, z, y4 \cdot y2\right) \cdot y1\right) \cdot k\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-254}:\\ \;\;\;\;\left(\mathsf{fma}\left(a, x, \left(-k\right) \cdot y4\right) \cdot b\right) \cdot y\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-306}:\\ \;\;\;\;\mathsf{fma}\left(c, x, \left(-y5\right) \cdot k\right) \cdot \left(y2 \cdot y0\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-233}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right) \cdot y4\right) \cdot y1\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-84}:\\ \;\;\;\;\left(\mathsf{fma}\left(-y3, y5, b \cdot x\right) \cdot a\right) \cdot y\\ \mathbf{elif}\;t \leq 185000000000:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, z, y4 \cdot y2\right) \cdot y1\right) \cdot k\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{+150}:\\ \;\;\;\;\left(\mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right) \cdot y1\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(x, y, \left(-t\right) \cdot z\right) \cdot b\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 38.3% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y3 \cdot z - y2 \cdot x\\ \mathbf{if}\;i \leq -9.5 \cdot 10^{+232}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, a, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1\\ \mathbf{elif}\;i \leq -1 \cdot 10^{+192}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y1, \left(-t\right) \cdot c\right) \cdot y4\right) \cdot y2\\ \mathbf{elif}\;i \leq -7.5 \cdot 10^{+90}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y, \left(-t\right) \cdot j\right) \cdot i\right) \cdot y5\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{-295}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, y1, \mathsf{fma}\left(y \cdot x - t \cdot z, b, \left(y2 \cdot t - y3 \cdot y\right) \cdot y5\right)\right) \cdot a\\ \mathbf{elif}\;i \leq 1.35 \cdot 10^{-176}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot j - y2 \cdot k, y5, \left(\left(-x\right) \cdot j\right) \cdot b\right) \cdot y0\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{+251}:\\ \;\;\;\;\mathsf{fma}\left(y5 \cdot i - y4 \cdot b, k, \mathsf{fma}\left(-y3, y5, b \cdot x\right) \cdot a\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y5, \left(-c\right) \cdot x\right) \cdot i\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y3 z) (* y2 x))))
   (if (<= i -9.5e+232)
     (*
      (fma t_1 a (fma (- (* y2 k) (* y3 j)) y4 (* (- (* j x) (* k z)) i)))
      y1)
     (if (<= i -1e+192)
       (* (* (fma k y1 (* (- t) c)) y4) y2)
       (if (<= i -7.5e+90)
         (* (* (fma k y (* (- t) j)) i) y5)
         (if (<= i 4.8e-295)
           (*
            (fma
             t_1
             y1
             (fma (- (* y x) (* t z)) b (* (- (* y2 t) (* y3 y)) y5)))
            a)
           (if (<= i 1.35e-176)
             (* (fma (- (* y3 j) (* y2 k)) y5 (* (* (- x) j) b)) y0)
             (if (<= i 1.1e+251)
               (*
                (fma (- (* y5 i) (* y4 b)) k (* (fma (- y3) y5 (* b x)) a))
                y)
               (* (* (fma k y5 (* (- c) x)) i) y)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y3 * z) - (y2 * x);
	double tmp;
	if (i <= -9.5e+232) {
		tmp = fma(t_1, a, fma(((y2 * k) - (y3 * j)), y4, (((j * x) - (k * z)) * i))) * y1;
	} else if (i <= -1e+192) {
		tmp = (fma(k, y1, (-t * c)) * y4) * y2;
	} else if (i <= -7.5e+90) {
		tmp = (fma(k, y, (-t * j)) * i) * y5;
	} else if (i <= 4.8e-295) {
		tmp = fma(t_1, y1, fma(((y * x) - (t * z)), b, (((y2 * t) - (y3 * y)) * y5))) * a;
	} else if (i <= 1.35e-176) {
		tmp = fma(((y3 * j) - (y2 * k)), y5, ((-x * j) * b)) * y0;
	} else if (i <= 1.1e+251) {
		tmp = fma(((y5 * i) - (y4 * b)), k, (fma(-y3, y5, (b * x)) * a)) * y;
	} else {
		tmp = (fma(k, y5, (-c * x)) * i) * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y3 * z) - Float64(y2 * x))
	tmp = 0.0
	if (i <= -9.5e+232)
		tmp = Float64(fma(t_1, a, fma(Float64(Float64(y2 * k) - Float64(y3 * j)), y4, Float64(Float64(Float64(j * x) - Float64(k * z)) * i))) * y1);
	elseif (i <= -1e+192)
		tmp = Float64(Float64(fma(k, y1, Float64(Float64(-t) * c)) * y4) * y2);
	elseif (i <= -7.5e+90)
		tmp = Float64(Float64(fma(k, y, Float64(Float64(-t) * j)) * i) * y5);
	elseif (i <= 4.8e-295)
		tmp = Float64(fma(t_1, y1, fma(Float64(Float64(y * x) - Float64(t * z)), b, Float64(Float64(Float64(y2 * t) - Float64(y3 * y)) * y5))) * a);
	elseif (i <= 1.35e-176)
		tmp = Float64(fma(Float64(Float64(y3 * j) - Float64(y2 * k)), y5, Float64(Float64(Float64(-x) * j) * b)) * y0);
	elseif (i <= 1.1e+251)
		tmp = Float64(fma(Float64(Float64(y5 * i) - Float64(y4 * b)), k, Float64(fma(Float64(-y3), y5, Float64(b * x)) * a)) * y);
	else
		tmp = Float64(Float64(fma(k, y5, Float64(Float64(-c) * x)) * i) * y);
	end
	return 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[(y3 * z), $MachinePrecision] - N[(y2 * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -9.5e+232], N[(N[(t$95$1 * a + N[(N[(N[(y2 * k), $MachinePrecision] - N[(y3 * j), $MachinePrecision]), $MachinePrecision] * y4 + N[(N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision], If[LessEqual[i, -1e+192], N[(N[(N[(k * y1 + N[((-t) * c), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision] * y2), $MachinePrecision], If[LessEqual[i, -7.5e+90], N[(N[(N[(k * y + N[((-t) * j), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision] * y5), $MachinePrecision], If[LessEqual[i, 4.8e-295], N[(N[(t$95$1 * y1 + N[(N[(N[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision] * b + N[(N[(N[(y2 * t), $MachinePrecision] - N[(y3 * y), $MachinePrecision]), $MachinePrecision] * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[i, 1.35e-176], N[(N[(N[(N[(y3 * j), $MachinePrecision] - N[(y2 * k), $MachinePrecision]), $MachinePrecision] * y5 + N[(N[((-x) * j), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] * y0), $MachinePrecision], If[LessEqual[i, 1.1e+251], N[(N[(N[(N[(y5 * i), $MachinePrecision] - N[(y4 * b), $MachinePrecision]), $MachinePrecision] * k + N[(N[((-y3) * y5 + N[(b * x), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], N[(N[(N[(k * y5 + N[((-c) * x), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision] * y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if i < -9.4999999999999996e232

   1. Initial program 28.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 64.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   if -9.4999999999999996e232 < i < -1.00000000000000004e192

   1. Initial program 24.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Applied rewrites 63.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y4 \cdot y1 - y0 \cdot y5, k, \mathsf{fma}\left(c \cdot y0 - y1 \cdot a, x, \left(-t\right) \cdot \left(c \cdot y4 - y5 \cdot a\right)\right)\right) \cdot y2} \]

   6. Taylor expanded in y4 around inf

      \[\leadsto \left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right) \cdot y2 \]
   7. Step-by-step derivation

   8. Applied rewrites 75.5%

      \[\leadsto \left(y4 \cdot \mathsf{fma}\left(k, y1, -c \cdot t\right)\right) \cdot y2 \]

   if -1.00000000000000004e192 < i < -7.50000000000000014e90

   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 y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

   5. Applied rewrites 64.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(j \cdot t - k \cdot y\right), i, \mathsf{fma}\left(-y0, k \cdot y2 - j \cdot y3, \left(t \cdot y2 - y \cdot y3\right) \cdot a\right)\right) \cdot y5} \]

   6. Taylor expanded in i around inf

      \[\leadsto \left(i \cdot \left(k \cdot y - j \cdot t\right)\right) \cdot y5 \]
   7. Step-by-step derivation

   8. Applied rewrites 71.9%

      \[\leadsto \left(i \cdot \mathsf{fma}\left(k, y, \left(-j\right) \cdot t\right)\right) \cdot y5 \]

   if -7.50000000000000014e90 < i < 4.7999999999999996e-295

   1. Initial program 40.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot a} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot a} \]

   5. Applied rewrites 59.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), y1, \mathsf{fma}\left(y \cdot x - t \cdot z, b, \left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]

   if 4.7999999999999996e-295 < i < 1.3499999999999999e-176

   1. Initial program 22.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y0} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y0} \]

   5. Applied rewrites 55.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(k \cdot y2 - j \cdot y3\right), y5, \mathsf{fma}\left(c, y2 \cdot x - z \cdot y3, \left(-b\right) \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y0} \]

   6. Taylor expanded in j around inf

      \[\leadsto \mathsf{fma}\left(-\left(k \cdot y2 - j \cdot y3\right), y5, -1 \cdot \left(b \cdot \left(j \cdot x\right)\right)\right) \cdot y0 \]
   7. Step-by-step derivation

   8. Applied rewrites 55.9%

      \[\leadsto \mathsf{fma}\left(-\left(k \cdot y2 - j \cdot y3\right), y5, -b \cdot \left(j \cdot x\right)\right) \cdot y0 \]

   if 1.3499999999999999e-176 < i < 1.1e251

   1. Initial program 30.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 57.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - c \cdot i, x, \left(c \cdot y4 - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, a \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 56.2%

      \[\leadsto \mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, a \cdot \mathsf{fma}\left(-y3, y5, b \cdot x\right)\right) \cdot y \]

   if 1.1e251 < i

   1. Initial program 7.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 21.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - c \cdot i, x, \left(c \cdot y4 - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in i around inf

      \[\leadsto \left(i \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 64.5%

      \[\leadsto \left(i \cdot \mathsf{fma}\left(k, y5, -c \cdot x\right)\right) \cdot y \]
3. Recombined 7 regimes into one program.

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -9.5 \cdot 10^{+232}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot z - y2 \cdot x, a, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1\\ \mathbf{elif}\;i \leq -1 \cdot 10^{+192}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y1, \left(-t\right) \cdot c\right) \cdot y4\right) \cdot y2\\ \mathbf{elif}\;i \leq -7.5 \cdot 10^{+90}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y, \left(-t\right) \cdot j\right) \cdot i\right) \cdot y5\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{-295}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot z - y2 \cdot x, y1, \mathsf{fma}\left(y \cdot x - t \cdot z, b, \left(y2 \cdot t - y3 \cdot y\right) \cdot y5\right)\right) \cdot a\\ \mathbf{elif}\;i \leq 1.35 \cdot 10^{-176}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot j - y2 \cdot k, y5, \left(\left(-x\right) \cdot j\right) \cdot b\right) \cdot y0\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{+251}:\\ \;\;\;\;\mathsf{fma}\left(y5 \cdot i - y4 \cdot b, k, \mathsf{fma}\left(-y3, y5, b \cdot x\right) \cdot a\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y5, \left(-c\right) \cdot x\right) \cdot i\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 30.6% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\mathsf{fma}\left(-i, k, y3 \cdot a\right) \cdot z\right) \cdot y1\\ t_2 := \left(\mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right) \cdot y4\right) \cdot y1\\ t_3 := \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right)\\ \mathbf{if}\;y4 \leq -2.35 \cdot 10^{-20}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y4 \leq -9.5 \cdot 10^{-72}:\\ \;\;\;\;\left(a \cdot t\right) \cdot \mathsf{fma}\left(-b, z, y5 \cdot y2\right)\\ \mathbf{elif}\;y4 \leq -8.4 \cdot 10^{-112}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y4 \leq -2 \cdot 10^{-207}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq -5 \cdot 10^{-270}:\\ \;\;\;\;\left(t\_3 \cdot a\right) \cdot y5\\ \mathbf{elif}\;y4 \leq 7.4 \cdot 10^{-99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq 1.2 \cdot 10^{+27}:\\ \;\;\;\;\mathsf{fma}\left(c, x, \left(-y5\right) \cdot k\right) \cdot \left(y2 \cdot y0\right)\\ \mathbf{elif}\;y4 \leq 5.2 \cdot 10^{+69}:\\ \;\;\;\;\left(t\_3 \cdot y5\right) \cdot a\\ \mathbf{elif}\;y4 \leq 5 \cdot 10^{+263}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y, \left(-t\right) \cdot j\right) \cdot i\right) \cdot y5\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* (fma (- i) k (* y3 a)) z) y1))
        (t_2 (* (* (fma k y2 (* (- j) y3)) y4) y1))
        (t_3 (fma t y2 (* (- y) y3))))
   (if (<= y4 -2.35e-20)
     t_2
     (if (<= y4 -9.5e-72)
       (* (* a t) (fma (- b) z (* y5 y2)))
       (if (<= y4 -8.4e-112)
         t_2
         (if (<= y4 -2e-207)
           t_1
           (if (<= y4 -5e-270)
             (* (* t_3 a) y5)
             (if (<= y4 7.4e-99)
               t_1
               (if (<= y4 1.2e+27)
                 (* (fma c x (* (- y5) k)) (* y2 y0))
                 (if (<= y4 5.2e+69)
                   (* (* t_3 y5) a)
                   (if (<= y4 5e+263)
                     (* (* (fma k y (* (- t) j)) i) y5)
                     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 = (fma(-i, k, (y3 * a)) * z) * y1;
	double t_2 = (fma(k, y2, (-j * y3)) * y4) * y1;
	double t_3 = fma(t, y2, (-y * y3));
	double tmp;
	if (y4 <= -2.35e-20) {
		tmp = t_2;
	} else if (y4 <= -9.5e-72) {
		tmp = (a * t) * fma(-b, z, (y5 * y2));
	} else if (y4 <= -8.4e-112) {
		tmp = t_2;
	} else if (y4 <= -2e-207) {
		tmp = t_1;
	} else if (y4 <= -5e-270) {
		tmp = (t_3 * a) * y5;
	} else if (y4 <= 7.4e-99) {
		tmp = t_1;
	} else if (y4 <= 1.2e+27) {
		tmp = fma(c, x, (-y5 * k)) * (y2 * y0);
	} else if (y4 <= 5.2e+69) {
		tmp = (t_3 * y5) * a;
	} else if (y4 <= 5e+263) {
		tmp = (fma(k, y, (-t * j)) * i) * y5;
	} 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(fma(Float64(-i), k, Float64(y3 * a)) * z) * y1)
	t_2 = Float64(Float64(fma(k, y2, Float64(Float64(-j) * y3)) * y4) * y1)
	t_3 = fma(t, y2, Float64(Float64(-y) * y3))
	tmp = 0.0
	if (y4 <= -2.35e-20)
		tmp = t_2;
	elseif (y4 <= -9.5e-72)
		tmp = Float64(Float64(a * t) * fma(Float64(-b), z, Float64(y5 * y2)));
	elseif (y4 <= -8.4e-112)
		tmp = t_2;
	elseif (y4 <= -2e-207)
		tmp = t_1;
	elseif (y4 <= -5e-270)
		tmp = Float64(Float64(t_3 * a) * y5);
	elseif (y4 <= 7.4e-99)
		tmp = t_1;
	elseif (y4 <= 1.2e+27)
		tmp = Float64(fma(c, x, Float64(Float64(-y5) * k)) * Float64(y2 * y0));
	elseif (y4 <= 5.2e+69)
		tmp = Float64(Float64(t_3 * y5) * a);
	elseif (y4 <= 5e+263)
		tmp = Float64(Float64(fma(k, y, Float64(Float64(-t) * j)) * i) * y5);
	else
		tmp = t_2;
	end
	return 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[(N[((-i) * k + N[(y3 * a), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] * y1), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(k * y2 + N[((-j) * y3), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision] * y1), $MachinePrecision]}, Block[{t$95$3 = N[(t * y2 + N[((-y) * y3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -2.35e-20], t$95$2, If[LessEqual[y4, -9.5e-72], N[(N[(a * t), $MachinePrecision] * N[((-b) * z + N[(y5 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -8.4e-112], t$95$2, If[LessEqual[y4, -2e-207], t$95$1, If[LessEqual[y4, -5e-270], N[(N[(t$95$3 * a), $MachinePrecision] * y5), $MachinePrecision], If[LessEqual[y4, 7.4e-99], t$95$1, If[LessEqual[y4, 1.2e+27], N[(N[(c * x + N[((-y5) * k), $MachinePrecision]), $MachinePrecision] * N[(y2 * y0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 5.2e+69], N[(N[(t$95$3 * y5), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[y4, 5e+263], N[(N[(N[(k * y + N[((-t) * j), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision] * y5), $MachinePrecision], t$95$2]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y4 < -2.35000000000000007e-20 or -9.4999999999999998e-72 < y4 < -8.4000000000000002e-112 or 5.00000000000000022e263 < y4

   1. Initial program 29.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 46.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in y4 around inf

      \[\leadsto \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \cdot y1 \]
   7. Step-by-step derivation

   8. Applied rewrites 49.4%

      \[\leadsto \left(y4 \cdot \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right)\right) \cdot y1 \]

   if -2.35000000000000007e-20 < y4 < -9.4999999999999998e-72

   1. Initial program 40.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot a} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot a} \]

   5. Applied rewrites 70.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), y1, \mathsf{fma}\left(y \cdot x - t \cdot z, b, \left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]

   6. Taylor expanded in t around inf

      \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(-1 \cdot \left(b \cdot z\right) + y2 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 71.2%

      \[\leadsto \left(a \cdot t\right) \cdot \color{blue}{\mathsf{fma}\left(-b, z, y2 \cdot y5\right)} \]

   if -8.4000000000000002e-112 < y4 < -1.99999999999999985e-207 or -4.9999999999999998e-270 < y4 < 7.400000000000001e-99

   1. Initial program 30.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 41.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 21.3%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-1, y3 \cdot y4, i \cdot x\right)\right)} \]

   9. Taylor expanded in z around inf

      \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(i \cdot k\right) + a \cdot y3\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 55.7%

       \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \mathsf{fma}\left(-i, k, a \cdot y3\right)\right)} \]

   if -1.99999999999999985e-207 < y4 < -4.9999999999999998e-270

   1. Initial program 59.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

   5. Applied rewrites 49.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(j \cdot t - k \cdot y\right), i, \mathsf{fma}\left(-y0, k \cdot y2 - j \cdot y3, \left(t \cdot y2 - y \cdot y3\right) \cdot a\right)\right) \cdot y5} \]

   6. Taylor expanded in a around inf

      \[\leadsto \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y5 \]
   7. Step-by-step derivation

   8. Applied rewrites 61.3%

      \[\leadsto \left(a \cdot \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right)\right) \cdot y5 \]

   if 7.400000000000001e-99 < y4 < 1.19999999999999999e27

   1. Initial program 19.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Applied rewrites 54.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y4 \cdot y1 - y0 \cdot y5, k, \mathsf{fma}\left(c \cdot y0 - y1 \cdot a, x, \left(-t\right) \cdot \left(c \cdot y4 - y5 \cdot a\right)\right)\right) \cdot y2} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto y0 \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(k \cdot y5\right) + c \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 45.3%

      \[\leadsto \left(y0 \cdot y2\right) \cdot \color{blue}{\mathsf{fma}\left(c, x, -k \cdot y5\right)} \]

   if 1.19999999999999999e27 < y4 < 5.2000000000000004e69

   1. Initial program 0.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

   5. Applied rewrites 56.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(j \cdot t - k \cdot y\right), i, \mathsf{fma}\left(-y0, k \cdot y2 - j \cdot y3, \left(t \cdot y2 - y \cdot y3\right) \cdot a\right)\right) \cdot y5} \]

   6. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 56.3%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right)\right)} \]

   if 5.2000000000000004e69 < y4 < 5.00000000000000022e263

   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 y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

   5. Applied rewrites 57.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(j \cdot t - k \cdot y\right), i, \mathsf{fma}\left(-y0, k \cdot y2 - j \cdot y3, \left(t \cdot y2 - y \cdot y3\right) \cdot a\right)\right) \cdot y5} \]

   6. Taylor expanded in i around inf

      \[\leadsto \left(i \cdot \left(k \cdot y - j \cdot t\right)\right) \cdot y5 \]
   7. Step-by-step derivation

   8. Applied rewrites 48.2%

      \[\leadsto \left(i \cdot \mathsf{fma}\left(k, y, \left(-j\right) \cdot t\right)\right) \cdot y5 \]
3. Recombined 7 regimes into one program.

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -2.35 \cdot 10^{-20}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right) \cdot y4\right) \cdot y1\\ \mathbf{elif}\;y4 \leq -9.5 \cdot 10^{-72}:\\ \;\;\;\;\left(a \cdot t\right) \cdot \mathsf{fma}\left(-b, z, y5 \cdot y2\right)\\ \mathbf{elif}\;y4 \leq -8.4 \cdot 10^{-112}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right) \cdot y4\right) \cdot y1\\ \mathbf{elif}\;y4 \leq -2 \cdot 10^{-207}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, k, y3 \cdot a\right) \cdot z\right) \cdot y1\\ \mathbf{elif}\;y4 \leq -5 \cdot 10^{-270}:\\ \;\;\;\;\left(\mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right) \cdot a\right) \cdot y5\\ \mathbf{elif}\;y4 \leq 7.4 \cdot 10^{-99}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, k, y3 \cdot a\right) \cdot z\right) \cdot y1\\ \mathbf{elif}\;y4 \leq 1.2 \cdot 10^{+27}:\\ \;\;\;\;\mathsf{fma}\left(c, x, \left(-y5\right) \cdot k\right) \cdot \left(y2 \cdot y0\right)\\ \mathbf{elif}\;y4 \leq 5.2 \cdot 10^{+69}:\\ \;\;\;\;\left(\mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right) \cdot y5\right) \cdot a\\ \mathbf{elif}\;y4 \leq 5 \cdot 10^{+263}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y, \left(-t\right) \cdot j\right) \cdot i\right) \cdot y5\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right) \cdot y4\right) \cdot y1\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 35.1% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -4.1 \cdot 10^{+43}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y, \left(-t\right) \cdot j\right) \cdot i\right) \cdot y5\\ \mathbf{elif}\;i \leq -2.6 \cdot 10^{-69}:\\ \;\;\;\;\left(\mathsf{fma}\left(x, y, \left(-t\right) \cdot z\right) \cdot b\right) \cdot a\\ \mathbf{elif}\;i \leq 2 \cdot 10^{-298}:\\ \;\;\;\;\left(\mathsf{fma}\left(-x, y1, y5 \cdot t\right) \cdot y2\right) \cdot a\\ \mathbf{elif}\;i \leq 1.35 \cdot 10^{-176}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot j - y2 \cdot k, y5, \left(\left(-x\right) \cdot j\right) \cdot b\right) \cdot y0\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{+251}:\\ \;\;\;\;\mathsf{fma}\left(y5 \cdot i - y4 \cdot b, k, \mathsf{fma}\left(-y3, y5, b \cdot x\right) \cdot a\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y5, \left(-c\right) \cdot x\right) \cdot i\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= i -4.1e+43)
   (* (* (fma k y (* (- t) j)) i) y5)
   (if (<= i -2.6e-69)
     (* (* (fma x y (* (- t) z)) b) a)
     (if (<= i 2e-298)
       (* (* (fma (- x) y1 (* y5 t)) y2) a)
       (if (<= i 1.35e-176)
         (* (fma (- (* y3 j) (* y2 k)) y5 (* (* (- x) j) b)) y0)
         (if (<= i 1.1e+251)
           (* (fma (- (* y5 i) (* y4 b)) k (* (fma (- y3) y5 (* b x)) a)) y)
           (* (* (fma k y5 (* (- c) x)) i) y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (i <= -4.1e+43) {
		tmp = (fma(k, y, (-t * j)) * i) * y5;
	} else if (i <= -2.6e-69) {
		tmp = (fma(x, y, (-t * z)) * b) * a;
	} else if (i <= 2e-298) {
		tmp = (fma(-x, y1, (y5 * t)) * y2) * a;
	} else if (i <= 1.35e-176) {
		tmp = fma(((y3 * j) - (y2 * k)), y5, ((-x * j) * b)) * y0;
	} else if (i <= 1.1e+251) {
		tmp = fma(((y5 * i) - (y4 * b)), k, (fma(-y3, y5, (b * x)) * a)) * y;
	} else {
		tmp = (fma(k, y5, (-c * x)) * i) * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (i <= -4.1e+43)
		tmp = Float64(Float64(fma(k, y, Float64(Float64(-t) * j)) * i) * y5);
	elseif (i <= -2.6e-69)
		tmp = Float64(Float64(fma(x, y, Float64(Float64(-t) * z)) * b) * a);
	elseif (i <= 2e-298)
		tmp = Float64(Float64(fma(Float64(-x), y1, Float64(y5 * t)) * y2) * a);
	elseif (i <= 1.35e-176)
		tmp = Float64(fma(Float64(Float64(y3 * j) - Float64(y2 * k)), y5, Float64(Float64(Float64(-x) * j) * b)) * y0);
	elseif (i <= 1.1e+251)
		tmp = Float64(fma(Float64(Float64(y5 * i) - Float64(y4 * b)), k, Float64(fma(Float64(-y3), y5, Float64(b * x)) * a)) * y);
	else
		tmp = Float64(Float64(fma(k, y5, Float64(Float64(-c) * x)) * i) * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[i, -4.1e+43], N[(N[(N[(k * y + N[((-t) * j), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision] * y5), $MachinePrecision], If[LessEqual[i, -2.6e-69], N[(N[(N[(x * y + N[((-t) * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[i, 2e-298], N[(N[(N[((-x) * y1 + N[(y5 * t), $MachinePrecision]), $MachinePrecision] * y2), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[i, 1.35e-176], N[(N[(N[(N[(y3 * j), $MachinePrecision] - N[(y2 * k), $MachinePrecision]), $MachinePrecision] * y5 + N[(N[((-x) * j), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] * y0), $MachinePrecision], If[LessEqual[i, 1.1e+251], N[(N[(N[(N[(y5 * i), $MachinePrecision] - N[(y4 * b), $MachinePrecision]), $MachinePrecision] * k + N[(N[((-y3) * y5 + N[(b * x), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], N[(N[(N[(k * y5 + N[((-c) * x), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision] * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -4.1e43

   1. Initial program 29.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

   5. Applied rewrites 54.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(j \cdot t - k \cdot y\right), i, \mathsf{fma}\left(-y0, k \cdot y2 - j \cdot y3, \left(t \cdot y2 - y \cdot y3\right) \cdot a\right)\right) \cdot y5} \]

   6. Taylor expanded in i around inf

      \[\leadsto \left(i \cdot \left(k \cdot y - j \cdot t\right)\right) \cdot y5 \]
   7. Step-by-step derivation

   8. Applied rewrites 56.6%

      \[\leadsto \left(i \cdot \mathsf{fma}\left(k, y, \left(-j\right) \cdot t\right)\right) \cdot y5 \]

   if -4.1e43 < i < -2.6000000000000002e-69

   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 a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot a} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot a} \]

   5. Applied rewrites 59.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), y1, \mathsf{fma}\left(y \cdot x - t \cdot z, b, \left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]

   6. Taylor expanded in b around inf

      \[\leadsto \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) \cdot a \]
   7. Step-by-step derivation

   8. Applied rewrites 54.9%

      \[\leadsto \left(b \cdot \mathsf{fma}\left(x, y, \left(-t\right) \cdot z\right)\right) \cdot a \]

   if -2.6000000000000002e-69 < i < 1.99999999999999982e-298

   1. Initial program 40.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot a} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot a} \]

   5. Applied rewrites 56.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), y1, \mathsf{fma}\left(y \cdot x - t \cdot z, b, \left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto \left(y2 \cdot \left(-1 \cdot \left(x \cdot y1\right) + t \cdot y5\right)\right) \cdot a \]
   7. Step-by-step derivation

   8. Applied rewrites 48.2%

      \[\leadsto \left(y2 \cdot \mathsf{fma}\left(-x, y1, t \cdot y5\right)\right) \cdot a \]

   if 1.99999999999999982e-298 < i < 1.3499999999999999e-176

   1. Initial program 22.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y0} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y0} \]

   5. Applied rewrites 55.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(k \cdot y2 - j \cdot y3\right), y5, \mathsf{fma}\left(c, y2 \cdot x - z \cdot y3, \left(-b\right) \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y0} \]

   6. Taylor expanded in j around inf

      \[\leadsto \mathsf{fma}\left(-\left(k \cdot y2 - j \cdot y3\right), y5, -1 \cdot \left(b \cdot \left(j \cdot x\right)\right)\right) \cdot y0 \]
   7. Step-by-step derivation

   8. Applied rewrites 55.9%

      \[\leadsto \mathsf{fma}\left(-\left(k \cdot y2 - j \cdot y3\right), y5, -b \cdot \left(j \cdot x\right)\right) \cdot y0 \]

   if 1.3499999999999999e-176 < i < 1.1e251

   1. Initial program 30.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 57.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - c \cdot i, x, \left(c \cdot y4 - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, a \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 56.2%

      \[\leadsto \mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, a \cdot \mathsf{fma}\left(-y3, y5, b \cdot x\right)\right) \cdot y \]

   if 1.1e251 < i

   1. Initial program 7.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 21.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - c \cdot i, x, \left(c \cdot y4 - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in i around inf

      \[\leadsto \left(i \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 64.5%

      \[\leadsto \left(i \cdot \mathsf{fma}\left(k, y5, -c \cdot x\right)\right) \cdot y \]
3. Recombined 6 regimes into one program.

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4.1 \cdot 10^{+43}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y, \left(-t\right) \cdot j\right) \cdot i\right) \cdot y5\\ \mathbf{elif}\;i \leq -2.6 \cdot 10^{-69}:\\ \;\;\;\;\left(\mathsf{fma}\left(x, y, \left(-t\right) \cdot z\right) \cdot b\right) \cdot a\\ \mathbf{elif}\;i \leq 2 \cdot 10^{-298}:\\ \;\;\;\;\left(\mathsf{fma}\left(-x, y1, y5 \cdot t\right) \cdot y2\right) \cdot a\\ \mathbf{elif}\;i \leq 1.35 \cdot 10^{-176}:\\ \;\;\;\;\mathsf{fma}\left(y3 \cdot j - y2 \cdot k, y5, \left(\left(-x\right) \cdot j\right) \cdot b\right) \cdot y0\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{+251}:\\ \;\;\;\;\mathsf{fma}\left(y5 \cdot i - y4 \cdot b, k, \mathsf{fma}\left(-y3, y5, b \cdot x\right) \cdot a\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y5, \left(-c\right) \cdot x\right) \cdot i\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 29.6% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\mathsf{fma}\left(-i, t, y3 \cdot y0\right) \cdot y5\right) \cdot j\\ t_2 := \left(-y\right) \cdot y3\\ \mathbf{if}\;y3 \leq -3.8 \cdot 10^{+230}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y3 \leq -1.7 \cdot 10^{+184}:\\ \;\;\;\;\left(\mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right) \cdot y1\right) \cdot a\\ \mathbf{elif}\;y3 \leq -1.95 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y3 \leq -5.8 \cdot 10^{-123}:\\ \;\;\;\;\left(a \cdot t\right) \cdot \mathsf{fma}\left(-b, z, y5 \cdot y2\right)\\ \mathbf{elif}\;y3 \leq -1.1 \cdot 10^{-214}:\\ \;\;\;\;\left(\mathsf{fma}\left(j, x, \left(-k\right) \cdot z\right) \cdot y1\right) \cdot i\\ \mathbf{elif}\;y3 \leq -2 \cdot 10^{-256}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y, \left(-t\right) \cdot j\right) \cdot i\right) \cdot y5\\ \mathbf{elif}\;y3 \leq 1.1 \cdot 10^{+18}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, z, y4 \cdot y2\right) \cdot y1\right) \cdot k\\ \mathbf{elif}\;y3 \leq 1.3 \cdot 10^{+216}:\\ \;\;\;\;\left(\mathsf{fma}\left(t, y2, t\_2\right) \cdot y5\right) \cdot a\\ \mathbf{elif}\;y3 \leq 1.25 \cdot 10^{+257}:\\ \;\;\;\;\left(\left(b \cdot y\right) \cdot a\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(t\_2 \cdot y5\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* (fma (- i) t (* y3 y0)) y5) j)) (t_2 (* (- y) y3)))
   (if (<= y3 -3.8e+230)
     t_1
     (if (<= y3 -1.7e+184)
       (* (* (fma y3 z (* (- x) y2)) y1) a)
       (if (<= y3 -1.95e+34)
         t_1
         (if (<= y3 -5.8e-123)
           (* (* a t) (fma (- b) z (* y5 y2)))
           (if (<= y3 -1.1e-214)
             (* (* (fma j x (* (- k) z)) y1) i)
             (if (<= y3 -2e-256)
               (* (* (fma k y (* (- t) j)) i) y5)
               (if (<= y3 1.1e+18)
                 (* (* (fma (- i) z (* y4 y2)) y1) k)
                 (if (<= y3 1.3e+216)
                   (* (* (fma t y2 t_2) y5) a)
                   (if (<= y3 1.25e+257)
                     (* (* (* b y) a) x)
                     (* (* t_2 y5) 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 = (fma(-i, t, (y3 * y0)) * y5) * j;
	double t_2 = -y * y3;
	double tmp;
	if (y3 <= -3.8e+230) {
		tmp = t_1;
	} else if (y3 <= -1.7e+184) {
		tmp = (fma(y3, z, (-x * y2)) * y1) * a;
	} else if (y3 <= -1.95e+34) {
		tmp = t_1;
	} else if (y3 <= -5.8e-123) {
		tmp = (a * t) * fma(-b, z, (y5 * y2));
	} else if (y3 <= -1.1e-214) {
		tmp = (fma(j, x, (-k * z)) * y1) * i;
	} else if (y3 <= -2e-256) {
		tmp = (fma(k, y, (-t * j)) * i) * y5;
	} else if (y3 <= 1.1e+18) {
		tmp = (fma(-i, z, (y4 * y2)) * y1) * k;
	} else if (y3 <= 1.3e+216) {
		tmp = (fma(t, y2, t_2) * y5) * a;
	} else if (y3 <= 1.25e+257) {
		tmp = ((b * y) * a) * x;
	} else {
		tmp = (t_2 * y5) * 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(fma(Float64(-i), t, Float64(y3 * y0)) * y5) * j)
	t_2 = Float64(Float64(-y) * y3)
	tmp = 0.0
	if (y3 <= -3.8e+230)
		tmp = t_1;
	elseif (y3 <= -1.7e+184)
		tmp = Float64(Float64(fma(y3, z, Float64(Float64(-x) * y2)) * y1) * a);
	elseif (y3 <= -1.95e+34)
		tmp = t_1;
	elseif (y3 <= -5.8e-123)
		tmp = Float64(Float64(a * t) * fma(Float64(-b), z, Float64(y5 * y2)));
	elseif (y3 <= -1.1e-214)
		tmp = Float64(Float64(fma(j, x, Float64(Float64(-k) * z)) * y1) * i);
	elseif (y3 <= -2e-256)
		tmp = Float64(Float64(fma(k, y, Float64(Float64(-t) * j)) * i) * y5);
	elseif (y3 <= 1.1e+18)
		tmp = Float64(Float64(fma(Float64(-i), z, Float64(y4 * y2)) * y1) * k);
	elseif (y3 <= 1.3e+216)
		tmp = Float64(Float64(fma(t, y2, t_2) * y5) * a);
	elseif (y3 <= 1.25e+257)
		tmp = Float64(Float64(Float64(b * y) * a) * x);
	else
		tmp = Float64(Float64(t_2 * y5) * a);
	end
	return 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[(N[((-i) * t + N[(y3 * y0), $MachinePrecision]), $MachinePrecision] * y5), $MachinePrecision] * j), $MachinePrecision]}, Block[{t$95$2 = N[((-y) * y3), $MachinePrecision]}, If[LessEqual[y3, -3.8e+230], t$95$1, If[LessEqual[y3, -1.7e+184], N[(N[(N[(y3 * z + N[((-x) * y2), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[y3, -1.95e+34], t$95$1, If[LessEqual[y3, -5.8e-123], N[(N[(a * t), $MachinePrecision] * N[((-b) * z + N[(y5 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -1.1e-214], N[(N[(N[(j * x + N[((-k) * z), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision] * i), $MachinePrecision], If[LessEqual[y3, -2e-256], N[(N[(N[(k * y + N[((-t) * j), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision] * y5), $MachinePrecision], If[LessEqual[y3, 1.1e+18], N[(N[(N[((-i) * z + N[(y4 * y2), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision] * k), $MachinePrecision], If[LessEqual[y3, 1.3e+216], N[(N[(N[(t * y2 + t$95$2), $MachinePrecision] * y5), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[y3, 1.25e+257], N[(N[(N[(b * y), $MachinePrecision] * a), $MachinePrecision] * x), $MachinePrecision], N[(N[(t$95$2 * y5), $MachinePrecision] * a), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y3 < -3.8e230 or -1.7000000000000001e184 < y3 < -1.9500000000000001e34

   1. Initial program 31.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

   5. Applied rewrites 53.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(j \cdot t - k \cdot y\right), i, \mathsf{fma}\left(-y0, k \cdot y2 - j \cdot y3, \left(t \cdot y2 - y \cdot y3\right) \cdot a\right)\right) \cdot y5} \]

   6. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 32.7%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right)\right)} \]

   9. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 52.1%

       \[\leadsto j \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(-i, t, y0 \cdot y3\right)\right)} \]

   if -3.8e230 < y3 < -1.7000000000000001e184

   1. Initial program 27.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 45.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 63.7%

      \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right)\right)} \]

   if -1.9500000000000001e34 < y3 < -5.80000000000000007e-123

   1. Initial program 33.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot a} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot a} \]

   5. Applied rewrites 52.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), y1, \mathsf{fma}\left(y \cdot x - t \cdot z, b, \left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]

   6. Taylor expanded in t around inf

      \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(-1 \cdot \left(b \cdot z\right) + y2 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 47.4%

      \[\leadsto \left(a \cdot t\right) \cdot \color{blue}{\mathsf{fma}\left(-b, z, y2 \cdot y5\right)} \]

   if -5.80000000000000007e-123 < y3 < -1.10000000000000001e-214

   1. Initial program 40.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 55.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in i around inf

      \[\leadsto i \cdot \color{blue}{\left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 59.7%

      \[\leadsto i \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(j, x, \left(-k\right) \cdot z\right)\right)} \]

   if -1.10000000000000001e-214 < y3 < -1.99999999999999995e-256

   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 y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

   5. Applied rewrites 51.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(j \cdot t - k \cdot y\right), i, \mathsf{fma}\left(-y0, k \cdot y2 - j \cdot y3, \left(t \cdot y2 - y \cdot y3\right) \cdot a\right)\right) \cdot y5} \]

   6. Taylor expanded in i around inf

      \[\leadsto \left(i \cdot \left(k \cdot y - j \cdot t\right)\right) \cdot y5 \]
   7. Step-by-step derivation

   8. Applied rewrites 51.0%

      \[\leadsto \left(i \cdot \mathsf{fma}\left(k, y, \left(-j\right) \cdot t\right)\right) \cdot y5 \]

   if -1.99999999999999995e-256 < y3 < 1.1e18

   1. Initial program 32.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 44.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 15.4%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-1, y3 \cdot y4, i \cdot x\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto k \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(i \cdot z\right) + y2 \cdot y4\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 47.0%

       \[\leadsto k \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-i, z, y2 \cdot y4\right)\right)} \]

   if 1.1e18 < y3 < 1.2999999999999999e216

   1. Initial program 28.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

   5. Applied rewrites 50.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(j \cdot t - k \cdot y\right), i, \mathsf{fma}\left(-y0, k \cdot y2 - j \cdot y3, \left(t \cdot y2 - y \cdot y3\right) \cdot a\right)\right) \cdot y5} \]

   6. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 44.5%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right)\right)} \]

   if 1.2999999999999999e216 < y3 < 1.25000000000000007e257

   1. Initial program 0.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot x} \]

   5. Applied rewrites 50.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot a - c \cdot i, y, \mathsf{fma}\left(c \cdot y0 - y1 \cdot a, y2, \left(-j\right) \cdot \left(y0 \cdot b - i \cdot y1\right)\right)\right) \cdot x} \]

   6. Taylor expanded in y around inf

      \[\leadsto \left(y \cdot \left(a \cdot b - c \cdot i\right)\right) \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 66.7%

      \[\leadsto \left(y \cdot \mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right)\right) \cdot x \]

   9. Taylor expanded in c around 0

      \[\leadsto \left(a \cdot \left(b \cdot y\right)\right) \cdot x \]
   10. Step-by-step derivation

   11. Applied rewrites 84.1%

       \[\leadsto \left(a \cdot \left(b \cdot y\right)\right) \cdot x \]

   if 1.25000000000000007e257 < y3

   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 y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

   5. Applied rewrites 41.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(j \cdot t - k \cdot y\right), i, \mathsf{fma}\left(-y0, k \cdot y2 - j \cdot y3, \left(t \cdot y2 - y \cdot y3\right) \cdot a\right)\right) \cdot y5} \]

   6. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 75.6%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right)\right)} \]

   9. Taylor expanded in t around 0

      \[\leadsto a \cdot \left(-1 \cdot \left(y \cdot \color{blue}{\left(y3 \cdot y5\right)}\right)\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 75.6%

       \[\leadsto a \cdot \left(-\left(y \cdot y3\right) \cdot y5\right) \]
3. Recombined 9 regimes into one program.

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -3.8 \cdot 10^{+230}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, t, y3 \cdot y0\right) \cdot y5\right) \cdot j\\ \mathbf{elif}\;y3 \leq -1.7 \cdot 10^{+184}:\\ \;\;\;\;\left(\mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right) \cdot y1\right) \cdot a\\ \mathbf{elif}\;y3 \leq -1.95 \cdot 10^{+34}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, t, y3 \cdot y0\right) \cdot y5\right) \cdot j\\ \mathbf{elif}\;y3 \leq -5.8 \cdot 10^{-123}:\\ \;\;\;\;\left(a \cdot t\right) \cdot \mathsf{fma}\left(-b, z, y5 \cdot y2\right)\\ \mathbf{elif}\;y3 \leq -1.1 \cdot 10^{-214}:\\ \;\;\;\;\left(\mathsf{fma}\left(j, x, \left(-k\right) \cdot z\right) \cdot y1\right) \cdot i\\ \mathbf{elif}\;y3 \leq -2 \cdot 10^{-256}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y, \left(-t\right) \cdot j\right) \cdot i\right) \cdot y5\\ \mathbf{elif}\;y3 \leq 1.1 \cdot 10^{+18}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, z, y4 \cdot y2\right) \cdot y1\right) \cdot k\\ \mathbf{elif}\;y3 \leq 1.3 \cdot 10^{+216}:\\ \;\;\;\;\left(\mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right) \cdot y5\right) \cdot a\\ \mathbf{elif}\;y3 \leq 1.25 \cdot 10^{+257}:\\ \;\;\;\;\left(\left(b \cdot y\right) \cdot a\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(-y\right) \cdot y3\right) \cdot y5\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 31.0% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right) \cdot y4\right) \cdot y1\\ t_2 := \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right)\\ t_3 := \left(\mathsf{fma}\left(-i, k, y3 \cdot a\right) \cdot z\right) \cdot y1\\ \mathbf{if}\;y4 \leq -7.6 \cdot 10^{-40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq -1.55 \cdot 10^{-101}:\\ \;\;\;\;\left(\mathsf{fma}\left(x, y, \left(-t\right) \cdot z\right) \cdot b\right) \cdot a\\ \mathbf{elif}\;y4 \leq -2 \cdot 10^{-207}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y4 \leq -5 \cdot 10^{-270}:\\ \;\;\;\;\left(t\_2 \cdot a\right) \cdot y5\\ \mathbf{elif}\;y4 \leq 7.4 \cdot 10^{-99}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y4 \leq 1.2 \cdot 10^{+27}:\\ \;\;\;\;\mathsf{fma}\left(c, x, \left(-y5\right) \cdot k\right) \cdot \left(y2 \cdot y0\right)\\ \mathbf{elif}\;y4 \leq 5.2 \cdot 10^{+69}:\\ \;\;\;\;\left(t\_2 \cdot y5\right) \cdot a\\ \mathbf{elif}\;y4 \leq 5 \cdot 10^{+263}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y, \left(-t\right) \cdot j\right) \cdot i\right) \cdot y5\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* (fma k y2 (* (- j) y3)) y4) y1))
        (t_2 (fma t y2 (* (- y) y3)))
        (t_3 (* (* (fma (- i) k (* y3 a)) z) y1)))
   (if (<= y4 -7.6e-40)
     t_1
     (if (<= y4 -1.55e-101)
       (* (* (fma x y (* (- t) z)) b) a)
       (if (<= y4 -2e-207)
         t_3
         (if (<= y4 -5e-270)
           (* (* t_2 a) y5)
           (if (<= y4 7.4e-99)
             t_3
             (if (<= y4 1.2e+27)
               (* (fma c x (* (- y5) k)) (* y2 y0))
               (if (<= y4 5.2e+69)
                 (* (* t_2 y5) a)
                 (if (<= y4 5e+263)
                   (* (* (fma k y (* (- t) j)) i) y5)
                   t_1))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (fma(k, y2, (-j * y3)) * y4) * y1;
	double t_2 = fma(t, y2, (-y * y3));
	double t_3 = (fma(-i, k, (y3 * a)) * z) * y1;
	double tmp;
	if (y4 <= -7.6e-40) {
		tmp = t_1;
	} else if (y4 <= -1.55e-101) {
		tmp = (fma(x, y, (-t * z)) * b) * a;
	} else if (y4 <= -2e-207) {
		tmp = t_3;
	} else if (y4 <= -5e-270) {
		tmp = (t_2 * a) * y5;
	} else if (y4 <= 7.4e-99) {
		tmp = t_3;
	} else if (y4 <= 1.2e+27) {
		tmp = fma(c, x, (-y5 * k)) * (y2 * y0);
	} else if (y4 <= 5.2e+69) {
		tmp = (t_2 * y5) * a;
	} else if (y4 <= 5e+263) {
		tmp = (fma(k, y, (-t * j)) * i) * y5;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(fma(k, y2, Float64(Float64(-j) * y3)) * y4) * y1)
	t_2 = fma(t, y2, Float64(Float64(-y) * y3))
	t_3 = Float64(Float64(fma(Float64(-i), k, Float64(y3 * a)) * z) * y1)
	tmp = 0.0
	if (y4 <= -7.6e-40)
		tmp = t_1;
	elseif (y4 <= -1.55e-101)
		tmp = Float64(Float64(fma(x, y, Float64(Float64(-t) * z)) * b) * a);
	elseif (y4 <= -2e-207)
		tmp = t_3;
	elseif (y4 <= -5e-270)
		tmp = Float64(Float64(t_2 * a) * y5);
	elseif (y4 <= 7.4e-99)
		tmp = t_3;
	elseif (y4 <= 1.2e+27)
		tmp = Float64(fma(c, x, Float64(Float64(-y5) * k)) * Float64(y2 * y0));
	elseif (y4 <= 5.2e+69)
		tmp = Float64(Float64(t_2 * y5) * a);
	elseif (y4 <= 5e+263)
		tmp = Float64(Float64(fma(k, y, Float64(Float64(-t) * j)) * i) * y5);
	else
		tmp = t_1;
	end
	return 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[(N[(k * y2 + N[((-j) * y3), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision] * y1), $MachinePrecision]}, Block[{t$95$2 = N[(t * y2 + N[((-y) * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[((-i) * k + N[(y3 * a), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] * y1), $MachinePrecision]}, If[LessEqual[y4, -7.6e-40], t$95$1, If[LessEqual[y4, -1.55e-101], N[(N[(N[(x * y + N[((-t) * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[y4, -2e-207], t$95$3, If[LessEqual[y4, -5e-270], N[(N[(t$95$2 * a), $MachinePrecision] * y5), $MachinePrecision], If[LessEqual[y4, 7.4e-99], t$95$3, If[LessEqual[y4, 1.2e+27], N[(N[(c * x + N[((-y5) * k), $MachinePrecision]), $MachinePrecision] * N[(y2 * y0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 5.2e+69], N[(N[(t$95$2 * y5), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[y4, 5e+263], N[(N[(N[(k * y + N[((-t) * j), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision] * y5), $MachinePrecision], t$95$1]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y4 < -7.5999999999999998e-40 or 5.00000000000000022e263 < y4

   1. Initial program 27.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 47.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in y4 around inf

      \[\leadsto \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \cdot y1 \]
   7. Step-by-step derivation

   8. Applied rewrites 48.3%

      \[\leadsto \left(y4 \cdot \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right)\right) \cdot y1 \]

   if -7.5999999999999998e-40 < y4 < -1.54999999999999987e-101

   1. Initial program 45.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot a} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot a} \]

   5. Applied rewrites 55.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), y1, \mathsf{fma}\left(y \cdot x - t \cdot z, b, \left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]

   6. Taylor expanded in b around inf

      \[\leadsto \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) \cdot a \]
   7. Step-by-step derivation

   8. Applied rewrites 76.2%

      \[\leadsto \left(b \cdot \mathsf{fma}\left(x, y, \left(-t\right) \cdot z\right)\right) \cdot a \]

   if -1.54999999999999987e-101 < y4 < -1.99999999999999985e-207 or -4.9999999999999998e-270 < y4 < 7.400000000000001e-99

   1. Initial program 32.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 44.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 21.9%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-1, y3 \cdot y4, i \cdot x\right)\right)} \]

   9. Taylor expanded in z around inf

      \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(i \cdot k\right) + a \cdot y3\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 54.7%

       \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \mathsf{fma}\left(-i, k, a \cdot y3\right)\right)} \]

   if -1.99999999999999985e-207 < y4 < -4.9999999999999998e-270

   1. Initial program 59.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

   5. Applied rewrites 49.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(j \cdot t - k \cdot y\right), i, \mathsf{fma}\left(-y0, k \cdot y2 - j \cdot y3, \left(t \cdot y2 - y \cdot y3\right) \cdot a\right)\right) \cdot y5} \]

   6. Taylor expanded in a around inf

      \[\leadsto \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y5 \]
   7. Step-by-step derivation

   8. Applied rewrites 61.3%

      \[\leadsto \left(a \cdot \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right)\right) \cdot y5 \]

   if 7.400000000000001e-99 < y4 < 1.19999999999999999e27

   1. Initial program 19.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Applied rewrites 54.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y4 \cdot y1 - y0 \cdot y5, k, \mathsf{fma}\left(c \cdot y0 - y1 \cdot a, x, \left(-t\right) \cdot \left(c \cdot y4 - y5 \cdot a\right)\right)\right) \cdot y2} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto y0 \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(k \cdot y5\right) + c \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 45.3%

      \[\leadsto \left(y0 \cdot y2\right) \cdot \color{blue}{\mathsf{fma}\left(c, x, -k \cdot y5\right)} \]

   if 1.19999999999999999e27 < y4 < 5.2000000000000004e69

   1. Initial program 0.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

   5. Applied rewrites 56.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(j \cdot t - k \cdot y\right), i, \mathsf{fma}\left(-y0, k \cdot y2 - j \cdot y3, \left(t \cdot y2 - y \cdot y3\right) \cdot a\right)\right) \cdot y5} \]

   6. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 56.3%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right)\right)} \]

   if 5.2000000000000004e69 < y4 < 5.00000000000000022e263

   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 y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

   5. Applied rewrites 57.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(j \cdot t - k \cdot y\right), i, \mathsf{fma}\left(-y0, k \cdot y2 - j \cdot y3, \left(t \cdot y2 - y \cdot y3\right) \cdot a\right)\right) \cdot y5} \]

   6. Taylor expanded in i around inf

      \[\leadsto \left(i \cdot \left(k \cdot y - j \cdot t\right)\right) \cdot y5 \]
   7. Step-by-step derivation

   8. Applied rewrites 48.2%

      \[\leadsto \left(i \cdot \mathsf{fma}\left(k, y, \left(-j\right) \cdot t\right)\right) \cdot y5 \]
3. Recombined 7 regimes into one program.

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -7.6 \cdot 10^{-40}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right) \cdot y4\right) \cdot y1\\ \mathbf{elif}\;y4 \leq -1.55 \cdot 10^{-101}:\\ \;\;\;\;\left(\mathsf{fma}\left(x, y, \left(-t\right) \cdot z\right) \cdot b\right) \cdot a\\ \mathbf{elif}\;y4 \leq -2 \cdot 10^{-207}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, k, y3 \cdot a\right) \cdot z\right) \cdot y1\\ \mathbf{elif}\;y4 \leq -5 \cdot 10^{-270}:\\ \;\;\;\;\left(\mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right) \cdot a\right) \cdot y5\\ \mathbf{elif}\;y4 \leq 7.4 \cdot 10^{-99}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, k, y3 \cdot a\right) \cdot z\right) \cdot y1\\ \mathbf{elif}\;y4 \leq 1.2 \cdot 10^{+27}:\\ \;\;\;\;\mathsf{fma}\left(c, x, \left(-y5\right) \cdot k\right) \cdot \left(y2 \cdot y0\right)\\ \mathbf{elif}\;y4 \leq 5.2 \cdot 10^{+69}:\\ \;\;\;\;\left(\mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right) \cdot y5\right) \cdot a\\ \mathbf{elif}\;y4 \leq 5 \cdot 10^{+263}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y, \left(-t\right) \cdot j\right) \cdot i\right) \cdot y5\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right) \cdot y4\right) \cdot y1\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 32.7% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right) \cdot y4\right) \cdot y1\\ t_2 := \left(\mathsf{fma}\left(-y3, y5, b \cdot x\right) \cdot a\right) \cdot y\\ t_3 := \mathsf{fma}\left(-b, z, y5 \cdot y2\right)\\ \mathbf{if}\;a \leq -7.8 \cdot 10^{-38}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-54}:\\ \;\;\;\;\left(a \cdot t\right) \cdot t\_3\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-83}:\\ \;\;\;\;\mathsf{fma}\left(i, y, \left(-y0\right) \cdot y2\right) \cdot \left(y5 \cdot k\right)\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-205}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-211}:\\ \;\;\;\;\left(\mathsf{fma}\left(j, x, \left(-k\right) \cdot z\right) \cdot y1\right) \cdot i\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-117}:\\ \;\;\;\;\left(t\_3 \cdot t\right) \cdot a\\ \mathbf{elif}\;a \leq 31000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* (fma k y2 (* (- j) y3)) y4) y1))
        (t_2 (* (* (fma (- y3) y5 (* b x)) a) y))
        (t_3 (fma (- b) z (* y5 y2))))
   (if (<= a -7.8e-38)
     t_2
     (if (<= a -5.2e-54)
       (* (* a t) t_3)
       (if (<= a -2.7e-83)
         (* (fma i y (* (- y0) y2)) (* y5 k))
         (if (<= a -2.2e-205)
           t_1
           (if (<= a 1.5e-211)
             (* (* (fma j x (* (- k) z)) y1) i)
             (if (<= a 1.9e-117)
               (* (* t_3 t) a)
               (if (<= a 31000000000.0) 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 = (fma(k, y2, (-j * y3)) * y4) * y1;
	double t_2 = (fma(-y3, y5, (b * x)) * a) * y;
	double t_3 = fma(-b, z, (y5 * y2));
	double tmp;
	if (a <= -7.8e-38) {
		tmp = t_2;
	} else if (a <= -5.2e-54) {
		tmp = (a * t) * t_3;
	} else if (a <= -2.7e-83) {
		tmp = fma(i, y, (-y0 * y2)) * (y5 * k);
	} else if (a <= -2.2e-205) {
		tmp = t_1;
	} else if (a <= 1.5e-211) {
		tmp = (fma(j, x, (-k * z)) * y1) * i;
	} else if (a <= 1.9e-117) {
		tmp = (t_3 * t) * a;
	} else if (a <= 31000000000.0) {
		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(Float64(fma(k, y2, Float64(Float64(-j) * y3)) * y4) * y1)
	t_2 = Float64(Float64(fma(Float64(-y3), y5, Float64(b * x)) * a) * y)
	t_3 = fma(Float64(-b), z, Float64(y5 * y2))
	tmp = 0.0
	if (a <= -7.8e-38)
		tmp = t_2;
	elseif (a <= -5.2e-54)
		tmp = Float64(Float64(a * t) * t_3);
	elseif (a <= -2.7e-83)
		tmp = Float64(fma(i, y, Float64(Float64(-y0) * y2)) * Float64(y5 * k));
	elseif (a <= -2.2e-205)
		tmp = t_1;
	elseif (a <= 1.5e-211)
		tmp = Float64(Float64(fma(j, x, Float64(Float64(-k) * z)) * y1) * i);
	elseif (a <= 1.9e-117)
		tmp = Float64(Float64(t_3 * t) * a);
	elseif (a <= 31000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return 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[(N[(k * y2 + N[((-j) * y3), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision] * y1), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[((-y3) * y5 + N[(b * x), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$3 = N[((-b) * z + N[(y5 * y2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.8e-38], t$95$2, If[LessEqual[a, -5.2e-54], N[(N[(a * t), $MachinePrecision] * t$95$3), $MachinePrecision], If[LessEqual[a, -2.7e-83], N[(N[(i * y + N[((-y0) * y2), $MachinePrecision]), $MachinePrecision] * N[(y5 * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.2e-205], t$95$1, If[LessEqual[a, 1.5e-211], N[(N[(N[(j * x + N[((-k) * z), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision] * i), $MachinePrecision], If[LessEqual[a, 1.9e-117], N[(N[(t$95$3 * t), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[a, 31000000000.0], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -7.7999999999999998e-38 or 3.1e10 < a

   1. Initial program 23.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 43.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - c \cdot i, x, \left(c \cdot y4 - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in a around inf

      \[\leadsto \left(a \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 47.7%

      \[\leadsto \left(a \cdot \mathsf{fma}\left(-y3, y5, b \cdot x\right)\right) \cdot y \]

   if -7.7999999999999998e-38 < a < -5.20000000000000004e-54

   1. Initial program 40.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot a} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot a} \]

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), y1, \mathsf{fma}\left(y \cdot x - t \cdot z, b, \left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]

   6. Taylor expanded in t around inf

      \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(-1 \cdot \left(b \cdot z\right) + y2 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 100.0%

      \[\leadsto \left(a \cdot t\right) \cdot \color{blue}{\mathsf{fma}\left(-b, z, y2 \cdot y5\right)} \]

   if -5.20000000000000004e-54 < a < -2.69999999999999991e-83

   1. Initial program 20.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

   5. Applied rewrites 21.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(j \cdot t - k \cdot y\right), i, \mathsf{fma}\left(-y0, k \cdot y2 - j \cdot y3, \left(t \cdot y2 - y \cdot y3\right) \cdot a\right)\right) \cdot y5} \]

   6. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 2.0%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto k \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 80.0%

       \[\leadsto \left(k \cdot y5\right) \cdot \color{blue}{\mathsf{fma}\left(i, y, -y0 \cdot y2\right)} \]

   if -2.69999999999999991e-83 < a < -2.20000000000000009e-205 or 1.89999999999999986e-117 < a < 3.1e10

   1. Initial program 30.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 40.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in y4 around inf

      \[\leadsto \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \cdot y1 \]
   7. Step-by-step derivation

   8. Applied rewrites 55.0%

      \[\leadsto \left(y4 \cdot \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right)\right) \cdot y1 \]

   if -2.20000000000000009e-205 < a < 1.50000000000000002e-211

   1. Initial program 55.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 59.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in i around inf

      \[\leadsto i \cdot \color{blue}{\left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 52.2%

      \[\leadsto i \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(j, x, \left(-k\right) \cdot z\right)\right)} \]

   if 1.50000000000000002e-211 < a < 1.89999999999999986e-117

   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 a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot a} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot a} \]

   5. Applied rewrites 38.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), y1, \mathsf{fma}\left(y \cdot x - t \cdot z, b, \left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]

   6. Taylor expanded in t around inf

      \[\leadsto \left(t \cdot \left(-1 \cdot \left(b \cdot z\right) + y2 \cdot y5\right)\right) \cdot a \]
   7. Step-by-step derivation

   8. Applied rewrites 50.9%

      \[\leadsto \left(t \cdot \mathsf{fma}\left(-b, z, y2 \cdot y5\right)\right) \cdot a \]
3. Recombined 6 regimes into one program.

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{-38}:\\ \;\;\;\;\left(\mathsf{fma}\left(-y3, y5, b \cdot x\right) \cdot a\right) \cdot y\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-54}:\\ \;\;\;\;\left(a \cdot t\right) \cdot \mathsf{fma}\left(-b, z, y5 \cdot y2\right)\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-83}:\\ \;\;\;\;\mathsf{fma}\left(i, y, \left(-y0\right) \cdot y2\right) \cdot \left(y5 \cdot k\right)\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-205}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right) \cdot y4\right) \cdot y1\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-211}:\\ \;\;\;\;\left(\mathsf{fma}\left(j, x, \left(-k\right) \cdot z\right) \cdot y1\right) \cdot i\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-117}:\\ \;\;\;\;\left(\mathsf{fma}\left(-b, z, y5 \cdot y2\right) \cdot t\right) \cdot a\\ \mathbf{elif}\;a \leq 31000000000:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right) \cdot y4\right) \cdot y1\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(-y3, y5, b \cdot x\right) \cdot a\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 31: 26.1% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(i, y, \left(-y0\right) \cdot y2\right) \cdot \left(y5 \cdot k\right)\\ t_2 := \left(\mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right) \cdot y5\right) \cdot a\\ t_3 := \left(\mathsf{fma}\left(-i, t, y3 \cdot y0\right) \cdot y5\right) \cdot j\\ \mathbf{if}\;y5 \leq -2.8 \cdot 10^{+124}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y5 \leq -350:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y5 \leq -2.8 \cdot 10^{-93}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y5 \leq 2.8 \cdot 10^{-188}:\\ \;\;\;\;\left(\left(b \cdot y\right) \cdot a\right) \cdot x\\ \mathbf{elif}\;y5 \leq 7.5 \cdot 10^{+123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y5 \leq 8.5 \cdot 10^{+185}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y5 \leq 3.7 \cdot 10^{+239}:\\ \;\;\;\;\left(\mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right) \cdot y1\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (fma i y (* (- y0) y2)) (* y5 k)))
        (t_2 (* (* (fma t y2 (* (- y) y3)) y5) a))
        (t_3 (* (* (fma (- i) t (* y3 y0)) y5) j)))
   (if (<= y5 -2.8e+124)
     t_2
     (if (<= y5 -350.0)
       t_1
       (if (<= y5 -2.8e-93)
         t_2
         (if (<= y5 2.8e-188)
           (* (* (* b y) a) x)
           (if (<= y5 7.5e+123)
             t_1
             (if (<= y5 8.5e+185)
               t_3
               (if (<= y5 3.7e+239)
                 (* (* (fma y3 z (* (- x) y2)) y1) a)
                 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 = fma(i, y, (-y0 * y2)) * (y5 * k);
	double t_2 = (fma(t, y2, (-y * y3)) * y5) * a;
	double t_3 = (fma(-i, t, (y3 * y0)) * y5) * j;
	double tmp;
	if (y5 <= -2.8e+124) {
		tmp = t_2;
	} else if (y5 <= -350.0) {
		tmp = t_1;
	} else if (y5 <= -2.8e-93) {
		tmp = t_2;
	} else if (y5 <= 2.8e-188) {
		tmp = ((b * y) * a) * x;
	} else if (y5 <= 7.5e+123) {
		tmp = t_1;
	} else if (y5 <= 8.5e+185) {
		tmp = t_3;
	} else if (y5 <= 3.7e+239) {
		tmp = (fma(y3, z, (-x * y2)) * y1) * a;
	} 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(fma(i, y, Float64(Float64(-y0) * y2)) * Float64(y5 * k))
	t_2 = Float64(Float64(fma(t, y2, Float64(Float64(-y) * y3)) * y5) * a)
	t_3 = Float64(Float64(fma(Float64(-i), t, Float64(y3 * y0)) * y5) * j)
	tmp = 0.0
	if (y5 <= -2.8e+124)
		tmp = t_2;
	elseif (y5 <= -350.0)
		tmp = t_1;
	elseif (y5 <= -2.8e-93)
		tmp = t_2;
	elseif (y5 <= 2.8e-188)
		tmp = Float64(Float64(Float64(b * y) * a) * x);
	elseif (y5 <= 7.5e+123)
		tmp = t_1;
	elseif (y5 <= 8.5e+185)
		tmp = t_3;
	elseif (y5 <= 3.7e+239)
		tmp = Float64(Float64(fma(y3, z, Float64(Float64(-x) * y2)) * y1) * a);
	else
		tmp = t_3;
	end
	return 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 * y + N[((-y0) * y2), $MachinePrecision]), $MachinePrecision] * N[(y5 * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t * y2 + N[((-y) * y3), $MachinePrecision]), $MachinePrecision] * y5), $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[((-i) * t + N[(y3 * y0), $MachinePrecision]), $MachinePrecision] * y5), $MachinePrecision] * j), $MachinePrecision]}, If[LessEqual[y5, -2.8e+124], t$95$2, If[LessEqual[y5, -350.0], t$95$1, If[LessEqual[y5, -2.8e-93], t$95$2, If[LessEqual[y5, 2.8e-188], N[(N[(N[(b * y), $MachinePrecision] * a), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[y5, 7.5e+123], t$95$1, If[LessEqual[y5, 8.5e+185], t$95$3, If[LessEqual[y5, 3.7e+239], N[(N[(N[(y3 * z + N[((-x) * y2), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision] * a), $MachinePrecision], t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y5 < -2.8e124 or -350 < y5 < -2.79999999999999998e-93

   1. Initial program 23.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

   5. Applied rewrites 51.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(j \cdot t - k \cdot y\right), i, \mathsf{fma}\left(-y0, k \cdot y2 - j \cdot y3, \left(t \cdot y2 - y \cdot y3\right) \cdot a\right)\right) \cdot y5} \]

   6. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 53.7%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right)\right)} \]

   if -2.8e124 < y5 < -350 or 2.8000000000000001e-188 < y5 < 7.4999999999999999e123

   1. Initial program 29.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

   5. Applied rewrites 37.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(j \cdot t - k \cdot y\right), i, \mathsf{fma}\left(-y0, k \cdot y2 - j \cdot y3, \left(t \cdot y2 - y \cdot y3\right) \cdot a\right)\right) \cdot y5} \]

   6. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 23.1%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto k \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 35.9%

       \[\leadsto \left(k \cdot y5\right) \cdot \color{blue}{\mathsf{fma}\left(i, y, -y0 \cdot y2\right)} \]

   if -2.79999999999999998e-93 < y5 < 2.8000000000000001e-188

   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 x around inf

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot x} \]

   5. Applied rewrites 51.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot a - c \cdot i, y, \mathsf{fma}\left(c \cdot y0 - y1 \cdot a, y2, \left(-j\right) \cdot \left(y0 \cdot b - i \cdot y1\right)\right)\right) \cdot x} \]

   6. Taylor expanded in y around inf

      \[\leadsto \left(y \cdot \left(a \cdot b - c \cdot i\right)\right) \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 40.4%

      \[\leadsto \left(y \cdot \mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right)\right) \cdot x \]

   9. Taylor expanded in c around 0

      \[\leadsto \left(a \cdot \left(b \cdot y\right)\right) \cdot x \]
   10. Step-by-step derivation

   11. Applied rewrites 37.2%

       \[\leadsto \left(a \cdot \left(b \cdot y\right)\right) \cdot x \]

   if 7.4999999999999999e123 < y5 < 8.50000000000000013e185 or 3.69999999999999998e239 < y5

   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 y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

   5. Applied rewrites 66.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(j \cdot t - k \cdot y\right), i, \mathsf{fma}\left(-y0, k \cdot y2 - j \cdot y3, \left(t \cdot y2 - y \cdot y3\right) \cdot a\right)\right) \cdot y5} \]

   6. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 34.1%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right)\right)} \]

   9. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 63.9%

       \[\leadsto j \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(-i, t, y0 \cdot y3\right)\right)} \]

   if 8.50000000000000013e185 < y5 < 3.69999999999999998e239

   1. Initial program 25.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 51.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 51.3%

      \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -2.8 \cdot 10^{+124}:\\ \;\;\;\;\left(\mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right) \cdot y5\right) \cdot a\\ \mathbf{elif}\;y5 \leq -350:\\ \;\;\;\;\mathsf{fma}\left(i, y, \left(-y0\right) \cdot y2\right) \cdot \left(y5 \cdot k\right)\\ \mathbf{elif}\;y5 \leq -2.8 \cdot 10^{-93}:\\ \;\;\;\;\left(\mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right) \cdot y5\right) \cdot a\\ \mathbf{elif}\;y5 \leq 2.8 \cdot 10^{-188}:\\ \;\;\;\;\left(\left(b \cdot y\right) \cdot a\right) \cdot x\\ \mathbf{elif}\;y5 \leq 7.5 \cdot 10^{+123}:\\ \;\;\;\;\mathsf{fma}\left(i, y, \left(-y0\right) \cdot y2\right) \cdot \left(y5 \cdot k\right)\\ \mathbf{elif}\;y5 \leq 8.5 \cdot 10^{+185}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, t, y3 \cdot y0\right) \cdot y5\right) \cdot j\\ \mathbf{elif}\;y5 \leq 3.7 \cdot 10^{+239}:\\ \;\;\;\;\left(\mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right) \cdot y1\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, t, y3 \cdot y0\right) \cdot y5\right) \cdot j\\ \end{array} \]
5. Add Preprocessing

Alternative 32: 29.5% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\mathsf{fma}\left(-i, t, y3 \cdot y0\right) \cdot y5\right) \cdot j\\ t_2 := \left(-y\right) \cdot y3\\ \mathbf{if}\;y3 \leq -3.8 \cdot 10^{+230}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y3 \leq -1.7 \cdot 10^{+184}:\\ \;\;\;\;\left(\mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right) \cdot y1\right) \cdot a\\ \mathbf{elif}\;y3 \leq -1.95 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y3 \leq -1.06 \cdot 10^{-131}:\\ \;\;\;\;\left(a \cdot t\right) \cdot \mathsf{fma}\left(-b, z, y5 \cdot y2\right)\\ \mathbf{elif}\;y3 \leq 1.1 \cdot 10^{+18}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, z, y4 \cdot y2\right) \cdot y1\right) \cdot k\\ \mathbf{elif}\;y3 \leq 1.3 \cdot 10^{+216}:\\ \;\;\;\;\left(\mathsf{fma}\left(t, y2, t\_2\right) \cdot y5\right) \cdot a\\ \mathbf{elif}\;y3 \leq 1.25 \cdot 10^{+257}:\\ \;\;\;\;\left(\left(b \cdot y\right) \cdot a\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(t\_2 \cdot y5\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* (fma (- i) t (* y3 y0)) y5) j)) (t_2 (* (- y) y3)))
   (if (<= y3 -3.8e+230)
     t_1
     (if (<= y3 -1.7e+184)
       (* (* (fma y3 z (* (- x) y2)) y1) a)
       (if (<= y3 -1.95e+34)
         t_1
         (if (<= y3 -1.06e-131)
           (* (* a t) (fma (- b) z (* y5 y2)))
           (if (<= y3 1.1e+18)
             (* (* (fma (- i) z (* y4 y2)) y1) k)
             (if (<= y3 1.3e+216)
               (* (* (fma t y2 t_2) y5) a)
               (if (<= y3 1.25e+257)
                 (* (* (* b y) a) x)
                 (* (* t_2 y5) 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 = (fma(-i, t, (y3 * y0)) * y5) * j;
	double t_2 = -y * y3;
	double tmp;
	if (y3 <= -3.8e+230) {
		tmp = t_1;
	} else if (y3 <= -1.7e+184) {
		tmp = (fma(y3, z, (-x * y2)) * y1) * a;
	} else if (y3 <= -1.95e+34) {
		tmp = t_1;
	} else if (y3 <= -1.06e-131) {
		tmp = (a * t) * fma(-b, z, (y5 * y2));
	} else if (y3 <= 1.1e+18) {
		tmp = (fma(-i, z, (y4 * y2)) * y1) * k;
	} else if (y3 <= 1.3e+216) {
		tmp = (fma(t, y2, t_2) * y5) * a;
	} else if (y3 <= 1.25e+257) {
		tmp = ((b * y) * a) * x;
	} else {
		tmp = (t_2 * y5) * 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(fma(Float64(-i), t, Float64(y3 * y0)) * y5) * j)
	t_2 = Float64(Float64(-y) * y3)
	tmp = 0.0
	if (y3 <= -3.8e+230)
		tmp = t_1;
	elseif (y3 <= -1.7e+184)
		tmp = Float64(Float64(fma(y3, z, Float64(Float64(-x) * y2)) * y1) * a);
	elseif (y3 <= -1.95e+34)
		tmp = t_1;
	elseif (y3 <= -1.06e-131)
		tmp = Float64(Float64(a * t) * fma(Float64(-b), z, Float64(y5 * y2)));
	elseif (y3 <= 1.1e+18)
		tmp = Float64(Float64(fma(Float64(-i), z, Float64(y4 * y2)) * y1) * k);
	elseif (y3 <= 1.3e+216)
		tmp = Float64(Float64(fma(t, y2, t_2) * y5) * a);
	elseif (y3 <= 1.25e+257)
		tmp = Float64(Float64(Float64(b * y) * a) * x);
	else
		tmp = Float64(Float64(t_2 * y5) * a);
	end
	return 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[(N[((-i) * t + N[(y3 * y0), $MachinePrecision]), $MachinePrecision] * y5), $MachinePrecision] * j), $MachinePrecision]}, Block[{t$95$2 = N[((-y) * y3), $MachinePrecision]}, If[LessEqual[y3, -3.8e+230], t$95$1, If[LessEqual[y3, -1.7e+184], N[(N[(N[(y3 * z + N[((-x) * y2), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[y3, -1.95e+34], t$95$1, If[LessEqual[y3, -1.06e-131], N[(N[(a * t), $MachinePrecision] * N[((-b) * z + N[(y5 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.1e+18], N[(N[(N[((-i) * z + N[(y4 * y2), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision] * k), $MachinePrecision], If[LessEqual[y3, 1.3e+216], N[(N[(N[(t * y2 + t$95$2), $MachinePrecision] * y5), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[y3, 1.25e+257], N[(N[(N[(b * y), $MachinePrecision] * a), $MachinePrecision] * x), $MachinePrecision], N[(N[(t$95$2 * y5), $MachinePrecision] * a), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y3 < -3.8e230 or -1.7000000000000001e184 < y3 < -1.9500000000000001e34

   1. Initial program 31.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

   5. Applied rewrites 53.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(j \cdot t - k \cdot y\right), i, \mathsf{fma}\left(-y0, k \cdot y2 - j \cdot y3, \left(t \cdot y2 - y \cdot y3\right) \cdot a\right)\right) \cdot y5} \]

   6. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 32.7%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right)\right)} \]

   9. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 52.1%

       \[\leadsto j \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(-i, t, y0 \cdot y3\right)\right)} \]

   if -3.8e230 < y3 < -1.7000000000000001e184

   1. Initial program 27.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 45.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 63.7%

      \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right)\right)} \]

   if -1.9500000000000001e34 < y3 < -1.06000000000000006e-131

   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 a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot a} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot a} \]

   5. Applied rewrites 50.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), y1, \mathsf{fma}\left(y \cdot x - t \cdot z, b, \left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]

   6. Taylor expanded in t around inf

      \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(-1 \cdot \left(b \cdot z\right) + y2 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 43.4%

      \[\leadsto \left(a \cdot t\right) \cdot \color{blue}{\mathsf{fma}\left(-b, z, y2 \cdot y5\right)} \]

   if -1.06000000000000006e-131 < y3 < 1.1e18

   1. Initial program 35.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 43.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 18.2%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-1, y3 \cdot y4, i \cdot x\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto k \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(i \cdot z\right) + y2 \cdot y4\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 46.6%

       \[\leadsto k \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-i, z, y2 \cdot y4\right)\right)} \]

   if 1.1e18 < y3 < 1.2999999999999999e216

   1. Initial program 28.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

   5. Applied rewrites 50.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(j \cdot t - k \cdot y\right), i, \mathsf{fma}\left(-y0, k \cdot y2 - j \cdot y3, \left(t \cdot y2 - y \cdot y3\right) \cdot a\right)\right) \cdot y5} \]

   6. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 44.5%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right)\right)} \]

   if 1.2999999999999999e216 < y3 < 1.25000000000000007e257

   1. Initial program 0.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot x} \]

   5. Applied rewrites 50.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot a - c \cdot i, y, \mathsf{fma}\left(c \cdot y0 - y1 \cdot a, y2, \left(-j\right) \cdot \left(y0 \cdot b - i \cdot y1\right)\right)\right) \cdot x} \]

   6. Taylor expanded in y around inf

      \[\leadsto \left(y \cdot \left(a \cdot b - c \cdot i\right)\right) \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 66.7%

      \[\leadsto \left(y \cdot \mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right)\right) \cdot x \]

   9. Taylor expanded in c around 0

      \[\leadsto \left(a \cdot \left(b \cdot y\right)\right) \cdot x \]
   10. Step-by-step derivation

   11. Applied rewrites 84.1%

       \[\leadsto \left(a \cdot \left(b \cdot y\right)\right) \cdot x \]

   if 1.25000000000000007e257 < y3

   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 y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

   5. Applied rewrites 41.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(j \cdot t - k \cdot y\right), i, \mathsf{fma}\left(-y0, k \cdot y2 - j \cdot y3, \left(t \cdot y2 - y \cdot y3\right) \cdot a\right)\right) \cdot y5} \]

   6. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 75.6%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right)\right)} \]

   9. Taylor expanded in t around 0

      \[\leadsto a \cdot \left(-1 \cdot \left(y \cdot \color{blue}{\left(y3 \cdot y5\right)}\right)\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 75.6%

       \[\leadsto a \cdot \left(-\left(y \cdot y3\right) \cdot y5\right) \]
3. Recombined 7 regimes into one program.

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -3.8 \cdot 10^{+230}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, t, y3 \cdot y0\right) \cdot y5\right) \cdot j\\ \mathbf{elif}\;y3 \leq -1.7 \cdot 10^{+184}:\\ \;\;\;\;\left(\mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right) \cdot y1\right) \cdot a\\ \mathbf{elif}\;y3 \leq -1.95 \cdot 10^{+34}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, t, y3 \cdot y0\right) \cdot y5\right) \cdot j\\ \mathbf{elif}\;y3 \leq -1.06 \cdot 10^{-131}:\\ \;\;\;\;\left(a \cdot t\right) \cdot \mathsf{fma}\left(-b, z, y5 \cdot y2\right)\\ \mathbf{elif}\;y3 \leq 1.1 \cdot 10^{+18}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, z, y4 \cdot y2\right) \cdot y1\right) \cdot k\\ \mathbf{elif}\;y3 \leq 1.3 \cdot 10^{+216}:\\ \;\;\;\;\left(\mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right) \cdot y5\right) \cdot a\\ \mathbf{elif}\;y3 \leq 1.25 \cdot 10^{+257}:\\ \;\;\;\;\left(\left(b \cdot y\right) \cdot a\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(-y\right) \cdot y3\right) \cdot y5\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 33: 29.5% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\mathsf{fma}\left(-i, t, y3 \cdot y0\right) \cdot y5\right) \cdot j\\ t_2 := \left(-y\right) \cdot y3\\ t_3 := \left(\mathsf{fma}\left(t, y2, t\_2\right) \cdot y5\right) \cdot a\\ \mathbf{if}\;y3 \leq -3.8 \cdot 10^{+230}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y3 \leq -1.7 \cdot 10^{+184}:\\ \;\;\;\;\left(\mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right) \cdot y1\right) \cdot a\\ \mathbf{elif}\;y3 \leq -4.6 \cdot 10^{+51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y3 \leq -2.25 \cdot 10^{-55}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y3 \leq 1.1 \cdot 10^{+18}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, z, y4 \cdot y2\right) \cdot y1\right) \cdot k\\ \mathbf{elif}\;y3 \leq 1.3 \cdot 10^{+216}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y3 \leq 1.25 \cdot 10^{+257}:\\ \;\;\;\;\left(\left(b \cdot y\right) \cdot a\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(t\_2 \cdot y5\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* (fma (- i) t (* y3 y0)) y5) j))
        (t_2 (* (- y) y3))
        (t_3 (* (* (fma t y2 t_2) y5) a)))
   (if (<= y3 -3.8e+230)
     t_1
     (if (<= y3 -1.7e+184)
       (* (* (fma y3 z (* (- x) y2)) y1) a)
       (if (<= y3 -4.6e+51)
         t_1
         (if (<= y3 -2.25e-55)
           t_3
           (if (<= y3 1.1e+18)
             (* (* (fma (- i) z (* y4 y2)) y1) k)
             (if (<= y3 1.3e+216)
               t_3
               (if (<= y3 1.25e+257)
                 (* (* (* b y) a) x)
                 (* (* t_2 y5) 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 = (fma(-i, t, (y3 * y0)) * y5) * j;
	double t_2 = -y * y3;
	double t_3 = (fma(t, y2, t_2) * y5) * a;
	double tmp;
	if (y3 <= -3.8e+230) {
		tmp = t_1;
	} else if (y3 <= -1.7e+184) {
		tmp = (fma(y3, z, (-x * y2)) * y1) * a;
	} else if (y3 <= -4.6e+51) {
		tmp = t_1;
	} else if (y3 <= -2.25e-55) {
		tmp = t_3;
	} else if (y3 <= 1.1e+18) {
		tmp = (fma(-i, z, (y4 * y2)) * y1) * k;
	} else if (y3 <= 1.3e+216) {
		tmp = t_3;
	} else if (y3 <= 1.25e+257) {
		tmp = ((b * y) * a) * x;
	} else {
		tmp = (t_2 * y5) * 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(fma(Float64(-i), t, Float64(y3 * y0)) * y5) * j)
	t_2 = Float64(Float64(-y) * y3)
	t_3 = Float64(Float64(fma(t, y2, t_2) * y5) * a)
	tmp = 0.0
	if (y3 <= -3.8e+230)
		tmp = t_1;
	elseif (y3 <= -1.7e+184)
		tmp = Float64(Float64(fma(y3, z, Float64(Float64(-x) * y2)) * y1) * a);
	elseif (y3 <= -4.6e+51)
		tmp = t_1;
	elseif (y3 <= -2.25e-55)
		tmp = t_3;
	elseif (y3 <= 1.1e+18)
		tmp = Float64(Float64(fma(Float64(-i), z, Float64(y4 * y2)) * y1) * k);
	elseif (y3 <= 1.3e+216)
		tmp = t_3;
	elseif (y3 <= 1.25e+257)
		tmp = Float64(Float64(Float64(b * y) * a) * x);
	else
		tmp = Float64(Float64(t_2 * y5) * a);
	end
	return 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[(N[((-i) * t + N[(y3 * y0), $MachinePrecision]), $MachinePrecision] * y5), $MachinePrecision] * j), $MachinePrecision]}, Block[{t$95$2 = N[((-y) * y3), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t * y2 + t$95$2), $MachinePrecision] * y5), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[y3, -3.8e+230], t$95$1, If[LessEqual[y3, -1.7e+184], N[(N[(N[(y3 * z + N[((-x) * y2), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[y3, -4.6e+51], t$95$1, If[LessEqual[y3, -2.25e-55], t$95$3, If[LessEqual[y3, 1.1e+18], N[(N[(N[((-i) * z + N[(y4 * y2), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision] * k), $MachinePrecision], If[LessEqual[y3, 1.3e+216], t$95$3, If[LessEqual[y3, 1.25e+257], N[(N[(N[(b * y), $MachinePrecision] * a), $MachinePrecision] * x), $MachinePrecision], N[(N[(t$95$2 * y5), $MachinePrecision] * a), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y3 < -3.8e230 or -1.7000000000000001e184 < y3 < -4.6000000000000001e51

   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 y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

   5. Applied rewrites 53.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(j \cdot t - k \cdot y\right), i, \mathsf{fma}\left(-y0, k \cdot y2 - j \cdot y3, \left(t \cdot y2 - y \cdot y3\right) \cdot a\right)\right) \cdot y5} \]

   6. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 29.7%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right)\right)} \]

   9. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 54.3%

       \[\leadsto j \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(-i, t, y0 \cdot y3\right)\right)} \]

   if -3.8e230 < y3 < -1.7000000000000001e184

   1. Initial program 27.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 45.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 63.7%

      \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right)\right)} \]

   if -4.6000000000000001e51 < y3 < -2.24999999999999985e-55 or 1.1e18 < y3 < 1.2999999999999999e216

   1. Initial program 33.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

   5. Applied rewrites 51.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(j \cdot t - k \cdot y\right), i, \mathsf{fma}\left(-y0, k \cdot y2 - j \cdot y3, \left(t \cdot y2 - y \cdot y3\right) \cdot a\right)\right) \cdot y5} \]

   6. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 47.6%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right)\right)} \]

   if -2.24999999999999985e-55 < y3 < 1.1e18

   1. Initial program 33.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 45.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 18.9%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-1, y3 \cdot y4, i \cdot x\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto k \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(i \cdot z\right) + y2 \cdot y4\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 43.3%

       \[\leadsto k \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-i, z, y2 \cdot y4\right)\right)} \]

   if 1.2999999999999999e216 < y3 < 1.25000000000000007e257

   1. Initial program 0.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot x} \]

   5. Applied rewrites 50.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot a - c \cdot i, y, \mathsf{fma}\left(c \cdot y0 - y1 \cdot a, y2, \left(-j\right) \cdot \left(y0 \cdot b - i \cdot y1\right)\right)\right) \cdot x} \]

   6. Taylor expanded in y around inf

      \[\leadsto \left(y \cdot \left(a \cdot b - c \cdot i\right)\right) \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 66.7%

      \[\leadsto \left(y \cdot \mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right)\right) \cdot x \]

   9. Taylor expanded in c around 0

      \[\leadsto \left(a \cdot \left(b \cdot y\right)\right) \cdot x \]
   10. Step-by-step derivation

   11. Applied rewrites 84.1%

       \[\leadsto \left(a \cdot \left(b \cdot y\right)\right) \cdot x \]

   if 1.25000000000000007e257 < y3

   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 y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

   5. Applied rewrites 41.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(j \cdot t - k \cdot y\right), i, \mathsf{fma}\left(-y0, k \cdot y2 - j \cdot y3, \left(t \cdot y2 - y \cdot y3\right) \cdot a\right)\right) \cdot y5} \]

   6. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 75.6%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right)\right)} \]

   9. Taylor expanded in t around 0

      \[\leadsto a \cdot \left(-1 \cdot \left(y \cdot \color{blue}{\left(y3 \cdot y5\right)}\right)\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 75.6%

       \[\leadsto a \cdot \left(-\left(y \cdot y3\right) \cdot y5\right) \]
3. Recombined 6 regimes into one program.

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -3.8 \cdot 10^{+230}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, t, y3 \cdot y0\right) \cdot y5\right) \cdot j\\ \mathbf{elif}\;y3 \leq -1.7 \cdot 10^{+184}:\\ \;\;\;\;\left(\mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right) \cdot y1\right) \cdot a\\ \mathbf{elif}\;y3 \leq -4.6 \cdot 10^{+51}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, t, y3 \cdot y0\right) \cdot y5\right) \cdot j\\ \mathbf{elif}\;y3 \leq -2.25 \cdot 10^{-55}:\\ \;\;\;\;\left(\mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right) \cdot y5\right) \cdot a\\ \mathbf{elif}\;y3 \leq 1.1 \cdot 10^{+18}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, z, y4 \cdot y2\right) \cdot y1\right) \cdot k\\ \mathbf{elif}\;y3 \leq 1.3 \cdot 10^{+216}:\\ \;\;\;\;\left(\mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right) \cdot y5\right) \cdot a\\ \mathbf{elif}\;y3 \leq 1.25 \cdot 10^{+257}:\\ \;\;\;\;\left(\left(b \cdot y\right) \cdot a\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(-y\right) \cdot y3\right) \cdot y5\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 34: 30.2% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\mathsf{fma}\left(-i, t, y3 \cdot y0\right) \cdot y5\right) \cdot j\\ t_2 := \left(-y\right) \cdot y3\\ t_3 := \left(\mathsf{fma}\left(t, y2, t\_2\right) \cdot y5\right) \cdot a\\ \mathbf{if}\;y3 \leq -3.8 \cdot 10^{+230}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y3 \leq -1.7 \cdot 10^{+184}:\\ \;\;\;\;\left(\mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right) \cdot y1\right) \cdot a\\ \mathbf{elif}\;y3 \leq -4.6 \cdot 10^{+51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y3 \leq -7.2 \cdot 10^{-58}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y3 \leq 650000000000:\\ \;\;\;\;\left(\mathsf{fma}\left(j, x, \left(-k\right) \cdot z\right) \cdot y1\right) \cdot i\\ \mathbf{elif}\;y3 \leq 1.3 \cdot 10^{+216}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y3 \leq 1.25 \cdot 10^{+257}:\\ \;\;\;\;\left(\left(b \cdot y\right) \cdot a\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(t\_2 \cdot y5\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* (fma (- i) t (* y3 y0)) y5) j))
        (t_2 (* (- y) y3))
        (t_3 (* (* (fma t y2 t_2) y5) a)))
   (if (<= y3 -3.8e+230)
     t_1
     (if (<= y3 -1.7e+184)
       (* (* (fma y3 z (* (- x) y2)) y1) a)
       (if (<= y3 -4.6e+51)
         t_1
         (if (<= y3 -7.2e-58)
           t_3
           (if (<= y3 650000000000.0)
             (* (* (fma j x (* (- k) z)) y1) i)
             (if (<= y3 1.3e+216)
               t_3
               (if (<= y3 1.25e+257)
                 (* (* (* b y) a) x)
                 (* (* t_2 y5) 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 = (fma(-i, t, (y3 * y0)) * y5) * j;
	double t_2 = -y * y3;
	double t_3 = (fma(t, y2, t_2) * y5) * a;
	double tmp;
	if (y3 <= -3.8e+230) {
		tmp = t_1;
	} else if (y3 <= -1.7e+184) {
		tmp = (fma(y3, z, (-x * y2)) * y1) * a;
	} else if (y3 <= -4.6e+51) {
		tmp = t_1;
	} else if (y3 <= -7.2e-58) {
		tmp = t_3;
	} else if (y3 <= 650000000000.0) {
		tmp = (fma(j, x, (-k * z)) * y1) * i;
	} else if (y3 <= 1.3e+216) {
		tmp = t_3;
	} else if (y3 <= 1.25e+257) {
		tmp = ((b * y) * a) * x;
	} else {
		tmp = (t_2 * y5) * 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(fma(Float64(-i), t, Float64(y3 * y0)) * y5) * j)
	t_2 = Float64(Float64(-y) * y3)
	t_3 = Float64(Float64(fma(t, y2, t_2) * y5) * a)
	tmp = 0.0
	if (y3 <= -3.8e+230)
		tmp = t_1;
	elseif (y3 <= -1.7e+184)
		tmp = Float64(Float64(fma(y3, z, Float64(Float64(-x) * y2)) * y1) * a);
	elseif (y3 <= -4.6e+51)
		tmp = t_1;
	elseif (y3 <= -7.2e-58)
		tmp = t_3;
	elseif (y3 <= 650000000000.0)
		tmp = Float64(Float64(fma(j, x, Float64(Float64(-k) * z)) * y1) * i);
	elseif (y3 <= 1.3e+216)
		tmp = t_3;
	elseif (y3 <= 1.25e+257)
		tmp = Float64(Float64(Float64(b * y) * a) * x);
	else
		tmp = Float64(Float64(t_2 * y5) * a);
	end
	return 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[(N[((-i) * t + N[(y3 * y0), $MachinePrecision]), $MachinePrecision] * y5), $MachinePrecision] * j), $MachinePrecision]}, Block[{t$95$2 = N[((-y) * y3), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t * y2 + t$95$2), $MachinePrecision] * y5), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[y3, -3.8e+230], t$95$1, If[LessEqual[y3, -1.7e+184], N[(N[(N[(y3 * z + N[((-x) * y2), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[y3, -4.6e+51], t$95$1, If[LessEqual[y3, -7.2e-58], t$95$3, If[LessEqual[y3, 650000000000.0], N[(N[(N[(j * x + N[((-k) * z), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision] * i), $MachinePrecision], If[LessEqual[y3, 1.3e+216], t$95$3, If[LessEqual[y3, 1.25e+257], N[(N[(N[(b * y), $MachinePrecision] * a), $MachinePrecision] * x), $MachinePrecision], N[(N[(t$95$2 * y5), $MachinePrecision] * a), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y3 < -3.8e230 or -1.7000000000000001e184 < y3 < -4.6000000000000001e51

   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 y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

   5. Applied rewrites 53.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(j \cdot t - k \cdot y\right), i, \mathsf{fma}\left(-y0, k \cdot y2 - j \cdot y3, \left(t \cdot y2 - y \cdot y3\right) \cdot a\right)\right) \cdot y5} \]

   6. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 29.7%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right)\right)} \]

   9. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 54.3%

       \[\leadsto j \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(-i, t, y0 \cdot y3\right)\right)} \]

   if -3.8e230 < y3 < -1.7000000000000001e184

   1. Initial program 27.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 45.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 63.7%

      \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right)\right)} \]

   if -4.6000000000000001e51 < y3 < -7.20000000000000019e-58 or 6.5e11 < y3 < 1.2999999999999999e216

   1. Initial program 32.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

   5. Applied rewrites 50.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(j \cdot t - k \cdot y\right), i, \mathsf{fma}\left(-y0, k \cdot y2 - j \cdot y3, \left(t \cdot y2 - y \cdot y3\right) \cdot a\right)\right) \cdot y5} \]

   6. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 46.8%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right)\right)} \]

   if -7.20000000000000019e-58 < y3 < 6.5e11

   1. Initial program 33.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 44.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in i around inf

      \[\leadsto i \cdot \color{blue}{\left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 32.9%

      \[\leadsto i \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(j, x, \left(-k\right) \cdot z\right)\right)} \]

   if 1.2999999999999999e216 < y3 < 1.25000000000000007e257

   1. Initial program 0.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot x} \]

   5. Applied rewrites 50.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot a - c \cdot i, y, \mathsf{fma}\left(c \cdot y0 - y1 \cdot a, y2, \left(-j\right) \cdot \left(y0 \cdot b - i \cdot y1\right)\right)\right) \cdot x} \]

   6. Taylor expanded in y around inf

      \[\leadsto \left(y \cdot \left(a \cdot b - c \cdot i\right)\right) \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 66.7%

      \[\leadsto \left(y \cdot \mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right)\right) \cdot x \]

   9. Taylor expanded in c around 0

      \[\leadsto \left(a \cdot \left(b \cdot y\right)\right) \cdot x \]
   10. Step-by-step derivation

   11. Applied rewrites 84.1%

       \[\leadsto \left(a \cdot \left(b \cdot y\right)\right) \cdot x \]

   if 1.25000000000000007e257 < y3

   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 y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

   5. Applied rewrites 41.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(j \cdot t - k \cdot y\right), i, \mathsf{fma}\left(-y0, k \cdot y2 - j \cdot y3, \left(t \cdot y2 - y \cdot y3\right) \cdot a\right)\right) \cdot y5} \]

   6. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 75.6%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right)\right)} \]

   9. Taylor expanded in t around 0

      \[\leadsto a \cdot \left(-1 \cdot \left(y \cdot \color{blue}{\left(y3 \cdot y5\right)}\right)\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 75.6%

       \[\leadsto a \cdot \left(-\left(y \cdot y3\right) \cdot y5\right) \]
3. Recombined 6 regimes into one program.

4. Final simplification 44.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -3.8 \cdot 10^{+230}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, t, y3 \cdot y0\right) \cdot y5\right) \cdot j\\ \mathbf{elif}\;y3 \leq -1.7 \cdot 10^{+184}:\\ \;\;\;\;\left(\mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right) \cdot y1\right) \cdot a\\ \mathbf{elif}\;y3 \leq -4.6 \cdot 10^{+51}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, t, y3 \cdot y0\right) \cdot y5\right) \cdot j\\ \mathbf{elif}\;y3 \leq -7.2 \cdot 10^{-58}:\\ \;\;\;\;\left(\mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right) \cdot y5\right) \cdot a\\ \mathbf{elif}\;y3 \leq 650000000000:\\ \;\;\;\;\left(\mathsf{fma}\left(j, x, \left(-k\right) \cdot z\right) \cdot y1\right) \cdot i\\ \mathbf{elif}\;y3 \leq 1.3 \cdot 10^{+216}:\\ \;\;\;\;\left(\mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right) \cdot y5\right) \cdot a\\ \mathbf{elif}\;y3 \leq 1.25 \cdot 10^{+257}:\\ \;\;\;\;\left(\left(b \cdot y\right) \cdot a\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(-y\right) \cdot y3\right) \cdot y5\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 35: 20.5% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(b \cdot y\right) \cdot a\right) \cdot x\\ t_2 := \left(\left(y5 \cdot k\right) \cdot i\right) \cdot y\\ \mathbf{if}\;c \leq -1.56 \cdot 10^{+68}:\\ \;\;\;\;\left(\left(\left(-y\right) \cdot i\right) \cdot c\right) \cdot x\\ \mathbf{elif}\;c \leq -8.8 \cdot 10^{-61}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -4.8 \cdot 10^{-196}:\\ \;\;\;\;\left(\left(y3 \cdot z\right) \cdot y1\right) \cdot a\\ \mathbf{elif}\;c \leq 2.15 \cdot 10^{-293}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{-173}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 1.08 \cdot 10^{-91}:\\ \;\;\;\;\left(\left(y3 \cdot z\right) \cdot a\right) \cdot y1\\ \mathbf{elif}\;c \leq 3 \cdot 10^{+228}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(-x\right) \cdot i\right) \cdot c\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* (* b y) a) x)) (t_2 (* (* (* y5 k) i) y)))
   (if (<= c -1.56e+68)
     (* (* (* (- y) i) c) x)
     (if (<= c -8.8e-61)
       t_2
       (if (<= c -4.8e-196)
         (* (* (* y3 z) y1) a)
         (if (<= c 2.15e-293)
           t_2
           (if (<= c 5.5e-173)
             t_1
             (if (<= c 1.08e-91)
               (* (* (* y3 z) a) y1)
               (if (<= c 3e+228) t_1 (* (* (* (- x) i) c) y))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = ((b * y) * a) * x;
	double t_2 = ((y5 * k) * i) * y;
	double tmp;
	if (c <= -1.56e+68) {
		tmp = ((-y * i) * c) * x;
	} else if (c <= -8.8e-61) {
		tmp = t_2;
	} else if (c <= -4.8e-196) {
		tmp = ((y3 * z) * y1) * a;
	} else if (c <= 2.15e-293) {
		tmp = t_2;
	} else if (c <= 5.5e-173) {
		tmp = t_1;
	} else if (c <= 1.08e-91) {
		tmp = ((y3 * z) * a) * y1;
	} else if (c <= 3e+228) {
		tmp = t_1;
	} else {
		tmp = ((-x * i) * c) * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((b * y) * a) * x
    t_2 = ((y5 * k) * i) * y
    if (c <= (-1.56d+68)) then
        tmp = ((-y * i) * c) * x
    else if (c <= (-8.8d-61)) then
        tmp = t_2
    else if (c <= (-4.8d-196)) then
        tmp = ((y3 * z) * y1) * a
    else if (c <= 2.15d-293) then
        tmp = t_2
    else if (c <= 5.5d-173) then
        tmp = t_1
    else if (c <= 1.08d-91) then
        tmp = ((y3 * z) * a) * y1
    else if (c <= 3d+228) then
        tmp = t_1
    else
        tmp = ((-x * i) * c) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = ((b * y) * a) * x;
	double t_2 = ((y5 * k) * i) * y;
	double tmp;
	if (c <= -1.56e+68) {
		tmp = ((-y * i) * c) * x;
	} else if (c <= -8.8e-61) {
		tmp = t_2;
	} else if (c <= -4.8e-196) {
		tmp = ((y3 * z) * y1) * a;
	} else if (c <= 2.15e-293) {
		tmp = t_2;
	} else if (c <= 5.5e-173) {
		tmp = t_1;
	} else if (c <= 1.08e-91) {
		tmp = ((y3 * z) * a) * y1;
	} else if (c <= 3e+228) {
		tmp = t_1;
	} else {
		tmp = ((-x * i) * c) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = ((b * y) * a) * x
	t_2 = ((y5 * k) * i) * y
	tmp = 0
	if c <= -1.56e+68:
		tmp = ((-y * i) * c) * x
	elif c <= -8.8e-61:
		tmp = t_2
	elif c <= -4.8e-196:
		tmp = ((y3 * z) * y1) * a
	elif c <= 2.15e-293:
		tmp = t_2
	elif c <= 5.5e-173:
		tmp = t_1
	elif c <= 1.08e-91:
		tmp = ((y3 * z) * a) * y1
	elif c <= 3e+228:
		tmp = t_1
	else:
		tmp = ((-x * i) * c) * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(Float64(b * y) * a) * x)
	t_2 = Float64(Float64(Float64(y5 * k) * i) * y)
	tmp = 0.0
	if (c <= -1.56e+68)
		tmp = Float64(Float64(Float64(Float64(-y) * i) * c) * x);
	elseif (c <= -8.8e-61)
		tmp = t_2;
	elseif (c <= -4.8e-196)
		tmp = Float64(Float64(Float64(y3 * z) * y1) * a);
	elseif (c <= 2.15e-293)
		tmp = t_2;
	elseif (c <= 5.5e-173)
		tmp = t_1;
	elseif (c <= 1.08e-91)
		tmp = Float64(Float64(Float64(y3 * z) * a) * y1);
	elseif (c <= 3e+228)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(Float64(-x) * i) * c) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = ((b * y) * a) * x;
	t_2 = ((y5 * k) * i) * y;
	tmp = 0.0;
	if (c <= -1.56e+68)
		tmp = ((-y * i) * c) * x;
	elseif (c <= -8.8e-61)
		tmp = t_2;
	elseif (c <= -4.8e-196)
		tmp = ((y3 * z) * y1) * a;
	elseif (c <= 2.15e-293)
		tmp = t_2;
	elseif (c <= 5.5e-173)
		tmp = t_1;
	elseif (c <= 1.08e-91)
		tmp = ((y3 * z) * a) * y1;
	elseif (c <= 3e+228)
		tmp = t_1;
	else
		tmp = ((-x * i) * c) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(N[(b * y), $MachinePrecision] * a), $MachinePrecision] * x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y5 * k), $MachinePrecision] * i), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[c, -1.56e+68], N[(N[(N[((-y) * i), $MachinePrecision] * c), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[c, -8.8e-61], t$95$2, If[LessEqual[c, -4.8e-196], N[(N[(N[(y3 * z), $MachinePrecision] * y1), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[c, 2.15e-293], t$95$2, If[LessEqual[c, 5.5e-173], t$95$1, If[LessEqual[c, 1.08e-91], N[(N[(N[(y3 * z), $MachinePrecision] * a), $MachinePrecision] * y1), $MachinePrecision], If[LessEqual[c, 3e+228], t$95$1, N[(N[(N[((-x) * i), $MachinePrecision] * c), $MachinePrecision] * y), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -1.56000000000000003e68

   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 x around inf

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot x} \]

   5. Applied rewrites 36.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot a - c \cdot i, y, \mathsf{fma}\left(c \cdot y0 - y1 \cdot a, y2, \left(-j\right) \cdot \left(y0 \cdot b - i \cdot y1\right)\right)\right) \cdot x} \]

   6. Taylor expanded in y around inf

      \[\leadsto \left(y \cdot \left(a \cdot b - c \cdot i\right)\right) \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 36.6%

      \[\leadsto \left(y \cdot \mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right)\right) \cdot x \]

   9. Taylor expanded in c around inf

      \[\leadsto \left(-1 \cdot \left(c \cdot \left(i \cdot y\right)\right)\right) \cdot x \]
   10. Step-by-step derivation

   11. Applied rewrites 27.8%

       \[\leadsto \left(-c \cdot \left(i \cdot y\right)\right) \cdot x \]

   if -1.56000000000000003e68 < c < -8.80000000000000035e-61 or -4.80000000000000041e-196 < c < 2.1499999999999999e-293

   1. Initial program 38.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 51.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - c \cdot i, x, \left(c \cdot y4 - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in i around inf

      \[\leadsto \left(i \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 37.3%

      \[\leadsto \left(i \cdot \mathsf{fma}\left(k, y5, -c \cdot x\right)\right) \cdot y \]

   9. Taylor expanded in c around 0

      \[\leadsto \left(i \cdot \left(k \cdot y5\right)\right) \cdot y \]
   10. Step-by-step derivation

   11. Applied rewrites 37.3%

       \[\leadsto \left(i \cdot \left(k \cdot y5\right)\right) \cdot y \]

   if -8.80000000000000035e-61 < c < -4.80000000000000041e-196

   1. Initial program 54.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 43.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 16.9%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-1, y3 \cdot y4, i \cdot x\right)\right)} \]

   9. Taylor expanded in z around inf

      \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(i \cdot k\right) + a \cdot y3\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 24.6%

       \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \mathsf{fma}\left(-i, k, a \cdot y3\right)\right)} \]

   12. Taylor expanded in a around inf

       \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(y3 \cdot z\right)}\right) \]
   13. Step-by-step derivation

   14. Applied rewrites 24.2%

       \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(y3 \cdot z\right)}\right) \]

   if 2.1499999999999999e-293 < c < 5.50000000000000022e-173 or 1.07999999999999998e-91 < c < 3.0000000000000001e228

   1. Initial program 32.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot x} \]

   5. Applied rewrites 37.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot a - c \cdot i, y, \mathsf{fma}\left(c \cdot y0 - y1 \cdot a, y2, \left(-j\right) \cdot \left(y0 \cdot b - i \cdot y1\right)\right)\right) \cdot x} \]

   6. Taylor expanded in y around inf

      \[\leadsto \left(y \cdot \left(a \cdot b - c \cdot i\right)\right) \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 39.8%

      \[\leadsto \left(y \cdot \mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right)\right) \cdot x \]

   9. Taylor expanded in c around 0

      \[\leadsto \left(a \cdot \left(b \cdot y\right)\right) \cdot x \]
   10. Step-by-step derivation

   11. Applied rewrites 38.8%

       \[\leadsto \left(a \cdot \left(b \cdot y\right)\right) \cdot x \]

   if 5.50000000000000022e-173 < c < 1.07999999999999998e-91

   1. Initial program 29.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 57.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 31.1%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-1, y3 \cdot y4, i \cdot x\right)\right)} \]

   9. Taylor expanded in z around inf

      \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(i \cdot k\right) + a \cdot y3\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 57.8%

       \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \mathsf{fma}\left(-i, k, a \cdot y3\right)\right)} \]

   12. Taylor expanded in a around inf

       \[\leadsto y1 \cdot \left(a \cdot \left(y3 \cdot \color{blue}{z}\right)\right) \]
   13. Step-by-step derivation

   14. Applied rewrites 50.9%

       \[\leadsto y1 \cdot \left(a \cdot \left(y3 \cdot \color{blue}{z}\right)\right) \]

   if 3.0000000000000001e228 < c

   1. Initial program 5.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 21.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - c \cdot i, x, \left(c \cdot y4 - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in i around inf

      \[\leadsto \left(i \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 68.9%

      \[\leadsto \left(i \cdot \mathsf{fma}\left(k, y5, -c \cdot x\right)\right) \cdot y \]

   9. Taylor expanded in c around inf

      \[\leadsto \left(-1 \cdot \left(c \cdot \left(i \cdot x\right)\right)\right) \cdot y \]
   10. Step-by-step derivation

   11. Applied rewrites 43.0%

       \[\leadsto \left(-c \cdot \left(i \cdot x\right)\right) \cdot y \]
3. Recombined 6 regimes into one program.

4. Final simplification 36.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.56 \cdot 10^{+68}:\\ \;\;\;\;\left(\left(\left(-y\right) \cdot i\right) \cdot c\right) \cdot x\\ \mathbf{elif}\;c \leq -8.8 \cdot 10^{-61}:\\ \;\;\;\;\left(\left(y5 \cdot k\right) \cdot i\right) \cdot y\\ \mathbf{elif}\;c \leq -4.8 \cdot 10^{-196}:\\ \;\;\;\;\left(\left(y3 \cdot z\right) \cdot y1\right) \cdot a\\ \mathbf{elif}\;c \leq 2.15 \cdot 10^{-293}:\\ \;\;\;\;\left(\left(y5 \cdot k\right) \cdot i\right) \cdot y\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{-173}:\\ \;\;\;\;\left(\left(b \cdot y\right) \cdot a\right) \cdot x\\ \mathbf{elif}\;c \leq 1.08 \cdot 10^{-91}:\\ \;\;\;\;\left(\left(y3 \cdot z\right) \cdot a\right) \cdot y1\\ \mathbf{elif}\;c \leq 3 \cdot 10^{+228}:\\ \;\;\;\;\left(\left(b \cdot y\right) \cdot a\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(-x\right) \cdot i\right) \cdot c\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 36: 17.8% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(b \cdot y\right) \cdot a\right) \cdot x\\ t_2 := \left(\left(y5 \cdot k\right) \cdot i\right) \cdot y\\ \mathbf{if}\;c \leq -5 \cdot 10^{+67}:\\ \;\;\;\;\left(\left(y2 \cdot t\right) \cdot y5\right) \cdot a\\ \mathbf{elif}\;c \leq -8.8 \cdot 10^{-61}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -4.8 \cdot 10^{-196}:\\ \;\;\;\;\left(\left(y3 \cdot z\right) \cdot y1\right) \cdot a\\ \mathbf{elif}\;c \leq 2.15 \cdot 10^{-293}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{-173}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 1.08 \cdot 10^{-91}:\\ \;\;\;\;\left(\left(y3 \cdot z\right) \cdot a\right) \cdot y1\\ \mathbf{elif}\;c \leq 3 \cdot 10^{+228}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(-x\right) \cdot i\right) \cdot c\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* (* b y) a) x)) (t_2 (* (* (* y5 k) i) y)))
   (if (<= c -5e+67)
     (* (* (* y2 t) y5) a)
     (if (<= c -8.8e-61)
       t_2
       (if (<= c -4.8e-196)
         (* (* (* y3 z) y1) a)
         (if (<= c 2.15e-293)
           t_2
           (if (<= c 5.5e-173)
             t_1
             (if (<= c 1.08e-91)
               (* (* (* y3 z) a) y1)
               (if (<= c 3e+228) t_1 (* (* (* (- x) i) c) y))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = ((b * y) * a) * x;
	double t_2 = ((y5 * k) * i) * y;
	double tmp;
	if (c <= -5e+67) {
		tmp = ((y2 * t) * y5) * a;
	} else if (c <= -8.8e-61) {
		tmp = t_2;
	} else if (c <= -4.8e-196) {
		tmp = ((y3 * z) * y1) * a;
	} else if (c <= 2.15e-293) {
		tmp = t_2;
	} else if (c <= 5.5e-173) {
		tmp = t_1;
	} else if (c <= 1.08e-91) {
		tmp = ((y3 * z) * a) * y1;
	} else if (c <= 3e+228) {
		tmp = t_1;
	} else {
		tmp = ((-x * i) * c) * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((b * y) * a) * x
    t_2 = ((y5 * k) * i) * y
    if (c <= (-5d+67)) then
        tmp = ((y2 * t) * y5) * a
    else if (c <= (-8.8d-61)) then
        tmp = t_2
    else if (c <= (-4.8d-196)) then
        tmp = ((y3 * z) * y1) * a
    else if (c <= 2.15d-293) then
        tmp = t_2
    else if (c <= 5.5d-173) then
        tmp = t_1
    else if (c <= 1.08d-91) then
        tmp = ((y3 * z) * a) * y1
    else if (c <= 3d+228) then
        tmp = t_1
    else
        tmp = ((-x * i) * c) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = ((b * y) * a) * x;
	double t_2 = ((y5 * k) * i) * y;
	double tmp;
	if (c <= -5e+67) {
		tmp = ((y2 * t) * y5) * a;
	} else if (c <= -8.8e-61) {
		tmp = t_2;
	} else if (c <= -4.8e-196) {
		tmp = ((y3 * z) * y1) * a;
	} else if (c <= 2.15e-293) {
		tmp = t_2;
	} else if (c <= 5.5e-173) {
		tmp = t_1;
	} else if (c <= 1.08e-91) {
		tmp = ((y3 * z) * a) * y1;
	} else if (c <= 3e+228) {
		tmp = t_1;
	} else {
		tmp = ((-x * i) * c) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = ((b * y) * a) * x
	t_2 = ((y5 * k) * i) * y
	tmp = 0
	if c <= -5e+67:
		tmp = ((y2 * t) * y5) * a
	elif c <= -8.8e-61:
		tmp = t_2
	elif c <= -4.8e-196:
		tmp = ((y3 * z) * y1) * a
	elif c <= 2.15e-293:
		tmp = t_2
	elif c <= 5.5e-173:
		tmp = t_1
	elif c <= 1.08e-91:
		tmp = ((y3 * z) * a) * y1
	elif c <= 3e+228:
		tmp = t_1
	else:
		tmp = ((-x * i) * c) * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(Float64(b * y) * a) * x)
	t_2 = Float64(Float64(Float64(y5 * k) * i) * y)
	tmp = 0.0
	if (c <= -5e+67)
		tmp = Float64(Float64(Float64(y2 * t) * y5) * a);
	elseif (c <= -8.8e-61)
		tmp = t_2;
	elseif (c <= -4.8e-196)
		tmp = Float64(Float64(Float64(y3 * z) * y1) * a);
	elseif (c <= 2.15e-293)
		tmp = t_2;
	elseif (c <= 5.5e-173)
		tmp = t_1;
	elseif (c <= 1.08e-91)
		tmp = Float64(Float64(Float64(y3 * z) * a) * y1);
	elseif (c <= 3e+228)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(Float64(-x) * i) * c) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = ((b * y) * a) * x;
	t_2 = ((y5 * k) * i) * y;
	tmp = 0.0;
	if (c <= -5e+67)
		tmp = ((y2 * t) * y5) * a;
	elseif (c <= -8.8e-61)
		tmp = t_2;
	elseif (c <= -4.8e-196)
		tmp = ((y3 * z) * y1) * a;
	elseif (c <= 2.15e-293)
		tmp = t_2;
	elseif (c <= 5.5e-173)
		tmp = t_1;
	elseif (c <= 1.08e-91)
		tmp = ((y3 * z) * a) * y1;
	elseif (c <= 3e+228)
		tmp = t_1;
	else
		tmp = ((-x * i) * c) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(N[(b * y), $MachinePrecision] * a), $MachinePrecision] * x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y5 * k), $MachinePrecision] * i), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[c, -5e+67], N[(N[(N[(y2 * t), $MachinePrecision] * y5), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[c, -8.8e-61], t$95$2, If[LessEqual[c, -4.8e-196], N[(N[(N[(y3 * z), $MachinePrecision] * y1), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[c, 2.15e-293], t$95$2, If[LessEqual[c, 5.5e-173], t$95$1, If[LessEqual[c, 1.08e-91], N[(N[(N[(y3 * z), $MachinePrecision] * a), $MachinePrecision] * y1), $MachinePrecision], If[LessEqual[c, 3e+228], t$95$1, N[(N[(N[((-x) * i), $MachinePrecision] * c), $MachinePrecision] * y), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -4.99999999999999976e67

   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 y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

   5. Applied rewrites 36.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(j \cdot t - k \cdot y\right), i, \mathsf{fma}\left(-y0, k \cdot y2 - j \cdot y3, \left(t \cdot y2 - y \cdot y3\right) \cdot a\right)\right) \cdot y5} \]

   6. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 36.4%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right)\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot \color{blue}{y5}\right)\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 27.3%

       \[\leadsto a \cdot \left(\left(t \cdot y2\right) \cdot y5\right) \]

   if -4.99999999999999976e67 < c < -8.80000000000000035e-61 or -4.80000000000000041e-196 < c < 2.1499999999999999e-293

   1. Initial program 38.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 51.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - c \cdot i, x, \left(c \cdot y4 - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in i around inf

      \[\leadsto \left(i \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 37.3%

      \[\leadsto \left(i \cdot \mathsf{fma}\left(k, y5, -c \cdot x\right)\right) \cdot y \]

   9. Taylor expanded in c around 0

      \[\leadsto \left(i \cdot \left(k \cdot y5\right)\right) \cdot y \]
   10. Step-by-step derivation

   11. Applied rewrites 37.3%

       \[\leadsto \left(i \cdot \left(k \cdot y5\right)\right) \cdot y \]

   if -8.80000000000000035e-61 < c < -4.80000000000000041e-196

   1. Initial program 54.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 43.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 16.9%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-1, y3 \cdot y4, i \cdot x\right)\right)} \]

   9. Taylor expanded in z around inf

      \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(i \cdot k\right) + a \cdot y3\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 24.6%

       \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \mathsf{fma}\left(-i, k, a \cdot y3\right)\right)} \]

   12. Taylor expanded in a around inf

       \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(y3 \cdot z\right)}\right) \]
   13. Step-by-step derivation

   14. Applied rewrites 24.2%

       \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(y3 \cdot z\right)}\right) \]

   if 2.1499999999999999e-293 < c < 5.50000000000000022e-173 or 1.07999999999999998e-91 < c < 3.0000000000000001e228

   1. Initial program 32.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot x} \]

   5. Applied rewrites 37.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot a - c \cdot i, y, \mathsf{fma}\left(c \cdot y0 - y1 \cdot a, y2, \left(-j\right) \cdot \left(y0 \cdot b - i \cdot y1\right)\right)\right) \cdot x} \]

   6. Taylor expanded in y around inf

      \[\leadsto \left(y \cdot \left(a \cdot b - c \cdot i\right)\right) \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 39.8%

      \[\leadsto \left(y \cdot \mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right)\right) \cdot x \]

   9. Taylor expanded in c around 0

      \[\leadsto \left(a \cdot \left(b \cdot y\right)\right) \cdot x \]
   10. Step-by-step derivation

   11. Applied rewrites 38.8%

       \[\leadsto \left(a \cdot \left(b \cdot y\right)\right) \cdot x \]

   if 5.50000000000000022e-173 < c < 1.07999999999999998e-91

   1. Initial program 29.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 57.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 31.1%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-1, y3 \cdot y4, i \cdot x\right)\right)} \]

   9. Taylor expanded in z around inf

      \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(i \cdot k\right) + a \cdot y3\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 57.8%

       \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \mathsf{fma}\left(-i, k, a \cdot y3\right)\right)} \]

   12. Taylor expanded in a around inf

       \[\leadsto y1 \cdot \left(a \cdot \left(y3 \cdot \color{blue}{z}\right)\right) \]
   13. Step-by-step derivation

   14. Applied rewrites 50.9%

       \[\leadsto y1 \cdot \left(a \cdot \left(y3 \cdot \color{blue}{z}\right)\right) \]

   if 3.0000000000000001e228 < c

   1. Initial program 5.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 21.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - c \cdot i, x, \left(c \cdot y4 - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in i around inf

      \[\leadsto \left(i \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 68.9%

      \[\leadsto \left(i \cdot \mathsf{fma}\left(k, y5, -c \cdot x\right)\right) \cdot y \]

   9. Taylor expanded in c around inf

      \[\leadsto \left(-1 \cdot \left(c \cdot \left(i \cdot x\right)\right)\right) \cdot y \]
   10. Step-by-step derivation

   11. Applied rewrites 43.0%

       \[\leadsto \left(-c \cdot \left(i \cdot x\right)\right) \cdot y \]
3. Recombined 6 regimes into one program.

4. Final simplification 36.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5 \cdot 10^{+67}:\\ \;\;\;\;\left(\left(y2 \cdot t\right) \cdot y5\right) \cdot a\\ \mathbf{elif}\;c \leq -8.8 \cdot 10^{-61}:\\ \;\;\;\;\left(\left(y5 \cdot k\right) \cdot i\right) \cdot y\\ \mathbf{elif}\;c \leq -4.8 \cdot 10^{-196}:\\ \;\;\;\;\left(\left(y3 \cdot z\right) \cdot y1\right) \cdot a\\ \mathbf{elif}\;c \leq 2.15 \cdot 10^{-293}:\\ \;\;\;\;\left(\left(y5 \cdot k\right) \cdot i\right) \cdot y\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{-173}:\\ \;\;\;\;\left(\left(b \cdot y\right) \cdot a\right) \cdot x\\ \mathbf{elif}\;c \leq 1.08 \cdot 10^{-91}:\\ \;\;\;\;\left(\left(y3 \cdot z\right) \cdot a\right) \cdot y1\\ \mathbf{elif}\;c \leq 3 \cdot 10^{+228}:\\ \;\;\;\;\left(\left(b \cdot y\right) \cdot a\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(-x\right) \cdot i\right) \cdot c\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 37: 28.9% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{+142}:\\ \;\;\;\;\left(\mathsf{fma}\left(j, x, \left(-k\right) \cdot z\right) \cdot i\right) \cdot y1\\ \mathbf{elif}\;x \leq -3.35 \cdot 10^{-43}:\\ \;\;\;\;\left(\mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right) \cdot y1\right) \cdot a\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-307}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y, \left(-t\right) \cdot j\right) \cdot i\right) \cdot y5\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-160}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, k, y3 \cdot a\right) \cdot z\right) \cdot y1\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+80}:\\ \;\;\;\;\left(\mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right) \cdot y5\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, z, y4 \cdot y2\right) \cdot y1\right) \cdot k\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -3.1e+142)
   (* (* (fma j x (* (- k) z)) i) y1)
   (if (<= x -3.35e-43)
     (* (* (fma y3 z (* (- x) y2)) y1) a)
     (if (<= x -2e-307)
       (* (* (fma k y (* (- t) j)) i) y5)
       (if (<= x 1.85e-160)
         (* (* (fma (- i) k (* y3 a)) z) y1)
         (if (<= x 7.5e+80)
           (* (* (fma t y2 (* (- y) y3)) y5) a)
           (* (* (fma (- i) z (* y4 y2)) y1) k)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -3.1e+142) {
		tmp = (fma(j, x, (-k * z)) * i) * y1;
	} else if (x <= -3.35e-43) {
		tmp = (fma(y3, z, (-x * y2)) * y1) * a;
	} else if (x <= -2e-307) {
		tmp = (fma(k, y, (-t * j)) * i) * y5;
	} else if (x <= 1.85e-160) {
		tmp = (fma(-i, k, (y3 * a)) * z) * y1;
	} else if (x <= 7.5e+80) {
		tmp = (fma(t, y2, (-y * y3)) * y5) * a;
	} else {
		tmp = (fma(-i, z, (y4 * y2)) * y1) * k;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (x <= -3.1e+142)
		tmp = Float64(Float64(fma(j, x, Float64(Float64(-k) * z)) * i) * y1);
	elseif (x <= -3.35e-43)
		tmp = Float64(Float64(fma(y3, z, Float64(Float64(-x) * y2)) * y1) * a);
	elseif (x <= -2e-307)
		tmp = Float64(Float64(fma(k, y, Float64(Float64(-t) * j)) * i) * y5);
	elseif (x <= 1.85e-160)
		tmp = Float64(Float64(fma(Float64(-i), k, Float64(y3 * a)) * z) * y1);
	elseif (x <= 7.5e+80)
		tmp = Float64(Float64(fma(t, y2, Float64(Float64(-y) * y3)) * y5) * a);
	else
		tmp = Float64(Float64(fma(Float64(-i), z, Float64(y4 * y2)) * y1) * k);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[x, -3.1e+142], N[(N[(N[(j * x + N[((-k) * z), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision] * y1), $MachinePrecision], If[LessEqual[x, -3.35e-43], N[(N[(N[(y3 * z + N[((-x) * y2), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[x, -2e-307], N[(N[(N[(k * y + N[((-t) * j), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision] * y5), $MachinePrecision], If[LessEqual[x, 1.85e-160], N[(N[(N[((-i) * k + N[(y3 * a), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] * y1), $MachinePrecision], If[LessEqual[x, 7.5e+80], N[(N[(N[(t * y2 + N[((-y) * y3), $MachinePrecision]), $MachinePrecision] * y5), $MachinePrecision] * a), $MachinePrecision], N[(N[(N[((-i) * z + N[(y4 * y2), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision] * k), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -3.0999999999999999e142

   1. Initial program 22.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 32.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in i around inf

      \[\leadsto \left(i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1 \]
   7. Step-by-step derivation

   8. Applied rewrites 46.1%

      \[\leadsto \left(i \cdot \mathsf{fma}\left(j, x, \left(-k\right) \cdot z\right)\right) \cdot y1 \]

   if -3.0999999999999999e142 < x < -3.3499999999999999e-43

   1. Initial program 34.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 48.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 43.3%

      \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right)\right)} \]

   if -3.3499999999999999e-43 < x < -1.99999999999999982e-307

   1. Initial program 28.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

   5. Applied rewrites 58.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(j \cdot t - k \cdot y\right), i, \mathsf{fma}\left(-y0, k \cdot y2 - j \cdot y3, \left(t \cdot y2 - y \cdot y3\right) \cdot a\right)\right) \cdot y5} \]

   6. Taylor expanded in i around inf

      \[\leadsto \left(i \cdot \left(k \cdot y - j \cdot t\right)\right) \cdot y5 \]
   7. Step-by-step derivation

   8. Applied rewrites 45.9%

      \[\leadsto \left(i \cdot \mathsf{fma}\left(k, y, \left(-j\right) \cdot t\right)\right) \cdot y5 \]

   if -1.99999999999999982e-307 < x < 1.84999999999999988e-160

   1. Initial program 44.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 56.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 15.2%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-1, y3 \cdot y4, i \cdot x\right)\right)} \]

   9. Taylor expanded in z around inf

      \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(i \cdot k\right) + a \cdot y3\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 45.4%

       \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \mathsf{fma}\left(-i, k, a \cdot y3\right)\right)} \]

   if 1.84999999999999988e-160 < x < 7.49999999999999994e80

   1. Initial program 30.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

   5. Applied rewrites 49.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(j \cdot t - k \cdot y\right), i, \mathsf{fma}\left(-y0, k \cdot y2 - j \cdot y3, \left(t \cdot y2 - y \cdot y3\right) \cdot a\right)\right) \cdot y5} \]

   6. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 49.9%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right)\right)} \]

   if 7.49999999999999994e80 < x

   1. Initial program 27.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 39.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 37.2%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-1, y3 \cdot y4, i \cdot x\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto k \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(i \cdot z\right) + y2 \cdot y4\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 40.6%

       \[\leadsto k \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-i, z, y2 \cdot y4\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{+142}:\\ \;\;\;\;\left(\mathsf{fma}\left(j, x, \left(-k\right) \cdot z\right) \cdot i\right) \cdot y1\\ \mathbf{elif}\;x \leq -3.35 \cdot 10^{-43}:\\ \;\;\;\;\left(\mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right) \cdot y1\right) \cdot a\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-307}:\\ \;\;\;\;\left(\mathsf{fma}\left(k, y, \left(-t\right) \cdot j\right) \cdot i\right) \cdot y5\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-160}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, k, y3 \cdot a\right) \cdot z\right) \cdot y1\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+80}:\\ \;\;\;\;\left(\mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right) \cdot y5\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, z, y4 \cdot y2\right) \cdot y1\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 38: 16.7% accurate, 3.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(b \cdot y\right) \cdot a\right) \cdot x\\ t_2 := \left(\left(y5 \cdot k\right) \cdot i\right) \cdot y\\ \mathbf{if}\;c \leq -5 \cdot 10^{+67}:\\ \;\;\;\;\left(\left(y2 \cdot t\right) \cdot y5\right) \cdot a\\ \mathbf{elif}\;c \leq -8.8 \cdot 10^{-61}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -4.8 \cdot 10^{-196}:\\ \;\;\;\;\left(\left(y3 \cdot z\right) \cdot y1\right) \cdot a\\ \mathbf{elif}\;c \leq 2.15 \cdot 10^{-293}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{-173}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 1.08 \cdot 10^{-91}:\\ \;\;\;\;\left(\left(y3 \cdot z\right) \cdot a\right) \cdot y1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* (* b y) a) x)) (t_2 (* (* (* y5 k) i) y)))
   (if (<= c -5e+67)
     (* (* (* y2 t) y5) a)
     (if (<= c -8.8e-61)
       t_2
       (if (<= c -4.8e-196)
         (* (* (* y3 z) y1) a)
         (if (<= c 2.15e-293)
           t_2
           (if (<= c 5.5e-173)
             t_1
             (if (<= c 1.08e-91) (* (* (* y3 z) a) y1) 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 * y) * a) * x;
	double t_2 = ((y5 * k) * i) * y;
	double tmp;
	if (c <= -5e+67) {
		tmp = ((y2 * t) * y5) * a;
	} else if (c <= -8.8e-61) {
		tmp = t_2;
	} else if (c <= -4.8e-196) {
		tmp = ((y3 * z) * y1) * a;
	} else if (c <= 2.15e-293) {
		tmp = t_2;
	} else if (c <= 5.5e-173) {
		tmp = t_1;
	} else if (c <= 1.08e-91) {
		tmp = ((y3 * z) * a) * y1;
	} 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 = ((b * y) * a) * x
    t_2 = ((y5 * k) * i) * y
    if (c <= (-5d+67)) then
        tmp = ((y2 * t) * y5) * a
    else if (c <= (-8.8d-61)) then
        tmp = t_2
    else if (c <= (-4.8d-196)) then
        tmp = ((y3 * z) * y1) * a
    else if (c <= 2.15d-293) then
        tmp = t_2
    else if (c <= 5.5d-173) then
        tmp = t_1
    else if (c <= 1.08d-91) then
        tmp = ((y3 * z) * a) * y1
    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 * y) * a) * x;
	double t_2 = ((y5 * k) * i) * y;
	double tmp;
	if (c <= -5e+67) {
		tmp = ((y2 * t) * y5) * a;
	} else if (c <= -8.8e-61) {
		tmp = t_2;
	} else if (c <= -4.8e-196) {
		tmp = ((y3 * z) * y1) * a;
	} else if (c <= 2.15e-293) {
		tmp = t_2;
	} else if (c <= 5.5e-173) {
		tmp = t_1;
	} else if (c <= 1.08e-91) {
		tmp = ((y3 * z) * a) * y1;
	} 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 * y) * a) * x
	t_2 = ((y5 * k) * i) * y
	tmp = 0
	if c <= -5e+67:
		tmp = ((y2 * t) * y5) * a
	elif c <= -8.8e-61:
		tmp = t_2
	elif c <= -4.8e-196:
		tmp = ((y3 * z) * y1) * a
	elif c <= 2.15e-293:
		tmp = t_2
	elif c <= 5.5e-173:
		tmp = t_1
	elif c <= 1.08e-91:
		tmp = ((y3 * z) * a) * y1
	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(Float64(b * y) * a) * x)
	t_2 = Float64(Float64(Float64(y5 * k) * i) * y)
	tmp = 0.0
	if (c <= -5e+67)
		tmp = Float64(Float64(Float64(y2 * t) * y5) * a);
	elseif (c <= -8.8e-61)
		tmp = t_2;
	elseif (c <= -4.8e-196)
		tmp = Float64(Float64(Float64(y3 * z) * y1) * a);
	elseif (c <= 2.15e-293)
		tmp = t_2;
	elseif (c <= 5.5e-173)
		tmp = t_1;
	elseif (c <= 1.08e-91)
		tmp = Float64(Float64(Float64(y3 * z) * a) * y1);
	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 * y) * a) * x;
	t_2 = ((y5 * k) * i) * y;
	tmp = 0.0;
	if (c <= -5e+67)
		tmp = ((y2 * t) * y5) * a;
	elseif (c <= -8.8e-61)
		tmp = t_2;
	elseif (c <= -4.8e-196)
		tmp = ((y3 * z) * y1) * a;
	elseif (c <= 2.15e-293)
		tmp = t_2;
	elseif (c <= 5.5e-173)
		tmp = t_1;
	elseif (c <= 1.08e-91)
		tmp = ((y3 * z) * a) * y1;
	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[(N[(b * y), $MachinePrecision] * a), $MachinePrecision] * x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y5 * k), $MachinePrecision] * i), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[c, -5e+67], N[(N[(N[(y2 * t), $MachinePrecision] * y5), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[c, -8.8e-61], t$95$2, If[LessEqual[c, -4.8e-196], N[(N[(N[(y3 * z), $MachinePrecision] * y1), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[c, 2.15e-293], t$95$2, If[LessEqual[c, 5.5e-173], t$95$1, If[LessEqual[c, 1.08e-91], N[(N[(N[(y3 * z), $MachinePrecision] * a), $MachinePrecision] * y1), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -4.99999999999999976e67

   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 y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

   5. Applied rewrites 36.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(j \cdot t - k \cdot y\right), i, \mathsf{fma}\left(-y0, k \cdot y2 - j \cdot y3, \left(t \cdot y2 - y \cdot y3\right) \cdot a\right)\right) \cdot y5} \]

   6. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 36.4%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right)\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot \color{blue}{y5}\right)\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 27.3%

       \[\leadsto a \cdot \left(\left(t \cdot y2\right) \cdot y5\right) \]

   if -4.99999999999999976e67 < c < -8.80000000000000035e-61 or -4.80000000000000041e-196 < c < 2.1499999999999999e-293

   1. Initial program 38.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 51.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - c \cdot i, x, \left(c \cdot y4 - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in i around inf

      \[\leadsto \left(i \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 37.3%

      \[\leadsto \left(i \cdot \mathsf{fma}\left(k, y5, -c \cdot x\right)\right) \cdot y \]

   9. Taylor expanded in c around 0

      \[\leadsto \left(i \cdot \left(k \cdot y5\right)\right) \cdot y \]
   10. Step-by-step derivation

   11. Applied rewrites 37.3%

       \[\leadsto \left(i \cdot \left(k \cdot y5\right)\right) \cdot y \]

   if -8.80000000000000035e-61 < c < -4.80000000000000041e-196

   1. Initial program 54.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 43.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 16.9%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-1, y3 \cdot y4, i \cdot x\right)\right)} \]

   9. Taylor expanded in z around inf

      \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(i \cdot k\right) + a \cdot y3\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 24.6%

       \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \mathsf{fma}\left(-i, k, a \cdot y3\right)\right)} \]

   12. Taylor expanded in a around inf

       \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(y3 \cdot z\right)}\right) \]
   13. Step-by-step derivation

   14. Applied rewrites 24.2%

       \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(y3 \cdot z\right)}\right) \]

   if 2.1499999999999999e-293 < c < 5.50000000000000022e-173 or 1.07999999999999998e-91 < c

   1. Initial program 27.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot x} \]

   5. Applied rewrites 35.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot a - c \cdot i, y, \mathsf{fma}\left(c \cdot y0 - y1 \cdot a, y2, \left(-j\right) \cdot \left(y0 \cdot b - i \cdot y1\right)\right)\right) \cdot x} \]

   6. Taylor expanded in y around inf

      \[\leadsto \left(y \cdot \left(a \cdot b - c \cdot i\right)\right) \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 41.3%

      \[\leadsto \left(y \cdot \mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right)\right) \cdot x \]

   9. Taylor expanded in c around 0

      \[\leadsto \left(a \cdot \left(b \cdot y\right)\right) \cdot x \]
   10. Step-by-step derivation

   11. Applied rewrites 34.9%

       \[\leadsto \left(a \cdot \left(b \cdot y\right)\right) \cdot x \]

   if 5.50000000000000022e-173 < c < 1.07999999999999998e-91

   1. Initial program 29.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 57.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 31.1%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-1, y3 \cdot y4, i \cdot x\right)\right)} \]

   9. Taylor expanded in z around inf

      \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(i \cdot k\right) + a \cdot y3\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 57.8%

       \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \mathsf{fma}\left(-i, k, a \cdot y3\right)\right)} \]

   12. Taylor expanded in a around inf

       \[\leadsto y1 \cdot \left(a \cdot \left(y3 \cdot \color{blue}{z}\right)\right) \]
   13. Step-by-step derivation

   14. Applied rewrites 50.9%

       \[\leadsto y1 \cdot \left(a \cdot \left(y3 \cdot \color{blue}{z}\right)\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 34.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5 \cdot 10^{+67}:\\ \;\;\;\;\left(\left(y2 \cdot t\right) \cdot y5\right) \cdot a\\ \mathbf{elif}\;c \leq -8.8 \cdot 10^{-61}:\\ \;\;\;\;\left(\left(y5 \cdot k\right) \cdot i\right) \cdot y\\ \mathbf{elif}\;c \leq -4.8 \cdot 10^{-196}:\\ \;\;\;\;\left(\left(y3 \cdot z\right) \cdot y1\right) \cdot a\\ \mathbf{elif}\;c \leq 2.15 \cdot 10^{-293}:\\ \;\;\;\;\left(\left(y5 \cdot k\right) \cdot i\right) \cdot y\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{-173}:\\ \;\;\;\;\left(\left(b \cdot y\right) \cdot a\right) \cdot x\\ \mathbf{elif}\;c \leq 1.08 \cdot 10^{-91}:\\ \;\;\;\;\left(\left(y3 \cdot z\right) \cdot a\right) \cdot y1\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot y\right) \cdot a\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 39: 28.3% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{-51}:\\ \;\;\;\;\left(\mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right) \cdot y5\right) \cdot a\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-82}:\\ \;\;\;\;\mathsf{fma}\left(i, y, \left(-y0\right) \cdot y2\right) \cdot \left(y5 \cdot k\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-22}:\\ \;\;\;\;\left(\left(\left(-y3\right) \cdot y4\right) \cdot y1\right) \cdot j\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+50}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, t, y3 \cdot y0\right) \cdot y5\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot y\right) \cdot a\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= a -2.1e-51)
   (* (* (fma t y2 (* (- y) y3)) y5) a)
   (if (<= a 9.2e-82)
     (* (fma i y (* (- y0) y2)) (* y5 k))
     (if (<= a 1.05e-22)
       (* (* (* (- y3) y4) y1) j)
       (if (<= a 3.5e+50)
         (* (* (fma (- i) t (* y3 y0)) y5) j)
         (* (* (* b y) a) x))))))

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 <= -2.1e-51) {
		tmp = (fma(t, y2, (-y * y3)) * y5) * a;
	} else if (a <= 9.2e-82) {
		tmp = fma(i, y, (-y0 * y2)) * (y5 * k);
	} else if (a <= 1.05e-22) {
		tmp = ((-y3 * y4) * y1) * j;
	} else if (a <= 3.5e+50) {
		tmp = (fma(-i, t, (y3 * y0)) * y5) * j;
	} else {
		tmp = ((b * y) * a) * x;
	}
	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 <= -2.1e-51)
		tmp = Float64(Float64(fma(t, y2, Float64(Float64(-y) * y3)) * y5) * a);
	elseif (a <= 9.2e-82)
		tmp = Float64(fma(i, y, Float64(Float64(-y0) * y2)) * Float64(y5 * k));
	elseif (a <= 1.05e-22)
		tmp = Float64(Float64(Float64(Float64(-y3) * y4) * y1) * j);
	elseif (a <= 3.5e+50)
		tmp = Float64(Float64(fma(Float64(-i), t, Float64(y3 * y0)) * y5) * j);
	else
		tmp = Float64(Float64(Float64(b * y) * a) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[a, -2.1e-51], N[(N[(N[(t * y2 + N[((-y) * y3), $MachinePrecision]), $MachinePrecision] * y5), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[a, 9.2e-82], N[(N[(i * y + N[((-y0) * y2), $MachinePrecision]), $MachinePrecision] * N[(y5 * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.05e-22], N[(N[(N[((-y3) * y4), $MachinePrecision] * y1), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[a, 3.5e+50], N[(N[(N[((-i) * t + N[(y3 * y0), $MachinePrecision]), $MachinePrecision] * y5), $MachinePrecision] * j), $MachinePrecision], N[(N[(N[(b * y), $MachinePrecision] * a), $MachinePrecision] * x), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.10000000000000002e-51

   1. Initial program 22.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

   5. Applied rewrites 42.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(j \cdot t - k \cdot y\right), i, \mathsf{fma}\left(-y0, k \cdot y2 - j \cdot y3, \left(t \cdot y2 - y \cdot y3\right) \cdot a\right)\right) \cdot y5} \]

   6. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 37.0%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right)\right)} \]

   if -2.10000000000000002e-51 < a < 9.19999999999999988e-82

   1. Initial program 40.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

   5. Applied rewrites 41.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(j \cdot t - k \cdot y\right), i, \mathsf{fma}\left(-y0, k \cdot y2 - j \cdot y3, \left(t \cdot y2 - y \cdot y3\right) \cdot a\right)\right) \cdot y5} \]

   6. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 17.8%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto k \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 35.7%

       \[\leadsto \left(k \cdot y5\right) \cdot \color{blue}{\mathsf{fma}\left(i, y, -y0 \cdot y2\right)} \]

   if 9.19999999999999988e-82 < a < 1.05000000000000004e-22

   1. Initial program 36.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 46.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 55.8%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-1, y3 \cdot y4, i \cdot x\right)\right)} \]

   9. Taylor expanded in y4 around inf

      \[\leadsto j \cdot \left(y1 \cdot \left(-1 \cdot \left(y3 \cdot \color{blue}{y4}\right)\right)\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 55.2%

       \[\leadsto j \cdot \left(y1 \cdot \left(\left(-y3\right) \cdot y4\right)\right) \]

   if 1.05000000000000004e-22 < a < 3.50000000000000006e50

   1. Initial program 44.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

   5. Applied rewrites 78.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(j \cdot t - k \cdot y\right), i, \mathsf{fma}\left(-y0, k \cdot y2 - j \cdot y3, \left(t \cdot y2 - y \cdot y3\right) \cdot a\right)\right) \cdot y5} \]

   6. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 24.0%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right)\right)} \]

   9. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 40.2%

       \[\leadsto j \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(-i, t, y0 \cdot y3\right)\right)} \]

   if 3.50000000000000006e50 < a

   1. Initial program 22.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot x} \]

   5. Applied rewrites 42.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot a - c \cdot i, y, \mathsf{fma}\left(c \cdot y0 - y1 \cdot a, y2, \left(-j\right) \cdot \left(y0 \cdot b - i \cdot y1\right)\right)\right) \cdot x} \]

   6. Taylor expanded in y around inf

      \[\leadsto \left(y \cdot \left(a \cdot b - c \cdot i\right)\right) \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 44.3%

      \[\leadsto \left(y \cdot \mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right)\right) \cdot x \]

   9. Taylor expanded in c around 0

      \[\leadsto \left(a \cdot \left(b \cdot y\right)\right) \cdot x \]
   10. Step-by-step derivation

   11. Applied rewrites 36.8%

       \[\leadsto \left(a \cdot \left(b \cdot y\right)\right) \cdot x \]
3. Recombined 5 regimes into one program.

4. Final simplification 37.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{-51}:\\ \;\;\;\;\left(\mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right) \cdot y5\right) \cdot a\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-82}:\\ \;\;\;\;\mathsf{fma}\left(i, y, \left(-y0\right) \cdot y2\right) \cdot \left(y5 \cdot k\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-22}:\\ \;\;\;\;\left(\left(\left(-y3\right) \cdot y4\right) \cdot y1\right) \cdot j\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+50}:\\ \;\;\;\;\left(\mathsf{fma}\left(-i, t, y3 \cdot y0\right) \cdot y5\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot y\right) \cdot a\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 40: 26.0% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(j \cdot x\right) \cdot y1\right) \cdot i\\ t_2 := \left(\left(b \cdot y\right) \cdot a\right) \cdot x\\ \mathbf{if}\;x \leq -4.7 \cdot 10^{+142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{+86}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-81}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+161}:\\ \;\;\;\;\left(\mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right) \cdot y5\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* (* j x) y1) i)) (t_2 (* (* (* b y) a) x)))
   (if (<= x -4.7e+142)
     t_1
     (if (<= x -2.8e+86)
       t_2
       (if (<= x -7e-81)
         t_1
         (if (<= x 1.6e+161) (* (* (fma t y2 (* (- y) y3)) y5) a) 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 * x) * y1) * i;
	double t_2 = ((b * y) * a) * x;
	double tmp;
	if (x <= -4.7e+142) {
		tmp = t_1;
	} else if (x <= -2.8e+86) {
		tmp = t_2;
	} else if (x <= -7e-81) {
		tmp = t_1;
	} else if (x <= 1.6e+161) {
		tmp = (fma(t, y2, (-y * y3)) * y5) * a;
	} 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(Float64(j * x) * y1) * i)
	t_2 = Float64(Float64(Float64(b * y) * a) * x)
	tmp = 0.0
	if (x <= -4.7e+142)
		tmp = t_1;
	elseif (x <= -2.8e+86)
		tmp = t_2;
	elseif (x <= -7e-81)
		tmp = t_1;
	elseif (x <= 1.6e+161)
		tmp = Float64(Float64(fma(t, y2, Float64(Float64(-y) * y3)) * y5) * a);
	else
		tmp = t_2;
	end
	return 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[(N[(j * x), $MachinePrecision] * y1), $MachinePrecision] * i), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(b * y), $MachinePrecision] * a), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -4.7e+142], t$95$1, If[LessEqual[x, -2.8e+86], t$95$2, If[LessEqual[x, -7e-81], t$95$1, If[LessEqual[x, 1.6e+161], N[(N[(N[(t * y2 + N[((-y) * y3), $MachinePrecision]), $MachinePrecision] * y5), $MachinePrecision] * a), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.7e142 or -2.80000000000000004e86 < x < -6.99999999999999973e-81

   1. Initial program 29.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 35.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 33.3%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-1, y3 \cdot y4, i \cdot x\right)\right)} \]

   9. Taylor expanded in y4 around 0

      \[\leadsto i \cdot \left(j \cdot \color{blue}{\left(x \cdot y1\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 33.3%

       \[\leadsto i \cdot \left(\left(j \cdot x\right) \cdot \color{blue}{y1}\right) \]

   if -4.7e142 < x < -2.80000000000000004e86 or 1.60000000000000001e161 < x

   1. Initial program 22.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot x} \]

   5. Applied rewrites 48.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot a - c \cdot i, y, \mathsf{fma}\left(c \cdot y0 - y1 \cdot a, y2, \left(-j\right) \cdot \left(y0 \cdot b - i \cdot y1\right)\right)\right) \cdot x} \]

   6. Taylor expanded in y around inf

      \[\leadsto \left(y \cdot \left(a \cdot b - c \cdot i\right)\right) \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 57.5%

      \[\leadsto \left(y \cdot \mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right)\right) \cdot x \]

   9. Taylor expanded in c around 0

      \[\leadsto \left(a \cdot \left(b \cdot y\right)\right) \cdot x \]
   10. Step-by-step derivation

   11. Applied rewrites 41.7%

       \[\leadsto \left(a \cdot \left(b \cdot y\right)\right) \cdot x \]

   if -6.99999999999999973e-81 < x < 1.60000000000000001e161

   1. Initial program 34.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

   5. Applied rewrites 48.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(j \cdot t - k \cdot y\right), i, \mathsf{fma}\left(-y0, k \cdot y2 - j \cdot y3, \left(t \cdot y2 - y \cdot y3\right) \cdot a\right)\right) \cdot y5} \]

   6. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 35.8%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 36.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.7 \cdot 10^{+142}:\\ \;\;\;\;\left(\left(j \cdot x\right) \cdot y1\right) \cdot i\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{+86}:\\ \;\;\;\;\left(\left(b \cdot y\right) \cdot a\right) \cdot x\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-81}:\\ \;\;\;\;\left(\left(j \cdot x\right) \cdot y1\right) \cdot i\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+161}:\\ \;\;\;\;\left(\mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right) \cdot y5\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot y\right) \cdot a\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 41: 20.2% accurate, 5.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{-51}:\\ \;\;\;\;\left(\left(y3 \cdot z\right) \cdot y1\right) \cdot a\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-199}:\\ \;\;\;\;\left(\left(y5 \cdot k\right) \cdot i\right) \cdot y\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-7}:\\ \;\;\;\;\left(\left(j \cdot x\right) \cdot y1\right) \cdot i\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y2 \cdot t\right) \cdot y5\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= a -1.7e-51)
   (* (* (* y3 z) y1) a)
   (if (<= a -8e-199)
     (* (* (* y5 k) i) y)
     (if (<= a 2.8e-7) (* (* (* j x) y1) i) (* (* (* y2 t) y5) a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (a <= -1.7e-51) {
		tmp = ((y3 * z) * y1) * a;
	} else if (a <= -8e-199) {
		tmp = ((y5 * k) * i) * y;
	} else if (a <= 2.8e-7) {
		tmp = ((j * x) * y1) * i;
	} else {
		tmp = ((y2 * t) * y5) * a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (a <= (-1.7d-51)) then
        tmp = ((y3 * z) * y1) * a
    else if (a <= (-8d-199)) then
        tmp = ((y5 * k) * i) * y
    else if (a <= 2.8d-7) then
        tmp = ((j * x) * y1) * i
    else
        tmp = ((y2 * t) * y5) * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (a <= -1.7e-51) {
		tmp = ((y3 * z) * y1) * a;
	} else if (a <= -8e-199) {
		tmp = ((y5 * k) * i) * y;
	} else if (a <= 2.8e-7) {
		tmp = ((j * x) * y1) * i;
	} else {
		tmp = ((y2 * t) * y5) * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if a <= -1.7e-51:
		tmp = ((y3 * z) * y1) * a
	elif a <= -8e-199:
		tmp = ((y5 * k) * i) * y
	elif a <= 2.8e-7:
		tmp = ((j * x) * y1) * i
	else:
		tmp = ((y2 * t) * y5) * a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (a <= -1.7e-51)
		tmp = Float64(Float64(Float64(y3 * z) * y1) * a);
	elseif (a <= -8e-199)
		tmp = Float64(Float64(Float64(y5 * k) * i) * y);
	elseif (a <= 2.8e-7)
		tmp = Float64(Float64(Float64(j * x) * y1) * i);
	else
		tmp = Float64(Float64(Float64(y2 * t) * y5) * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (a <= -1.7e-51)
		tmp = ((y3 * z) * y1) * a;
	elseif (a <= -8e-199)
		tmp = ((y5 * k) * i) * y;
	elseif (a <= 2.8e-7)
		tmp = ((j * x) * y1) * i;
	else
		tmp = ((y2 * t) * y5) * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[a, -1.7e-51], N[(N[(N[(y3 * z), $MachinePrecision] * y1), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[a, -8e-199], N[(N[(N[(y5 * k), $MachinePrecision] * i), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[a, 2.8e-7], N[(N[(N[(j * x), $MachinePrecision] * y1), $MachinePrecision] * i), $MachinePrecision], N[(N[(N[(y2 * t), $MachinePrecision] * y5), $MachinePrecision] * a), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.70000000000000001e-51

   1. Initial program 22.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 40.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 17.7%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-1, y3 \cdot y4, i \cdot x\right)\right)} \]

   9. Taylor expanded in z around inf

      \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(i \cdot k\right) + a \cdot y3\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 40.7%

       \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \mathsf{fma}\left(-i, k, a \cdot y3\right)\right)} \]

   12. Taylor expanded in a around inf

       \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(y3 \cdot z\right)}\right) \]
   13. Step-by-step derivation

   14. Applied rewrites 29.8%

       \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(y3 \cdot z\right)}\right) \]

   if -1.70000000000000001e-51 < a < -7.99999999999999986e-199

   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 y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 41.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - c \cdot i, x, \left(c \cdot y4 - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in i around inf

      \[\leadsto \left(i \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 35.4%

      \[\leadsto \left(i \cdot \mathsf{fma}\left(k, y5, -c \cdot x\right)\right) \cdot y \]

   9. Taylor expanded in c around 0

      \[\leadsto \left(i \cdot \left(k \cdot y5\right)\right) \cdot y \]
   10. Step-by-step derivation

   11. Applied rewrites 31.3%

       \[\leadsto \left(i \cdot \left(k \cdot y5\right)\right) \cdot y \]

   if -7.99999999999999986e-199 < a < 2.80000000000000019e-7

   1. Initial program 44.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 45.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 35.3%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-1, y3 \cdot y4, i \cdot x\right)\right)} \]

   9. Taylor expanded in y4 around 0

      \[\leadsto i \cdot \left(j \cdot \color{blue}{\left(x \cdot y1\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 29.0%

       \[\leadsto i \cdot \left(\left(j \cdot x\right) \cdot \color{blue}{y1}\right) \]

   if 2.80000000000000019e-7 < a

   1. Initial program 27.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

   5. Applied rewrites 47.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(j \cdot t - k \cdot y\right), i, \mathsf{fma}\left(-y0, k \cdot y2 - j \cdot y3, \left(t \cdot y2 - y \cdot y3\right) \cdot a\right)\right) \cdot y5} \]

   6. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 32.0%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right)\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot \color{blue}{y5}\right)\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 28.3%

       \[\leadsto a \cdot \left(\left(t \cdot y2\right) \cdot y5\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 29.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{-51}:\\ \;\;\;\;\left(\left(y3 \cdot z\right) \cdot y1\right) \cdot a\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-199}:\\ \;\;\;\;\left(\left(y5 \cdot k\right) \cdot i\right) \cdot y\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-7}:\\ \;\;\;\;\left(\left(j \cdot x\right) \cdot y1\right) \cdot i\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y2 \cdot t\right) \cdot y5\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 42: 19.9% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{-178}:\\ \;\;\;\;\left(\left(y3 \cdot z\right) \cdot a\right) \cdot y1\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-7}:\\ \;\;\;\;\left(\left(j \cdot x\right) \cdot y1\right) \cdot i\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y2 \cdot t\right) \cdot y5\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= a -1.7e-178)
   (* (* (* y3 z) a) y1)
   (if (<= a 2.8e-7) (* (* (* j x) y1) i) (* (* (* y2 t) y5) a))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (a <= -1.7e-178) {
		tmp = ((y3 * z) * a) * y1;
	} else if (a <= 2.8e-7) {
		tmp = ((j * x) * y1) * i;
	} else {
		tmp = ((y2 * t) * y5) * a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (a <= (-1.7d-178)) then
        tmp = ((y3 * z) * a) * y1
    else if (a <= 2.8d-7) then
        tmp = ((j * x) * y1) * i
    else
        tmp = ((y2 * t) * y5) * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (a <= -1.7e-178) {
		tmp = ((y3 * z) * a) * y1;
	} else if (a <= 2.8e-7) {
		tmp = ((j * x) * y1) * i;
	} else {
		tmp = ((y2 * t) * y5) * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if a <= -1.7e-178:
		tmp = ((y3 * z) * a) * y1
	elif a <= 2.8e-7:
		tmp = ((j * x) * y1) * i
	else:
		tmp = ((y2 * t) * y5) * a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (a <= -1.7e-178)
		tmp = Float64(Float64(Float64(y3 * z) * a) * y1);
	elseif (a <= 2.8e-7)
		tmp = Float64(Float64(Float64(j * x) * y1) * i);
	else
		tmp = Float64(Float64(Float64(y2 * t) * y5) * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (a <= -1.7e-178)
		tmp = ((y3 * z) * a) * y1;
	elseif (a <= 2.8e-7)
		tmp = ((j * x) * y1) * i;
	else
		tmp = ((y2 * t) * y5) * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[a, -1.7e-178], N[(N[(N[(y3 * z), $MachinePrecision] * a), $MachinePrecision] * y1), $MachinePrecision], If[LessEqual[a, 2.8e-7], N[(N[(N[(j * x), $MachinePrecision] * y1), $MachinePrecision] * i), $MachinePrecision], N[(N[(N[(y2 * t), $MachinePrecision] * y5), $MachinePrecision] * a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.69999999999999986e-178

   1. Initial program 24.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 41.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 17.8%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-1, y3 \cdot y4, i \cdot x\right)\right)} \]

   9. Taylor expanded in z around inf

      \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(i \cdot k\right) + a \cdot y3\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 37.3%

       \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \mathsf{fma}\left(-i, k, a \cdot y3\right)\right)} \]

   12. Taylor expanded in a around inf

       \[\leadsto y1 \cdot \left(a \cdot \left(y3 \cdot \color{blue}{z}\right)\right) \]
   13. Step-by-step derivation

   14. Applied rewrites 25.2%

       \[\leadsto y1 \cdot \left(a \cdot \left(y3 \cdot \color{blue}{z}\right)\right) \]

   if -1.69999999999999986e-178 < a < 2.80000000000000019e-7

   1. Initial program 42.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 47.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 36.6%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-1, y3 \cdot y4, i \cdot x\right)\right)} \]

   9. Taylor expanded in y4 around 0

      \[\leadsto i \cdot \left(j \cdot \color{blue}{\left(x \cdot y1\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 29.2%

       \[\leadsto i \cdot \left(\left(j \cdot x\right) \cdot \color{blue}{y1}\right) \]

   if 2.80000000000000019e-7 < a

   1. Initial program 27.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

   5. Applied rewrites 47.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(j \cdot t - k \cdot y\right), i, \mathsf{fma}\left(-y0, k \cdot y2 - j \cdot y3, \left(t \cdot y2 - y \cdot y3\right) \cdot a\right)\right) \cdot y5} \]

   6. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 32.0%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right)\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot \color{blue}{y5}\right)\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 28.3%

       \[\leadsto a \cdot \left(\left(t \cdot y2\right) \cdot y5\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 27.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{-178}:\\ \;\;\;\;\left(\left(y3 \cdot z\right) \cdot a\right) \cdot y1\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-7}:\\ \;\;\;\;\left(\left(j \cdot x\right) \cdot y1\right) \cdot i\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y2 \cdot t\right) \cdot y5\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 43: 19.6% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{-180}:\\ \;\;\;\;\left(\left(y3 \cdot z\right) \cdot y1\right) \cdot a\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-7}:\\ \;\;\;\;\left(\left(j \cdot x\right) \cdot y1\right) \cdot i\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y2 \cdot t\right) \cdot y5\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= a -3.8e-180)
   (* (* (* y3 z) y1) a)
   (if (<= a 2.8e-7) (* (* (* j x) y1) i) (* (* (* y2 t) y5) a))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (a <= -3.8e-180) {
		tmp = ((y3 * z) * y1) * a;
	} else if (a <= 2.8e-7) {
		tmp = ((j * x) * y1) * i;
	} else {
		tmp = ((y2 * t) * y5) * a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (a <= (-3.8d-180)) then
        tmp = ((y3 * z) * y1) * a
    else if (a <= 2.8d-7) then
        tmp = ((j * x) * y1) * i
    else
        tmp = ((y2 * t) * y5) * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (a <= -3.8e-180) {
		tmp = ((y3 * z) * y1) * a;
	} else if (a <= 2.8e-7) {
		tmp = ((j * x) * y1) * i;
	} else {
		tmp = ((y2 * t) * y5) * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if a <= -3.8e-180:
		tmp = ((y3 * z) * y1) * a
	elif a <= 2.8e-7:
		tmp = ((j * x) * y1) * i
	else:
		tmp = ((y2 * t) * y5) * a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (a <= -3.8e-180)
		tmp = Float64(Float64(Float64(y3 * z) * y1) * a);
	elseif (a <= 2.8e-7)
		tmp = Float64(Float64(Float64(j * x) * y1) * i);
	else
		tmp = Float64(Float64(Float64(y2 * t) * y5) * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (a <= -3.8e-180)
		tmp = ((y3 * z) * y1) * a;
	elseif (a <= 2.8e-7)
		tmp = ((j * x) * y1) * i;
	else
		tmp = ((y2 * t) * y5) * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[a, -3.8e-180], N[(N[(N[(y3 * z), $MachinePrecision] * y1), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[a, 2.8e-7], N[(N[(N[(j * x), $MachinePrecision] * y1), $MachinePrecision] * i), $MachinePrecision], N[(N[(N[(y2 * t), $MachinePrecision] * y5), $MachinePrecision] * a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.79999999999999999e-180

   1. Initial program 24.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 41.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 17.8%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-1, y3 \cdot y4, i \cdot x\right)\right)} \]

   9. Taylor expanded in z around inf

      \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(i \cdot k\right) + a \cdot y3\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 37.3%

       \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \mathsf{fma}\left(-i, k, a \cdot y3\right)\right)} \]

   12. Taylor expanded in a around inf

       \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(y3 \cdot z\right)}\right) \]
   13. Step-by-step derivation

   14. Applied rewrites 25.2%

       \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(y3 \cdot z\right)}\right) \]

   if -3.79999999999999999e-180 < a < 2.80000000000000019e-7

   1. Initial program 42.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 47.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 36.6%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-1, y3 \cdot y4, i \cdot x\right)\right)} \]

   9. Taylor expanded in y4 around 0

      \[\leadsto i \cdot \left(j \cdot \color{blue}{\left(x \cdot y1\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 29.2%

       \[\leadsto i \cdot \left(\left(j \cdot x\right) \cdot \color{blue}{y1}\right) \]

   if 2.80000000000000019e-7 < a

   1. Initial program 27.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

   5. Applied rewrites 47.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(j \cdot t - k \cdot y\right), i, \mathsf{fma}\left(-y0, k \cdot y2 - j \cdot y3, \left(t \cdot y2 - y \cdot y3\right) \cdot a\right)\right) \cdot y5} \]

   6. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 32.0%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right)\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot \color{blue}{y5}\right)\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 28.3%

       \[\leadsto a \cdot \left(\left(t \cdot y2\right) \cdot y5\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 27.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{-180}:\\ \;\;\;\;\left(\left(y3 \cdot z\right) \cdot y1\right) \cdot a\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-7}:\\ \;\;\;\;\left(\left(j \cdot x\right) \cdot y1\right) \cdot i\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y2 \cdot t\right) \cdot y5\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 44: 21.8% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(j \cdot x\right) \cdot y1\right) \cdot i\\ \mathbf{if}\;x \leq -2.8 \cdot 10^{-118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+82}:\\ \;\;\;\;\left(\left(y2 \cdot t\right) \cdot y5\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* (* j x) y1) i)))
   (if (<= x -2.8e-118) t_1 (if (<= x 7.2e+82) (* (* (* y2 t) y5) a) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = ((j * x) * y1) * i;
	double tmp;
	if (x <= -2.8e-118) {
		tmp = t_1;
	} else if (x <= 7.2e+82) {
		tmp = ((y2 * t) * y5) * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((j * x) * y1) * i
    if (x <= (-2.8d-118)) then
        tmp = t_1
    else if (x <= 7.2d+82) then
        tmp = ((y2 * t) * y5) * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = ((j * x) * y1) * i;
	double tmp;
	if (x <= -2.8e-118) {
		tmp = t_1;
	} else if (x <= 7.2e+82) {
		tmp = ((y2 * t) * y5) * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = ((j * x) * y1) * i
	tmp = 0
	if x <= -2.8e-118:
		tmp = t_1
	elif x <= 7.2e+82:
		tmp = ((y2 * t) * y5) * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(Float64(j * x) * y1) * i)
	tmp = 0.0
	if (x <= -2.8e-118)
		tmp = t_1;
	elseif (x <= 7.2e+82)
		tmp = Float64(Float64(Float64(y2 * t) * y5) * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = ((j * x) * y1) * i;
	tmp = 0.0;
	if (x <= -2.8e-118)
		tmp = t_1;
	elseif (x <= 7.2e+82)
		tmp = ((y2 * t) * y5) * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(N[(j * x), $MachinePrecision] * y1), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[x, -2.8e-118], t$95$1, If[LessEqual[x, 7.2e+82], N[(N[(N[(y2 * t), $MachinePrecision] * y5), $MachinePrecision] * a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.8e-118 or 7.20000000000000028e82 < x

   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 y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 38.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - z \cdot y3\right), a, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 30.6%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-1, y3 \cdot y4, i \cdot x\right)\right)} \]

   9. Taylor expanded in y4 around 0

      \[\leadsto i \cdot \left(j \cdot \color{blue}{\left(x \cdot y1\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 27.0%

       \[\leadsto i \cdot \left(\left(j \cdot x\right) \cdot \color{blue}{y1}\right) \]

   if -2.8e-118 < x < 7.20000000000000028e82

   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 y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

   5. Applied rewrites 46.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(j \cdot t - k \cdot y\right), i, \mathsf{fma}\left(-y0, k \cdot y2 - j \cdot y3, \left(t \cdot y2 - y \cdot y3\right) \cdot a\right)\right) \cdot y5} \]

   6. Taylor expanded in a around inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 34.9%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right)\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot \color{blue}{y5}\right)\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 26.4%

       \[\leadsto a \cdot \left(\left(t \cdot y2\right) \cdot y5\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 26.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-118}:\\ \;\;\;\;\left(\left(j \cdot x\right) \cdot y1\right) \cdot i\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+82}:\\ \;\;\;\;\left(\left(y2 \cdot t\right) \cdot y5\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(\left(j \cdot x\right) \cdot y1\right) \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 45: 16.8% accurate, 12.6× speedup

Math

\[\begin{array}{l} \\ \left(\left(y2 \cdot t\right) \cdot y5\right) \cdot a \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* (* (* y2 t) y5) 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) {
	return ((y2 * t) * y5) * a;
}

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 = ((y2 * t) * y5) * a
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 ((y2 * t) * y5) * a;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return ((y2 * t) * y5) * a

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(Float64(Float64(y2 * t) * y5) * a)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = ((y2 * t) * y5) * a;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(N[(N[(y2 * t), $MachinePrecision] * y5), $MachinePrecision] * a), $MachinePrecision]

Derivation

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 y5 around inf

   \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
4. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

   2. lower-*.f64 N/A

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot y5} \]

5. Applied rewrites 42.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(j \cdot t - k \cdot y\right), i, \mathsf{fma}\left(-y0, k \cdot y2 - j \cdot y3, \left(t \cdot y2 - y \cdot y3\right) \cdot a\right)\right) \cdot y5} \]

6. Taylor expanded in a around inf

   \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
7. Step-by-step derivation

8. Applied rewrites 28.8%

   \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right)\right)} \]

9. Taylor expanded in t around inf

   \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot \color{blue}{y5}\right)\right) \]
10. Step-by-step derivation

11. Applied rewrites 19.0%

    \[\leadsto a \cdot \left(\left(t \cdot y2\right) \cdot y5\right) \]

12. Final simplification 19.0%

    \[\leadsto \left(\left(y2 \cdot t\right) \cdot y5\right) \cdot a \]
13. Add Preprocessing

Developer Target 1: 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 2024249 
(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
  (! :herbie-platform default (if (< y4 -7206256231996481000000000000000000000000000000000000000000000) (- (- (* (- (* 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 (- (* y4 c) (* y5 a)))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (if (< y4 -3364603505246317/1000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (- (- (* (* 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 -3000016263921529/2500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (+ (- (* (- (* 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 1343792624811499/200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (- (- (* (* 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 29872667587737/6250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (+ (- (* (- (* 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 4570448308253367/20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (- (- (* (* 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)))))