Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 29.5% → 38.3%

Time: 2.1min

Alternatives: 45

Speedup: 4.1×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 29.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 38.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot y4 - i \cdot y5\\ t_2 := y \cdot y3 - t \cdot y2\\ t_3 := c \cdot i - a \cdot b\\ t_4 := t \cdot j - y \cdot k\\ t_5 := y4 \cdot \left(\left(b \cdot t_4 + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot t_2\right)\\ t_6 := i \cdot y1 - b \cdot y0\\ t_7 := a \cdot y1 - c \cdot y0\\ t_8 := y0 \cdot y5 - y1 \cdot y4\\ t_9 := y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot t_8 + z \cdot t_7\right)\right)\\ \mathbf{if}\;c \leq -4.6 \cdot 10^{+98}:\\ \;\;\;\;c \cdot \left(\left(x \cdot \left(y0 \cdot y2\right) - y0 \cdot \left(z \cdot y3\right)\right) + y4 \cdot t_2\right)\\ \mathbf{elif}\;c \leq -8.2 \cdot 10^{+40}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot t_3 + y3 \cdot t_7\right)\right)\\ \mathbf{elif}\;c \leq -8.5 \cdot 10^{-53}:\\ \;\;\;\;t_9\\ \mathbf{elif}\;c \leq -1.25 \cdot 10^{-67}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - i \cdot \left(t \cdot j\right)\right)\\ \mathbf{elif}\;c \leq -1.75 \cdot 10^{-134}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(c \cdot \left(z \cdot t - x \cdot y\right) - y5 \cdot t_4\right)\right)\\ \mathbf{elif}\;c \leq -1.45 \cdot 10^{-235}:\\ \;\;\;\;t \cdot \left(\left(j \cdot t_1 + z \cdot t_3\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq -2.75 \cdot 10^{-297}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) - z \cdot t_6\right)\\ \mathbf{elif}\;c \leq 1.65 \cdot 10^{-248}:\\ \;\;\;\;j \cdot \left(\left(t \cdot t_1 + y3 \cdot t_8\right) + x \cdot t_6\right)\\ \mathbf{elif}\;c \leq 6 \cdot 10^{-177}:\\ \;\;\;\;t_9\\ \mathbf{elif}\;c \leq 1.65 \cdot 10^{-111}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{-37}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{+50}:\\ \;\;\;\;y5 \cdot \left(y2 \cdot \left(t \cdot a - k \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{+82}:\\ \;\;\;\;t_9\\ \mathbf{elif}\;c \leq 7.8 \cdot 10^{+245}:\\ \;\;\;\;\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0\right)\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* b y4) (* i y5)))
        (t_2 (- (* y y3) (* t y2)))
        (t_3 (- (* c i) (* a b)))
        (t_4 (- (* t j) (* y k)))
        (t_5 (* y4 (+ (+ (* b t_4) (* y1 (- (* k y2) (* j y3)))) (* c t_2))))
        (t_6 (- (* i y1) (* b y0)))
        (t_7 (- (* a y1) (* c y0)))
        (t_8 (- (* y0 y5) (* y1 y4)))
        (t_9 (* y3 (+ (* y (- (* c y4) (* a y5))) (+ (* j t_8) (* z t_7))))))
   (if (<= c -4.6e+98)
     (* c (+ (- (* x (* y0 y2)) (* y0 (* z y3))) (* y4 t_2)))
     (if (<= c -8.2e+40)
       (* z (+ (* k (- (* b y0) (* i y1))) (+ (* t t_3) (* y3 t_7))))
       (if (<= c -8.5e-53)
         t_9
         (if (<= c -1.25e-67)
           (* y5 (- (* a (- (* t y2) (* y y3))) (* i (* t j))))
           (if (<= c -1.75e-134)
             (*
              i
              (+
               (* y1 (- (* x j) (* z k)))
               (- (* c (- (* z t) (* x y))) (* y5 t_4))))
             (if (<= c -1.45e-235)
               (* t (+ (+ (* j t_1) (* z t_3)) (* y2 (- (* a y5) (* c y4)))))
               (if (<= c -2.75e-297)
                 (*
                  k
                  (-
                   (+
                    (* y2 (- (* y1 y4) (* y0 y5)))
                    (* y (- (* i y5) (* b y4))))
                   (* z t_6)))
                 (if (<= c 1.65e-248)
                   (* j (+ (+ (* t t_1) (* y3 t_8)) (* x t_6)))
                   (if (<= c 6e-177)
                     t_9
                     (if (<= c 1.65e-111)
                       (*
                        b
                        (+
                         (* a (- (* x y) (* z t)))
                         (* y0 (- (* z k) (* x j)))))
                       (if (<= c 3.2e-37)
                         t_5
                         (if (<= c 2.5e+50)
                           (* y5 (* y2 (- (* t a) (* k y0))))
                           (if (<= c 8.5e+82)
                             t_9
                             (if (<= c 7.8e+245)
                               (* (- (* x y2) (* z y3)) (* c y0))
                               t_5))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (b * y4) - (i * y5);
	double t_2 = (y * y3) - (t * y2);
	double t_3 = (c * i) - (a * b);
	double t_4 = (t * j) - (y * k);
	double t_5 = y4 * (((b * t_4) + (y1 * ((k * y2) - (j * y3)))) + (c * t_2));
	double t_6 = (i * y1) - (b * y0);
	double t_7 = (a * y1) - (c * y0);
	double t_8 = (y0 * y5) - (y1 * y4);
	double t_9 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_8) + (z * t_7)));
	double tmp;
	if (c <= -4.6e+98) {
		tmp = c * (((x * (y0 * y2)) - (y0 * (z * y3))) + (y4 * t_2));
	} else if (c <= -8.2e+40) {
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * t_3) + (y3 * t_7)));
	} else if (c <= -8.5e-53) {
		tmp = t_9;
	} else if (c <= -1.25e-67) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) - (i * (t * j)));
	} else if (c <= -1.75e-134) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((c * ((z * t) - (x * y))) - (y5 * t_4)));
	} else if (c <= -1.45e-235) {
		tmp = t * (((j * t_1) + (z * t_3)) + (y2 * ((a * y5) - (c * y4))));
	} else if (c <= -2.75e-297) {
		tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) - (z * t_6));
	} else if (c <= 1.65e-248) {
		tmp = j * (((t * t_1) + (y3 * t_8)) + (x * t_6));
	} else if (c <= 6e-177) {
		tmp = t_9;
	} else if (c <= 1.65e-111) {
		tmp = b * ((a * ((x * y) - (z * t))) + (y0 * ((z * k) - (x * j))));
	} else if (c <= 3.2e-37) {
		tmp = t_5;
	} else if (c <= 2.5e+50) {
		tmp = y5 * (y2 * ((t * a) - (k * y0)));
	} else if (c <= 8.5e+82) {
		tmp = t_9;
	} else if (c <= 7.8e+245) {
		tmp = ((x * y2) - (z * y3)) * (c * y0);
	} else {
		tmp = t_5;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = (b * y4) - (i * y5)
    t_2 = (y * y3) - (t * y2)
    t_3 = (c * i) - (a * b)
    t_4 = (t * j) - (y * k)
    t_5 = y4 * (((b * t_4) + (y1 * ((k * y2) - (j * y3)))) + (c * t_2))
    t_6 = (i * y1) - (b * y0)
    t_7 = (a * y1) - (c * y0)
    t_8 = (y0 * y5) - (y1 * y4)
    t_9 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_8) + (z * t_7)))
    if (c <= (-4.6d+98)) then
        tmp = c * (((x * (y0 * y2)) - (y0 * (z * y3))) + (y4 * t_2))
    else if (c <= (-8.2d+40)) then
        tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * t_3) + (y3 * t_7)))
    else if (c <= (-8.5d-53)) then
        tmp = t_9
    else if (c <= (-1.25d-67)) then
        tmp = y5 * ((a * ((t * y2) - (y * y3))) - (i * (t * j)))
    else if (c <= (-1.75d-134)) then
        tmp = i * ((y1 * ((x * j) - (z * k))) + ((c * ((z * t) - (x * y))) - (y5 * t_4)))
    else if (c <= (-1.45d-235)) then
        tmp = t * (((j * t_1) + (z * t_3)) + (y2 * ((a * y5) - (c * y4))))
    else if (c <= (-2.75d-297)) then
        tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) - (z * t_6))
    else if (c <= 1.65d-248) then
        tmp = j * (((t * t_1) + (y3 * t_8)) + (x * t_6))
    else if (c <= 6d-177) then
        tmp = t_9
    else if (c <= 1.65d-111) then
        tmp = b * ((a * ((x * y) - (z * t))) + (y0 * ((z * k) - (x * j))))
    else if (c <= 3.2d-37) then
        tmp = t_5
    else if (c <= 2.5d+50) then
        tmp = y5 * (y2 * ((t * a) - (k * y0)))
    else if (c <= 8.5d+82) then
        tmp = t_9
    else if (c <= 7.8d+245) then
        tmp = ((x * y2) - (z * y3)) * (c * y0)
    else
        tmp = t_5
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (b * y4) - (i * y5);
	double t_2 = (y * y3) - (t * y2);
	double t_3 = (c * i) - (a * b);
	double t_4 = (t * j) - (y * k);
	double t_5 = y4 * (((b * t_4) + (y1 * ((k * y2) - (j * y3)))) + (c * t_2));
	double t_6 = (i * y1) - (b * y0);
	double t_7 = (a * y1) - (c * y0);
	double t_8 = (y0 * y5) - (y1 * y4);
	double t_9 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_8) + (z * t_7)));
	double tmp;
	if (c <= -4.6e+98) {
		tmp = c * (((x * (y0 * y2)) - (y0 * (z * y3))) + (y4 * t_2));
	} else if (c <= -8.2e+40) {
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * t_3) + (y3 * t_7)));
	} else if (c <= -8.5e-53) {
		tmp = t_9;
	} else if (c <= -1.25e-67) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) - (i * (t * j)));
	} else if (c <= -1.75e-134) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((c * ((z * t) - (x * y))) - (y5 * t_4)));
	} else if (c <= -1.45e-235) {
		tmp = t * (((j * t_1) + (z * t_3)) + (y2 * ((a * y5) - (c * y4))));
	} else if (c <= -2.75e-297) {
		tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) - (z * t_6));
	} else if (c <= 1.65e-248) {
		tmp = j * (((t * t_1) + (y3 * t_8)) + (x * t_6));
	} else if (c <= 6e-177) {
		tmp = t_9;
	} else if (c <= 1.65e-111) {
		tmp = b * ((a * ((x * y) - (z * t))) + (y0 * ((z * k) - (x * j))));
	} else if (c <= 3.2e-37) {
		tmp = t_5;
	} else if (c <= 2.5e+50) {
		tmp = y5 * (y2 * ((t * a) - (k * y0)));
	} else if (c <= 8.5e+82) {
		tmp = t_9;
	} else if (c <= 7.8e+245) {
		tmp = ((x * y2) - (z * y3)) * (c * y0);
	} else {
		tmp = t_5;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (b * y4) - (i * y5)
	t_2 = (y * y3) - (t * y2)
	t_3 = (c * i) - (a * b)
	t_4 = (t * j) - (y * k)
	t_5 = y4 * (((b * t_4) + (y1 * ((k * y2) - (j * y3)))) + (c * t_2))
	t_6 = (i * y1) - (b * y0)
	t_7 = (a * y1) - (c * y0)
	t_8 = (y0 * y5) - (y1 * y4)
	t_9 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_8) + (z * t_7)))
	tmp = 0
	if c <= -4.6e+98:
		tmp = c * (((x * (y0 * y2)) - (y0 * (z * y3))) + (y4 * t_2))
	elif c <= -8.2e+40:
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * t_3) + (y3 * t_7)))
	elif c <= -8.5e-53:
		tmp = t_9
	elif c <= -1.25e-67:
		tmp = y5 * ((a * ((t * y2) - (y * y3))) - (i * (t * j)))
	elif c <= -1.75e-134:
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((c * ((z * t) - (x * y))) - (y5 * t_4)))
	elif c <= -1.45e-235:
		tmp = t * (((j * t_1) + (z * t_3)) + (y2 * ((a * y5) - (c * y4))))
	elif c <= -2.75e-297:
		tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) - (z * t_6))
	elif c <= 1.65e-248:
		tmp = j * (((t * t_1) + (y3 * t_8)) + (x * t_6))
	elif c <= 6e-177:
		tmp = t_9
	elif c <= 1.65e-111:
		tmp = b * ((a * ((x * y) - (z * t))) + (y0 * ((z * k) - (x * j))))
	elif c <= 3.2e-37:
		tmp = t_5
	elif c <= 2.5e+50:
		tmp = y5 * (y2 * ((t * a) - (k * y0)))
	elif c <= 8.5e+82:
		tmp = t_9
	elif c <= 7.8e+245:
		tmp = ((x * y2) - (z * y3)) * (c * y0)
	else:
		tmp = t_5
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(b * y4) - Float64(i * y5))
	t_2 = Float64(Float64(y * y3) - Float64(t * y2))
	t_3 = Float64(Float64(c * i) - Float64(a * b))
	t_4 = Float64(Float64(t * j) - Float64(y * k))
	t_5 = Float64(y4 * Float64(Float64(Float64(b * t_4) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * t_2)))
	t_6 = Float64(Float64(i * y1) - Float64(b * y0))
	t_7 = Float64(Float64(a * y1) - Float64(c * y0))
	t_8 = Float64(Float64(y0 * y5) - Float64(y1 * y4))
	t_9 = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(j * t_8) + Float64(z * t_7))))
	tmp = 0.0
	if (c <= -4.6e+98)
		tmp = Float64(c * Float64(Float64(Float64(x * Float64(y0 * y2)) - Float64(y0 * Float64(z * y3))) + Float64(y4 * t_2)));
	elseif (c <= -8.2e+40)
		tmp = Float64(z * Float64(Float64(k * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(Float64(t * t_3) + Float64(y3 * t_7))));
	elseif (c <= -8.5e-53)
		tmp = t_9;
	elseif (c <= -1.25e-67)
		tmp = Float64(y5 * Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) - Float64(i * Float64(t * j))));
	elseif (c <= -1.75e-134)
		tmp = Float64(i * Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) + Float64(Float64(c * Float64(Float64(z * t) - Float64(x * y))) - Float64(y5 * t_4))));
	elseif (c <= -1.45e-235)
		tmp = Float64(t * Float64(Float64(Float64(j * t_1) + Float64(z * t_3)) + Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (c <= -2.75e-297)
		tmp = Float64(k * Float64(Float64(Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(y * Float64(Float64(i * y5) - Float64(b * y4)))) - Float64(z * t_6)));
	elseif (c <= 1.65e-248)
		tmp = Float64(j * Float64(Float64(Float64(t * t_1) + Float64(y3 * t_8)) + Float64(x * t_6)));
	elseif (c <= 6e-177)
		tmp = t_9;
	elseif (c <= 1.65e-111)
		tmp = Float64(b * Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (c <= 3.2e-37)
		tmp = t_5;
	elseif (c <= 2.5e+50)
		tmp = Float64(y5 * Float64(y2 * Float64(Float64(t * a) - Float64(k * y0))));
	elseif (c <= 8.5e+82)
		tmp = t_9;
	elseif (c <= 7.8e+245)
		tmp = Float64(Float64(Float64(x * y2) - Float64(z * y3)) * Float64(c * y0));
	else
		tmp = t_5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (b * y4) - (i * y5);
	t_2 = (y * y3) - (t * y2);
	t_3 = (c * i) - (a * b);
	t_4 = (t * j) - (y * k);
	t_5 = y4 * (((b * t_4) + (y1 * ((k * y2) - (j * y3)))) + (c * t_2));
	t_6 = (i * y1) - (b * y0);
	t_7 = (a * y1) - (c * y0);
	t_8 = (y0 * y5) - (y1 * y4);
	t_9 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_8) + (z * t_7)));
	tmp = 0.0;
	if (c <= -4.6e+98)
		tmp = c * (((x * (y0 * y2)) - (y0 * (z * y3))) + (y4 * t_2));
	elseif (c <= -8.2e+40)
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * t_3) + (y3 * t_7)));
	elseif (c <= -8.5e-53)
		tmp = t_9;
	elseif (c <= -1.25e-67)
		tmp = y5 * ((a * ((t * y2) - (y * y3))) - (i * (t * j)));
	elseif (c <= -1.75e-134)
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((c * ((z * t) - (x * y))) - (y5 * t_4)));
	elseif (c <= -1.45e-235)
		tmp = t * (((j * t_1) + (z * t_3)) + (y2 * ((a * y5) - (c * y4))));
	elseif (c <= -2.75e-297)
		tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) - (z * t_6));
	elseif (c <= 1.65e-248)
		tmp = j * (((t * t_1) + (y3 * t_8)) + (x * t_6));
	elseif (c <= 6e-177)
		tmp = t_9;
	elseif (c <= 1.65e-111)
		tmp = b * ((a * ((x * y) - (z * t))) + (y0 * ((z * k) - (x * j))));
	elseif (c <= 3.2e-37)
		tmp = t_5;
	elseif (c <= 2.5e+50)
		tmp = y5 * (y2 * ((t * a) - (k * y0)));
	elseif (c <= 8.5e+82)
		tmp = t_9;
	elseif (c <= 7.8e+245)
		tmp = ((x * y2) - (z * y3)) * (c * y0);
	else
		tmp = t_5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y4 * N[(N[(N[(b * t$95$4), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * t$95$8), $MachinePrecision] + N[(z * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4.6e+98], N[(c * N[(N[(N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision] - N[(y0 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -8.2e+40], N[(z * N[(N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t * t$95$3), $MachinePrecision] + N[(y3 * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -8.5e-53], t$95$9, If[LessEqual[c, -1.25e-67], N[(y5 * N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.75e-134], N[(i * N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(c * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y5 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.45e-235], N[(t * N[(N[(N[(j * t$95$1), $MachinePrecision] + N[(z * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.75e-297], N[(k * N[(N[(N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.65e-248], N[(j * N[(N[(N[(t * t$95$1), $MachinePrecision] + N[(y3 * t$95$8), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6e-177], t$95$9, If[LessEqual[c, 1.65e-111], N[(b * N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.2e-37], t$95$5, If[LessEqual[c, 2.5e+50], N[(y5 * N[(y2 * N[(N[(t * a), $MachinePrecision] - N[(k * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 8.5e+82], t$95$9, If[LessEqual[c, 7.8e+245], N[(N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision] * N[(c * y0), $MachinePrecision]), $MachinePrecision], t$95$5]]]]]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 12 regimes

2. if c < -4.60000000000000026e98

   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. Taylor expanded in c around inf 58.1%

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

      1. +-commutative 58.1%

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

      2. mul-1-neg 58.1%

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

      3. unsub-neg 58.1%

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

      4. *-commutative 58.1%

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

      5. *-commutative 58.1%

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

      6. *-commutative 58.1%

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

      7. *-commutative 58.1%

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

   4. Simplified 58.1%

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

   5. Taylor expanded in y2 around 0 58.2%

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

   6. Taylor expanded in i around 0 65.1%

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

   if -4.60000000000000026e98 < c < -8.2000000000000003e40

   1. Initial program 50.4%

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

   2. Taylor expanded in z around -inf 69.4%

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

   if -8.2000000000000003e40 < c < -8.50000000000000044e-53 or 1.6500000000000001e-248 < c < 6.00000000000000015e-177 or 2.5e50 < c < 8.4999999999999995e82

   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. Taylor expanded in y3 around -inf 75.3%

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

   if -8.50000000000000044e-53 < c < -1.25e-67

   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. Taylor expanded in y5 around -inf 80.0%

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

   3. Taylor expanded in t around inf 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   if -1.25e-67 < c < -1.7499999999999999e-134

   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. Taylor expanded in i around -inf 83.9%

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

   if -1.7499999999999999e-134 < c < -1.45000000000000004e-235

   1. Initial program 43.1%

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

   2. Taylor expanded in t around inf 63.0%

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

      1. +-commutative 63.0%

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

      2. mul-1-neg 63.0%

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

      3. unsub-neg 63.0%

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

      4. *-commutative 63.0%

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

   4. Simplified 63.0%

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

   if -1.45000000000000004e-235 < c < -2.75000000000000015e-297

   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. Taylor expanded in k around -inf 57.0%

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

      1. mul-1-neg 57.0%

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

      2. *-commutative 57.0%

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

      3. sub-neg 57.0%

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

      4. +-commutative 57.0%

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

      5. mul-1-neg 57.0%

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

      6. distribute-rgt-neg-in 57.0%

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

   4. Simplified 57.0%

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

   if -2.75000000000000015e-297 < c < 1.6500000000000001e-248

   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. Taylor expanded in j around inf 63.3%

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

   4. Simplified 63.3%

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

   if 6.00000000000000015e-177 < c < 1.65e-111

   1. Initial program 53.6%

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

   2. Taylor expanded in b around inf 52.7%

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

   3. Taylor expanded in y4 around 0 68.1%

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

      1. *-commutative 68.1%

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

      2. *-commutative 68.1%

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

      3. *-commutative 68.1%

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

   5. Simplified 68.1%

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

   if 1.65e-111 < c < 3.1999999999999999e-37 or 7.7999999999999996e245 < c

   1. Initial program 30.4%

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

   2. Taylor expanded in y4 around inf 74.5%

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

   if 3.1999999999999999e-37 < c < 2.5e50

   1. Initial program 35.5%

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

   2. Taylor expanded in y5 around -inf 39.9%

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

   3. Taylor expanded in y2 around inf 75.2%

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

      1. *-commutative 75.2%

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

   5. Simplified 75.2%

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

   if 8.4999999999999995e82 < c < 7.7999999999999996e245

   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. Taylor expanded in c around inf 50.4%

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

      1. +-commutative 50.4%

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

      2. mul-1-neg 50.4%

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

      3. unsub-neg 50.4%

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

      4. *-commutative 50.4%

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

      5. *-commutative 50.4%

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

      6. *-commutative 50.4%

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

      7. *-commutative 50.4%

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

   4. Simplified 50.4%

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

   5. Taylor expanded in y0 around inf 54.1%

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

      1. associate-*r* 56.4%

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

      2. *-commutative 56.4%

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

      3. *-commutative 56.4%

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

      4. *-commutative 56.4%

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

      5. *-commutative 56.4%

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

      6. *-commutative 56.4%

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

   7. Simplified 56.4%

      \[\leadsto \color{blue}{\left(x \cdot y2 - y3 \cdot z\right) \cdot \left(c \cdot y0\right)} \]
3. Recombined 12 regimes into one program.

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.6 \cdot 10^{+98}:\\ \;\;\;\;c \cdot \left(\left(x \cdot \left(y0 \cdot y2\right) - y0 \cdot \left(z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -8.2 \cdot 10^{+40}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot \left(c \cdot i - a \cdot b\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;c \leq -8.5 \cdot 10^{-53}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;c \leq -1.25 \cdot 10^{-67}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - i \cdot \left(t \cdot j\right)\right)\\ \mathbf{elif}\;c \leq -1.75 \cdot 10^{-134}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(c \cdot \left(z \cdot t - x \cdot y\right) - y5 \cdot \left(t \cdot j - y \cdot k\right)\right)\right)\\ \mathbf{elif}\;c \leq -1.45 \cdot 10^{-235}:\\ \;\;\;\;t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + z \cdot \left(c \cdot i - a \cdot b\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq -2.75 \cdot 10^{-297}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) - z \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq 1.65 \cdot 10^{-248}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq 6 \cdot 10^{-177}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.65 \cdot 10^{-111}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{-37}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{+50}:\\ \;\;\;\;y5 \cdot \left(y2 \cdot \left(t \cdot a - k \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{+82}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;c \leq 7.8 \cdot 10^{+245}:\\ \;\;\;\;\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \end{array} \]

Alternative 2: 52.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 90.8%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in c around inf 37.3%

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

      1. +-commutative 37.3%

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

      2. mul-1-neg 37.3%

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

      3. unsub-neg 37.3%

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

      4. *-commutative 37.3%

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

      5. *-commutative 37.3%

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

      6. *-commutative 37.3%

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

      7. *-commutative 37.3%

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

   4. Simplified 37.3%

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

   5. Taylor expanded in i around 0 39.4%

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

      1. *-commutative 39.4%

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

      2. *-commutative 39.4%

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

   7. Simplified 39.4%

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

4. Final simplification 58.7%

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

Alternative 3: 40.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot y4 - i \cdot y5\\ t_2 := y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\\ t_3 := t \cdot y2 - y \cdot y3\\ t_4 := c \cdot i - a \cdot b\\ t_5 := i \cdot y1 - b \cdot y0\\ t_6 := a \cdot y5 - c \cdot y4\\ t_7 := j \cdot y3 - k \cdot y2\\ t_8 := x \cdot y2 - z \cdot y3\\ t_9 := y0 \cdot t_8\\ t_10 := t_9 + i \cdot \left(z \cdot t - x \cdot y\right)\\ t_11 := z \cdot k - x \cdot j\\ t_12 := y0 \cdot \left(\left(c \cdot t_8 + y5 \cdot t_7\right) + b \cdot t_11\right)\\ \mathbf{if}\;j \leq -4.1 \cdot 10^{+88}:\\ \;\;\;\;x \cdot \left(j \cdot t_5\right)\\ \mathbf{elif}\;j \leq -6.5 \cdot 10^{+40}:\\ \;\;\;\;y5 \cdot \left(\left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot t_7\right) + a \cdot t_3\right)\\ \mathbf{elif}\;j \leq -8 \cdot 10^{-51}:\\ \;\;\;\;c \cdot \left(t_9 + t_2\right)\\ \mathbf{elif}\;j \leq -8 \cdot 10^{-139}:\\ \;\;\;\;t_12\\ \mathbf{elif}\;j \leq -7.2 \cdot 10^{-292}:\\ \;\;\;\;c \cdot \left(t_10 + t_2\right)\\ \mathbf{elif}\;j \leq 5.5 \cdot 10^{-145}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(c \cdot t_10 + t_3 \cdot t_6\right)\\ \mathbf{elif}\;j \leq 2.75 \cdot 10^{-78}:\\ \;\;\;\;t \cdot \left(\left(j \cdot t_1 + z \cdot t_4\right) + y2 \cdot t_6\right)\\ \mathbf{elif}\;j \leq 1.9 \cdot 10^{-60}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot t_4 + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;j \leq 6 \cdot 10^{-16}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 120:\\ \;\;\;\;t_12\\ \mathbf{elif}\;j \leq 4.1 \cdot 10^{+93}:\\ \;\;\;\;b \cdot \left(\left(y4 \cdot \left(t \cdot j - y \cdot k\right) + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot t_11\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(\left(t \cdot t_1 + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot t_5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* b y4) (* i y5)))
        (t_2 (* y4 (- (* y y3) (* t y2))))
        (t_3 (- (* t y2) (* y y3)))
        (t_4 (- (* c i) (* a b)))
        (t_5 (- (* i y1) (* b y0)))
        (t_6 (- (* a y5) (* c y4)))
        (t_7 (- (* j y3) (* k y2)))
        (t_8 (- (* x y2) (* z y3)))
        (t_9 (* y0 t_8))
        (t_10 (+ t_9 (* i (- (* z t) (* x y)))))
        (t_11 (- (* z k) (* x j)))
        (t_12 (* y0 (+ (+ (* c t_8) (* y5 t_7)) (* b t_11)))))
   (if (<= j -4.1e+88)
     (* x (* j t_5))
     (if (<= j -6.5e+40)
       (* y5 (+ (+ (* i (- (* y k) (* t j))) (* y0 t_7)) (* a t_3)))
       (if (<= j -8e-51)
         (* c (+ t_9 t_2))
         (if (<= j -8e-139)
           t_12
           (if (<= j -7.2e-292)
             (* c (+ t_10 t_2))
             (if (<= j 5.5e-145)
               (+
                (* (- (* k y2) (* j y3)) (- (* y1 y4) (* y0 y5)))
                (+ (* c t_10) (* t_3 t_6)))
               (if (<= j 2.75e-78)
                 (* t (+ (+ (* j t_1) (* z t_4)) (* y2 t_6)))
                 (if (<= j 1.9e-60)
                   (*
                    z
                    (+
                     (* k (- (* b y0) (* i y1)))
                     (+ (* t t_4) (* y3 (- (* a y1) (* c y0))))))
                   (if (<= j 6e-16)
                     (* a (* y1 (- (* z y3) (* x y2))))
                     (if (<= j 120.0)
                       t_12
                       (if (<= j 4.1e+93)
                         (*
                          b
                          (+
                           (+
                            (* y4 (- (* t j) (* y k)))
                            (* a (- (* x y) (* z t))))
                           (* y0 t_11)))
                         (*
                          j
                          (+
                           (+ (* t t_1) (* y3 (- (* y0 y5) (* y1 y4))))
                           (* x t_5))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (b * y4) - (i * y5);
	double t_2 = y4 * ((y * y3) - (t * y2));
	double t_3 = (t * y2) - (y * y3);
	double t_4 = (c * i) - (a * b);
	double t_5 = (i * y1) - (b * y0);
	double t_6 = (a * y5) - (c * y4);
	double t_7 = (j * y3) - (k * y2);
	double t_8 = (x * y2) - (z * y3);
	double t_9 = y0 * t_8;
	double t_10 = t_9 + (i * ((z * t) - (x * y)));
	double t_11 = (z * k) - (x * j);
	double t_12 = y0 * (((c * t_8) + (y5 * t_7)) + (b * t_11));
	double tmp;
	if (j <= -4.1e+88) {
		tmp = x * (j * t_5);
	} else if (j <= -6.5e+40) {
		tmp = y5 * (((i * ((y * k) - (t * j))) + (y0 * t_7)) + (a * t_3));
	} else if (j <= -8e-51) {
		tmp = c * (t_9 + t_2);
	} else if (j <= -8e-139) {
		tmp = t_12;
	} else if (j <= -7.2e-292) {
		tmp = c * (t_10 + t_2);
	} else if (j <= 5.5e-145) {
		tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + ((c * t_10) + (t_3 * t_6));
	} else if (j <= 2.75e-78) {
		tmp = t * (((j * t_1) + (z * t_4)) + (y2 * t_6));
	} else if (j <= 1.9e-60) {
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * t_4) + (y3 * ((a * y1) - (c * y0)))));
	} else if (j <= 6e-16) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (j <= 120.0) {
		tmp = t_12;
	} else if (j <= 4.1e+93) {
		tmp = b * (((y4 * ((t * j) - (y * k))) + (a * ((x * y) - (z * t)))) + (y0 * t_11));
	} else {
		tmp = j * (((t * t_1) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_10
    real(8) :: t_11
    real(8) :: t_12
    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 = (b * y4) - (i * y5)
    t_2 = y4 * ((y * y3) - (t * y2))
    t_3 = (t * y2) - (y * y3)
    t_4 = (c * i) - (a * b)
    t_5 = (i * y1) - (b * y0)
    t_6 = (a * y5) - (c * y4)
    t_7 = (j * y3) - (k * y2)
    t_8 = (x * y2) - (z * y3)
    t_9 = y0 * t_8
    t_10 = t_9 + (i * ((z * t) - (x * y)))
    t_11 = (z * k) - (x * j)
    t_12 = y0 * (((c * t_8) + (y5 * t_7)) + (b * t_11))
    if (j <= (-4.1d+88)) then
        tmp = x * (j * t_5)
    else if (j <= (-6.5d+40)) then
        tmp = y5 * (((i * ((y * k) - (t * j))) + (y0 * t_7)) + (a * t_3))
    else if (j <= (-8d-51)) then
        tmp = c * (t_9 + t_2)
    else if (j <= (-8d-139)) then
        tmp = t_12
    else if (j <= (-7.2d-292)) then
        tmp = c * (t_10 + t_2)
    else if (j <= 5.5d-145) then
        tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + ((c * t_10) + (t_3 * t_6))
    else if (j <= 2.75d-78) then
        tmp = t * (((j * t_1) + (z * t_4)) + (y2 * t_6))
    else if (j <= 1.9d-60) then
        tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * t_4) + (y3 * ((a * y1) - (c * y0)))))
    else if (j <= 6d-16) then
        tmp = a * (y1 * ((z * y3) - (x * y2)))
    else if (j <= 120.0d0) then
        tmp = t_12
    else if (j <= 4.1d+93) then
        tmp = b * (((y4 * ((t * j) - (y * k))) + (a * ((x * y) - (z * t)))) + (y0 * t_11))
    else
        tmp = j * (((t * t_1) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (b * y4) - (i * y5);
	double t_2 = y4 * ((y * y3) - (t * y2));
	double t_3 = (t * y2) - (y * y3);
	double t_4 = (c * i) - (a * b);
	double t_5 = (i * y1) - (b * y0);
	double t_6 = (a * y5) - (c * y4);
	double t_7 = (j * y3) - (k * y2);
	double t_8 = (x * y2) - (z * y3);
	double t_9 = y0 * t_8;
	double t_10 = t_9 + (i * ((z * t) - (x * y)));
	double t_11 = (z * k) - (x * j);
	double t_12 = y0 * (((c * t_8) + (y5 * t_7)) + (b * t_11));
	double tmp;
	if (j <= -4.1e+88) {
		tmp = x * (j * t_5);
	} else if (j <= -6.5e+40) {
		tmp = y5 * (((i * ((y * k) - (t * j))) + (y0 * t_7)) + (a * t_3));
	} else if (j <= -8e-51) {
		tmp = c * (t_9 + t_2);
	} else if (j <= -8e-139) {
		tmp = t_12;
	} else if (j <= -7.2e-292) {
		tmp = c * (t_10 + t_2);
	} else if (j <= 5.5e-145) {
		tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + ((c * t_10) + (t_3 * t_6));
	} else if (j <= 2.75e-78) {
		tmp = t * (((j * t_1) + (z * t_4)) + (y2 * t_6));
	} else if (j <= 1.9e-60) {
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * t_4) + (y3 * ((a * y1) - (c * y0)))));
	} else if (j <= 6e-16) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (j <= 120.0) {
		tmp = t_12;
	} else if (j <= 4.1e+93) {
		tmp = b * (((y4 * ((t * j) - (y * k))) + (a * ((x * y) - (z * t)))) + (y0 * t_11));
	} else {
		tmp = j * (((t * t_1) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (b * y4) - (i * y5)
	t_2 = y4 * ((y * y3) - (t * y2))
	t_3 = (t * y2) - (y * y3)
	t_4 = (c * i) - (a * b)
	t_5 = (i * y1) - (b * y0)
	t_6 = (a * y5) - (c * y4)
	t_7 = (j * y3) - (k * y2)
	t_8 = (x * y2) - (z * y3)
	t_9 = y0 * t_8
	t_10 = t_9 + (i * ((z * t) - (x * y)))
	t_11 = (z * k) - (x * j)
	t_12 = y0 * (((c * t_8) + (y5 * t_7)) + (b * t_11))
	tmp = 0
	if j <= -4.1e+88:
		tmp = x * (j * t_5)
	elif j <= -6.5e+40:
		tmp = y5 * (((i * ((y * k) - (t * j))) + (y0 * t_7)) + (a * t_3))
	elif j <= -8e-51:
		tmp = c * (t_9 + t_2)
	elif j <= -8e-139:
		tmp = t_12
	elif j <= -7.2e-292:
		tmp = c * (t_10 + t_2)
	elif j <= 5.5e-145:
		tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + ((c * t_10) + (t_3 * t_6))
	elif j <= 2.75e-78:
		tmp = t * (((j * t_1) + (z * t_4)) + (y2 * t_6))
	elif j <= 1.9e-60:
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * t_4) + (y3 * ((a * y1) - (c * y0)))))
	elif j <= 6e-16:
		tmp = a * (y1 * ((z * y3) - (x * y2)))
	elif j <= 120.0:
		tmp = t_12
	elif j <= 4.1e+93:
		tmp = b * (((y4 * ((t * j) - (y * k))) + (a * ((x * y) - (z * t)))) + (y0 * t_11))
	else:
		tmp = j * (((t * t_1) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(b * y4) - Float64(i * y5))
	t_2 = Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))
	t_3 = Float64(Float64(t * y2) - Float64(y * y3))
	t_4 = Float64(Float64(c * i) - Float64(a * b))
	t_5 = Float64(Float64(i * y1) - Float64(b * y0))
	t_6 = Float64(Float64(a * y5) - Float64(c * y4))
	t_7 = Float64(Float64(j * y3) - Float64(k * y2))
	t_8 = Float64(Float64(x * y2) - Float64(z * y3))
	t_9 = Float64(y0 * t_8)
	t_10 = Float64(t_9 + Float64(i * Float64(Float64(z * t) - Float64(x * y))))
	t_11 = Float64(Float64(z * k) - Float64(x * j))
	t_12 = Float64(y0 * Float64(Float64(Float64(c * t_8) + Float64(y5 * t_7)) + Float64(b * t_11)))
	tmp = 0.0
	if (j <= -4.1e+88)
		tmp = Float64(x * Float64(j * t_5));
	elseif (j <= -6.5e+40)
		tmp = Float64(y5 * Float64(Float64(Float64(i * Float64(Float64(y * k) - Float64(t * j))) + Float64(y0 * t_7)) + Float64(a * t_3)));
	elseif (j <= -8e-51)
		tmp = Float64(c * Float64(t_9 + t_2));
	elseif (j <= -8e-139)
		tmp = t_12;
	elseif (j <= -7.2e-292)
		tmp = Float64(c * Float64(t_10 + t_2));
	elseif (j <= 5.5e-145)
		tmp = Float64(Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(Float64(c * t_10) + Float64(t_3 * t_6)));
	elseif (j <= 2.75e-78)
		tmp = Float64(t * Float64(Float64(Float64(j * t_1) + Float64(z * t_4)) + Float64(y2 * t_6)));
	elseif (j <= 1.9e-60)
		tmp = Float64(z * Float64(Float64(k * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(Float64(t * t_4) + Float64(y3 * Float64(Float64(a * y1) - Float64(c * y0))))));
	elseif (j <= 6e-16)
		tmp = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))));
	elseif (j <= 120.0)
		tmp = t_12;
	elseif (j <= 4.1e+93)
		tmp = Float64(b * Float64(Float64(Float64(y4 * Float64(Float64(t * j) - Float64(y * k))) + Float64(a * Float64(Float64(x * y) - Float64(z * t)))) + Float64(y0 * t_11)));
	else
		tmp = Float64(j * Float64(Float64(Float64(t * t_1) + Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) + Float64(x * t_5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (b * y4) - (i * y5);
	t_2 = y4 * ((y * y3) - (t * y2));
	t_3 = (t * y2) - (y * y3);
	t_4 = (c * i) - (a * b);
	t_5 = (i * y1) - (b * y0);
	t_6 = (a * y5) - (c * y4);
	t_7 = (j * y3) - (k * y2);
	t_8 = (x * y2) - (z * y3);
	t_9 = y0 * t_8;
	t_10 = t_9 + (i * ((z * t) - (x * y)));
	t_11 = (z * k) - (x * j);
	t_12 = y0 * (((c * t_8) + (y5 * t_7)) + (b * t_11));
	tmp = 0.0;
	if (j <= -4.1e+88)
		tmp = x * (j * t_5);
	elseif (j <= -6.5e+40)
		tmp = y5 * (((i * ((y * k) - (t * j))) + (y0 * t_7)) + (a * t_3));
	elseif (j <= -8e-51)
		tmp = c * (t_9 + t_2);
	elseif (j <= -8e-139)
		tmp = t_12;
	elseif (j <= -7.2e-292)
		tmp = c * (t_10 + t_2);
	elseif (j <= 5.5e-145)
		tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + ((c * t_10) + (t_3 * t_6));
	elseif (j <= 2.75e-78)
		tmp = t * (((j * t_1) + (z * t_4)) + (y2 * t_6));
	elseif (j <= 1.9e-60)
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * t_4) + (y3 * ((a * y1) - (c * y0)))));
	elseif (j <= 6e-16)
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	elseif (j <= 120.0)
		tmp = t_12;
	elseif (j <= 4.1e+93)
		tmp = b * (((y4 * ((t * j) - (y * k))) + (a * ((x * y) - (z * t)))) + (y0 * t_11));
	else
		tmp = j * (((t * t_1) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(y0 * t$95$8), $MachinePrecision]}, Block[{t$95$10 = N[(t$95$9 + N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$11 = N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$12 = N[(y0 * N[(N[(N[(c * t$95$8), $MachinePrecision] + N[(y5 * t$95$7), $MachinePrecision]), $MachinePrecision] + N[(b * t$95$11), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -4.1e+88], N[(x * N[(j * t$95$5), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -6.5e+40], N[(y5 * N[(N[(N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$7), $MachinePrecision]), $MachinePrecision] + N[(a * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -8e-51], N[(c * N[(t$95$9 + t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -8e-139], t$95$12, If[LessEqual[j, -7.2e-292], N[(c * N[(t$95$10 + t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.5e-145], N[(N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(c * t$95$10), $MachinePrecision] + N[(t$95$3 * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.75e-78], N[(t * N[(N[(N[(j * t$95$1), $MachinePrecision] + N[(z * t$95$4), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.9e-60], N[(z * N[(N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t * t$95$4), $MachinePrecision] + N[(y3 * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6e-16], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 120.0], t$95$12, If[LessEqual[j, 4.1e+93], N[(b * N[(N[(N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$11), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(N[(N[(t * t$95$1), $MachinePrecision] + N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 11 regimes

2. if j < -4.10000000000000028e88

   1. Initial program 12.6%

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

   2. Taylor expanded in x around inf 40.1%

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

   3. Taylor expanded in j around inf 65.5%

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

      1. *-commutative 65.5%

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

      2. *-commutative 65.5%

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

   5. Simplified 65.5%

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

   if -4.10000000000000028e88 < j < -6.5000000000000001e40

   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. Taylor expanded in y5 around -inf 75.0%

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

   if -6.5000000000000001e40 < j < -8.0000000000000001e-51

   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. Taylor expanded in c around inf 46.8%

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

      1. +-commutative 46.8%

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

      2. mul-1-neg 46.8%

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

      3. unsub-neg 46.8%

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

      4. *-commutative 46.8%

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

      5. *-commutative 46.8%

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

      6. *-commutative 46.8%

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

      7. *-commutative 46.8%

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

   4. Simplified 46.8%

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

   5. Taylor expanded in i around 0 52.0%

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

      1. *-commutative 52.0%

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

      2. *-commutative 52.0%

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

   7. Simplified 52.0%

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

   if -8.0000000000000001e-51 < j < -8.00000000000000024e-139 or 5.99999999999999987e-16 < j < 120

   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. Taylor expanded in y0 around inf 71.7%

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

      1. sub-neg 71.7%

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

      2. +-commutative 71.7%

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

      3. mul-1-neg 71.7%

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

   4. Simplified 71.7%

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

   if -8.00000000000000024e-139 < j < -7.2000000000000004e-292

   1. Initial program 48.4%

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

   2. Taylor expanded in c around inf 68.3%

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

      1. +-commutative 68.3%

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

      2. mul-1-neg 68.3%

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

      3. unsub-neg 68.3%

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

      4. *-commutative 68.3%

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

      5. *-commutative 68.3%

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

      6. *-commutative 68.3%

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

      7. *-commutative 68.3%

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

   4. Simplified 68.3%

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

   if -7.2000000000000004e-292 < j < 5.50000000000000015e-145

   1. Initial program 43.0%

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

   2. Taylor expanded in c around inf 60.5%

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

      1. +-commutative 60.5%

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

      2. mul-1-neg 60.5%

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

      3. unsub-neg 60.5%

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

      4. *-commutative 60.5%

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

      5. *-commutative 60.5%

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

      6. *-commutative 60.5%

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

   4. Simplified 60.5%

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

   if 5.50000000000000015e-145 < j < 2.75000000000000009e-78

   1. Initial program 61.3%

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

   2. Taylor expanded in t around inf 77.5%

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

      1. +-commutative 77.5%

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

      2. mul-1-neg 77.5%

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

      3. unsub-neg 77.5%

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

      4. *-commutative 77.5%

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

   4. Simplified 77.5%

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

   if 2.75000000000000009e-78 < j < 1.89999999999999997e-60

   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. Taylor expanded in z around -inf 99.6%

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

   if 1.89999999999999997e-60 < j < 5.99999999999999987e-16

   1. Initial program 12.2%

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

   2. Taylor expanded in a around -inf 56.1%

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

      1. mul-1-neg 56.1%

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

      2. distribute-rgt-neg-in 56.1%

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

      3. +-commutative 56.1%

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

      4. mul-1-neg 56.1%

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

      5. unsub-neg 56.1%

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

      6. *-commutative 56.1%

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

      7. *-commutative 56.1%

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

      8. *-commutative 56.1%

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

   4. Simplified 56.1%

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

   5. Taylor expanded in y1 around inf 78.3%

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

   if 120 < j < 4.1000000000000001e93

   1. Initial program 22.5%

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

   2. Taylor expanded in b around inf 56.3%

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

   if 4.1000000000000001e93 < j

   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. Taylor expanded in j around inf 68.9%

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

   4. Simplified 68.9%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]
3. Recombined 11 regimes into one program.

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4.1 \cdot 10^{+88}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq -6.5 \cdot 10^{+40}:\\ \;\;\;\;y5 \cdot \left(\left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq -8 \cdot 10^{-51}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq -8 \cdot 10^{-139}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -7.2 \cdot 10^{-292}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + i \cdot \left(z \cdot t - x \cdot y\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 5.5 \cdot 10^{-145}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + i \cdot \left(z \cdot t - x \cdot y\right)\right) + \left(t \cdot y2 - y \cdot y3\right) \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 2.75 \cdot 10^{-78}:\\ \;\;\;\;t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + z \cdot \left(c \cdot i - a \cdot b\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 1.9 \cdot 10^{-60}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot \left(c \cdot i - a \cdot b\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;j \leq 6 \cdot 10^{-16}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 120:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;j \leq 4.1 \cdot 10^{+93}:\\ \;\;\;\;b \cdot \left(\left(y4 \cdot \left(t \cdot j - y \cdot k\right) + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \end{array} \]

Alternative 4: 37.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot y3 - t \cdot y2\\ t_2 := t \cdot j - y \cdot k\\ t_3 := b \cdot y4 - i \cdot y5\\ t_4 := y4 \cdot \left(\left(b \cdot t_2 + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot t_1\right)\\ t_5 := y0 \cdot y5 - y1 \cdot y4\\ t_6 := y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot t_5 + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ t_7 := i \cdot y1 - b \cdot y0\\ \mathbf{if}\;c \leq -3 \cdot 10^{+116}:\\ \;\;\;\;c \cdot \left(\left(x \cdot \left(y0 \cdot y2\right) - y0 \cdot \left(z \cdot y3\right)\right) + y4 \cdot t_1\right)\\ \mathbf{elif}\;c \leq -1.3 \cdot 10^{-51}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;c \leq -4.5 \cdot 10^{-75}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - i \cdot \left(t \cdot j\right)\right)\\ \mathbf{elif}\;c \leq -3.6 \cdot 10^{-130}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(c \cdot \left(z \cdot t - x \cdot y\right) - y5 \cdot t_2\right)\right)\\ \mathbf{elif}\;c \leq -7.8 \cdot 10^{-236}:\\ \;\;\;\;t \cdot \left(\left(j \cdot t_3 + z \cdot \left(c \cdot i - a \cdot b\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq -9.4 \cdot 10^{-299}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) - z \cdot t_7\right)\\ \mathbf{elif}\;c \leq 5 \cdot 10^{-250}:\\ \;\;\;\;j \cdot \left(\left(t \cdot t_3 + y3 \cdot t_5\right) + x \cdot t_7\right)\\ \mathbf{elif}\;c \leq 3.1 \cdot 10^{-177}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;c \leq 6 \cdot 10^{-112}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{-35}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq 2.15 \cdot 10^{+52}:\\ \;\;\;\;y5 \cdot \left(y2 \cdot \left(t \cdot a - k \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq 5.6 \cdot 10^{+82}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;c \leq 4 \cdot 10^{+245}:\\ \;\;\;\;\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0\right)\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y y3) (* t y2)))
        (t_2 (- (* t j) (* y k)))
        (t_3 (- (* b y4) (* i y5)))
        (t_4 (* y4 (+ (+ (* b t_2) (* y1 (- (* k y2) (* j y3)))) (* c t_1))))
        (t_5 (- (* y0 y5) (* y1 y4)))
        (t_6
         (*
          y3
          (+
           (* y (- (* c y4) (* a y5)))
           (+ (* j t_5) (* z (- (* a y1) (* c y0)))))))
        (t_7 (- (* i y1) (* b y0))))
   (if (<= c -3e+116)
     (* c (+ (- (* x (* y0 y2)) (* y0 (* z y3))) (* y4 t_1)))
     (if (<= c -1.3e-51)
       t_6
       (if (<= c -4.5e-75)
         (* y5 (- (* a (- (* t y2) (* y y3))) (* i (* t j))))
         (if (<= c -3.6e-130)
           (*
            i
            (+
             (* y1 (- (* x j) (* z k)))
             (- (* c (- (* z t) (* x y))) (* y5 t_2))))
           (if (<= c -7.8e-236)
             (*
              t
              (+
               (+ (* j t_3) (* z (- (* c i) (* a b))))
               (* y2 (- (* a y5) (* c y4)))))
             (if (<= c -9.4e-299)
               (*
                k
                (-
                 (+ (* y2 (- (* y1 y4) (* y0 y5))) (* y (- (* i y5) (* b y4))))
                 (* z t_7)))
               (if (<= c 5e-250)
                 (* j (+ (+ (* t t_3) (* y3 t_5)) (* x t_7)))
                 (if (<= c 3.1e-177)
                   t_6
                   (if (<= c 6e-112)
                     (*
                      b
                      (+ (* a (- (* x y) (* z t))) (* y0 (- (* z k) (* x j)))))
                     (if (<= c 8.5e-35)
                       t_4
                       (if (<= c 2.15e+52)
                         (* y5 (* y2 (- (* t a) (* k y0))))
                         (if (<= c 5.6e+82)
                           t_6
                           (if (<= c 4e+245)
                             (* (- (* x y2) (* z y3)) (* c y0))
                             t_4)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * y3) - (t * y2);
	double t_2 = (t * j) - (y * k);
	double t_3 = (b * y4) - (i * y5);
	double t_4 = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) + (c * t_1));
	double t_5 = (y0 * y5) - (y1 * y4);
	double t_6 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_5) + (z * ((a * y1) - (c * y0)))));
	double t_7 = (i * y1) - (b * y0);
	double tmp;
	if (c <= -3e+116) {
		tmp = c * (((x * (y0 * y2)) - (y0 * (z * y3))) + (y4 * t_1));
	} else if (c <= -1.3e-51) {
		tmp = t_6;
	} else if (c <= -4.5e-75) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) - (i * (t * j)));
	} else if (c <= -3.6e-130) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((c * ((z * t) - (x * y))) - (y5 * t_2)));
	} else if (c <= -7.8e-236) {
		tmp = t * (((j * t_3) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))));
	} else if (c <= -9.4e-299) {
		tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) - (z * t_7));
	} else if (c <= 5e-250) {
		tmp = j * (((t * t_3) + (y3 * t_5)) + (x * t_7));
	} else if (c <= 3.1e-177) {
		tmp = t_6;
	} else if (c <= 6e-112) {
		tmp = b * ((a * ((x * y) - (z * t))) + (y0 * ((z * k) - (x * j))));
	} else if (c <= 8.5e-35) {
		tmp = t_4;
	} else if (c <= 2.15e+52) {
		tmp = y5 * (y2 * ((t * a) - (k * y0)));
	} else if (c <= 5.6e+82) {
		tmp = t_6;
	} else if (c <= 4e+245) {
		tmp = ((x * y2) - (z * y3)) * (c * y0);
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_1 = (y * y3) - (t * y2)
    t_2 = (t * j) - (y * k)
    t_3 = (b * y4) - (i * y5)
    t_4 = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) + (c * t_1))
    t_5 = (y0 * y5) - (y1 * y4)
    t_6 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_5) + (z * ((a * y1) - (c * y0)))))
    t_7 = (i * y1) - (b * y0)
    if (c <= (-3d+116)) then
        tmp = c * (((x * (y0 * y2)) - (y0 * (z * y3))) + (y4 * t_1))
    else if (c <= (-1.3d-51)) then
        tmp = t_6
    else if (c <= (-4.5d-75)) then
        tmp = y5 * ((a * ((t * y2) - (y * y3))) - (i * (t * j)))
    else if (c <= (-3.6d-130)) then
        tmp = i * ((y1 * ((x * j) - (z * k))) + ((c * ((z * t) - (x * y))) - (y5 * t_2)))
    else if (c <= (-7.8d-236)) then
        tmp = t * (((j * t_3) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))))
    else if (c <= (-9.4d-299)) then
        tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) - (z * t_7))
    else if (c <= 5d-250) then
        tmp = j * (((t * t_3) + (y3 * t_5)) + (x * t_7))
    else if (c <= 3.1d-177) then
        tmp = t_6
    else if (c <= 6d-112) then
        tmp = b * ((a * ((x * y) - (z * t))) + (y0 * ((z * k) - (x * j))))
    else if (c <= 8.5d-35) then
        tmp = t_4
    else if (c <= 2.15d+52) then
        tmp = y5 * (y2 * ((t * a) - (k * y0)))
    else if (c <= 5.6d+82) then
        tmp = t_6
    else if (c <= 4d+245) then
        tmp = ((x * y2) - (z * y3)) * (c * y0)
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * y3) - (t * y2);
	double t_2 = (t * j) - (y * k);
	double t_3 = (b * y4) - (i * y5);
	double t_4 = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) + (c * t_1));
	double t_5 = (y0 * y5) - (y1 * y4);
	double t_6 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_5) + (z * ((a * y1) - (c * y0)))));
	double t_7 = (i * y1) - (b * y0);
	double tmp;
	if (c <= -3e+116) {
		tmp = c * (((x * (y0 * y2)) - (y0 * (z * y3))) + (y4 * t_1));
	} else if (c <= -1.3e-51) {
		tmp = t_6;
	} else if (c <= -4.5e-75) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) - (i * (t * j)));
	} else if (c <= -3.6e-130) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((c * ((z * t) - (x * y))) - (y5 * t_2)));
	} else if (c <= -7.8e-236) {
		tmp = t * (((j * t_3) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))));
	} else if (c <= -9.4e-299) {
		tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) - (z * t_7));
	} else if (c <= 5e-250) {
		tmp = j * (((t * t_3) + (y3 * t_5)) + (x * t_7));
	} else if (c <= 3.1e-177) {
		tmp = t_6;
	} else if (c <= 6e-112) {
		tmp = b * ((a * ((x * y) - (z * t))) + (y0 * ((z * k) - (x * j))));
	} else if (c <= 8.5e-35) {
		tmp = t_4;
	} else if (c <= 2.15e+52) {
		tmp = y5 * (y2 * ((t * a) - (k * y0)));
	} else if (c <= 5.6e+82) {
		tmp = t_6;
	} else if (c <= 4e+245) {
		tmp = ((x * y2) - (z * y3)) * (c * y0);
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y * y3) - (t * y2)
	t_2 = (t * j) - (y * k)
	t_3 = (b * y4) - (i * y5)
	t_4 = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) + (c * t_1))
	t_5 = (y0 * y5) - (y1 * y4)
	t_6 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_5) + (z * ((a * y1) - (c * y0)))))
	t_7 = (i * y1) - (b * y0)
	tmp = 0
	if c <= -3e+116:
		tmp = c * (((x * (y0 * y2)) - (y0 * (z * y3))) + (y4 * t_1))
	elif c <= -1.3e-51:
		tmp = t_6
	elif c <= -4.5e-75:
		tmp = y5 * ((a * ((t * y2) - (y * y3))) - (i * (t * j)))
	elif c <= -3.6e-130:
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((c * ((z * t) - (x * y))) - (y5 * t_2)))
	elif c <= -7.8e-236:
		tmp = t * (((j * t_3) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))))
	elif c <= -9.4e-299:
		tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) - (z * t_7))
	elif c <= 5e-250:
		tmp = j * (((t * t_3) + (y3 * t_5)) + (x * t_7))
	elif c <= 3.1e-177:
		tmp = t_6
	elif c <= 6e-112:
		tmp = b * ((a * ((x * y) - (z * t))) + (y0 * ((z * k) - (x * j))))
	elif c <= 8.5e-35:
		tmp = t_4
	elif c <= 2.15e+52:
		tmp = y5 * (y2 * ((t * a) - (k * y0)))
	elif c <= 5.6e+82:
		tmp = t_6
	elif c <= 4e+245:
		tmp = ((x * y2) - (z * y3)) * (c * y0)
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y * y3) - Float64(t * y2))
	t_2 = Float64(Float64(t * j) - Float64(y * k))
	t_3 = Float64(Float64(b * y4) - Float64(i * y5))
	t_4 = Float64(y4 * Float64(Float64(Float64(b * t_2) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * t_1)))
	t_5 = Float64(Float64(y0 * y5) - Float64(y1 * y4))
	t_6 = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(j * t_5) + Float64(z * Float64(Float64(a * y1) - Float64(c * y0))))))
	t_7 = Float64(Float64(i * y1) - Float64(b * y0))
	tmp = 0.0
	if (c <= -3e+116)
		tmp = Float64(c * Float64(Float64(Float64(x * Float64(y0 * y2)) - Float64(y0 * Float64(z * y3))) + Float64(y4 * t_1)));
	elseif (c <= -1.3e-51)
		tmp = t_6;
	elseif (c <= -4.5e-75)
		tmp = Float64(y5 * Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) - Float64(i * Float64(t * j))));
	elseif (c <= -3.6e-130)
		tmp = Float64(i * Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) + Float64(Float64(c * Float64(Float64(z * t) - Float64(x * y))) - Float64(y5 * t_2))));
	elseif (c <= -7.8e-236)
		tmp = Float64(t * Float64(Float64(Float64(j * t_3) + Float64(z * Float64(Float64(c * i) - Float64(a * b)))) + Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (c <= -9.4e-299)
		tmp = Float64(k * Float64(Float64(Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(y * Float64(Float64(i * y5) - Float64(b * y4)))) - Float64(z * t_7)));
	elseif (c <= 5e-250)
		tmp = Float64(j * Float64(Float64(Float64(t * t_3) + Float64(y3 * t_5)) + Float64(x * t_7)));
	elseif (c <= 3.1e-177)
		tmp = t_6;
	elseif (c <= 6e-112)
		tmp = Float64(b * Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (c <= 8.5e-35)
		tmp = t_4;
	elseif (c <= 2.15e+52)
		tmp = Float64(y5 * Float64(y2 * Float64(Float64(t * a) - Float64(k * y0))));
	elseif (c <= 5.6e+82)
		tmp = t_6;
	elseif (c <= 4e+245)
		tmp = Float64(Float64(Float64(x * y2) - Float64(z * y3)) * Float64(c * y0));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y * y3) - (t * y2);
	t_2 = (t * j) - (y * k);
	t_3 = (b * y4) - (i * y5);
	t_4 = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) + (c * t_1));
	t_5 = (y0 * y5) - (y1 * y4);
	t_6 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_5) + (z * ((a * y1) - (c * y0)))));
	t_7 = (i * y1) - (b * y0);
	tmp = 0.0;
	if (c <= -3e+116)
		tmp = c * (((x * (y0 * y2)) - (y0 * (z * y3))) + (y4 * t_1));
	elseif (c <= -1.3e-51)
		tmp = t_6;
	elseif (c <= -4.5e-75)
		tmp = y5 * ((a * ((t * y2) - (y * y3))) - (i * (t * j)));
	elseif (c <= -3.6e-130)
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((c * ((z * t) - (x * y))) - (y5 * t_2)));
	elseif (c <= -7.8e-236)
		tmp = t * (((j * t_3) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))));
	elseif (c <= -9.4e-299)
		tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) - (z * t_7));
	elseif (c <= 5e-250)
		tmp = j * (((t * t_3) + (y3 * t_5)) + (x * t_7));
	elseif (c <= 3.1e-177)
		tmp = t_6;
	elseif (c <= 6e-112)
		tmp = b * ((a * ((x * y) - (z * t))) + (y0 * ((z * k) - (x * j))));
	elseif (c <= 8.5e-35)
		tmp = t_4;
	elseif (c <= 2.15e+52)
		tmp = y5 * (y2 * ((t * a) - (k * y0)));
	elseif (c <= 5.6e+82)
		tmp = t_6;
	elseif (c <= 4e+245)
		tmp = ((x * y2) - (z * y3)) * (c * y0);
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y4 * N[(N[(N[(b * t$95$2), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * t$95$5), $MachinePrecision] + N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3e+116], N[(c * N[(N[(N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision] - N[(y0 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.3e-51], t$95$6, If[LessEqual[c, -4.5e-75], N[(y5 * N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3.6e-130], N[(i * N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(c * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y5 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -7.8e-236], N[(t * N[(N[(N[(j * t$95$3), $MachinePrecision] + N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -9.4e-299], N[(k * N[(N[(N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5e-250], N[(j * N[(N[(N[(t * t$95$3), $MachinePrecision] + N[(y3 * t$95$5), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.1e-177], t$95$6, If[LessEqual[c, 6e-112], N[(b * N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 8.5e-35], t$95$4, If[LessEqual[c, 2.15e+52], N[(y5 * N[(y2 * N[(N[(t * a), $MachinePrecision] - N[(k * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.6e+82], t$95$6, If[LessEqual[c, 4e+245], N[(N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision] * N[(c * y0), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 11 regimes

2. if c < -2.9999999999999999e116

   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. Taylor expanded in c around inf 58.1%

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

      1. +-commutative 58.1%

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

      2. mul-1-neg 58.1%

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

      3. unsub-neg 58.1%

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

      4. *-commutative 58.1%

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

      5. *-commutative 58.1%

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

      6. *-commutative 58.1%

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

      7. *-commutative 58.1%

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

   4. Simplified 58.1%

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

   5. Taylor expanded in y2 around 0 58.2%

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

   6. Taylor expanded in i around 0 65.1%

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

   if -2.9999999999999999e116 < c < -1.3e-51 or 5.00000000000000027e-250 < c < 3.10000000000000018e-177 or 2.15e52 < c < 5.6000000000000001e82

   1. Initial program 37.4%

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

   2. Taylor expanded in y3 around -inf 61.5%

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

   if -1.3e-51 < c < -4.5000000000000003e-75

   1. Initial program 14.3%

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

   2. Taylor expanded in y5 around -inf 85.7%

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

   3. Taylor expanded in t around inf 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   if -4.5000000000000003e-75 < c < -3.6000000000000001e-130

   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. Taylor expanded in i around -inf 80.7%

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

   if -3.6000000000000001e-130 < c < -7.8000000000000001e-236

   1. Initial program 43.1%

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

   2. Taylor expanded in t around inf 63.0%

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

      1. +-commutative 63.0%

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

      2. mul-1-neg 63.0%

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

      3. unsub-neg 63.0%

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

      4. *-commutative 63.0%

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

   4. Simplified 63.0%

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

   if -7.8000000000000001e-236 < c < -9.3999999999999995e-299

   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. Taylor expanded in k around -inf 57.0%

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

      1. mul-1-neg 57.0%

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

      2. *-commutative 57.0%

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

      3. sub-neg 57.0%

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

      4. +-commutative 57.0%

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

      5. mul-1-neg 57.0%

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

      6. distribute-rgt-neg-in 57.0%

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

   4. Simplified 57.0%

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

   if -9.3999999999999995e-299 < c < 5.00000000000000027e-250

   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. Taylor expanded in j around inf 63.3%

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

   4. Simplified 63.3%

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

   if 3.10000000000000018e-177 < c < 6.0000000000000002e-112

   1. Initial program 53.6%

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

   2. Taylor expanded in b around inf 52.7%

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

   3. Taylor expanded in y4 around 0 68.1%

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

      1. *-commutative 68.1%

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

      2. *-commutative 68.1%

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

      3. *-commutative 68.1%

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

   5. Simplified 68.1%

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

   if 6.0000000000000002e-112 < c < 8.5000000000000001e-35 or 4.00000000000000018e245 < c

   1. Initial program 30.4%

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

   2. Taylor expanded in y4 around inf 74.5%

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

   if 8.5000000000000001e-35 < c < 2.15e52

   1. Initial program 35.5%

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

   2. Taylor expanded in y5 around -inf 39.9%

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

   3. Taylor expanded in y2 around inf 75.2%

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

      1. *-commutative 75.2%

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

   5. Simplified 75.2%

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

   if 5.6000000000000001e82 < c < 4.00000000000000018e245

   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. Taylor expanded in c around inf 50.4%

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

      1. +-commutative 50.4%

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

      2. mul-1-neg 50.4%

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

      3. unsub-neg 50.4%

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

      4. *-commutative 50.4%

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

      5. *-commutative 50.4%

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

      6. *-commutative 50.4%

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

      7. *-commutative 50.4%

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

   4. Simplified 50.4%

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

   5. Taylor expanded in y0 around inf 54.1%

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

      1. associate-*r* 56.4%

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

      2. *-commutative 56.4%

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

      3. *-commutative 56.4%

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

      4. *-commutative 56.4%

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

      5. *-commutative 56.4%

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

      6. *-commutative 56.4%

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

   7. Simplified 56.4%

      \[\leadsto \color{blue}{\left(x \cdot y2 - y3 \cdot z\right) \cdot \left(c \cdot y0\right)} \]
3. Recombined 11 regimes into one program.

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3 \cdot 10^{+116}:\\ \;\;\;\;c \cdot \left(\left(x \cdot \left(y0 \cdot y2\right) - y0 \cdot \left(z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -1.3 \cdot 10^{-51}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;c \leq -4.5 \cdot 10^{-75}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - i \cdot \left(t \cdot j\right)\right)\\ \mathbf{elif}\;c \leq -3.6 \cdot 10^{-130}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(c \cdot \left(z \cdot t - x \cdot y\right) - y5 \cdot \left(t \cdot j - y \cdot k\right)\right)\right)\\ \mathbf{elif}\;c \leq -7.8 \cdot 10^{-236}:\\ \;\;\;\;t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + z \cdot \left(c \cdot i - a \cdot b\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq -9.4 \cdot 10^{-299}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) - z \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq 5 \cdot 10^{-250}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq 3.1 \cdot 10^{-177}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;c \leq 6 \cdot 10^{-112}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{-35}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq 2.15 \cdot 10^{+52}:\\ \;\;\;\;y5 \cdot \left(y2 \cdot \left(t \cdot a - k \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq 5.6 \cdot 10^{+82}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;c \leq 4 \cdot 10^{+245}:\\ \;\;\;\;\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \end{array} \]

Alternative 5: 35.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot y2 - j \cdot y3\\ t_2 := y \cdot y3 - t \cdot y2\\ t_3 := z \cdot t - x \cdot y\\ t_4 := x \cdot y2 - z \cdot y3\\ t_5 := x \cdot j - z \cdot k\\ t_6 := t \cdot j - y \cdot k\\ t_7 := i \cdot \left(y1 \cdot t_5 + \left(c \cdot t_3 - y5 \cdot t_6\right)\right)\\ t_8 := c \cdot \left(\left(y0 \cdot t_4 + i \cdot t_3\right) + y4 \cdot t_2\right)\\ t_9 := x \cdot y - z \cdot t\\ \mathbf{if}\;b \leq -3.2 \cdot 10^{+212}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{-251}:\\ \;\;\;\;y1 \cdot \left(i \cdot t_5 + \left(y4 \cdot t_1 - a \cdot t_4\right)\right)\\ \mathbf{elif}\;b \leq 8.8 \cdot 10^{-226}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-132}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(b \cdot t_9 + y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{-11}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{+110}:\\ \;\;\;\;b \cdot \left(\left(y4 \cdot t_6 + a \cdot t_9\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{+127}:\\ \;\;\;\;y5 \cdot \left(y2 \cdot \left(t \cdot a - k \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{+171}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right) - y0 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+259}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot t_6 + y1 \cdot t_1\right) + c \cdot t_2\right)\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{+274}:\\ \;\;\;\;t_7\\ \mathbf{else}:\\ \;\;\;\;t_8\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* k y2) (* j y3)))
        (t_2 (- (* y y3) (* t y2)))
        (t_3 (- (* z t) (* x y)))
        (t_4 (- (* x y2) (* z y3)))
        (t_5 (- (* x j) (* z k)))
        (t_6 (- (* t j) (* y k)))
        (t_7 (* i (+ (* y1 t_5) (- (* c t_3) (* y5 t_6)))))
        (t_8 (* c (+ (+ (* y0 t_4) (* i t_3)) (* y4 t_2))))
        (t_9 (- (* x y) (* z t))))
   (if (<= b -3.2e+212)
     t_7
     (if (<= b -2.4e+38)
       (* x (* y0 (- (* c y2) (* b j))))
       (if (<= b -8.2e-251)
         (* y1 (+ (* i t_5) (- (* y4 t_1) (* a t_4))))
         (if (<= b 8.8e-226)
           t_8
           (if (<= b 1.55e-132)
             (*
              a
              (+
               (* y5 (- (* t y2) (* y y3)))
               (+ (* b t_9) (* y1 (- (* z y3) (* x y2))))))
             (if (<= b 1.85e-11)
               t_7
               (if (<= b 5.4e+110)
                 (* b (+ (+ (* y4 t_6) (* a t_9)) (* y0 (- (* z k) (* x j)))))
                 (if (<= b 2.15e+127)
                   (* y5 (* y2 (- (* t a) (* k y0))))
                   (if (<= b 1.55e+171)
                     (* c (- (* x (* y0 y2)) (* y0 (* z y3))))
                     (if (<= b 3.8e+259)
                       (* y4 (+ (+ (* b t_6) (* y1 t_1)) (* c t_2)))
                       (if (<= b 2.15e+274) t_7 t_8)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (k * y2) - (j * y3);
	double t_2 = (y * y3) - (t * y2);
	double t_3 = (z * t) - (x * y);
	double t_4 = (x * y2) - (z * y3);
	double t_5 = (x * j) - (z * k);
	double t_6 = (t * j) - (y * k);
	double t_7 = i * ((y1 * t_5) + ((c * t_3) - (y5 * t_6)));
	double t_8 = c * (((y0 * t_4) + (i * t_3)) + (y4 * t_2));
	double t_9 = (x * y) - (z * t);
	double tmp;
	if (b <= -3.2e+212) {
		tmp = t_7;
	} else if (b <= -2.4e+38) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (b <= -8.2e-251) {
		tmp = y1 * ((i * t_5) + ((y4 * t_1) - (a * t_4)));
	} else if (b <= 8.8e-226) {
		tmp = t_8;
	} else if (b <= 1.55e-132) {
		tmp = a * ((y5 * ((t * y2) - (y * y3))) + ((b * t_9) + (y1 * ((z * y3) - (x * y2)))));
	} else if (b <= 1.85e-11) {
		tmp = t_7;
	} else if (b <= 5.4e+110) {
		tmp = b * (((y4 * t_6) + (a * t_9)) + (y0 * ((z * k) - (x * j))));
	} else if (b <= 2.15e+127) {
		tmp = y5 * (y2 * ((t * a) - (k * y0)));
	} else if (b <= 1.55e+171) {
		tmp = c * ((x * (y0 * y2)) - (y0 * (z * y3)));
	} else if (b <= 3.8e+259) {
		tmp = y4 * (((b * t_6) + (y1 * t_1)) + (c * t_2));
	} else if (b <= 2.15e+274) {
		tmp = t_7;
	} else {
		tmp = t_8;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = (k * y2) - (j * y3)
    t_2 = (y * y3) - (t * y2)
    t_3 = (z * t) - (x * y)
    t_4 = (x * y2) - (z * y3)
    t_5 = (x * j) - (z * k)
    t_6 = (t * j) - (y * k)
    t_7 = i * ((y1 * t_5) + ((c * t_3) - (y5 * t_6)))
    t_8 = c * (((y0 * t_4) + (i * t_3)) + (y4 * t_2))
    t_9 = (x * y) - (z * t)
    if (b <= (-3.2d+212)) then
        tmp = t_7
    else if (b <= (-2.4d+38)) then
        tmp = x * (y0 * ((c * y2) - (b * j)))
    else if (b <= (-8.2d-251)) then
        tmp = y1 * ((i * t_5) + ((y4 * t_1) - (a * t_4)))
    else if (b <= 8.8d-226) then
        tmp = t_8
    else if (b <= 1.55d-132) then
        tmp = a * ((y5 * ((t * y2) - (y * y3))) + ((b * t_9) + (y1 * ((z * y3) - (x * y2)))))
    else if (b <= 1.85d-11) then
        tmp = t_7
    else if (b <= 5.4d+110) then
        tmp = b * (((y4 * t_6) + (a * t_9)) + (y0 * ((z * k) - (x * j))))
    else if (b <= 2.15d+127) then
        tmp = y5 * (y2 * ((t * a) - (k * y0)))
    else if (b <= 1.55d+171) then
        tmp = c * ((x * (y0 * y2)) - (y0 * (z * y3)))
    else if (b <= 3.8d+259) then
        tmp = y4 * (((b * t_6) + (y1 * t_1)) + (c * t_2))
    else if (b <= 2.15d+274) then
        tmp = t_7
    else
        tmp = t_8
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (k * y2) - (j * y3);
	double t_2 = (y * y3) - (t * y2);
	double t_3 = (z * t) - (x * y);
	double t_4 = (x * y2) - (z * y3);
	double t_5 = (x * j) - (z * k);
	double t_6 = (t * j) - (y * k);
	double t_7 = i * ((y1 * t_5) + ((c * t_3) - (y5 * t_6)));
	double t_8 = c * (((y0 * t_4) + (i * t_3)) + (y4 * t_2));
	double t_9 = (x * y) - (z * t);
	double tmp;
	if (b <= -3.2e+212) {
		tmp = t_7;
	} else if (b <= -2.4e+38) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (b <= -8.2e-251) {
		tmp = y1 * ((i * t_5) + ((y4 * t_1) - (a * t_4)));
	} else if (b <= 8.8e-226) {
		tmp = t_8;
	} else if (b <= 1.55e-132) {
		tmp = a * ((y5 * ((t * y2) - (y * y3))) + ((b * t_9) + (y1 * ((z * y3) - (x * y2)))));
	} else if (b <= 1.85e-11) {
		tmp = t_7;
	} else if (b <= 5.4e+110) {
		tmp = b * (((y4 * t_6) + (a * t_9)) + (y0 * ((z * k) - (x * j))));
	} else if (b <= 2.15e+127) {
		tmp = y5 * (y2 * ((t * a) - (k * y0)));
	} else if (b <= 1.55e+171) {
		tmp = c * ((x * (y0 * y2)) - (y0 * (z * y3)));
	} else if (b <= 3.8e+259) {
		tmp = y4 * (((b * t_6) + (y1 * t_1)) + (c * t_2));
	} else if (b <= 2.15e+274) {
		tmp = t_7;
	} else {
		tmp = t_8;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (k * y2) - (j * y3)
	t_2 = (y * y3) - (t * y2)
	t_3 = (z * t) - (x * y)
	t_4 = (x * y2) - (z * y3)
	t_5 = (x * j) - (z * k)
	t_6 = (t * j) - (y * k)
	t_7 = i * ((y1 * t_5) + ((c * t_3) - (y5 * t_6)))
	t_8 = c * (((y0 * t_4) + (i * t_3)) + (y4 * t_2))
	t_9 = (x * y) - (z * t)
	tmp = 0
	if b <= -3.2e+212:
		tmp = t_7
	elif b <= -2.4e+38:
		tmp = x * (y0 * ((c * y2) - (b * j)))
	elif b <= -8.2e-251:
		tmp = y1 * ((i * t_5) + ((y4 * t_1) - (a * t_4)))
	elif b <= 8.8e-226:
		tmp = t_8
	elif b <= 1.55e-132:
		tmp = a * ((y5 * ((t * y2) - (y * y3))) + ((b * t_9) + (y1 * ((z * y3) - (x * y2)))))
	elif b <= 1.85e-11:
		tmp = t_7
	elif b <= 5.4e+110:
		tmp = b * (((y4 * t_6) + (a * t_9)) + (y0 * ((z * k) - (x * j))))
	elif b <= 2.15e+127:
		tmp = y5 * (y2 * ((t * a) - (k * y0)))
	elif b <= 1.55e+171:
		tmp = c * ((x * (y0 * y2)) - (y0 * (z * y3)))
	elif b <= 3.8e+259:
		tmp = y4 * (((b * t_6) + (y1 * t_1)) + (c * t_2))
	elif b <= 2.15e+274:
		tmp = t_7
	else:
		tmp = t_8
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(k * y2) - Float64(j * y3))
	t_2 = Float64(Float64(y * y3) - Float64(t * y2))
	t_3 = Float64(Float64(z * t) - Float64(x * y))
	t_4 = Float64(Float64(x * y2) - Float64(z * y3))
	t_5 = Float64(Float64(x * j) - Float64(z * k))
	t_6 = Float64(Float64(t * j) - Float64(y * k))
	t_7 = Float64(i * Float64(Float64(y1 * t_5) + Float64(Float64(c * t_3) - Float64(y5 * t_6))))
	t_8 = Float64(c * Float64(Float64(Float64(y0 * t_4) + Float64(i * t_3)) + Float64(y4 * t_2)))
	t_9 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if (b <= -3.2e+212)
		tmp = t_7;
	elseif (b <= -2.4e+38)
		tmp = Float64(x * Float64(y0 * Float64(Float64(c * y2) - Float64(b * j))));
	elseif (b <= -8.2e-251)
		tmp = Float64(y1 * Float64(Float64(i * t_5) + Float64(Float64(y4 * t_1) - Float64(a * t_4))));
	elseif (b <= 8.8e-226)
		tmp = t_8;
	elseif (b <= 1.55e-132)
		tmp = Float64(a * Float64(Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(Float64(b * t_9) + Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))))));
	elseif (b <= 1.85e-11)
		tmp = t_7;
	elseif (b <= 5.4e+110)
		tmp = Float64(b * Float64(Float64(Float64(y4 * t_6) + Float64(a * t_9)) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (b <= 2.15e+127)
		tmp = Float64(y5 * Float64(y2 * Float64(Float64(t * a) - Float64(k * y0))));
	elseif (b <= 1.55e+171)
		tmp = Float64(c * Float64(Float64(x * Float64(y0 * y2)) - Float64(y0 * Float64(z * y3))));
	elseif (b <= 3.8e+259)
		tmp = Float64(y4 * Float64(Float64(Float64(b * t_6) + Float64(y1 * t_1)) + Float64(c * t_2)));
	elseif (b <= 2.15e+274)
		tmp = t_7;
	else
		tmp = t_8;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (k * y2) - (j * y3);
	t_2 = (y * y3) - (t * y2);
	t_3 = (z * t) - (x * y);
	t_4 = (x * y2) - (z * y3);
	t_5 = (x * j) - (z * k);
	t_6 = (t * j) - (y * k);
	t_7 = i * ((y1 * t_5) + ((c * t_3) - (y5 * t_6)));
	t_8 = c * (((y0 * t_4) + (i * t_3)) + (y4 * t_2));
	t_9 = (x * y) - (z * t);
	tmp = 0.0;
	if (b <= -3.2e+212)
		tmp = t_7;
	elseif (b <= -2.4e+38)
		tmp = x * (y0 * ((c * y2) - (b * j)));
	elseif (b <= -8.2e-251)
		tmp = y1 * ((i * t_5) + ((y4 * t_1) - (a * t_4)));
	elseif (b <= 8.8e-226)
		tmp = t_8;
	elseif (b <= 1.55e-132)
		tmp = a * ((y5 * ((t * y2) - (y * y3))) + ((b * t_9) + (y1 * ((z * y3) - (x * y2)))));
	elseif (b <= 1.85e-11)
		tmp = t_7;
	elseif (b <= 5.4e+110)
		tmp = b * (((y4 * t_6) + (a * t_9)) + (y0 * ((z * k) - (x * j))));
	elseif (b <= 2.15e+127)
		tmp = y5 * (y2 * ((t * a) - (k * y0)));
	elseif (b <= 1.55e+171)
		tmp = c * ((x * (y0 * y2)) - (y0 * (z * y3)));
	elseif (b <= 3.8e+259)
		tmp = y4 * (((b * t_6) + (y1 * t_1)) + (c * t_2));
	elseif (b <= 2.15e+274)
		tmp = t_7;
	else
		tmp = t_8;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(i * N[(N[(y1 * t$95$5), $MachinePrecision] + N[(N[(c * t$95$3), $MachinePrecision] - N[(y5 * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(c * N[(N[(N[(y0 * t$95$4), $MachinePrecision] + N[(i * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.2e+212], t$95$7, If[LessEqual[b, -2.4e+38], N[(x * N[(y0 * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -8.2e-251], N[(y1 * N[(N[(i * t$95$5), $MachinePrecision] + N[(N[(y4 * t$95$1), $MachinePrecision] - N[(a * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.8e-226], t$95$8, If[LessEqual[b, 1.55e-132], N[(a * N[(N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(b * t$95$9), $MachinePrecision] + N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.85e-11], t$95$7, If[LessEqual[b, 5.4e+110], N[(b * N[(N[(N[(y4 * t$95$6), $MachinePrecision] + N[(a * t$95$9), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.15e+127], N[(y5 * N[(y2 * N[(N[(t * a), $MachinePrecision] - N[(k * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.55e+171], N[(c * N[(N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision] - N[(y0 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.8e+259], N[(y4 * N[(N[(N[(b * t$95$6), $MachinePrecision] + N[(y1 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.15e+274], t$95$7, t$95$8]]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if b < -3.1999999999999999e212 or 1.55000000000000004e-132 < b < 1.8500000000000001e-11 or 3.8e259 < b < 2.14999999999999994e274

   1. Initial program 25.4%

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

   2. Taylor expanded in i around -inf 63.3%

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

   if -3.1999999999999999e212 < b < -2.40000000000000017e38

   1. Initial program 20.6%

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

   2. Taylor expanded in x around inf 27.7%

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

   3. Taylor expanded in y0 around inf 55.8%

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

      1. *-commutative 55.8%

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

   5. Simplified 55.8%

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

   if -2.40000000000000017e38 < b < -8.1999999999999997e-251

   1. Initial program 32.9%

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

   2. Taylor expanded in y1 around -inf 51.9%

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

      1. mul-1-neg 51.9%

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

      2. *-commutative 51.9%

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

      3. distribute-rgt-neg-in 51.9%

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

   4. Simplified 51.9%

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

   if -8.1999999999999997e-251 < b < 8.8e-226 or 2.14999999999999994e274 < b

   1. Initial program 36.3%

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

   2. Taylor expanded in c around inf 71.9%

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

      1. +-commutative 71.9%

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

      2. mul-1-neg 71.9%

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

      3. unsub-neg 71.9%

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

      4. *-commutative 71.9%

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

      5. *-commutative 71.9%

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

      6. *-commutative 71.9%

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

      7. *-commutative 71.9%

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

   4. Simplified 71.9%

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

   if 8.8e-226 < b < 1.55000000000000004e-132

   1. Initial program 47.6%

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

   2. Taylor expanded in a around -inf 53.4%

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

      1. mul-1-neg 53.4%

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

      2. distribute-rgt-neg-in 53.4%

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

      3. +-commutative 53.4%

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

      4. mul-1-neg 53.4%

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

      5. unsub-neg 53.4%

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

      6. *-commutative 53.4%

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

      7. *-commutative 53.4%

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

      8. *-commutative 53.4%

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

   4. Simplified 53.4%

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

   if 1.8500000000000001e-11 < b < 5.40000000000000019e110

   1. Initial program 57.1%

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

   2. Taylor expanded in b around inf 64.6%

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

   if 5.40000000000000019e110 < b < 2.14999999999999992e127

   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. Taylor expanded in y5 around -inf 38.2%

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

   3. Taylor expanded in y2 around inf 62.7%

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

      1. *-commutative 62.7%

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

   5. Simplified 62.7%

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

   if 2.14999999999999992e127 < b < 1.5499999999999999e171

   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. Taylor expanded in c around inf 47.3%

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

      1. +-commutative 47.3%

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

      2. mul-1-neg 47.3%

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

      3. unsub-neg 47.3%

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

      4. *-commutative 47.3%

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

      5. *-commutative 47.3%

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

      6. *-commutative 47.3%

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

      7. *-commutative 47.3%

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

   4. Simplified 47.3%

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

   5. Taylor expanded in y0 around inf 72.8%

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

   6. Taylor expanded in x around 0 72.8%

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

   if 1.5499999999999999e171 < b < 3.8e259

   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. Taylor expanded in y4 around inf 71.2%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.2 \cdot 10^{+212}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(c \cdot \left(z \cdot t - x \cdot y\right) - y5 \cdot \left(t \cdot j - y \cdot k\right)\right)\right)\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{-251}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\right)\\ \mathbf{elif}\;b \leq 8.8 \cdot 10^{-226}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + i \cdot \left(z \cdot t - x \cdot y\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-132}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(b \cdot \left(x \cdot y - z \cdot t\right) + y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{-11}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(c \cdot \left(z \cdot t - x \cdot y\right) - y5 \cdot \left(t \cdot j - y \cdot k\right)\right)\right)\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{+110}:\\ \;\;\;\;b \cdot \left(\left(y4 \cdot \left(t \cdot j - y \cdot k\right) + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{+127}:\\ \;\;\;\;y5 \cdot \left(y2 \cdot \left(t \cdot a - k \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{+171}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right) - y0 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+259}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{+274}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(c \cdot \left(z \cdot t - x \cdot y\right) - y5 \cdot \left(t \cdot j - y \cdot k\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + i \cdot \left(z \cdot t - x \cdot y\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \end{array} \]

Alternative 6: 41.0% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y2 - z \cdot y3\\ t_2 := y0 \cdot \left(\left(c \cdot t_1 + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ t_3 := i \cdot y1 - b \cdot y0\\ t_4 := b \cdot y4 - i \cdot y5\\ \mathbf{if}\;j \leq -5.5 \cdot 10^{+91}:\\ \;\;\;\;x \cdot \left(j \cdot t_3\right)\\ \mathbf{elif}\;j \leq -3.2 \cdot 10^{-139}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{-218}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot t_1 + i \cdot \left(z \cdot t - x \cdot y\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 3 \cdot 10^{-159}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) - z \cdot t_3\right)\\ \mathbf{elif}\;j \leq 1.65 \cdot 10^{-79}:\\ \;\;\;\;t \cdot \left(\left(j \cdot t_4 + z \cdot \left(c \cdot i - a \cdot b\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 4 \cdot 10^{+33}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(\left(t \cdot t_4 + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot t_3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* x y2) (* z y3)))
        (t_2
         (*
          y0
          (+
           (+ (* c t_1) (* y5 (- (* j y3) (* k y2))))
           (* b (- (* z k) (* x j))))))
        (t_3 (- (* i y1) (* b y0)))
        (t_4 (- (* b y4) (* i y5))))
   (if (<= j -5.5e+91)
     (* x (* j t_3))
     (if (<= j -3.2e-139)
       t_2
       (if (<= j 3.8e-218)
         (*
          c
          (+
           (+ (* y0 t_1) (* i (- (* z t) (* x y))))
           (* y4 (- (* y y3) (* t y2)))))
         (if (<= j 3e-159)
           (*
            k
            (-
             (+ (* y2 (- (* y1 y4) (* y0 y5))) (* y (- (* i y5) (* b y4))))
             (* z t_3)))
           (if (<= j 1.65e-79)
             (*
              t
              (+
               (+ (* j t_4) (* z (- (* c i) (* a b))))
               (* y2 (- (* a y5) (* c y4)))))
             (if (<= j 4e+33)
               t_2
               (*
                j
                (+
                 (+ (* t t_4) (* y3 (- (* y0 y5) (* y1 y4))))
                 (* x t_3)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (x * y2) - (z * y3);
	double t_2 = y0 * (((c * t_1) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))));
	double t_3 = (i * y1) - (b * y0);
	double t_4 = (b * y4) - (i * y5);
	double tmp;
	if (j <= -5.5e+91) {
		tmp = x * (j * t_3);
	} else if (j <= -3.2e-139) {
		tmp = t_2;
	} else if (j <= 3.8e-218) {
		tmp = c * (((y0 * t_1) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (j <= 3e-159) {
		tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) - (z * t_3));
	} else if (j <= 1.65e-79) {
		tmp = t * (((j * t_4) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))));
	} else if (j <= 4e+33) {
		tmp = t_2;
	} else {
		tmp = j * (((t * t_4) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_3));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (x * y2) - (z * y3)
    t_2 = y0 * (((c * t_1) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))))
    t_3 = (i * y1) - (b * y0)
    t_4 = (b * y4) - (i * y5)
    if (j <= (-5.5d+91)) then
        tmp = x * (j * t_3)
    else if (j <= (-3.2d-139)) then
        tmp = t_2
    else if (j <= 3.8d-218) then
        tmp = c * (((y0 * t_1) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))))
    else if (j <= 3d-159) then
        tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) - (z * t_3))
    else if (j <= 1.65d-79) then
        tmp = t * (((j * t_4) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))))
    else if (j <= 4d+33) then
        tmp = t_2
    else
        tmp = j * (((t * t_4) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_3))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (x * y2) - (z * y3);
	double t_2 = y0 * (((c * t_1) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))));
	double t_3 = (i * y1) - (b * y0);
	double t_4 = (b * y4) - (i * y5);
	double tmp;
	if (j <= -5.5e+91) {
		tmp = x * (j * t_3);
	} else if (j <= -3.2e-139) {
		tmp = t_2;
	} else if (j <= 3.8e-218) {
		tmp = c * (((y0 * t_1) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (j <= 3e-159) {
		tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) - (z * t_3));
	} else if (j <= 1.65e-79) {
		tmp = t * (((j * t_4) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))));
	} else if (j <= 4e+33) {
		tmp = t_2;
	} else {
		tmp = j * (((t * t_4) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_3));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (x * y2) - (z * y3)
	t_2 = y0 * (((c * t_1) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))))
	t_3 = (i * y1) - (b * y0)
	t_4 = (b * y4) - (i * y5)
	tmp = 0
	if j <= -5.5e+91:
		tmp = x * (j * t_3)
	elif j <= -3.2e-139:
		tmp = t_2
	elif j <= 3.8e-218:
		tmp = c * (((y0 * t_1) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))))
	elif j <= 3e-159:
		tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) - (z * t_3))
	elif j <= 1.65e-79:
		tmp = t * (((j * t_4) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))))
	elif j <= 4e+33:
		tmp = t_2
	else:
		tmp = j * (((t * t_4) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_3))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(x * y2) - Float64(z * y3))
	t_2 = Float64(y0 * Float64(Float64(Float64(c * t_1) + Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2)))) + Float64(b * Float64(Float64(z * k) - Float64(x * j)))))
	t_3 = Float64(Float64(i * y1) - Float64(b * y0))
	t_4 = Float64(Float64(b * y4) - Float64(i * y5))
	tmp = 0.0
	if (j <= -5.5e+91)
		tmp = Float64(x * Float64(j * t_3));
	elseif (j <= -3.2e-139)
		tmp = t_2;
	elseif (j <= 3.8e-218)
		tmp = Float64(c * Float64(Float64(Float64(y0 * t_1) + Float64(i * Float64(Float64(z * t) - Float64(x * y)))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (j <= 3e-159)
		tmp = Float64(k * Float64(Float64(Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(y * Float64(Float64(i * y5) - Float64(b * y4)))) - Float64(z * t_3)));
	elseif (j <= 1.65e-79)
		tmp = Float64(t * Float64(Float64(Float64(j * t_4) + Float64(z * Float64(Float64(c * i) - Float64(a * b)))) + Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (j <= 4e+33)
		tmp = t_2;
	else
		tmp = Float64(j * Float64(Float64(Float64(t * t_4) + Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) + Float64(x * t_3)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (x * y2) - (z * y3);
	t_2 = y0 * (((c * t_1) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))));
	t_3 = (i * y1) - (b * y0);
	t_4 = (b * y4) - (i * y5);
	tmp = 0.0;
	if (j <= -5.5e+91)
		tmp = x * (j * t_3);
	elseif (j <= -3.2e-139)
		tmp = t_2;
	elseif (j <= 3.8e-218)
		tmp = c * (((y0 * t_1) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	elseif (j <= 3e-159)
		tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) - (z * t_3));
	elseif (j <= 1.65e-79)
		tmp = t * (((j * t_4) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))));
	elseif (j <= 4e+33)
		tmp = t_2;
	else
		tmp = j * (((t * t_4) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_3));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y0 * N[(N[(N[(c * t$95$1), $MachinePrecision] + N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -5.5e+91], N[(x * N[(j * t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.2e-139], t$95$2, If[LessEqual[j, 3.8e-218], N[(c * N[(N[(N[(y0 * t$95$1), $MachinePrecision] + N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3e-159], N[(k * N[(N[(N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.65e-79], N[(t * N[(N[(N[(j * t$95$4), $MachinePrecision] + N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4e+33], t$95$2, N[(j * N[(N[(N[(t * t$95$4), $MachinePrecision] + N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -5.4999999999999998e91

   1. Initial program 12.6%

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

   2. Taylor expanded in x around inf 40.1%

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

   3. Taylor expanded in j around inf 65.5%

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

      1. *-commutative 65.5%

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

      2. *-commutative 65.5%

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

   5. Simplified 65.5%

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

   if -5.4999999999999998e91 < j < -3.1999999999999999e-139 or 1.6499999999999999e-79 < j < 3.9999999999999998e33

   1. Initial program 24.1%

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

   2. Taylor expanded in y0 around inf 50.8%

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

      1. sub-neg 50.8%

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

      2. +-commutative 50.8%

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

      3. mul-1-neg 50.8%

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

   4. Simplified 50.8%

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

   if -3.1999999999999999e-139 < j < 3.7999999999999999e-218

   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. Taylor expanded in c around inf 61.4%

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

      1. +-commutative 61.4%

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

      2. mul-1-neg 61.4%

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

      3. unsub-neg 61.4%

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

      4. *-commutative 61.4%

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

      5. *-commutative 61.4%

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

      6. *-commutative 61.4%

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

      7. *-commutative 61.4%

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

   4. Simplified 61.4%

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

   if 3.7999999999999999e-218 < j < 3.00000000000000009e-159

   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. Taylor expanded in k around -inf 67.6%

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

      1. mul-1-neg 67.6%

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

      2. *-commutative 67.6%

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

      3. sub-neg 67.6%

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

      4. +-commutative 67.6%

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

      5. mul-1-neg 67.6%

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

      6. distribute-rgt-neg-in 67.6%

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

   4. Simplified 67.6%

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

   if 3.00000000000000009e-159 < j < 1.6499999999999999e-79

   1. Initial program 52.8%

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

   2. Taylor expanded in t around inf 71.0%

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

      1. +-commutative 71.0%

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

      2. mul-1-neg 71.0%

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

      3. unsub-neg 71.0%

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

      4. *-commutative 71.0%

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

   4. Simplified 71.0%

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

   if 3.9999999999999998e33 < j

   1. Initial program 41.4%

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

   2. Taylor expanded in j around inf 64.0%

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

   4. Simplified 64.0%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -5.5 \cdot 10^{+91}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq -3.2 \cdot 10^{-139}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{-218}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + i \cdot \left(z \cdot t - x \cdot y\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 3 \cdot 10^{-159}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) - z \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq 1.65 \cdot 10^{-79}:\\ \;\;\;\;t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + z \cdot \left(c \cdot i - a \cdot b\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 4 \cdot 10^{+33}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \end{array} \]

Alternative 7: 36.2% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\\ t_2 := x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ t_3 := y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\\ t_4 := y4 \cdot \left(t \cdot j - y \cdot k\right)\\ \mathbf{if}\;j \leq -2.8 \cdot 10^{+120}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -4 \cdot 10^{-289}:\\ \;\;\;\;c \cdot \left(\left(x \cdot \left(y0 \cdot y2\right) - y0 \cdot \left(z \cdot y3\right)\right) + t_3\right)\\ \mathbf{elif}\;j \leq 7.2 \cdot 10^{-284}:\\ \;\;\;\;y5 \cdot \left(y2 \cdot \left(t \cdot a - k \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq 6.2 \cdot 10^{-206}:\\ \;\;\;\;c \cdot \left(t_1 + t_3\right)\\ \mathbf{elif}\;j \leq 2.05 \cdot 10^{+93}:\\ \;\;\;\;b \cdot \left(\left(t_4 + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;j \leq 5.2 \cdot 10^{+140}:\\ \;\;\;\;c \cdot t_1\\ \mathbf{elif}\;j \leq 1.65 \cdot 10^{+191}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 7.5 \cdot 10^{+231}:\\ \;\;\;\;x \cdot \left(b \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y0 (- (* x y2) (* z y3))))
        (t_2 (* x (* j (- (* i y1) (* b y0)))))
        (t_3 (* y4 (- (* y y3) (* t y2))))
        (t_4 (* y4 (- (* t j) (* y k)))))
   (if (<= j -2.8e+120)
     t_2
     (if (<= j -4e-289)
       (* c (+ (- (* x (* y0 y2)) (* y0 (* z y3))) t_3))
       (if (<= j 7.2e-284)
         (* y5 (* y2 (- (* t a) (* k y0))))
         (if (<= j 6.2e-206)
           (* c (+ t_1 t_3))
           (if (<= j 2.05e+93)
             (*
              b
              (+ (+ t_4 (* a (- (* x y) (* z t)))) (* y0 (- (* z k) (* x j)))))
             (if (<= j 5.2e+140)
               (* c t_1)
               (if (<= j 1.65e+191)
                 t_2
                 (if (<= j 7.5e+231)
                   (* x (* b (- (* y a) (* j y0))))
                   (* b t_4)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * ((x * y2) - (z * y3));
	double t_2 = x * (j * ((i * y1) - (b * y0)));
	double t_3 = y4 * ((y * y3) - (t * y2));
	double t_4 = y4 * ((t * j) - (y * k));
	double tmp;
	if (j <= -2.8e+120) {
		tmp = t_2;
	} else if (j <= -4e-289) {
		tmp = c * (((x * (y0 * y2)) - (y0 * (z * y3))) + t_3);
	} else if (j <= 7.2e-284) {
		tmp = y5 * (y2 * ((t * a) - (k * y0)));
	} else if (j <= 6.2e-206) {
		tmp = c * (t_1 + t_3);
	} else if (j <= 2.05e+93) {
		tmp = b * ((t_4 + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))));
	} else if (j <= 5.2e+140) {
		tmp = c * t_1;
	} else if (j <= 1.65e+191) {
		tmp = t_2;
	} else if (j <= 7.5e+231) {
		tmp = x * (b * ((y * a) - (j * y0)));
	} else {
		tmp = b * t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = y0 * ((x * y2) - (z * y3))
    t_2 = x * (j * ((i * y1) - (b * y0)))
    t_3 = y4 * ((y * y3) - (t * y2))
    t_4 = y4 * ((t * j) - (y * k))
    if (j <= (-2.8d+120)) then
        tmp = t_2
    else if (j <= (-4d-289)) then
        tmp = c * (((x * (y0 * y2)) - (y0 * (z * y3))) + t_3)
    else if (j <= 7.2d-284) then
        tmp = y5 * (y2 * ((t * a) - (k * y0)))
    else if (j <= 6.2d-206) then
        tmp = c * (t_1 + t_3)
    else if (j <= 2.05d+93) then
        tmp = b * ((t_4 + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))))
    else if (j <= 5.2d+140) then
        tmp = c * t_1
    else if (j <= 1.65d+191) then
        tmp = t_2
    else if (j <= 7.5d+231) then
        tmp = x * (b * ((y * a) - (j * y0)))
    else
        tmp = b * t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * ((x * y2) - (z * y3));
	double t_2 = x * (j * ((i * y1) - (b * y0)));
	double t_3 = y4 * ((y * y3) - (t * y2));
	double t_4 = y4 * ((t * j) - (y * k));
	double tmp;
	if (j <= -2.8e+120) {
		tmp = t_2;
	} else if (j <= -4e-289) {
		tmp = c * (((x * (y0 * y2)) - (y0 * (z * y3))) + t_3);
	} else if (j <= 7.2e-284) {
		tmp = y5 * (y2 * ((t * a) - (k * y0)));
	} else if (j <= 6.2e-206) {
		tmp = c * (t_1 + t_3);
	} else if (j <= 2.05e+93) {
		tmp = b * ((t_4 + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))));
	} else if (j <= 5.2e+140) {
		tmp = c * t_1;
	} else if (j <= 1.65e+191) {
		tmp = t_2;
	} else if (j <= 7.5e+231) {
		tmp = x * (b * ((y * a) - (j * y0)));
	} else {
		tmp = b * t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y0 * ((x * y2) - (z * y3))
	t_2 = x * (j * ((i * y1) - (b * y0)))
	t_3 = y4 * ((y * y3) - (t * y2))
	t_4 = y4 * ((t * j) - (y * k))
	tmp = 0
	if j <= -2.8e+120:
		tmp = t_2
	elif j <= -4e-289:
		tmp = c * (((x * (y0 * y2)) - (y0 * (z * y3))) + t_3)
	elif j <= 7.2e-284:
		tmp = y5 * (y2 * ((t * a) - (k * y0)))
	elif j <= 6.2e-206:
		tmp = c * (t_1 + t_3)
	elif j <= 2.05e+93:
		tmp = b * ((t_4 + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))))
	elif j <= 5.2e+140:
		tmp = c * t_1
	elif j <= 1.65e+191:
		tmp = t_2
	elif j <= 7.5e+231:
		tmp = x * (b * ((y * a) - (j * y0)))
	else:
		tmp = b * t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3)))
	t_2 = Float64(x * Float64(j * Float64(Float64(i * y1) - Float64(b * y0))))
	t_3 = Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))
	t_4 = Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))
	tmp = 0.0
	if (j <= -2.8e+120)
		tmp = t_2;
	elseif (j <= -4e-289)
		tmp = Float64(c * Float64(Float64(Float64(x * Float64(y0 * y2)) - Float64(y0 * Float64(z * y3))) + t_3));
	elseif (j <= 7.2e-284)
		tmp = Float64(y5 * Float64(y2 * Float64(Float64(t * a) - Float64(k * y0))));
	elseif (j <= 6.2e-206)
		tmp = Float64(c * Float64(t_1 + t_3));
	elseif (j <= 2.05e+93)
		tmp = Float64(b * Float64(Float64(t_4 + Float64(a * Float64(Float64(x * y) - Float64(z * t)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (j <= 5.2e+140)
		tmp = Float64(c * t_1);
	elseif (j <= 1.65e+191)
		tmp = t_2;
	elseif (j <= 7.5e+231)
		tmp = Float64(x * Float64(b * Float64(Float64(y * a) - Float64(j * y0))));
	else
		tmp = Float64(b * t_4);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y0 * ((x * y2) - (z * y3));
	t_2 = x * (j * ((i * y1) - (b * y0)));
	t_3 = y4 * ((y * y3) - (t * y2));
	t_4 = y4 * ((t * j) - (y * k));
	tmp = 0.0;
	if (j <= -2.8e+120)
		tmp = t_2;
	elseif (j <= -4e-289)
		tmp = c * (((x * (y0 * y2)) - (y0 * (z * y3))) + t_3);
	elseif (j <= 7.2e-284)
		tmp = y5 * (y2 * ((t * a) - (k * y0)));
	elseif (j <= 6.2e-206)
		tmp = c * (t_1 + t_3);
	elseif (j <= 2.05e+93)
		tmp = b * ((t_4 + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))));
	elseif (j <= 5.2e+140)
		tmp = c * t_1;
	elseif (j <= 1.65e+191)
		tmp = t_2;
	elseif (j <= 7.5e+231)
		tmp = x * (b * ((y * a) - (j * y0)));
	else
		tmp = b * t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.8e+120], t$95$2, If[LessEqual[j, -4e-289], N[(c * N[(N[(N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision] - N[(y0 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7.2e-284], N[(y5 * N[(y2 * N[(N[(t * a), $MachinePrecision] - N[(k * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6.2e-206], N[(c * N[(t$95$1 + t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.05e+93], N[(b * N[(N[(t$95$4 + N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.2e+140], N[(c * t$95$1), $MachinePrecision], If[LessEqual[j, 1.65e+191], t$95$2, If[LessEqual[j, 7.5e+231], N[(x * N[(b * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * t$95$4), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if j < -2.8000000000000001e120 or 5.2000000000000002e140 < j < 1.6499999999999999e191

   1. Initial program 23.0%

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

   2. Taylor expanded in x around inf 42.2%

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

   3. Taylor expanded in j around inf 63.4%

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

      1. *-commutative 63.4%

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

      2. *-commutative 63.4%

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

   5. Simplified 63.4%

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

   if -2.8000000000000001e120 < j < -4e-289

   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. Taylor expanded in c around inf 47.7%

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

      1. +-commutative 47.7%

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

      2. mul-1-neg 47.7%

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

      3. unsub-neg 47.7%

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

      4. *-commutative 47.7%

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

      5. *-commutative 47.7%

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

      6. *-commutative 47.7%

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

      7. *-commutative 47.7%

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

   4. Simplified 47.7%

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

   5. Taylor expanded in y2 around 0 48.9%

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

   6. Taylor expanded in i around 0 44.7%

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

   if -4e-289 < j < 7.2000000000000004e-284

   1. Initial program 58.0%

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

   2. Taylor expanded in y5 around -inf 43.5%

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

   3. Taylor expanded in y2 around inf 86.2%

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

      1. *-commutative 86.2%

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

   5. Simplified 86.2%

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

   if 7.2000000000000004e-284 < j < 6.2000000000000005e-206

   1. Initial program 46.6%

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

   2. Taylor expanded in c around inf 47.8%

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

      1. +-commutative 47.8%

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

      2. mul-1-neg 47.8%

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

      3. unsub-neg 47.8%

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

      4. *-commutative 47.8%

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

      5. *-commutative 47.8%

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

      6. *-commutative 47.8%

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

      7. *-commutative 47.8%

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

   4. Simplified 47.8%

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

   5. Taylor expanded in i around 0 54.6%

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

      1. *-commutative 54.6%

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

      2. *-commutative 54.6%

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

   7. Simplified 54.6%

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

   if 6.2000000000000005e-206 < j < 2.0500000000000001e93

   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. Taylor expanded in b around inf 42.5%

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

   if 2.0500000000000001e93 < j < 5.2000000000000002e140

   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. Taylor expanded in c around inf 55.4%

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

      1. +-commutative 55.4%

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

      2. mul-1-neg 55.4%

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

      3. unsub-neg 55.4%

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

      4. *-commutative 55.4%

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

      5. *-commutative 55.4%

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

      6. *-commutative 55.4%

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

      7. *-commutative 55.4%

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

   4. Simplified 55.4%

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

   5. Taylor expanded in y0 around inf 78.6%

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

   if 1.6499999999999999e191 < j < 7.50000000000000008e231

   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. Taylor expanded in x around inf 43.5%

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

   3. Taylor expanded in b around inf 85.7%

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

      1. *-commutative 85.7%

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

   5. Simplified 85.7%

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

   if 7.50000000000000008e231 < j

   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. Taylor expanded in b around inf 38.3%

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

   3. Taylor expanded in y4 around inf 66.9%

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

      1. *-commutative 66.9%

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

   5. Simplified 66.9%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - y \cdot k\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.8 \cdot 10^{+120}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq -4 \cdot 10^{-289}:\\ \;\;\;\;c \cdot \left(\left(x \cdot \left(y0 \cdot y2\right) - y0 \cdot \left(z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 7.2 \cdot 10^{-284}:\\ \;\;\;\;y5 \cdot \left(y2 \cdot \left(t \cdot a - k \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq 6.2 \cdot 10^{-206}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 2.05 \cdot 10^{+93}:\\ \;\;\;\;b \cdot \left(\left(y4 \cdot \left(t \cdot j - y \cdot k\right) + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;j \leq 5.2 \cdot 10^{+140}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 1.65 \cdot 10^{+191}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq 7.5 \cdot 10^{+231}:\\ \;\;\;\;x \cdot \left(b \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \end{array} \]

Alternative 8: 36.2% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ t_2 := y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\\ t_3 := y4 \cdot \left(t \cdot j - y \cdot k\right)\\ \mathbf{if}\;j \leq -2.7 \cdot 10^{+132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 1.35 \cdot 10^{-221}:\\ \;\;\;\;c \cdot \left(\left(t_2 + i \cdot \left(z \cdot t - x \cdot y\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 1.05 \cdot 10^{-46}:\\ \;\;\;\;\left(t \cdot y2 - y \cdot y3\right) \cdot \left(a \cdot y5\right)\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{-25}:\\ \;\;\;\;\left(x \cdot y2\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\\ \mathbf{elif}\;j \leq 2 \cdot 10^{+90}:\\ \;\;\;\;b \cdot \left(\left(t_3 + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;j \leq 5.9 \cdot 10^{+140}:\\ \;\;\;\;c \cdot t_2\\ \mathbf{elif}\;j \leq 3.2 \cdot 10^{+192}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 1.6 \cdot 10^{+230}:\\ \;\;\;\;x \cdot \left(b \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* x (* j (- (* i y1) (* b y0)))))
        (t_2 (* y0 (- (* x y2) (* z y3))))
        (t_3 (* y4 (- (* t j) (* y k)))))
   (if (<= j -2.7e+132)
     t_1
     (if (<= j 1.35e-221)
       (* c (+ (+ t_2 (* i (- (* z t) (* x y)))) (* y4 (- (* y y3) (* t y2)))))
       (if (<= j 1.05e-46)
         (* (- (* t y2) (* y y3)) (* a y5))
         (if (<= j 1.5e-25)
           (* (* x y2) (- (* c y0) (* a y1)))
           (if (<= j 2e+90)
             (*
              b
              (+ (+ t_3 (* a (- (* x y) (* z t)))) (* y0 (- (* z k) (* x j)))))
             (if (<= j 5.9e+140)
               (* c t_2)
               (if (<= j 3.2e+192)
                 t_1
                 (if (<= j 1.6e+230)
                   (* x (* b (- (* y a) (* j y0))))
                   (* b t_3)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = x * (j * ((i * y1) - (b * y0)));
	double t_2 = y0 * ((x * y2) - (z * y3));
	double t_3 = y4 * ((t * j) - (y * k));
	double tmp;
	if (j <= -2.7e+132) {
		tmp = t_1;
	} else if (j <= 1.35e-221) {
		tmp = c * ((t_2 + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (j <= 1.05e-46) {
		tmp = ((t * y2) - (y * y3)) * (a * y5);
	} else if (j <= 1.5e-25) {
		tmp = (x * y2) * ((c * y0) - (a * y1));
	} else if (j <= 2e+90) {
		tmp = b * ((t_3 + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))));
	} else if (j <= 5.9e+140) {
		tmp = c * t_2;
	} else if (j <= 3.2e+192) {
		tmp = t_1;
	} else if (j <= 1.6e+230) {
		tmp = x * (b * ((y * a) - (j * y0)));
	} else {
		tmp = b * t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * (j * ((i * y1) - (b * y0)))
    t_2 = y0 * ((x * y2) - (z * y3))
    t_3 = y4 * ((t * j) - (y * k))
    if (j <= (-2.7d+132)) then
        tmp = t_1
    else if (j <= 1.35d-221) then
        tmp = c * ((t_2 + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))))
    else if (j <= 1.05d-46) then
        tmp = ((t * y2) - (y * y3)) * (a * y5)
    else if (j <= 1.5d-25) then
        tmp = (x * y2) * ((c * y0) - (a * y1))
    else if (j <= 2d+90) then
        tmp = b * ((t_3 + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))))
    else if (j <= 5.9d+140) then
        tmp = c * t_2
    else if (j <= 3.2d+192) then
        tmp = t_1
    else if (j <= 1.6d+230) then
        tmp = x * (b * ((y * a) - (j * y0)))
    else
        tmp = b * t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = x * (j * ((i * y1) - (b * y0)));
	double t_2 = y0 * ((x * y2) - (z * y3));
	double t_3 = y4 * ((t * j) - (y * k));
	double tmp;
	if (j <= -2.7e+132) {
		tmp = t_1;
	} else if (j <= 1.35e-221) {
		tmp = c * ((t_2 + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (j <= 1.05e-46) {
		tmp = ((t * y2) - (y * y3)) * (a * y5);
	} else if (j <= 1.5e-25) {
		tmp = (x * y2) * ((c * y0) - (a * y1));
	} else if (j <= 2e+90) {
		tmp = b * ((t_3 + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))));
	} else if (j <= 5.9e+140) {
		tmp = c * t_2;
	} else if (j <= 3.2e+192) {
		tmp = t_1;
	} else if (j <= 1.6e+230) {
		tmp = x * (b * ((y * a) - (j * y0)));
	} else {
		tmp = b * t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = x * (j * ((i * y1) - (b * y0)))
	t_2 = y0 * ((x * y2) - (z * y3))
	t_3 = y4 * ((t * j) - (y * k))
	tmp = 0
	if j <= -2.7e+132:
		tmp = t_1
	elif j <= 1.35e-221:
		tmp = c * ((t_2 + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))))
	elif j <= 1.05e-46:
		tmp = ((t * y2) - (y * y3)) * (a * y5)
	elif j <= 1.5e-25:
		tmp = (x * y2) * ((c * y0) - (a * y1))
	elif j <= 2e+90:
		tmp = b * ((t_3 + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))))
	elif j <= 5.9e+140:
		tmp = c * t_2
	elif j <= 3.2e+192:
		tmp = t_1
	elif j <= 1.6e+230:
		tmp = x * (b * ((y * a) - (j * y0)))
	else:
		tmp = b * 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(x * Float64(j * Float64(Float64(i * y1) - Float64(b * y0))))
	t_2 = Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3)))
	t_3 = Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))
	tmp = 0.0
	if (j <= -2.7e+132)
		tmp = t_1;
	elseif (j <= 1.35e-221)
		tmp = Float64(c * Float64(Float64(t_2 + Float64(i * Float64(Float64(z * t) - Float64(x * y)))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (j <= 1.05e-46)
		tmp = Float64(Float64(Float64(t * y2) - Float64(y * y3)) * Float64(a * y5));
	elseif (j <= 1.5e-25)
		tmp = Float64(Float64(x * y2) * Float64(Float64(c * y0) - Float64(a * y1)));
	elseif (j <= 2e+90)
		tmp = Float64(b * Float64(Float64(t_3 + Float64(a * Float64(Float64(x * y) - Float64(z * t)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (j <= 5.9e+140)
		tmp = Float64(c * t_2);
	elseif (j <= 3.2e+192)
		tmp = t_1;
	elseif (j <= 1.6e+230)
		tmp = Float64(x * Float64(b * Float64(Float64(y * a) - Float64(j * y0))));
	else
		tmp = Float64(b * t_3);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = x * (j * ((i * y1) - (b * y0)));
	t_2 = y0 * ((x * y2) - (z * y3));
	t_3 = y4 * ((t * j) - (y * k));
	tmp = 0.0;
	if (j <= -2.7e+132)
		tmp = t_1;
	elseif (j <= 1.35e-221)
		tmp = c * ((t_2 + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	elseif (j <= 1.05e-46)
		tmp = ((t * y2) - (y * y3)) * (a * y5);
	elseif (j <= 1.5e-25)
		tmp = (x * y2) * ((c * y0) - (a * y1));
	elseif (j <= 2e+90)
		tmp = b * ((t_3 + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))));
	elseif (j <= 5.9e+140)
		tmp = c * t_2;
	elseif (j <= 3.2e+192)
		tmp = t_1;
	elseif (j <= 1.6e+230)
		tmp = x * (b * ((y * a) - (j * y0)));
	else
		tmp = b * t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(x * N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.7e+132], t$95$1, If[LessEqual[j, 1.35e-221], N[(c * N[(N[(t$95$2 + N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.05e-46], N[(N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision] * N[(a * y5), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.5e-25], N[(N[(x * y2), $MachinePrecision] * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2e+90], N[(b * N[(N[(t$95$3 + N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.9e+140], N[(c * t$95$2), $MachinePrecision], If[LessEqual[j, 3.2e+192], t$95$1, If[LessEqual[j, 1.6e+230], N[(x * N[(b * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * t$95$3), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if j < -2.7e132 or 5.9000000000000003e140 < j < 3.20000000000000023e192

   1. Initial program 23.5%

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

   2. Taylor expanded in x around inf 43.1%

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

   3. Taylor expanded in j around inf 62.7%

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

      1. *-commutative 62.7%

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

      2. *-commutative 62.7%

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

   5. Simplified 62.7%

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

   if -2.7e132 < j < 1.35e-221

   1. Initial program 37.7%

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

   2. Taylor expanded in c around inf 48.8%

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

      1. +-commutative 48.8%

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

      2. mul-1-neg 48.8%

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

      3. unsub-neg 48.8%

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

      4. *-commutative 48.8%

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

      5. *-commutative 48.8%

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

      6. *-commutative 48.8%

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

      7. *-commutative 48.8%

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

   4. Simplified 48.8%

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

   if 1.35e-221 < j < 1.04999999999999994e-46

   1. Initial program 41.9%

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

   2. Taylor expanded in a around -inf 37.3%

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

      1. mul-1-neg 37.3%

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

      2. distribute-rgt-neg-in 37.3%

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

      3. +-commutative 37.3%

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

      4. mul-1-neg 37.3%

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

      5. unsub-neg 37.3%

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

      6. *-commutative 37.3%

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

      7. *-commutative 37.3%

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

      8. *-commutative 37.3%

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

   4. Simplified 37.3%

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

   5. Taylor expanded in y5 around inf 35.0%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 37.5%

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

      2. *-commutative 37.5%

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

   7. Simplified 37.5%

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

   if 1.04999999999999994e-46 < j < 1.4999999999999999e-25

   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. Taylor expanded in x around inf 83.9%

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

   3. Taylor expanded in y2 around inf 83.9%

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

      1. associate-*r* 100.0%

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

   5. Simplified 100.0%

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

   if 1.4999999999999999e-25 < j < 1.99999999999999993e90

   1. Initial program 20.2%

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

   2. Taylor expanded in b around inf 52.6%

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

   if 1.99999999999999993e90 < j < 5.9000000000000003e140

   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. Taylor expanded in c around inf 55.4%

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

      1. +-commutative 55.4%

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

      2. mul-1-neg 55.4%

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

      3. unsub-neg 55.4%

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

      4. *-commutative 55.4%

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

      5. *-commutative 55.4%

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

      6. *-commutative 55.4%

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

      7. *-commutative 55.4%

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

   4. Simplified 55.4%

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

   5. Taylor expanded in y0 around inf 78.6%

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

   if 3.20000000000000023e192 < j < 1.6e230

   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. Taylor expanded in x around inf 43.5%

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

   3. Taylor expanded in b around inf 85.7%

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

      1. *-commutative 85.7%

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

   5. Simplified 85.7%

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

   if 1.6e230 < j

   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. Taylor expanded in b around inf 38.3%

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

   3. Taylor expanded in y4 around inf 66.9%

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

      1. *-commutative 66.9%

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

   5. Simplified 66.9%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - y \cdot k\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.7 \cdot 10^{+132}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq 1.35 \cdot 10^{-221}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + i \cdot \left(z \cdot t - x \cdot y\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 1.05 \cdot 10^{-46}:\\ \;\;\;\;\left(t \cdot y2 - y \cdot y3\right) \cdot \left(a \cdot y5\right)\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{-25}:\\ \;\;\;\;\left(x \cdot y2\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\\ \mathbf{elif}\;j \leq 2 \cdot 10^{+90}:\\ \;\;\;\;b \cdot \left(\left(y4 \cdot \left(t \cdot j - y \cdot k\right) + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;j \leq 5.9 \cdot 10^{+140}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 3.2 \cdot 10^{+192}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq 1.6 \cdot 10^{+230}:\\ \;\;\;\;x \cdot \left(b \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \end{array} \]

Alternative 9: 39.2% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot y1 - b \cdot y0\\ \mathbf{if}\;j \leq -1.8 \cdot 10^{+130}:\\ \;\;\;\;x \cdot \left(j \cdot t_1\right)\\ \mathbf{elif}\;j \leq 2.25 \cdot 10^{-222}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + i \cdot \left(z \cdot t - x \cdot y\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 8.2 \cdot 10^{-43}:\\ \;\;\;\;\left(t \cdot y2 - y \cdot y3\right) \cdot \left(a \cdot y5\right)\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{-26}:\\ \;\;\;\;\left(x \cdot y2\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\\ \mathbf{elif}\;j \leq 2.65 \cdot 10^{+91}:\\ \;\;\;\;b \cdot \left(\left(y4 \cdot \left(t \cdot j - y \cdot k\right) + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* i y1) (* b y0))))
   (if (<= j -1.8e+130)
     (* x (* j t_1))
     (if (<= j 2.25e-222)
       (*
        c
        (+
         (+ (* y0 (- (* x y2) (* z y3))) (* i (- (* z t) (* x y))))
         (* y4 (- (* y y3) (* t y2)))))
       (if (<= j 8.2e-43)
         (* (- (* t y2) (* y y3)) (* a y5))
         (if (<= j 4.5e-26)
           (* (* x y2) (- (* c y0) (* a y1)))
           (if (<= j 2.65e+91)
             (*
              b
              (+
               (+ (* y4 (- (* t j) (* y k))) (* a (- (* x y) (* z t))))
               (* y0 (- (* z k) (* x j)))))
             (*
              j
              (+
               (+ (* t (- (* b y4) (* i y5))) (* y3 (- (* y0 y5) (* y1 y4))))
               (* x t_1))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (i * y1) - (b * y0);
	double tmp;
	if (j <= -1.8e+130) {
		tmp = x * (j * t_1);
	} else if (j <= 2.25e-222) {
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (j <= 8.2e-43) {
		tmp = ((t * y2) - (y * y3)) * (a * y5);
	} else if (j <= 4.5e-26) {
		tmp = (x * y2) * ((c * y0) - (a * y1));
	} else if (j <= 2.65e+91) {
		tmp = b * (((y4 * ((t * j) - (y * k))) + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))));
	} else {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (i * y1) - (b * y0)
    if (j <= (-1.8d+130)) then
        tmp = x * (j * t_1)
    else if (j <= 2.25d-222) then
        tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))))
    else if (j <= 8.2d-43) then
        tmp = ((t * y2) - (y * y3)) * (a * y5)
    else if (j <= 4.5d-26) then
        tmp = (x * y2) * ((c * y0) - (a * y1))
    else if (j <= 2.65d+91) then
        tmp = b * (((y4 * ((t * j) - (y * k))) + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))))
    else
        tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (i * y1) - (b * y0);
	double tmp;
	if (j <= -1.8e+130) {
		tmp = x * (j * t_1);
	} else if (j <= 2.25e-222) {
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (j <= 8.2e-43) {
		tmp = ((t * y2) - (y * y3)) * (a * y5);
	} else if (j <= 4.5e-26) {
		tmp = (x * y2) * ((c * y0) - (a * y1));
	} else if (j <= 2.65e+91) {
		tmp = b * (((y4 * ((t * j) - (y * k))) + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))));
	} else {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (i * y1) - (b * y0)
	tmp = 0
	if j <= -1.8e+130:
		tmp = x * (j * t_1)
	elif j <= 2.25e-222:
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))))
	elif j <= 8.2e-43:
		tmp = ((t * y2) - (y * y3)) * (a * y5)
	elif j <= 4.5e-26:
		tmp = (x * y2) * ((c * y0) - (a * y1))
	elif j <= 2.65e+91:
		tmp = b * (((y4 * ((t * j) - (y * k))) + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))))
	else:
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_1))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(i * y1) - Float64(b * y0))
	tmp = 0.0
	if (j <= -1.8e+130)
		tmp = Float64(x * Float64(j * t_1));
	elseif (j <= 2.25e-222)
		tmp = Float64(c * Float64(Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(i * Float64(Float64(z * t) - Float64(x * y)))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (j <= 8.2e-43)
		tmp = Float64(Float64(Float64(t * y2) - Float64(y * y3)) * Float64(a * y5));
	elseif (j <= 4.5e-26)
		tmp = Float64(Float64(x * y2) * Float64(Float64(c * y0) - Float64(a * y1)));
	elseif (j <= 2.65e+91)
		tmp = Float64(b * Float64(Float64(Float64(y4 * Float64(Float64(t * j) - Float64(y * k))) + Float64(a * Float64(Float64(x * y) - Float64(z * t)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	else
		tmp = Float64(j * Float64(Float64(Float64(t * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) + Float64(x * t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (i * y1) - (b * y0);
	tmp = 0.0;
	if (j <= -1.8e+130)
		tmp = x * (j * t_1);
	elseif (j <= 2.25e-222)
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	elseif (j <= 8.2e-43)
		tmp = ((t * y2) - (y * y3)) * (a * y5);
	elseif (j <= 4.5e-26)
		tmp = (x * y2) * ((c * y0) - (a * y1));
	elseif (j <= 2.65e+91)
		tmp = b * (((y4 * ((t * j) - (y * k))) + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))));
	else
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.8e+130], N[(x * N[(j * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.25e-222], N[(c * N[(N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.2e-43], N[(N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision] * N[(a * y5), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.5e-26], N[(N[(x * y2), $MachinePrecision] * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.65e+91], N[(b * N[(N[(N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(N[(N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -1.8000000000000001e130

   1. Initial program 14.0%

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

   2. Taylor expanded in x around inf 41.8%

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

   3. Taylor expanded in j around inf 67.2%

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

      1. *-commutative 67.2%

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

      2. *-commutative 67.2%

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

   5. Simplified 67.2%

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

   if -1.8000000000000001e130 < j < 2.25000000000000007e-222

   1. Initial program 37.7%

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

   2. Taylor expanded in c around inf 48.8%

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

      1. +-commutative 48.8%

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

      2. mul-1-neg 48.8%

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

      3. unsub-neg 48.8%

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

      4. *-commutative 48.8%

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

      5. *-commutative 48.8%

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

      6. *-commutative 48.8%

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

      7. *-commutative 48.8%

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

   4. Simplified 48.8%

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

   if 2.25000000000000007e-222 < j < 8.1999999999999996e-43

   1. Initial program 41.9%

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

   2. Taylor expanded in a around -inf 37.3%

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

      1. mul-1-neg 37.3%

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

      2. distribute-rgt-neg-in 37.3%

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

      3. +-commutative 37.3%

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

      4. mul-1-neg 37.3%

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

      5. unsub-neg 37.3%

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

      6. *-commutative 37.3%

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

      7. *-commutative 37.3%

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

      8. *-commutative 37.3%

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

   4. Simplified 37.3%

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

   5. Taylor expanded in y5 around inf 35.0%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 37.5%

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

      2. *-commutative 37.5%

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

   7. Simplified 37.5%

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

   if 8.1999999999999996e-43 < j < 4.4999999999999999e-26

   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. Taylor expanded in x around inf 83.9%

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

   3. Taylor expanded in y2 around inf 83.9%

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

      1. associate-*r* 100.0%

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

   5. Simplified 100.0%

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

   if 4.4999999999999999e-26 < j < 2.64999999999999998e91

   1. Initial program 20.2%

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

   2. Taylor expanded in b around inf 52.6%

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

   if 2.64999999999999998e91 < j

   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. Taylor expanded in j around inf 68.9%

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

   4. Simplified 68.9%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.8 \cdot 10^{+130}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq 2.25 \cdot 10^{-222}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + i \cdot \left(z \cdot t - x \cdot y\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 8.2 \cdot 10^{-43}:\\ \;\;\;\;\left(t \cdot y2 - y \cdot y3\right) \cdot \left(a \cdot y5\right)\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{-26}:\\ \;\;\;\;\left(x \cdot y2\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\\ \mathbf{elif}\;j \leq 2.65 \cdot 10^{+91}:\\ \;\;\;\;b \cdot \left(\left(y4 \cdot \left(t \cdot j - y \cdot k\right) + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \end{array} \]

Alternative 10: 41.1% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y2 - z \cdot y3\\ t_2 := y0 \cdot \left(\left(c \cdot t_1 + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ t_3 := i \cdot y1 - b \cdot y0\\ t_4 := b \cdot y4 - i \cdot y5\\ \mathbf{if}\;j \leq -4.1 \cdot 10^{+91}:\\ \;\;\;\;x \cdot \left(j \cdot t_3\right)\\ \mathbf{elif}\;j \leq -1.26 \cdot 10^{-138}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.25 \cdot 10^{-217}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot t_1 + i \cdot \left(z \cdot t - x \cdot y\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 4.4 \cdot 10^{-78}:\\ \;\;\;\;t \cdot \left(\left(j \cdot t_4 + z \cdot \left(c \cdot i - a \cdot b\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{+34}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(\left(t \cdot t_4 + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot t_3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* x y2) (* z y3)))
        (t_2
         (*
          y0
          (+
           (+ (* c t_1) (* y5 (- (* j y3) (* k y2))))
           (* b (- (* z k) (* x j))))))
        (t_3 (- (* i y1) (* b y0)))
        (t_4 (- (* b y4) (* i y5))))
   (if (<= j -4.1e+91)
     (* x (* j t_3))
     (if (<= j -1.26e-138)
       t_2
       (if (<= j 1.25e-217)
         (*
          c
          (+
           (+ (* y0 t_1) (* i (- (* z t) (* x y))))
           (* y4 (- (* y y3) (* t y2)))))
         (if (<= j 4.4e-78)
           (*
            t
            (+
             (+ (* j t_4) (* z (- (* c i) (* a b))))
             (* y2 (- (* a y5) (* c y4)))))
           (if (<= j 3.6e+34)
             t_2
             (*
              j
              (+
               (+ (* t t_4) (* y3 (- (* y0 y5) (* y1 y4))))
               (* x t_3))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (x * y2) - (z * y3);
	double t_2 = y0 * (((c * t_1) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))));
	double t_3 = (i * y1) - (b * y0);
	double t_4 = (b * y4) - (i * y5);
	double tmp;
	if (j <= -4.1e+91) {
		tmp = x * (j * t_3);
	} else if (j <= -1.26e-138) {
		tmp = t_2;
	} else if (j <= 1.25e-217) {
		tmp = c * (((y0 * t_1) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (j <= 4.4e-78) {
		tmp = t * (((j * t_4) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))));
	} else if (j <= 3.6e+34) {
		tmp = t_2;
	} else {
		tmp = j * (((t * t_4) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_3));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (x * y2) - (z * y3)
    t_2 = y0 * (((c * t_1) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))))
    t_3 = (i * y1) - (b * y0)
    t_4 = (b * y4) - (i * y5)
    if (j <= (-4.1d+91)) then
        tmp = x * (j * t_3)
    else if (j <= (-1.26d-138)) then
        tmp = t_2
    else if (j <= 1.25d-217) then
        tmp = c * (((y0 * t_1) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))))
    else if (j <= 4.4d-78) then
        tmp = t * (((j * t_4) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))))
    else if (j <= 3.6d+34) then
        tmp = t_2
    else
        tmp = j * (((t * t_4) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_3))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (x * y2) - (z * y3);
	double t_2 = y0 * (((c * t_1) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))));
	double t_3 = (i * y1) - (b * y0);
	double t_4 = (b * y4) - (i * y5);
	double tmp;
	if (j <= -4.1e+91) {
		tmp = x * (j * t_3);
	} else if (j <= -1.26e-138) {
		tmp = t_2;
	} else if (j <= 1.25e-217) {
		tmp = c * (((y0 * t_1) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (j <= 4.4e-78) {
		tmp = t * (((j * t_4) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))));
	} else if (j <= 3.6e+34) {
		tmp = t_2;
	} else {
		tmp = j * (((t * t_4) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_3));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (x * y2) - (z * y3)
	t_2 = y0 * (((c * t_1) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))))
	t_3 = (i * y1) - (b * y0)
	t_4 = (b * y4) - (i * y5)
	tmp = 0
	if j <= -4.1e+91:
		tmp = x * (j * t_3)
	elif j <= -1.26e-138:
		tmp = t_2
	elif j <= 1.25e-217:
		tmp = c * (((y0 * t_1) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))))
	elif j <= 4.4e-78:
		tmp = t * (((j * t_4) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))))
	elif j <= 3.6e+34:
		tmp = t_2
	else:
		tmp = j * (((t * t_4) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_3))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(x * y2) - Float64(z * y3))
	t_2 = Float64(y0 * Float64(Float64(Float64(c * t_1) + Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2)))) + Float64(b * Float64(Float64(z * k) - Float64(x * j)))))
	t_3 = Float64(Float64(i * y1) - Float64(b * y0))
	t_4 = Float64(Float64(b * y4) - Float64(i * y5))
	tmp = 0.0
	if (j <= -4.1e+91)
		tmp = Float64(x * Float64(j * t_3));
	elseif (j <= -1.26e-138)
		tmp = t_2;
	elseif (j <= 1.25e-217)
		tmp = Float64(c * Float64(Float64(Float64(y0 * t_1) + Float64(i * Float64(Float64(z * t) - Float64(x * y)))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (j <= 4.4e-78)
		tmp = Float64(t * Float64(Float64(Float64(j * t_4) + Float64(z * Float64(Float64(c * i) - Float64(a * b)))) + Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (j <= 3.6e+34)
		tmp = t_2;
	else
		tmp = Float64(j * Float64(Float64(Float64(t * t_4) + Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) + Float64(x * t_3)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (x * y2) - (z * y3);
	t_2 = y0 * (((c * t_1) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))));
	t_3 = (i * y1) - (b * y0);
	t_4 = (b * y4) - (i * y5);
	tmp = 0.0;
	if (j <= -4.1e+91)
		tmp = x * (j * t_3);
	elseif (j <= -1.26e-138)
		tmp = t_2;
	elseif (j <= 1.25e-217)
		tmp = c * (((y0 * t_1) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	elseif (j <= 4.4e-78)
		tmp = t * (((j * t_4) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))));
	elseif (j <= 3.6e+34)
		tmp = t_2;
	else
		tmp = j * (((t * t_4) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_3));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y0 * N[(N[(N[(c * t$95$1), $MachinePrecision] + N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -4.1e+91], N[(x * N[(j * t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.26e-138], t$95$2, If[LessEqual[j, 1.25e-217], N[(c * N[(N[(N[(y0 * t$95$1), $MachinePrecision] + N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.4e-78], N[(t * N[(N[(N[(j * t$95$4), $MachinePrecision] + N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.6e+34], t$95$2, N[(j * N[(N[(N[(t * t$95$4), $MachinePrecision] + N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -4.1000000000000002e91

   1. Initial program 12.6%

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

   2. Taylor expanded in x around inf 40.1%

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

   3. Taylor expanded in j around inf 65.5%

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

      1. *-commutative 65.5%

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

      2. *-commutative 65.5%

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

   5. Simplified 65.5%

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

   if -4.1000000000000002e91 < j < -1.26e-138 or 4.3999999999999998e-78 < j < 3.6e34

   1. Initial program 24.1%

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

   2. Taylor expanded in y0 around inf 50.8%

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

      1. sub-neg 50.8%

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

      2. +-commutative 50.8%

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

      3. mul-1-neg 50.8%

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

   4. Simplified 50.8%

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

   if -1.26e-138 < j < 1.2500000000000001e-217

   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. Taylor expanded in c around inf 61.4%

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

      1. +-commutative 61.4%

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

      2. mul-1-neg 61.4%

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

      3. unsub-neg 61.4%

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

      4. *-commutative 61.4%

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

      5. *-commutative 61.4%

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

      6. *-commutative 61.4%

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

      7. *-commutative 61.4%

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

   4. Simplified 61.4%

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

   if 1.2500000000000001e-217 < j < 4.3999999999999998e-78

   1. Initial program 44.7%

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

   2. Taylor expanded in t around inf 55.8%

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

      1. +-commutative 55.8%

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

      2. mul-1-neg 55.8%

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

      3. unsub-neg 55.8%

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

      4. *-commutative 55.8%

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

   4. Simplified 55.8%

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

   if 3.6e34 < j

   1. Initial program 41.4%

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

   2. Taylor expanded in j around inf 64.0%

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

   4. Simplified 64.0%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4.1 \cdot 10^{+91}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq -1.26 \cdot 10^{-138}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;j \leq 1.25 \cdot 10^{-217}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + i \cdot \left(z \cdot t - x \cdot y\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 4.4 \cdot 10^{-78}:\\ \;\;\;\;t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + z \cdot \left(c \cdot i - a \cdot b\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{+34}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \end{array} \]

Alternative 11: 41.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot y1 - b \cdot y0\\ t_2 := b \cdot y4 - i \cdot y5\\ \mathbf{if}\;j \leq -9.5 \cdot 10^{+132}:\\ \;\;\;\;x \cdot \left(j \cdot t_1\right)\\ \mathbf{elif}\;j \leq 3 \cdot 10^{-217}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + i \cdot \left(z \cdot t - x \cdot y\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 1.6 \cdot 10^{-41}:\\ \;\;\;\;t \cdot \left(\left(j \cdot t_2 + z \cdot \left(c \cdot i - a \cdot b\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 1.75 \cdot 10^{+92}:\\ \;\;\;\;b \cdot \left(\left(y4 \cdot \left(t \cdot j - y \cdot k\right) + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(\left(t \cdot t_2 + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* i y1) (* b y0))) (t_2 (- (* b y4) (* i y5))))
   (if (<= j -9.5e+132)
     (* x (* j t_1))
     (if (<= j 3e-217)
       (*
        c
        (+
         (+ (* y0 (- (* x y2) (* z y3))) (* i (- (* z t) (* x y))))
         (* y4 (- (* y y3) (* t y2)))))
       (if (<= j 1.6e-41)
         (*
          t
          (+
           (+ (* j t_2) (* z (- (* c i) (* a b))))
           (* y2 (- (* a y5) (* c y4)))))
         (if (<= j 1.75e+92)
           (*
            b
            (+
             (+ (* y4 (- (* t j) (* y k))) (* a (- (* x y) (* z t))))
             (* y0 (- (* z k) (* x j)))))
           (*
            j
            (+ (+ (* t t_2) (* y3 (- (* y0 y5) (* y1 y4)))) (* x t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (i * y1) - (b * y0);
	double t_2 = (b * y4) - (i * y5);
	double tmp;
	if (j <= -9.5e+132) {
		tmp = x * (j * t_1);
	} else if (j <= 3e-217) {
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (j <= 1.6e-41) {
		tmp = t * (((j * t_2) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))));
	} else if (j <= 1.75e+92) {
		tmp = b * (((y4 * ((t * j) - (y * k))) + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))));
	} else {
		tmp = j * (((t * t_2) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (i * y1) - (b * y0)
    t_2 = (b * y4) - (i * y5)
    if (j <= (-9.5d+132)) then
        tmp = x * (j * t_1)
    else if (j <= 3d-217) then
        tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))))
    else if (j <= 1.6d-41) then
        tmp = t * (((j * t_2) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))))
    else if (j <= 1.75d+92) then
        tmp = b * (((y4 * ((t * j) - (y * k))) + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))))
    else
        tmp = j * (((t * t_2) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (i * y1) - (b * y0);
	double t_2 = (b * y4) - (i * y5);
	double tmp;
	if (j <= -9.5e+132) {
		tmp = x * (j * t_1);
	} else if (j <= 3e-217) {
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (j <= 1.6e-41) {
		tmp = t * (((j * t_2) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))));
	} else if (j <= 1.75e+92) {
		tmp = b * (((y4 * ((t * j) - (y * k))) + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))));
	} else {
		tmp = j * (((t * t_2) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (i * y1) - (b * y0)
	t_2 = (b * y4) - (i * y5)
	tmp = 0
	if j <= -9.5e+132:
		tmp = x * (j * t_1)
	elif j <= 3e-217:
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))))
	elif j <= 1.6e-41:
		tmp = t * (((j * t_2) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))))
	elif j <= 1.75e+92:
		tmp = b * (((y4 * ((t * j) - (y * k))) + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))))
	else:
		tmp = j * (((t * t_2) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_1))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(i * y1) - Float64(b * y0))
	t_2 = Float64(Float64(b * y4) - Float64(i * y5))
	tmp = 0.0
	if (j <= -9.5e+132)
		tmp = Float64(x * Float64(j * t_1));
	elseif (j <= 3e-217)
		tmp = Float64(c * Float64(Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(i * Float64(Float64(z * t) - Float64(x * y)))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (j <= 1.6e-41)
		tmp = Float64(t * Float64(Float64(Float64(j * t_2) + Float64(z * Float64(Float64(c * i) - Float64(a * b)))) + Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (j <= 1.75e+92)
		tmp = Float64(b * Float64(Float64(Float64(y4 * Float64(Float64(t * j) - Float64(y * k))) + Float64(a * Float64(Float64(x * y) - Float64(z * t)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	else
		tmp = Float64(j * Float64(Float64(Float64(t * t_2) + Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) + Float64(x * t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (i * y1) - (b * y0);
	t_2 = (b * y4) - (i * y5);
	tmp = 0.0;
	if (j <= -9.5e+132)
		tmp = x * (j * t_1);
	elseif (j <= 3e-217)
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	elseif (j <= 1.6e-41)
		tmp = t * (((j * t_2) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))));
	elseif (j <= 1.75e+92)
		tmp = b * (((y4 * ((t * j) - (y * k))) + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))));
	else
		tmp = j * (((t * t_2) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -9.5e+132], N[(x * N[(j * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3e-217], N[(c * N[(N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.6e-41], N[(t * N[(N[(N[(j * t$95$2), $MachinePrecision] + N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.75e+92], N[(b * N[(N[(N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(N[(N[(t * t$95$2), $MachinePrecision] + N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -9.5000000000000005e132

   1. Initial program 14.0%

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

   2. Taylor expanded in x around inf 41.8%

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

   3. Taylor expanded in j around inf 67.2%

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

      1. *-commutative 67.2%

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

      2. *-commutative 67.2%

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

   5. Simplified 67.2%

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

   if -9.5000000000000005e132 < j < 3.00000000000000004e-217

   1. Initial program 37.4%

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

   2. Taylor expanded in c around inf 48.4%

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

      1. +-commutative 48.4%

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

      2. mul-1-neg 48.4%

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

      3. unsub-neg 48.4%

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

      4. *-commutative 48.4%

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

      5. *-commutative 48.4%

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

      6. *-commutative 48.4%

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

      7. *-commutative 48.4%

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

   4. Simplified 48.4%

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

   if 3.00000000000000004e-217 < j < 1.60000000000000006e-41

   1. Initial program 41.9%

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

   2. Taylor expanded in t around inf 48.1%

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

      1. +-commutative 48.1%

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

      2. mul-1-neg 48.1%

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

      3. unsub-neg 48.1%

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

      4. *-commutative 48.1%

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

   4. Simplified 48.1%

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

   if 1.60000000000000006e-41 < j < 1.74999999999999993e92

   1. Initial program 20.9%

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

   2. Taylor expanded in b around inf 52.2%

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

   if 1.74999999999999993e92 < j

   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. Taylor expanded in j around inf 68.9%

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

   4. Simplified 68.9%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -9.5 \cdot 10^{+132}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq 3 \cdot 10^{-217}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + i \cdot \left(z \cdot t - x \cdot y\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 1.6 \cdot 10^{-41}:\\ \;\;\;\;t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + z \cdot \left(c \cdot i - a \cdot b\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 1.75 \cdot 10^{+92}:\\ \;\;\;\;b \cdot \left(\left(y4 \cdot \left(t \cdot j - y \cdot k\right) + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \end{array} \]

Alternative 12: 29.9% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{if}\;y3 \leq -2.2 \cdot 10^{+253}:\\ \;\;\;\;c \cdot \left(\left(z \cdot y3\right) \cdot \left(-y0\right)\right)\\ \mathbf{elif}\;y3 \leq -1.3 \cdot 10^{+119}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;y3 \leq -1 \cdot 10^{-9}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(y2 \cdot y5 - z \cdot b\right)\\ \mathbf{elif}\;y3 \leq -4.8 \cdot 10^{-134}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq -3.2 \cdot 10^{-223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y3 \leq 7.5 \cdot 10^{-285}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y3 \leq 4.2 \cdot 10^{-251}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y3 \leq 1.05 \cdot 10^{-221}:\\ \;\;\;\;\left(b \cdot j\right) \cdot \left(t \cdot y4 - x \cdot y0\right)\\ \mathbf{elif}\;y3 \leq 2.8 \cdot 10^{-212}:\\ \;\;\;\;y5 \cdot \left(y2 \cdot \left(t \cdot a - k \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq 6.5 \cdot 10^{-156}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)\\ \mathbf{elif}\;y3 \leq 14000:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;y3 \leq 2.1 \cdot 10^{+98}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* t (* c (- (* z i) (* y2 y4))))))
   (if (<= y3 -2.2e+253)
     (* c (* (* z y3) (- y0)))
     (if (<= y3 -1.3e+119)
       (* a (* z (- (* y1 y3) (* t b))))
       (if (<= y3 -1e-9)
         (* (* t a) (- (* y2 y5) (* z b)))
         (if (<= y3 -4.8e-134)
           (* x (* j (- (* i y1) (* b y0))))
           (if (<= y3 -3.2e-223)
             t_1
             (if (<= y3 7.5e-285)
               (* x (* y (- (* a b) (* c i))))
               (if (<= y3 4.2e-251)
                 t_1
                 (if (<= y3 1.05e-221)
                   (* (* b j) (- (* t y4) (* x y0)))
                   (if (<= y3 2.8e-212)
                     (* y5 (* y2 (- (* t a) (* k y0))))
                     (if (<= y3 6.5e-156)
                       (* t (* y5 (- (* a y2) (* i j))))
                       (if (<= y3 14000.0)
                         (* x (* c (- (* y0 y2) (* y i))))
                         (if (<= y3 2.1e+98)
                           (* b (* y4 (- (* t j) (* y k))))
                           (* a (* y3 (- (* z y1) (* y y5))))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * (c * ((z * i) - (y2 * y4)));
	double tmp;
	if (y3 <= -2.2e+253) {
		tmp = c * ((z * y3) * -y0);
	} else if (y3 <= -1.3e+119) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (y3 <= -1e-9) {
		tmp = (t * a) * ((y2 * y5) - (z * b));
	} else if (y3 <= -4.8e-134) {
		tmp = x * (j * ((i * y1) - (b * y0)));
	} else if (y3 <= -3.2e-223) {
		tmp = t_1;
	} else if (y3 <= 7.5e-285) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y3 <= 4.2e-251) {
		tmp = t_1;
	} else if (y3 <= 1.05e-221) {
		tmp = (b * j) * ((t * y4) - (x * y0));
	} else if (y3 <= 2.8e-212) {
		tmp = y5 * (y2 * ((t * a) - (k * y0)));
	} else if (y3 <= 6.5e-156) {
		tmp = t * (y5 * ((a * y2) - (i * j)));
	} else if (y3 <= 14000.0) {
		tmp = x * (c * ((y0 * y2) - (y * i)));
	} else if (y3 <= 2.1e+98) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (c * ((z * i) - (y2 * y4)))
    if (y3 <= (-2.2d+253)) then
        tmp = c * ((z * y3) * -y0)
    else if (y3 <= (-1.3d+119)) then
        tmp = a * (z * ((y1 * y3) - (t * b)))
    else if (y3 <= (-1d-9)) then
        tmp = (t * a) * ((y2 * y5) - (z * b))
    else if (y3 <= (-4.8d-134)) then
        tmp = x * (j * ((i * y1) - (b * y0)))
    else if (y3 <= (-3.2d-223)) then
        tmp = t_1
    else if (y3 <= 7.5d-285) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (y3 <= 4.2d-251) then
        tmp = t_1
    else if (y3 <= 1.05d-221) then
        tmp = (b * j) * ((t * y4) - (x * y0))
    else if (y3 <= 2.8d-212) then
        tmp = y5 * (y2 * ((t * a) - (k * y0)))
    else if (y3 <= 6.5d-156) then
        tmp = t * (y5 * ((a * y2) - (i * j)))
    else if (y3 <= 14000.0d0) then
        tmp = x * (c * ((y0 * y2) - (y * i)))
    else if (y3 <= 2.1d+98) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else
        tmp = a * (y3 * ((z * y1) - (y * y5)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * (c * ((z * i) - (y2 * y4)));
	double tmp;
	if (y3 <= -2.2e+253) {
		tmp = c * ((z * y3) * -y0);
	} else if (y3 <= -1.3e+119) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (y3 <= -1e-9) {
		tmp = (t * a) * ((y2 * y5) - (z * b));
	} else if (y3 <= -4.8e-134) {
		tmp = x * (j * ((i * y1) - (b * y0)));
	} else if (y3 <= -3.2e-223) {
		tmp = t_1;
	} else if (y3 <= 7.5e-285) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y3 <= 4.2e-251) {
		tmp = t_1;
	} else if (y3 <= 1.05e-221) {
		tmp = (b * j) * ((t * y4) - (x * y0));
	} else if (y3 <= 2.8e-212) {
		tmp = y5 * (y2 * ((t * a) - (k * y0)));
	} else if (y3 <= 6.5e-156) {
		tmp = t * (y5 * ((a * y2) - (i * j)));
	} else if (y3 <= 14000.0) {
		tmp = x * (c * ((y0 * y2) - (y * i)));
	} else if (y3 <= 2.1e+98) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = t * (c * ((z * i) - (y2 * y4)))
	tmp = 0
	if y3 <= -2.2e+253:
		tmp = c * ((z * y3) * -y0)
	elif y3 <= -1.3e+119:
		tmp = a * (z * ((y1 * y3) - (t * b)))
	elif y3 <= -1e-9:
		tmp = (t * a) * ((y2 * y5) - (z * b))
	elif y3 <= -4.8e-134:
		tmp = x * (j * ((i * y1) - (b * y0)))
	elif y3 <= -3.2e-223:
		tmp = t_1
	elif y3 <= 7.5e-285:
		tmp = x * (y * ((a * b) - (c * i)))
	elif y3 <= 4.2e-251:
		tmp = t_1
	elif y3 <= 1.05e-221:
		tmp = (b * j) * ((t * y4) - (x * y0))
	elif y3 <= 2.8e-212:
		tmp = y5 * (y2 * ((t * a) - (k * y0)))
	elif y3 <= 6.5e-156:
		tmp = t * (y5 * ((a * y2) - (i * j)))
	elif y3 <= 14000.0:
		tmp = x * (c * ((y0 * y2) - (y * i)))
	elif y3 <= 2.1e+98:
		tmp = b * (y4 * ((t * j) - (y * k)))
	else:
		tmp = a * (y3 * ((z * y1) - (y * y5)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(t * Float64(c * Float64(Float64(z * i) - Float64(y2 * y4))))
	tmp = 0.0
	if (y3 <= -2.2e+253)
		tmp = Float64(c * Float64(Float64(z * y3) * Float64(-y0)));
	elseif (y3 <= -1.3e+119)
		tmp = Float64(a * Float64(z * Float64(Float64(y1 * y3) - Float64(t * b))));
	elseif (y3 <= -1e-9)
		tmp = Float64(Float64(t * a) * Float64(Float64(y2 * y5) - Float64(z * b)));
	elseif (y3 <= -4.8e-134)
		tmp = Float64(x * Float64(j * Float64(Float64(i * y1) - Float64(b * y0))));
	elseif (y3 <= -3.2e-223)
		tmp = t_1;
	elseif (y3 <= 7.5e-285)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (y3 <= 4.2e-251)
		tmp = t_1;
	elseif (y3 <= 1.05e-221)
		tmp = Float64(Float64(b * j) * Float64(Float64(t * y4) - Float64(x * y0)));
	elseif (y3 <= 2.8e-212)
		tmp = Float64(y5 * Float64(y2 * Float64(Float64(t * a) - Float64(k * y0))));
	elseif (y3 <= 6.5e-156)
		tmp = Float64(t * Float64(y5 * Float64(Float64(a * y2) - Float64(i * j))));
	elseif (y3 <= 14000.0)
		tmp = Float64(x * Float64(c * Float64(Float64(y0 * y2) - Float64(y * i))));
	elseif (y3 <= 2.1e+98)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	else
		tmp = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = t * (c * ((z * i) - (y2 * y4)));
	tmp = 0.0;
	if (y3 <= -2.2e+253)
		tmp = c * ((z * y3) * -y0);
	elseif (y3 <= -1.3e+119)
		tmp = a * (z * ((y1 * y3) - (t * b)));
	elseif (y3 <= -1e-9)
		tmp = (t * a) * ((y2 * y5) - (z * b));
	elseif (y3 <= -4.8e-134)
		tmp = x * (j * ((i * y1) - (b * y0)));
	elseif (y3 <= -3.2e-223)
		tmp = t_1;
	elseif (y3 <= 7.5e-285)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (y3 <= 4.2e-251)
		tmp = t_1;
	elseif (y3 <= 1.05e-221)
		tmp = (b * j) * ((t * y4) - (x * y0));
	elseif (y3 <= 2.8e-212)
		tmp = y5 * (y2 * ((t * a) - (k * y0)));
	elseif (y3 <= 6.5e-156)
		tmp = t * (y5 * ((a * y2) - (i * j)));
	elseif (y3 <= 14000.0)
		tmp = x * (c * ((y0 * y2) - (y * i)));
	elseif (y3 <= 2.1e+98)
		tmp = b * (y4 * ((t * j) - (y * k)));
	else
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(t * N[(c * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -2.2e+253], N[(c * N[(N[(z * y3), $MachinePrecision] * (-y0)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -1.3e+119], N[(a * N[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -1e-9], N[(N[(t * a), $MachinePrecision] * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -4.8e-134], N[(x * N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -3.2e-223], t$95$1, If[LessEqual[y3, 7.5e-285], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 4.2e-251], t$95$1, If[LessEqual[y3, 1.05e-221], N[(N[(b * j), $MachinePrecision] * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 2.8e-212], N[(y5 * N[(y2 * N[(N[(t * a), $MachinePrecision] - N[(k * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 6.5e-156], N[(t * N[(y5 * N[(N[(a * y2), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 14000.0], N[(x * N[(c * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 2.1e+98], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 12 regimes

2. if y3 < -2.20000000000000006e253

   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. Taylor expanded in c around inf 70.0%

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

      1. +-commutative 70.0%

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

      2. mul-1-neg 70.0%

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

      3. unsub-neg 70.0%

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

      4. *-commutative 70.0%

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

      5. *-commutative 70.0%

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

      6. *-commutative 70.0%

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

      7. *-commutative 70.0%

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

   4. Simplified 70.0%

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

   5. Taylor expanded in y0 around inf 70.2%

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

   6. Taylor expanded in x around 0 70.6%

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

      1. mul-1-neg 70.6%

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

      2. distribute-rgt-neg-in 70.6%

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

      3. distribute-lft-neg-in 70.6%

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

      4. *-commutative 70.6%

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

   8. Simplified 70.6%

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

   if -2.20000000000000006e253 < y3 < -1.3e119

   1. Initial program 23.7%

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

   2. Taylor expanded in a around -inf 34.5%

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

      1. mul-1-neg 34.5%

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

      2. distribute-rgt-neg-in 34.5%

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

      3. +-commutative 34.5%

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

      4. mul-1-neg 34.5%

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

      5. unsub-neg 34.5%

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

      6. *-commutative 34.5%

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

      7. *-commutative 34.5%

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

      8. *-commutative 34.5%

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

   4. Simplified 34.5%

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

   5. Taylor expanded in z around -inf 55.9%

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

      1. associate-*r* 55.9%

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

      2. neg-mul-1 55.9%

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

      3. *-commutative 55.9%

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

   7. Simplified 55.9%

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

   if -1.3e119 < y3 < -1.00000000000000006e-9

   1. Initial program 43.5%

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

   2. Taylor expanded in a around -inf 53.1%

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

      1. mul-1-neg 53.1%

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

      2. distribute-rgt-neg-in 53.1%

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

      3. +-commutative 53.1%

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

      4. mul-1-neg 53.1%

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

      5. unsub-neg 53.1%

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

      6. *-commutative 53.1%

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

      7. *-commutative 53.1%

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

      8. *-commutative 53.1%

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

   4. Simplified 53.1%

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

   5. Taylor expanded in t around inf 49.4%

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

      1. associate-*r* 53.4%

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

      2. +-commutative 53.4%

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

      3. mul-1-neg 53.4%

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

      4. unsub-neg 53.4%

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

      5. *-commutative 53.4%

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

      6. *-commutative 53.4%

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

   7. Simplified 53.4%

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

   if -1.00000000000000006e-9 < y3 < -4.80000000000000019e-134

   1. Initial program 39.1%

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

   2. Taylor expanded in x around inf 56.8%

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

   3. Taylor expanded in j around inf 57.2%

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

      1. *-commutative 57.2%

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

      2. *-commutative 57.2%

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

   5. Simplified 57.2%

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

   if -4.80000000000000019e-134 < y3 < -3.2000000000000001e-223 or 7.4999999999999999e-285 < y3 < 4.19999999999999964e-251

   1. Initial program 45.8%

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

   2. Taylor expanded in c around inf 59.2%

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

      1. +-commutative 59.2%

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

      2. mul-1-neg 59.2%

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

      3. unsub-neg 59.2%

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

      4. *-commutative 59.2%

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

      5. *-commutative 59.2%

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

      6. *-commutative 59.2%

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

      7. *-commutative 59.2%

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

   4. Simplified 59.2%

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

   5. Taylor expanded in t around -inf 55.1%

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

      1. *-commutative 55.1%

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

      2. associate-*l* 59.0%

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

      3. +-commutative 59.0%

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

      4. mul-1-neg 59.0%

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

      5. unsub-neg 59.0%

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

      6. *-commutative 59.0%

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

   7. Simplified 59.0%

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

   if -3.2000000000000001e-223 < y3 < 7.4999999999999999e-285

   1. Initial program 42.5%

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

   2. Taylor expanded in x around inf 42.9%

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

   3. Taylor expanded in y around inf 43.3%

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

   if 4.19999999999999964e-251 < y3 < 1.05e-221

   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. Taylor expanded in b around inf 67.2%

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

   3. Taylor expanded in j around inf 83.8%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 83.8%

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

      2. *-commutative 83.8%

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

      3. *-commutative 83.8%

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

      4. *-commutative 83.8%

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

   5. Simplified 83.8%

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

   if 1.05e-221 < y3 < 2.80000000000000014e-212

   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. Taylor expanded in y5 around -inf 33.3%

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

   3. Taylor expanded in y2 around inf 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   if 2.80000000000000014e-212 < y3 < 6.5000000000000002e-156

   1. Initial program 0.7%

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

   2. Taylor expanded in y5 around -inf 50.1%

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

   3. Taylor expanded in t around inf 63.1%

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

   if 6.5000000000000002e-156 < y3 < 14000

   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. Taylor expanded in x around inf 46.9%

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

   3. Taylor expanded in c around inf 51.6%

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

      1. +-commutative 51.6%

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

      2. mul-1-neg 51.6%

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

      3. unsub-neg 51.6%

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

      4. *-commutative 51.6%

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

   5. Simplified 51.6%

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

   if 14000 < y3 < 2.10000000000000004e98

   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. Taylor expanded in b around inf 72.2%

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

   3. Taylor expanded in y4 around inf 68.7%

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

      1. *-commutative 68.7%

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

   5. Simplified 68.7%

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

   if 2.10000000000000004e98 < y3

   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. Taylor expanded in a around -inf 32.4%

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

      1. mul-1-neg 32.4%

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

      2. distribute-rgt-neg-in 32.4%

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

      3. +-commutative 32.4%

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

      4. mul-1-neg 32.4%

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

      5. unsub-neg 32.4%

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

      6. *-commutative 32.4%

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

      7. *-commutative 32.4%

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

      8. *-commutative 32.4%

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

   4. Simplified 32.4%

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

   5. Taylor expanded in y3 around -inf 54.4%

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

      1. associate-*r* 54.4%

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

      2. neg-mul-1 54.4%

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

      3. *-commutative 54.4%

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

   7. Simplified 54.4%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - z \cdot y1\right)\right)} \]
3. Recombined 12 regimes into one program.

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -2.2 \cdot 10^{+253}:\\ \;\;\;\;c \cdot \left(\left(z \cdot y3\right) \cdot \left(-y0\right)\right)\\ \mathbf{elif}\;y3 \leq -1.3 \cdot 10^{+119}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;y3 \leq -1 \cdot 10^{-9}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(y2 \cdot y5 - z \cdot b\right)\\ \mathbf{elif}\;y3 \leq -4.8 \cdot 10^{-134}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq -3.2 \cdot 10^{-223}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 7.5 \cdot 10^{-285}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y3 \leq 4.2 \cdot 10^{-251}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 1.05 \cdot 10^{-221}:\\ \;\;\;\;\left(b \cdot j\right) \cdot \left(t \cdot y4 - x \cdot y0\right)\\ \mathbf{elif}\;y3 \leq 2.8 \cdot 10^{-212}:\\ \;\;\;\;y5 \cdot \left(y2 \cdot \left(t \cdot a - k \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq 6.5 \cdot 10^{-156}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)\\ \mathbf{elif}\;y3 \leq 14000:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;y3 \leq 2.1 \cdot 10^{+98}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \end{array} \]

Alternative 13: 31.3% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{+207}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq -2.56 \cdot 10^{-12}:\\ \;\;\;\;y5 \cdot \left(y2 \cdot \left(t \cdot a - k \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-85}:\\ \;\;\;\;\left(b \cdot j\right) \cdot \left(t \cdot y4 - x \cdot y0\right)\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-210}:\\ \;\;\;\;\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-121}:\\ \;\;\;\;\left(y3 \cdot y4\right) \cdot \left(y \cdot c - j \cdot y1\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-34}:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+121}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(y2 \cdot y5 - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= a -1.3e+207)
   (* a (* y (- (* x b) (* y3 y5))))
   (if (<= a -2.56e-12)
     (* y5 (* y2 (- (* t a) (* k y0))))
     (if (<= a -2.2e-85)
       (* (* b j) (- (* t y4) (* x y0)))
       (if (<= a 6.2e-210)
         (* (- (* x y2) (* z y3)) (* c y0))
         (if (<= a 1.6e-121)
           (* (* y3 y4) (- (* y c) (* j y1)))
           (if (<= a 8e-34)
             (* y2 (* c (- (* x y0) (* t y4))))
             (if (<= a 4.8e+121)
               (* b (+ (* a (- (* x y) (* z t))) (* y0 (- (* z k) (* x j)))))
               (* (* t a) (- (* y2 y5) (* z b)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (a <= -1.3e+207) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (a <= -2.56e-12) {
		tmp = y5 * (y2 * ((t * a) - (k * y0)));
	} else if (a <= -2.2e-85) {
		tmp = (b * j) * ((t * y4) - (x * y0));
	} else if (a <= 6.2e-210) {
		tmp = ((x * y2) - (z * y3)) * (c * y0);
	} else if (a <= 1.6e-121) {
		tmp = (y3 * y4) * ((y * c) - (j * y1));
	} else if (a <= 8e-34) {
		tmp = y2 * (c * ((x * y0) - (t * y4)));
	} else if (a <= 4.8e+121) {
		tmp = b * ((a * ((x * y) - (z * t))) + (y0 * ((z * k) - (x * j))));
	} else {
		tmp = (t * a) * ((y2 * y5) - (z * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (a <= (-1.3d+207)) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (a <= (-2.56d-12)) then
        tmp = y5 * (y2 * ((t * a) - (k * y0)))
    else if (a <= (-2.2d-85)) then
        tmp = (b * j) * ((t * y4) - (x * y0))
    else if (a <= 6.2d-210) then
        tmp = ((x * y2) - (z * y3)) * (c * y0)
    else if (a <= 1.6d-121) then
        tmp = (y3 * y4) * ((y * c) - (j * y1))
    else if (a <= 8d-34) then
        tmp = y2 * (c * ((x * y0) - (t * y4)))
    else if (a <= 4.8d+121) then
        tmp = b * ((a * ((x * y) - (z * t))) + (y0 * ((z * k) - (x * j))))
    else
        tmp = (t * a) * ((y2 * y5) - (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (a <= -1.3e+207) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (a <= -2.56e-12) {
		tmp = y5 * (y2 * ((t * a) - (k * y0)));
	} else if (a <= -2.2e-85) {
		tmp = (b * j) * ((t * y4) - (x * y0));
	} else if (a <= 6.2e-210) {
		tmp = ((x * y2) - (z * y3)) * (c * y0);
	} else if (a <= 1.6e-121) {
		tmp = (y3 * y4) * ((y * c) - (j * y1));
	} else if (a <= 8e-34) {
		tmp = y2 * (c * ((x * y0) - (t * y4)));
	} else if (a <= 4.8e+121) {
		tmp = b * ((a * ((x * y) - (z * t))) + (y0 * ((z * k) - (x * j))));
	} else {
		tmp = (t * a) * ((y2 * y5) - (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if a <= -1.3e+207:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif a <= -2.56e-12:
		tmp = y5 * (y2 * ((t * a) - (k * y0)))
	elif a <= -2.2e-85:
		tmp = (b * j) * ((t * y4) - (x * y0))
	elif a <= 6.2e-210:
		tmp = ((x * y2) - (z * y3)) * (c * y0)
	elif a <= 1.6e-121:
		tmp = (y3 * y4) * ((y * c) - (j * y1))
	elif a <= 8e-34:
		tmp = y2 * (c * ((x * y0) - (t * y4)))
	elif a <= 4.8e+121:
		tmp = b * ((a * ((x * y) - (z * t))) + (y0 * ((z * k) - (x * j))))
	else:
		tmp = (t * a) * ((y2 * y5) - (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (a <= -1.3e+207)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (a <= -2.56e-12)
		tmp = Float64(y5 * Float64(y2 * Float64(Float64(t * a) - Float64(k * y0))));
	elseif (a <= -2.2e-85)
		tmp = Float64(Float64(b * j) * Float64(Float64(t * y4) - Float64(x * y0)));
	elseif (a <= 6.2e-210)
		tmp = Float64(Float64(Float64(x * y2) - Float64(z * y3)) * Float64(c * y0));
	elseif (a <= 1.6e-121)
		tmp = Float64(Float64(y3 * y4) * Float64(Float64(y * c) - Float64(j * y1)));
	elseif (a <= 8e-34)
		tmp = Float64(y2 * Float64(c * Float64(Float64(x * y0) - Float64(t * y4))));
	elseif (a <= 4.8e+121)
		tmp = Float64(b * Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	else
		tmp = Float64(Float64(t * a) * Float64(Float64(y2 * y5) - Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (a <= -1.3e+207)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (a <= -2.56e-12)
		tmp = y5 * (y2 * ((t * a) - (k * y0)));
	elseif (a <= -2.2e-85)
		tmp = (b * j) * ((t * y4) - (x * y0));
	elseif (a <= 6.2e-210)
		tmp = ((x * y2) - (z * y3)) * (c * y0);
	elseif (a <= 1.6e-121)
		tmp = (y3 * y4) * ((y * c) - (j * y1));
	elseif (a <= 8e-34)
		tmp = y2 * (c * ((x * y0) - (t * y4)));
	elseif (a <= 4.8e+121)
		tmp = b * ((a * ((x * y) - (z * t))) + (y0 * ((z * k) - (x * j))));
	else
		tmp = (t * a) * ((y2 * y5) - (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[a, -1.3e+207], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.56e-12], N[(y5 * N[(y2 * N[(N[(t * a), $MachinePrecision] - N[(k * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.2e-85], N[(N[(b * j), $MachinePrecision] * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.2e-210], N[(N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision] * N[(c * y0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.6e-121], N[(N[(y3 * y4), $MachinePrecision] * N[(N[(y * c), $MachinePrecision] - N[(j * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8e-34], N[(y2 * N[(c * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.8e+121], N[(b * N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * a), $MachinePrecision] * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if a < -1.2999999999999999e207

   1. Initial program 34.9%

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

   2. Taylor expanded in a around -inf 60.4%

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

      1. mul-1-neg 60.4%

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

      2. distribute-rgt-neg-in 60.4%

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

      3. +-commutative 60.4%

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

      4. mul-1-neg 60.4%

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

      5. unsub-neg 60.4%

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

      6. *-commutative 60.4%

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

      7. *-commutative 60.4%

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

      8. *-commutative 60.4%

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

   4. Simplified 60.4%

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

   5. Taylor expanded in y around -inf 60.6%

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

      1. associate-*r* 60.6%

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

      2. neg-mul-1 60.6%

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

      3. +-commutative 60.6%

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

      4. mul-1-neg 60.6%

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

      5. unsub-neg 60.6%

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

   7. Simplified 60.6%

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

   if -1.2999999999999999e207 < a < -2.56e-12

   1. Initial program 22.0%

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

   2. Taylor expanded in y5 around -inf 39.4%

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

   3. Taylor expanded in y2 around inf 44.7%

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

      1. *-commutative 44.7%

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

   5. Simplified 44.7%

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

   if -2.56e-12 < a < -2.2e-85

   1. Initial program 39.5%

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

   2. Taylor expanded in b around inf 48.7%

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

   3. Taylor expanded in j around inf 44.6%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 52.9%

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

      2. *-commutative 52.9%

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

      3. *-commutative 52.9%

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

      4. *-commutative 52.9%

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

   5. Simplified 52.9%

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

   if -2.2e-85 < a < 6.19999999999999973e-210

   1. Initial program 37.2%

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

   2. Taylor expanded in c around inf 40.5%

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

      1. +-commutative 40.5%

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

      2. mul-1-neg 40.5%

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

      3. unsub-neg 40.5%

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

      4. *-commutative 40.5%

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

      5. *-commutative 40.5%

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

      6. *-commutative 40.5%

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

      7. *-commutative 40.5%

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

   4. Simplified 40.5%

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

   5. Taylor expanded in y0 around inf 43.5%

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

      1. associate-*r* 44.6%

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

      2. *-commutative 44.6%

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

      3. *-commutative 44.6%

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

      4. *-commutative 44.6%

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

      5. *-commutative 44.6%

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

      6. *-commutative 44.6%

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

   7. Simplified 44.6%

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

   if 6.19999999999999973e-210 < a < 1.60000000000000009e-121

   1. Initial program 64.2%

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

   2. Taylor expanded in y3 around -inf 52.2%

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

   3. Taylor expanded in y4 around inf 58.4%

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

      1. associate-*r* 58.4%

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

      2. *-commutative 58.4%

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

   5. Simplified 58.4%

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

   if 1.60000000000000009e-121 < a < 7.99999999999999942e-34

   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. Taylor expanded in c around inf 64.2%

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

      1. +-commutative 64.2%

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

      2. mul-1-neg 64.2%

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

      3. unsub-neg 64.2%

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

      4. *-commutative 64.2%

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

      5. *-commutative 64.2%

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

      6. *-commutative 64.2%

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

      7. *-commutative 64.2%

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

   4. Simplified 64.2%

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

   5. Taylor expanded in y2 around inf 64.6%

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

      1. *-commutative 64.6%

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

      2. associate-*l* 64.5%

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

      3. *-commutative 64.5%

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

   7. Simplified 64.5%

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

   if 7.99999999999999942e-34 < a < 4.8e121

   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. Taylor expanded in b around inf 46.9%

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

   3. Taylor expanded in y4 around 0 51.0%

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

      1. *-commutative 51.0%

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

      2. *-commutative 51.0%

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

      3. *-commutative 51.0%

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

   5. Simplified 51.0%

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

   if 4.8e121 < a

   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. Taylor expanded in a around -inf 62.8%

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

      1. mul-1-neg 62.8%

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

      2. distribute-rgt-neg-in 62.8%

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

      3. +-commutative 62.8%

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

      4. mul-1-neg 62.8%

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

      5. unsub-neg 62.8%

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

      6. *-commutative 62.8%

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

      7. *-commutative 62.8%

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

      8. *-commutative 62.8%

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

   4. Simplified 62.8%

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

   5. Taylor expanded in t around inf 48.9%

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

      1. associate-*r* 55.9%

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

      2. +-commutative 55.9%

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

      3. mul-1-neg 55.9%

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

      4. unsub-neg 55.9%

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

      5. *-commutative 55.9%

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

      6. *-commutative 55.9%

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

   7. Simplified 55.9%

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

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{+207}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq -2.56 \cdot 10^{-12}:\\ \;\;\;\;y5 \cdot \left(y2 \cdot \left(t \cdot a - k \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-85}:\\ \;\;\;\;\left(b \cdot j\right) \cdot \left(t \cdot y4 - x \cdot y0\right)\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-210}:\\ \;\;\;\;\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-121}:\\ \;\;\;\;\left(y3 \cdot y4\right) \cdot \left(y \cdot c - j \cdot y1\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-34}:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+121}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(y2 \cdot y5 - z \cdot b\right)\\ \end{array} \]

Alternative 14: 35.9% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.55 \cdot 10^{+206}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq -2.56 \cdot 10^{-12}:\\ \;\;\;\;y5 \cdot \left(y2 \cdot \left(t \cdot a - k \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-37}:\\ \;\;\;\;\left(b \cdot j\right) \cdot \left(t \cdot y4 - x \cdot y0\right)\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-34}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+122}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(y2 \cdot y5 - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= a -2.55e+206)
   (* a (* y (- (* x b) (* y3 y5))))
   (if (<= a -2.56e-12)
     (* y5 (* y2 (- (* t a) (* k y0))))
     (if (<= a -7e-37)
       (* (* b j) (- (* t y4) (* x y0)))
       (if (<= a 4e-34)
         (* c (+ (* y0 (- (* x y2) (* z y3))) (* y4 (- (* y y3) (* t y2)))))
         (if (<= a 1.15e+122)
           (* b (+ (* a (- (* x y) (* z t))) (* y0 (- (* z k) (* x j)))))
           (* (* t a) (- (* y2 y5) (* z b)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (a <= -2.55e+206) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (a <= -2.56e-12) {
		tmp = y5 * (y2 * ((t * a) - (k * y0)));
	} else if (a <= -7e-37) {
		tmp = (b * j) * ((t * y4) - (x * y0));
	} else if (a <= 4e-34) {
		tmp = c * ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2))));
	} else if (a <= 1.15e+122) {
		tmp = b * ((a * ((x * y) - (z * t))) + (y0 * ((z * k) - (x * j))));
	} else {
		tmp = (t * a) * ((y2 * y5) - (z * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (a <= (-2.55d+206)) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (a <= (-2.56d-12)) then
        tmp = y5 * (y2 * ((t * a) - (k * y0)))
    else if (a <= (-7d-37)) then
        tmp = (b * j) * ((t * y4) - (x * y0))
    else if (a <= 4d-34) then
        tmp = c * ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2))))
    else if (a <= 1.15d+122) then
        tmp = b * ((a * ((x * y) - (z * t))) + (y0 * ((z * k) - (x * j))))
    else
        tmp = (t * a) * ((y2 * y5) - (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (a <= -2.55e+206) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (a <= -2.56e-12) {
		tmp = y5 * (y2 * ((t * a) - (k * y0)));
	} else if (a <= -7e-37) {
		tmp = (b * j) * ((t * y4) - (x * y0));
	} else if (a <= 4e-34) {
		tmp = c * ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2))));
	} else if (a <= 1.15e+122) {
		tmp = b * ((a * ((x * y) - (z * t))) + (y0 * ((z * k) - (x * j))));
	} else {
		tmp = (t * a) * ((y2 * y5) - (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if a <= -2.55e+206:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif a <= -2.56e-12:
		tmp = y5 * (y2 * ((t * a) - (k * y0)))
	elif a <= -7e-37:
		tmp = (b * j) * ((t * y4) - (x * y0))
	elif a <= 4e-34:
		tmp = c * ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2))))
	elif a <= 1.15e+122:
		tmp = b * ((a * ((x * y) - (z * t))) + (y0 * ((z * k) - (x * j))))
	else:
		tmp = (t * a) * ((y2 * y5) - (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (a <= -2.55e+206)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (a <= -2.56e-12)
		tmp = Float64(y5 * Float64(y2 * Float64(Float64(t * a) - Float64(k * y0))));
	elseif (a <= -7e-37)
		tmp = Float64(Float64(b * j) * Float64(Float64(t * y4) - Float64(x * y0)));
	elseif (a <= 4e-34)
		tmp = Float64(c * Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (a <= 1.15e+122)
		tmp = Float64(b * Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	else
		tmp = Float64(Float64(t * a) * Float64(Float64(y2 * y5) - Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (a <= -2.55e+206)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (a <= -2.56e-12)
		tmp = y5 * (y2 * ((t * a) - (k * y0)));
	elseif (a <= -7e-37)
		tmp = (b * j) * ((t * y4) - (x * y0));
	elseif (a <= 4e-34)
		tmp = c * ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2))));
	elseif (a <= 1.15e+122)
		tmp = b * ((a * ((x * y) - (z * t))) + (y0 * ((z * k) - (x * j))));
	else
		tmp = (t * a) * ((y2 * y5) - (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[a, -2.55e+206], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.56e-12], N[(y5 * N[(y2 * N[(N[(t * a), $MachinePrecision] - N[(k * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -7e-37], N[(N[(b * j), $MachinePrecision] * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4e-34], N[(c * N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.15e+122], N[(b * N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * a), $MachinePrecision] * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -2.5500000000000002e206

   1. Initial program 34.9%

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

   2. Taylor expanded in a around -inf 60.4%

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

      1. mul-1-neg 60.4%

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

      2. distribute-rgt-neg-in 60.4%

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

      3. +-commutative 60.4%

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

      4. mul-1-neg 60.4%

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

      5. unsub-neg 60.4%

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

      6. *-commutative 60.4%

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

      7. *-commutative 60.4%

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

      8. *-commutative 60.4%

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

   4. Simplified 60.4%

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

   5. Taylor expanded in y around -inf 60.6%

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

      1. associate-*r* 60.6%

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

      2. neg-mul-1 60.6%

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

      3. +-commutative 60.6%

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

      4. mul-1-neg 60.6%

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

      5. unsub-neg 60.6%

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

   7. Simplified 60.6%

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

   if -2.5500000000000002e206 < a < -2.56e-12

   1. Initial program 22.0%

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

   2. Taylor expanded in y5 around -inf 39.4%

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

   3. Taylor expanded in y2 around inf 44.7%

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

      1. *-commutative 44.7%

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

   5. Simplified 44.7%

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

   if -2.56e-12 < a < -7.0000000000000003e-37

   1. Initial program 49.6%

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

   2. Taylor expanded in b around inf 66.9%

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

   3. Taylor expanded in j around inf 84.0%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 100.0%

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

      2. *-commutative 100.0%

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

      3. *-commutative 100.0%

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

      4. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   if -7.0000000000000003e-37 < a < 3.99999999999999971e-34

   1. Initial program 41.1%

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

   2. Taylor expanded in c around inf 45.1%

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

      1. +-commutative 45.1%

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

      2. mul-1-neg 45.1%

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

      3. unsub-neg 45.1%

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

      4. *-commutative 45.1%

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

      5. *-commutative 45.1%

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

      6. *-commutative 45.1%

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

      7. *-commutative 45.1%

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

   4. Simplified 45.1%

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

   5. Taylor expanded in i around 0 47.0%

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

      1. *-commutative 47.0%

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

      2. *-commutative 47.0%

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

   7. Simplified 47.0%

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

   if 3.99999999999999971e-34 < a < 1.15e122

   1. Initial program 22.5%

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

   2. Taylor expanded in b around inf 45.2%

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

   3. Taylor expanded in y4 around 0 49.1%

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

      1. *-commutative 49.1%

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

      2. *-commutative 49.1%

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

      3. *-commutative 49.1%

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

   5. Simplified 49.1%

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

   if 1.15e122 < a

   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. Taylor expanded in a around -inf 62.8%

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

      1. mul-1-neg 62.8%

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

      2. distribute-rgt-neg-in 62.8%

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

      3. +-commutative 62.8%

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

      4. mul-1-neg 62.8%

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

      5. unsub-neg 62.8%

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

      6. *-commutative 62.8%

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

      7. *-commutative 62.8%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative 62.8%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   4. Simplified 62.8%

      \[\leadsto \color{blue}{a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(y \cdot x - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   5. Taylor expanded in t around inf 48.9%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(-1 \cdot \left(b \cdot z\right) + y2 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 55.9%

         \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot \left(-1 \cdot \left(b \cdot z\right) + y2 \cdot y5\right)} \]

      2. +-commutative 55.9%

         \[\leadsto \left(a \cdot t\right) \cdot \color{blue}{\left(y2 \cdot y5 + -1 \cdot \left(b \cdot z\right)\right)} \]

      3. mul-1-neg 55.9%

         \[\leadsto \left(a \cdot t\right) \cdot \left(y2 \cdot y5 + \color{blue}{\left(-b \cdot z\right)}\right) \]

      4. unsub-neg 55.9%

         \[\leadsto \left(a \cdot t\right) \cdot \color{blue}{\left(y2 \cdot y5 - b \cdot z\right)} \]

      5. *-commutative 55.9%

         \[\leadsto \left(a \cdot t\right) \cdot \left(\color{blue}{y5 \cdot y2} - b \cdot z\right) \]

      6. *-commutative 55.9%

         \[\leadsto \left(a \cdot t\right) \cdot \left(y5 \cdot y2 - \color{blue}{z \cdot b}\right) \]

   7. Simplified 55.9%

      \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot \left(y5 \cdot y2 - z \cdot b\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.55 \cdot 10^{+206}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq -2.56 \cdot 10^{-12}:\\ \;\;\;\;y5 \cdot \left(y2 \cdot \left(t \cdot a - k \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-37}:\\ \;\;\;\;\left(b \cdot j\right) \cdot \left(t \cdot y4 - x \cdot y0\right)\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-34}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+122}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(y2 \cdot y5 - z \cdot b\right)\\ \end{array} \]

Alternative 15: 30.4% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ t_2 := a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{if}\;y1 \leq -1 \cdot 10^{+107}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y1 \leq -1.8 \cdot 10^{-97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y1 \leq 5.5 \cdot 10^{-296}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 5 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y1 \leq 2.5 \cdot 10^{+16}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq 2.6 \cdot 10^{+91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y1 \leq 1.55 \cdot 10^{+115}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq 1.1 \cdot 10^{+187}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y5 (- (* t y2) (* y y3)))))
        (t_2 (* a (* y1 (- (* z y3) (* x y2))))))
   (if (<= y1 -1e+107)
     t_2
     (if (<= y1 -1.8e-97)
       t_1
       (if (<= y1 5.5e-296)
         (* b (* y0 (- (* z k) (* x j))))
         (if (<= y1 5e-86)
           t_1
           (if (<= y1 2.5e+16)
             (* c (* y0 (* x y2)))
             (if (<= y1 2.6e+91)
               t_1
               (if (<= y1 1.55e+115)
                 (* i (* j (* x y1)))
                 (if (<= y1 1.1e+187) (* x (* c (* y0 y2))) 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 = a * (y5 * ((t * y2) - (y * y3)));
	double t_2 = a * (y1 * ((z * y3) - (x * y2)));
	double tmp;
	if (y1 <= -1e+107) {
		tmp = t_2;
	} else if (y1 <= -1.8e-97) {
		tmp = t_1;
	} else if (y1 <= 5.5e-296) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y1 <= 5e-86) {
		tmp = t_1;
	} else if (y1 <= 2.5e+16) {
		tmp = c * (y0 * (x * y2));
	} else if (y1 <= 2.6e+91) {
		tmp = t_1;
	} else if (y1 <= 1.55e+115) {
		tmp = i * (j * (x * y1));
	} else if (y1 <= 1.1e+187) {
		tmp = x * (c * (y0 * y2));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (y5 * ((t * y2) - (y * y3)))
    t_2 = a * (y1 * ((z * y3) - (x * y2)))
    if (y1 <= (-1d+107)) then
        tmp = t_2
    else if (y1 <= (-1.8d-97)) then
        tmp = t_1
    else if (y1 <= 5.5d-296) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (y1 <= 5d-86) then
        tmp = t_1
    else if (y1 <= 2.5d+16) then
        tmp = c * (y0 * (x * y2))
    else if (y1 <= 2.6d+91) then
        tmp = t_1
    else if (y1 <= 1.55d+115) then
        tmp = i * (j * (x * y1))
    else if (y1 <= 1.1d+187) then
        tmp = x * (c * (y0 * y2))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y5 * ((t * y2) - (y * y3)));
	double t_2 = a * (y1 * ((z * y3) - (x * y2)));
	double tmp;
	if (y1 <= -1e+107) {
		tmp = t_2;
	} else if (y1 <= -1.8e-97) {
		tmp = t_1;
	} else if (y1 <= 5.5e-296) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y1 <= 5e-86) {
		tmp = t_1;
	} else if (y1 <= 2.5e+16) {
		tmp = c * (y0 * (x * y2));
	} else if (y1 <= 2.6e+91) {
		tmp = t_1;
	} else if (y1 <= 1.55e+115) {
		tmp = i * (j * (x * y1));
	} else if (y1 <= 1.1e+187) {
		tmp = x * (c * (y0 * y2));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y5 * ((t * y2) - (y * y3)))
	t_2 = a * (y1 * ((z * y3) - (x * y2)))
	tmp = 0
	if y1 <= -1e+107:
		tmp = t_2
	elif y1 <= -1.8e-97:
		tmp = t_1
	elif y1 <= 5.5e-296:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif y1 <= 5e-86:
		tmp = t_1
	elif y1 <= 2.5e+16:
		tmp = c * (y0 * (x * y2))
	elif y1 <= 2.6e+91:
		tmp = t_1
	elif y1 <= 1.55e+115:
		tmp = i * (j * (x * y1))
	elif y1 <= 1.1e+187:
		tmp = x * (c * (y0 * y2))
	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(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))
	t_2 = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))))
	tmp = 0.0
	if (y1 <= -1e+107)
		tmp = t_2;
	elseif (y1 <= -1.8e-97)
		tmp = t_1;
	elseif (y1 <= 5.5e-296)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (y1 <= 5e-86)
		tmp = t_1;
	elseif (y1 <= 2.5e+16)
		tmp = Float64(c * Float64(y0 * Float64(x * y2)));
	elseif (y1 <= 2.6e+91)
		tmp = t_1;
	elseif (y1 <= 1.55e+115)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (y1 <= 1.1e+187)
		tmp = Float64(x * Float64(c * Float64(y0 * y2)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y5 * ((t * y2) - (y * y3)));
	t_2 = a * (y1 * ((z * y3) - (x * y2)));
	tmp = 0.0;
	if (y1 <= -1e+107)
		tmp = t_2;
	elseif (y1 <= -1.8e-97)
		tmp = t_1;
	elseif (y1 <= 5.5e-296)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (y1 <= 5e-86)
		tmp = t_1;
	elseif (y1 <= 2.5e+16)
		tmp = c * (y0 * (x * y2));
	elseif (y1 <= 2.6e+91)
		tmp = t_1;
	elseif (y1 <= 1.55e+115)
		tmp = i * (j * (x * y1));
	elseif (y1 <= 1.1e+187)
		tmp = x * (c * (y0 * y2));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -1e+107], t$95$2, If[LessEqual[y1, -1.8e-97], t$95$1, If[LessEqual[y1, 5.5e-296], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 5e-86], t$95$1, If[LessEqual[y1, 2.5e+16], N[(c * N[(y0 * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 2.6e+91], t$95$1, If[LessEqual[y1, 1.55e+115], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.1e+187], N[(x * N[(c * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y1 < -9.9999999999999997e106 or 1.0999999999999999e187 < y1

   1. Initial program 9.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around -inf 29.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 29.9%

         \[\leadsto \color{blue}{-a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. distribute-rgt-neg-in 29.9%

         \[\leadsto \color{blue}{a \cdot \left(-\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      3. +-commutative 29.9%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. mul-1-neg 29.9%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-b \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. unsub-neg 29.9%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 29.9%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. *-commutative 29.9%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative 29.9%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   4. Simplified 29.9%

      \[\leadsto \color{blue}{a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(y \cdot x - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   5. Taylor expanded in y1 around inf 53.9%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

   if -9.9999999999999997e106 < y1 < -1.79999999999999999e-97 or 5.5000000000000004e-296 < y1 < 4.9999999999999999e-86 or 2.5e16 < y1 < 2.6e91

   1. Initial program 41.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around -inf 41.1%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 41.1%

         \[\leadsto \color{blue}{-a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. distribute-rgt-neg-in 41.1%

         \[\leadsto \color{blue}{a \cdot \left(-\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      3. +-commutative 41.1%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. mul-1-neg 41.1%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-b \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. unsub-neg 41.1%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 41.1%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. *-commutative 41.1%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative 41.1%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   4. Simplified 41.1%

      \[\leadsto \color{blue}{a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(y \cdot x - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   5. Taylor expanded in y5 around inf 42.4%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   if -1.79999999999999999e-97 < y1 < 5.5000000000000004e-296

   1. Initial program 51.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf 47.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in y0 around inf 40.5%

      \[\leadsto b \cdot \color{blue}{\left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 40.5%

         \[\leadsto b \cdot \left(y0 \cdot \left(\color{blue}{z \cdot k} - j \cdot x\right)\right) \]

   5. Simplified 40.5%

      \[\leadsto b \cdot \color{blue}{\left(y0 \cdot \left(z \cdot k - j \cdot x\right)\right)} \]

   if 4.9999999999999999e-86 < y1 < 2.5e16

   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. Taylor expanded in c around inf 44.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 44.8%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 44.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 44.8%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 44.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 44.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 44.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 44.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 44.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 38.7%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 35.5%

      \[\leadsto c \cdot \color{blue}{\left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 35.5%

         \[\leadsto c \cdot \color{blue}{\left(\left(x \cdot y0\right) \cdot y2\right)} \]

      2. *-commutative 35.5%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot x\right)} \cdot y2\right) \]

      3. associate-*r* 35.6%

         \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2\right)\right)} \]

   8. Simplified 35.6%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2\right)\right)} \]

   if 2.6e91 < y1 < 1.55000000000000002e115

   1. Initial program 55.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in x around inf 77.8%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in j around inf 56.8%

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 56.8%

         \[\leadsto x \cdot \left(j \cdot \left(\color{blue}{y1 \cdot i} - b \cdot y0\right)\right) \]

      2. *-commutative 56.8%

         \[\leadsto x \cdot \left(j \cdot \left(y1 \cdot i - \color{blue}{y0 \cdot b}\right)\right) \]

   5. Simplified 56.8%

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(y1 \cdot i - y0 \cdot b\right)\right)} \]

   6. Taylor expanded in y1 around inf 57.9%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]

   if 1.55000000000000002e115 < y1 < 1.0999999999999999e187

   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. Taylor expanded in c around inf 53.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 53.4%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 53.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 53.4%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 53.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 53.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 53.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 53.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 53.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 53.1%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 43.7%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 43.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y0 \cdot y2\right)\right) \cdot c} \]

      2. associate-*l* 48.6%

         \[\leadsto \color{blue}{x \cdot \left(\left(y0 \cdot y2\right) \cdot c\right)} \]

   8. Simplified 48.6%

      \[\leadsto \color{blue}{x \cdot \left(\left(y0 \cdot y2\right) \cdot c\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 44.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -1 \cdot 10^{+107}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -1.8 \cdot 10^{-97}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq 5.5 \cdot 10^{-296}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 5 \cdot 10^{-86}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq 2.5 \cdot 10^{+16}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq 2.6 \cdot 10^{+91}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq 1.55 \cdot 10^{+115}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq 1.1 \cdot 10^{+187}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \end{array} \]

Alternative 16: 30.5% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ t_2 := b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{if}\;y4 \leq -4.4 \cdot 10^{+47}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y4 \leq -1.8 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y4 \leq -9.2 \cdot 10^{-26}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y4 \leq -2.1 \cdot 10^{-276}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y4 \leq 6 \cdot 10^{-167}:\\ \;\;\;\;\left(z \cdot y3\right) \cdot \left(c \cdot \left(-y0\right)\right)\\ \mathbf{elif}\;y4 \leq 3.2 \cdot 10^{-23}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y4 \leq 4 \cdot 10^{+98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y4 \leq 5 \cdot 10^{+109}:\\ \;\;\;\;\left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* b (- (* x y) (* z t)))))
        (t_2 (* b (* y4 (- (* t j) (* y k))))))
   (if (<= y4 -4.4e+47)
     t_2
     (if (<= y4 -1.8e+34)
       t_1
       (if (<= y4 -9.2e-26)
         t_2
         (if (<= y4 -2.1e-276)
           (* b (* y0 (- (* z k) (* x j))))
           (if (<= y4 6e-167)
             (* (* z y3) (* c (- y0)))
             (if (<= y4 3.2e-23)
               (* a (* y5 (- (* t y2) (* y y3))))
               (if (<= y4 4e+98)
                 t_1
                 (if (<= y4 5e+109) (* (- a) (* y (* y3 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 = a * (b * ((x * y) - (z * t)));
	double t_2 = b * (y4 * ((t * j) - (y * k)));
	double tmp;
	if (y4 <= -4.4e+47) {
		tmp = t_2;
	} else if (y4 <= -1.8e+34) {
		tmp = t_1;
	} else if (y4 <= -9.2e-26) {
		tmp = t_2;
	} else if (y4 <= -2.1e-276) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y4 <= 6e-167) {
		tmp = (z * y3) * (c * -y0);
	} else if (y4 <= 3.2e-23) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (y4 <= 4e+98) {
		tmp = t_1;
	} else if (y4 <= 5e+109) {
		tmp = -a * (y * (y3 * y5));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (b * ((x * y) - (z * t)))
    t_2 = b * (y4 * ((t * j) - (y * k)))
    if (y4 <= (-4.4d+47)) then
        tmp = t_2
    else if (y4 <= (-1.8d+34)) then
        tmp = t_1
    else if (y4 <= (-9.2d-26)) then
        tmp = t_2
    else if (y4 <= (-2.1d-276)) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (y4 <= 6d-167) then
        tmp = (z * y3) * (c * -y0)
    else if (y4 <= 3.2d-23) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else if (y4 <= 4d+98) then
        tmp = t_1
    else if (y4 <= 5d+109) then
        tmp = -a * (y * (y3 * y5))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (b * ((x * y) - (z * t)));
	double t_2 = b * (y4 * ((t * j) - (y * k)));
	double tmp;
	if (y4 <= -4.4e+47) {
		tmp = t_2;
	} else if (y4 <= -1.8e+34) {
		tmp = t_1;
	} else if (y4 <= -9.2e-26) {
		tmp = t_2;
	} else if (y4 <= -2.1e-276) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y4 <= 6e-167) {
		tmp = (z * y3) * (c * -y0);
	} else if (y4 <= 3.2e-23) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (y4 <= 4e+98) {
		tmp = t_1;
	} else if (y4 <= 5e+109) {
		tmp = -a * (y * (y3 * y5));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (b * ((x * y) - (z * t)))
	t_2 = b * (y4 * ((t * j) - (y * k)))
	tmp = 0
	if y4 <= -4.4e+47:
		tmp = t_2
	elif y4 <= -1.8e+34:
		tmp = t_1
	elif y4 <= -9.2e-26:
		tmp = t_2
	elif y4 <= -2.1e-276:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif y4 <= 6e-167:
		tmp = (z * y3) * (c * -y0)
	elif y4 <= 3.2e-23:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	elif y4 <= 4e+98:
		tmp = t_1
	elif y4 <= 5e+109:
		tmp = -a * (y * (y3 * 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(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))))
	t_2 = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))))
	tmp = 0.0
	if (y4 <= -4.4e+47)
		tmp = t_2;
	elseif (y4 <= -1.8e+34)
		tmp = t_1;
	elseif (y4 <= -9.2e-26)
		tmp = t_2;
	elseif (y4 <= -2.1e-276)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (y4 <= 6e-167)
		tmp = Float64(Float64(z * y3) * Float64(c * Float64(-y0)));
	elseif (y4 <= 3.2e-23)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (y4 <= 4e+98)
		tmp = t_1;
	elseif (y4 <= 5e+109)
		tmp = Float64(Float64(-a) * Float64(y * Float64(y3 * y5)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (b * ((x * y) - (z * t)));
	t_2 = b * (y4 * ((t * j) - (y * k)));
	tmp = 0.0;
	if (y4 <= -4.4e+47)
		tmp = t_2;
	elseif (y4 <= -1.8e+34)
		tmp = t_1;
	elseif (y4 <= -9.2e-26)
		tmp = t_2;
	elseif (y4 <= -2.1e-276)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (y4 <= 6e-167)
		tmp = (z * y3) * (c * -y0);
	elseif (y4 <= 3.2e-23)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	elseif (y4 <= 4e+98)
		tmp = t_1;
	elseif (y4 <= 5e+109)
		tmp = -a * (y * (y3 * y5));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -4.4e+47], t$95$2, If[LessEqual[y4, -1.8e+34], t$95$1, If[LessEqual[y4, -9.2e-26], t$95$2, If[LessEqual[y4, -2.1e-276], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 6e-167], N[(N[(z * y3), $MachinePrecision] * N[(c * (-y0)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 3.2e-23], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 4e+98], t$95$1, If[LessEqual[y4, 5e+109], N[((-a) * N[(y * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y4 < -4.3999999999999999e47 or -1.8e34 < y4 < -9.20000000000000035e-26 or 5.0000000000000001e109 < y4

   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. Taylor expanded in b around inf 40.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in y4 around inf 50.3%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 50.3%

         \[\leadsto b \cdot \left(y4 \cdot \left(j \cdot t - \color{blue}{y \cdot k}\right)\right) \]

   5. Simplified 50.3%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - y \cdot k\right)\right)} \]

   if -4.3999999999999999e47 < y4 < -1.8e34 or 3.19999999999999976e-23 < y4 < 3.99999999999999999e98

   1. Initial program 20.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf 32.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in a around inf 49.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if -9.20000000000000035e-26 < y4 < -2.1e-276

   1. Initial program 46.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf 38.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in y0 around inf 37.4%

      \[\leadsto b \cdot \color{blue}{\left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 37.4%

         \[\leadsto b \cdot \left(y0 \cdot \left(\color{blue}{z \cdot k} - j \cdot x\right)\right) \]

   5. Simplified 37.4%

      \[\leadsto b \cdot \color{blue}{\left(y0 \cdot \left(z \cdot k - j \cdot x\right)\right)} \]

   if -2.1e-276 < y4 < 5.9999999999999996e-167

   1. Initial program 37.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 38.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 38.4%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 38.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 38.4%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 38.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 38.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 38.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 38.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 38.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 49.9%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   6. Taylor expanded in x around 0 41.2%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 41.2%

         \[\leadsto \color{blue}{-c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)} \]

      2. associate-*r* 49.2%

         \[\leadsto -\color{blue}{\left(c \cdot y0\right) \cdot \left(y3 \cdot z\right)} \]

      3. distribute-rgt-neg-in 49.2%

         \[\leadsto \color{blue}{\left(c \cdot y0\right) \cdot \left(-y3 \cdot z\right)} \]

      4. distribute-lft-neg-in 49.2%

         \[\leadsto \left(c \cdot y0\right) \cdot \color{blue}{\left(\left(-y3\right) \cdot z\right)} \]

      5. *-commutative 49.2%

         \[\leadsto \left(c \cdot y0\right) \cdot \color{blue}{\left(z \cdot \left(-y3\right)\right)} \]

   8. Simplified 49.2%

      \[\leadsto \color{blue}{\left(c \cdot y0\right) \cdot \left(z \cdot \left(-y3\right)\right)} \]

   if 5.9999999999999996e-167 < y4 < 3.19999999999999976e-23

   1. Initial program 50.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around -inf 33.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 33.9%

         \[\leadsto \color{blue}{-a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. distribute-rgt-neg-in 33.9%

         \[\leadsto \color{blue}{a \cdot \left(-\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      3. +-commutative 33.9%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. mul-1-neg 33.9%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-b \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. unsub-neg 33.9%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 33.9%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. *-commutative 33.9%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative 33.9%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   4. Simplified 33.9%

      \[\leadsto \color{blue}{a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(y \cdot x - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   5. Taylor expanded in y5 around inf 41.0%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   if 3.99999999999999999e98 < y4 < 5.0000000000000001e109

   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. Taylor expanded in a around -inf 100.0%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 100.0%

         \[\leadsto \color{blue}{-a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. distribute-rgt-neg-in 100.0%

         \[\leadsto \color{blue}{a \cdot \left(-\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      3. +-commutative 100.0%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. mul-1-neg 100.0%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-b \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. unsub-neg 100.0%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 100.0%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. *-commutative 100.0%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative 100.0%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   4. Simplified 100.0%

      \[\leadsto \color{blue}{a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(y \cdot x - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   5. Taylor expanded in y around -inf 100.0%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 100.0%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)} \]

      2. neg-mul-1 100.0%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(y \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right) \]

      3. +-commutative 100.0%

         \[\leadsto \left(-a\right) \cdot \left(y \cdot \color{blue}{\left(y3 \cdot y5 + -1 \cdot \left(b \cdot x\right)\right)}\right) \]

      4. mul-1-neg 100.0%

         \[\leadsto \left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5 + \color{blue}{\left(-b \cdot x\right)}\right)\right) \]

      5. unsub-neg 100.0%

         \[\leadsto \left(-a\right) \cdot \left(y \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]

   7. Simplified 100.0%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)} \]

   8. Taylor expanded in y3 around inf 100.0%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 100.0%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)} \]

      2. neg-mul-1 100.0%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(y \cdot \left(y3 \cdot y5\right)\right) \]

   10. Simplified 100.0%

       \[\leadsto \color{blue}{\left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 47.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -4.4 \cdot 10^{+47}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y4 \leq -1.8 \cdot 10^{+34}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y4 \leq -9.2 \cdot 10^{-26}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y4 \leq -2.1 \cdot 10^{-276}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y4 \leq 6 \cdot 10^{-167}:\\ \;\;\;\;\left(z \cdot y3\right) \cdot \left(c \cdot \left(-y0\right)\right)\\ \mathbf{elif}\;y4 \leq 3.2 \cdot 10^{-23}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y4 \leq 4 \cdot 10^{+98}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y4 \leq 5 \cdot 10^{+109}:\\ \;\;\;\;\left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \end{array} \]

Alternative 17: 31.6% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{+55}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-306}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-181}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-30}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y \leq 0.26:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+39}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+151}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+219}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* t (* c (- (* z i) (* y2 y4))))))
   (if (<= y -2.7e+55)
     (* b (* y (- (* x a) (* k y4))))
     (if (<= y -2e-306)
       (* c (* y0 (- (* x y2) (* z y3))))
       (if (<= y 2.3e-181)
         t_1
         (if (<= y 1.95e-30)
           (* b (* y0 (- (* z k) (* x j))))
           (if (<= y 0.26)
             t_1
             (if (<= y 5.2e+39)
               (* c (* y (* y3 y4)))
               (if (<= y 5.2e+151)
                 (* x (* c (- (* y0 y2) (* y i))))
                 (if (<= y 4.5e+219)
                   (* b (* y4 (- (* t j) (* y k))))
                   (* (- a) (* y3 (* y y5)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * (c * ((z * i) - (y2 * y4)));
	double tmp;
	if (y <= -2.7e+55) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (y <= -2e-306) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (y <= 2.3e-181) {
		tmp = t_1;
	} else if (y <= 1.95e-30) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y <= 0.26) {
		tmp = t_1;
	} else if (y <= 5.2e+39) {
		tmp = c * (y * (y3 * y4));
	} else if (y <= 5.2e+151) {
		tmp = x * (c * ((y0 * y2) - (y * i)));
	} else if (y <= 4.5e+219) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else {
		tmp = -a * (y3 * (y * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (c * ((z * i) - (y2 * y4)))
    if (y <= (-2.7d+55)) then
        tmp = b * (y * ((x * a) - (k * y4)))
    else if (y <= (-2d-306)) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else if (y <= 2.3d-181) then
        tmp = t_1
    else if (y <= 1.95d-30) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (y <= 0.26d0) then
        tmp = t_1
    else if (y <= 5.2d+39) then
        tmp = c * (y * (y3 * y4))
    else if (y <= 5.2d+151) then
        tmp = x * (c * ((y0 * y2) - (y * i)))
    else if (y <= 4.5d+219) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else
        tmp = -a * (y3 * (y * y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * (c * ((z * i) - (y2 * y4)));
	double tmp;
	if (y <= -2.7e+55) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (y <= -2e-306) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (y <= 2.3e-181) {
		tmp = t_1;
	} else if (y <= 1.95e-30) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y <= 0.26) {
		tmp = t_1;
	} else if (y <= 5.2e+39) {
		tmp = c * (y * (y3 * y4));
	} else if (y <= 5.2e+151) {
		tmp = x * (c * ((y0 * y2) - (y * i)));
	} else if (y <= 4.5e+219) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else {
		tmp = -a * (y3 * (y * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = t * (c * ((z * i) - (y2 * y4)))
	tmp = 0
	if y <= -2.7e+55:
		tmp = b * (y * ((x * a) - (k * y4)))
	elif y <= -2e-306:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	elif y <= 2.3e-181:
		tmp = t_1
	elif y <= 1.95e-30:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif y <= 0.26:
		tmp = t_1
	elif y <= 5.2e+39:
		tmp = c * (y * (y3 * y4))
	elif y <= 5.2e+151:
		tmp = x * (c * ((y0 * y2) - (y * i)))
	elif y <= 4.5e+219:
		tmp = b * (y4 * ((t * j) - (y * k)))
	else:
		tmp = -a * (y3 * (y * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(t * Float64(c * Float64(Float64(z * i) - Float64(y2 * y4))))
	tmp = 0.0
	if (y <= -2.7e+55)
		tmp = Float64(b * Float64(y * Float64(Float64(x * a) - Float64(k * y4))));
	elseif (y <= -2e-306)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (y <= 2.3e-181)
		tmp = t_1;
	elseif (y <= 1.95e-30)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (y <= 0.26)
		tmp = t_1;
	elseif (y <= 5.2e+39)
		tmp = Float64(c * Float64(y * Float64(y3 * y4)));
	elseif (y <= 5.2e+151)
		tmp = Float64(x * Float64(c * Float64(Float64(y0 * y2) - Float64(y * i))));
	elseif (y <= 4.5e+219)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	else
		tmp = Float64(Float64(-a) * Float64(y3 * Float64(y * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = t * (c * ((z * i) - (y2 * y4)));
	tmp = 0.0;
	if (y <= -2.7e+55)
		tmp = b * (y * ((x * a) - (k * y4)));
	elseif (y <= -2e-306)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	elseif (y <= 2.3e-181)
		tmp = t_1;
	elseif (y <= 1.95e-30)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (y <= 0.26)
		tmp = t_1;
	elseif (y <= 5.2e+39)
		tmp = c * (y * (y3 * y4));
	elseif (y <= 5.2e+151)
		tmp = x * (c * ((y0 * y2) - (y * i)));
	elseif (y <= 4.5e+219)
		tmp = b * (y4 * ((t * j) - (y * k)));
	else
		tmp = -a * (y3 * (y * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(t * N[(c * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.7e+55], N[(b * N[(y * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2e-306], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e-181], t$95$1, If[LessEqual[y, 1.95e-30], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.26], t$95$1, If[LessEqual[y, 5.2e+39], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.2e+151], N[(x * N[(c * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e+219], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-a) * N[(y3 * N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y < -2.69999999999999977e55

   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. Taylor expanded in b around inf 48.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in y around inf 50.6%

      \[\leadsto b \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 50.6%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 50.6%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x + \color{blue}{\left(-k \cdot y4\right)}\right)\right) \]

      3. unsub-neg 50.6%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x - k \cdot y4\right)}\right) \]

      4. *-commutative 50.6%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x - \color{blue}{y4 \cdot k}\right)\right) \]

   5. Simplified 50.6%

      \[\leadsto b \cdot \color{blue}{\left(y \cdot \left(a \cdot x - y4 \cdot k\right)\right)} \]

   if -2.69999999999999977e55 < y < -2.00000000000000006e-306

   1. Initial program 28.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 48.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 48.6%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 48.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 48.6%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 48.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 48.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 48.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 48.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 48.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 44.6%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   if -2.00000000000000006e-306 < y < 2.29999999999999991e-181 or 1.9500000000000002e-30 < y < 0.26000000000000001

   1. Initial program 54.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 52.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 52.2%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 52.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 52.2%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 52.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 52.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 52.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 52.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 52.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in t around -inf 58.6%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(-1 \cdot \left(y2 \cdot y4\right) + i \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 58.6%

         \[\leadsto \color{blue}{\left(t \cdot \left(-1 \cdot \left(y2 \cdot y4\right) + i \cdot z\right)\right) \cdot c} \]

      2. associate-*l* 58.6%

         \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(y2 \cdot y4\right) + i \cdot z\right) \cdot c\right)} \]

      3. +-commutative 58.6%

         \[\leadsto t \cdot \left(\color{blue}{\left(i \cdot z + -1 \cdot \left(y2 \cdot y4\right)\right)} \cdot c\right) \]

      4. mul-1-neg 58.6%

         \[\leadsto t \cdot \left(\left(i \cdot z + \color{blue}{\left(-y2 \cdot y4\right)}\right) \cdot c\right) \]

      5. unsub-neg 58.6%

         \[\leadsto t \cdot \left(\color{blue}{\left(i \cdot z - y2 \cdot y4\right)} \cdot c\right) \]

      6. *-commutative 58.6%

         \[\leadsto t \cdot \left(\left(\color{blue}{z \cdot i} - y2 \cdot y4\right) \cdot c\right) \]

   7. Simplified 58.6%

      \[\leadsto \color{blue}{t \cdot \left(\left(z \cdot i - y2 \cdot y4\right) \cdot c\right)} \]

   if 2.29999999999999991e-181 < y < 1.9500000000000002e-30

   1. Initial program 39.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf 47.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in y0 around inf 41.8%

      \[\leadsto b \cdot \color{blue}{\left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 41.8%

         \[\leadsto b \cdot \left(y0 \cdot \left(\color{blue}{z \cdot k} - j \cdot x\right)\right) \]

   5. Simplified 41.8%

      \[\leadsto b \cdot \color{blue}{\left(y0 \cdot \left(z \cdot k - j \cdot x\right)\right)} \]

   if 0.26000000000000001 < y < 5.2e39

   1. Initial program 39.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y3 around -inf 31.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   3. Taylor expanded in y4 around inf 30.7%

      \[\leadsto -1 \cdot \color{blue}{\left(y3 \cdot \left(y4 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 30.7%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(y3 \cdot y4\right) \cdot \left(j \cdot y1 - c \cdot y\right)\right)} \]

      2. *-commutative 30.7%

         \[\leadsto -1 \cdot \left(\left(y3 \cdot y4\right) \cdot \left(\color{blue}{y1 \cdot j} - c \cdot y\right)\right) \]

   5. Simplified 30.7%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(y3 \cdot y4\right) \cdot \left(y1 \cdot j - c \cdot y\right)\right)} \]

   6. Taylor expanded in y1 around 0 40.0%

      \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 40.0%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(-1 \cdot c\right) \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\right)} \]

      2. neg-mul-1 40.0%

         \[\leadsto -1 \cdot \left(\color{blue}{\left(-c\right)} \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\right) \]

   8. Simplified 40.0%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(-c\right) \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\right)} \]

   if 5.2e39 < y < 5.20000000000000026e151

   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. Taylor expanded in x around inf 38.2%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in c around inf 55.4%

      \[\leadsto x \cdot \color{blue}{\left(c \cdot \left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 55.4%

         \[\leadsto x \cdot \left(c \cdot \color{blue}{\left(y0 \cdot y2 + -1 \cdot \left(i \cdot y\right)\right)}\right) \]

      2. mul-1-neg 55.4%

         \[\leadsto x \cdot \left(c \cdot \left(y0 \cdot y2 + \color{blue}{\left(-i \cdot y\right)}\right)\right) \]

      3. unsub-neg 55.4%

         \[\leadsto x \cdot \left(c \cdot \color{blue}{\left(y0 \cdot y2 - i \cdot y\right)}\right) \]

      4. *-commutative 55.4%

         \[\leadsto x \cdot \left(c \cdot \left(y0 \cdot y2 - \color{blue}{y \cdot i}\right)\right) \]

   5. Simplified 55.4%

      \[\leadsto x \cdot \color{blue}{\left(c \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)} \]

   if 5.20000000000000026e151 < y < 4.50000000000000023e219

   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. Taylor expanded in b around inf 45.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in y4 around inf 63.9%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 63.9%

         \[\leadsto b \cdot \left(y4 \cdot \left(j \cdot t - \color{blue}{y \cdot k}\right)\right) \]

   5. Simplified 63.9%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - y \cdot k\right)\right)} \]

   if 4.50000000000000023e219 < y

   1. Initial program 17.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around -inf 47.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 47.2%

         \[\leadsto \color{blue}{-a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. distribute-rgt-neg-in 47.2%

         \[\leadsto \color{blue}{a \cdot \left(-\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      3. +-commutative 47.2%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. mul-1-neg 47.2%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-b \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. unsub-neg 47.2%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 47.2%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. *-commutative 47.2%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative 47.2%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   4. Simplified 47.2%

      \[\leadsto \color{blue}{a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(y \cdot x - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   5. Taylor expanded in y around -inf 59.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 59.2%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)} \]

      2. neg-mul-1 59.2%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(y \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right) \]

      3. +-commutative 59.2%

         \[\leadsto \left(-a\right) \cdot \left(y \cdot \color{blue}{\left(y3 \cdot y5 + -1 \cdot \left(b \cdot x\right)\right)}\right) \]

      4. mul-1-neg 59.2%

         \[\leadsto \left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5 + \color{blue}{\left(-b \cdot x\right)}\right)\right) \]

      5. unsub-neg 59.2%

         \[\leadsto \left(-a\right) \cdot \left(y \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]

   7. Simplified 59.2%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)} \]

   8. Taylor expanded in y3 around inf 59.9%

      \[\leadsto \left(-a\right) \cdot \color{blue}{\left(y \cdot \left(y3 \cdot y5\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 60.0%

         \[\leadsto \left(-a\right) \cdot \color{blue}{\left(\left(y \cdot y3\right) \cdot y5\right)} \]

      2. *-commutative 60.0%

         \[\leadsto \left(-a\right) \cdot \left(\color{blue}{\left(y3 \cdot y\right)} \cdot y5\right) \]

      3. associate-*l* 71.3%

         \[\leadsto \left(-a\right) \cdot \color{blue}{\left(y3 \cdot \left(y \cdot y5\right)\right)} \]

   10. Simplified 71.3%

       \[\leadsto \left(-a\right) \cdot \color{blue}{\left(y3 \cdot \left(y \cdot y5\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+55}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-306}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-181}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-30}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y \leq 0.26:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+39}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+151}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+219}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5\right)\right)\\ \end{array} \]

Alternative 18: 32.0% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{if}\;y \leq -9.8 \cdot 10^{+54}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{-241}:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-306}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-212}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+152}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+228}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y0 (- (* x y2) (* z y3))))))
   (if (<= y -9.8e+54)
     (* b (* y (- (* x a) (* k y4))))
     (if (<= y -2.6e-54)
       t_1
       (if (<= y -1.12e-241)
         (* y2 (* c (- (* x y0) (* t y4))))
         (if (<= y -1.7e-306)
           t_1
           (if (<= y 1.85e-212)
             (* t (* c (- (* z i) (* y2 y4))))
             (if (<= y 2e+74)
               (* x (* y0 (- (* c y2) (* b j))))
               (if (<= y 8.2e+152)
                 (* x (* c (- (* y0 y2) (* y i))))
                 (if (<= y 1.4e+228)
                   (* b (* y4 (- (* t j) (* y k))))
                   (* (- a) (* y3 (* y y5)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y0 * ((x * y2) - (z * y3)));
	double tmp;
	if (y <= -9.8e+54) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (y <= -2.6e-54) {
		tmp = t_1;
	} else if (y <= -1.12e-241) {
		tmp = y2 * (c * ((x * y0) - (t * y4)));
	} else if (y <= -1.7e-306) {
		tmp = t_1;
	} else if (y <= 1.85e-212) {
		tmp = t * (c * ((z * i) - (y2 * y4)));
	} else if (y <= 2e+74) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (y <= 8.2e+152) {
		tmp = x * (c * ((y0 * y2) - (y * i)));
	} else if (y <= 1.4e+228) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else {
		tmp = -a * (y3 * (y * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (y0 * ((x * y2) - (z * y3)))
    if (y <= (-9.8d+54)) then
        tmp = b * (y * ((x * a) - (k * y4)))
    else if (y <= (-2.6d-54)) then
        tmp = t_1
    else if (y <= (-1.12d-241)) then
        tmp = y2 * (c * ((x * y0) - (t * y4)))
    else if (y <= (-1.7d-306)) then
        tmp = t_1
    else if (y <= 1.85d-212) then
        tmp = t * (c * ((z * i) - (y2 * y4)))
    else if (y <= 2d+74) then
        tmp = x * (y0 * ((c * y2) - (b * j)))
    else if (y <= 8.2d+152) then
        tmp = x * (c * ((y0 * y2) - (y * i)))
    else if (y <= 1.4d+228) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else
        tmp = -a * (y3 * (y * y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y0 * ((x * y2) - (z * y3)));
	double tmp;
	if (y <= -9.8e+54) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (y <= -2.6e-54) {
		tmp = t_1;
	} else if (y <= -1.12e-241) {
		tmp = y2 * (c * ((x * y0) - (t * y4)));
	} else if (y <= -1.7e-306) {
		tmp = t_1;
	} else if (y <= 1.85e-212) {
		tmp = t * (c * ((z * i) - (y2 * y4)));
	} else if (y <= 2e+74) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (y <= 8.2e+152) {
		tmp = x * (c * ((y0 * y2) - (y * i)));
	} else if (y <= 1.4e+228) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else {
		tmp = -a * (y3 * (y * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (y0 * ((x * y2) - (z * y3)))
	tmp = 0
	if y <= -9.8e+54:
		tmp = b * (y * ((x * a) - (k * y4)))
	elif y <= -2.6e-54:
		tmp = t_1
	elif y <= -1.12e-241:
		tmp = y2 * (c * ((x * y0) - (t * y4)))
	elif y <= -1.7e-306:
		tmp = t_1
	elif y <= 1.85e-212:
		tmp = t * (c * ((z * i) - (y2 * y4)))
	elif y <= 2e+74:
		tmp = x * (y0 * ((c * y2) - (b * j)))
	elif y <= 8.2e+152:
		tmp = x * (c * ((y0 * y2) - (y * i)))
	elif y <= 1.4e+228:
		tmp = b * (y4 * ((t * j) - (y * k)))
	else:
		tmp = -a * (y3 * (y * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))))
	tmp = 0.0
	if (y <= -9.8e+54)
		tmp = Float64(b * Float64(y * Float64(Float64(x * a) - Float64(k * y4))));
	elseif (y <= -2.6e-54)
		tmp = t_1;
	elseif (y <= -1.12e-241)
		tmp = Float64(y2 * Float64(c * Float64(Float64(x * y0) - Float64(t * y4))));
	elseif (y <= -1.7e-306)
		tmp = t_1;
	elseif (y <= 1.85e-212)
		tmp = Float64(t * Float64(c * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (y <= 2e+74)
		tmp = Float64(x * Float64(y0 * Float64(Float64(c * y2) - Float64(b * j))));
	elseif (y <= 8.2e+152)
		tmp = Float64(x * Float64(c * Float64(Float64(y0 * y2) - Float64(y * i))));
	elseif (y <= 1.4e+228)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	else
		tmp = Float64(Float64(-a) * Float64(y3 * Float64(y * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (y0 * ((x * y2) - (z * y3)));
	tmp = 0.0;
	if (y <= -9.8e+54)
		tmp = b * (y * ((x * a) - (k * y4)));
	elseif (y <= -2.6e-54)
		tmp = t_1;
	elseif (y <= -1.12e-241)
		tmp = y2 * (c * ((x * y0) - (t * y4)));
	elseif (y <= -1.7e-306)
		tmp = t_1;
	elseif (y <= 1.85e-212)
		tmp = t * (c * ((z * i) - (y2 * y4)));
	elseif (y <= 2e+74)
		tmp = x * (y0 * ((c * y2) - (b * j)));
	elseif (y <= 8.2e+152)
		tmp = x * (c * ((y0 * y2) - (y * i)));
	elseif (y <= 1.4e+228)
		tmp = b * (y4 * ((t * j) - (y * k)));
	else
		tmp = -a * (y3 * (y * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.8e+54], N[(b * N[(y * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.6e-54], t$95$1, If[LessEqual[y, -1.12e-241], N[(y2 * N[(c * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.7e-306], t$95$1, If[LessEqual[y, 1.85e-212], N[(t * N[(c * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e+74], N[(x * N[(y0 * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.2e+152], N[(x * N[(c * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e+228], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-a) * N[(y3 * N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y < -9.80000000000000002e54

   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. Taylor expanded in b around inf 48.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in y around inf 50.6%

      \[\leadsto b \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 50.6%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 50.6%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x + \color{blue}{\left(-k \cdot y4\right)}\right)\right) \]

      3. unsub-neg 50.6%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x - k \cdot y4\right)}\right) \]

      4. *-commutative 50.6%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x - \color{blue}{y4 \cdot k}\right)\right) \]

   5. Simplified 50.6%

      \[\leadsto b \cdot \color{blue}{\left(y \cdot \left(a \cdot x - y4 \cdot k\right)\right)} \]

   if -9.80000000000000002e54 < y < -2.60000000000000002e-54 or -1.11999999999999993e-241 < y < -1.6999999999999999e-306

   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. Taylor expanded in c around inf 45.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 45.2%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 45.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 45.2%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 45.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 45.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 45.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 45.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 45.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 54.0%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   if -2.60000000000000002e-54 < y < -1.11999999999999993e-241

   1. Initial program 21.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 51.5%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 51.5%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 51.5%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 51.5%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 51.5%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 51.5%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 51.5%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 51.5%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 51.5%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y2 around inf 50.9%

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 50.9%

         \[\leadsto \color{blue}{\left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right) \cdot c} \]

      2. associate-*l* 48.3%

         \[\leadsto \color{blue}{y2 \cdot \left(\left(x \cdot y0 - t \cdot y4\right) \cdot c\right)} \]

      3. *-commutative 48.3%

         \[\leadsto y2 \cdot \left(\left(\color{blue}{y0 \cdot x} - t \cdot y4\right) \cdot c\right) \]

   7. Simplified 48.3%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(y0 \cdot x - t \cdot y4\right) \cdot c\right)} \]

   if -1.6999999999999999e-306 < y < 1.84999999999999995e-212

   1. Initial program 61.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 50.5%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 50.5%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 50.5%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 50.5%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 50.5%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 50.5%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 50.5%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 50.5%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 50.5%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in t around -inf 61.9%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(-1 \cdot \left(y2 \cdot y4\right) + i \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 61.9%

         \[\leadsto \color{blue}{\left(t \cdot \left(-1 \cdot \left(y2 \cdot y4\right) + i \cdot z\right)\right) \cdot c} \]

      2. associate-*l* 61.9%

         \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(y2 \cdot y4\right) + i \cdot z\right) \cdot c\right)} \]

      3. +-commutative 61.9%

         \[\leadsto t \cdot \left(\color{blue}{\left(i \cdot z + -1 \cdot \left(y2 \cdot y4\right)\right)} \cdot c\right) \]

      4. mul-1-neg 61.9%

         \[\leadsto t \cdot \left(\left(i \cdot z + \color{blue}{\left(-y2 \cdot y4\right)}\right) \cdot c\right) \]

      5. unsub-neg 61.9%

         \[\leadsto t \cdot \left(\color{blue}{\left(i \cdot z - y2 \cdot y4\right)} \cdot c\right) \]

      6. *-commutative 61.9%

         \[\leadsto t \cdot \left(\left(\color{blue}{z \cdot i} - y2 \cdot y4\right) \cdot c\right) \]

   7. Simplified 61.9%

      \[\leadsto \color{blue}{t \cdot \left(\left(z \cdot i - y2 \cdot y4\right) \cdot c\right)} \]

   if 1.84999999999999995e-212 < y < 1.9999999999999999e74

   1. Initial program 38.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in x around inf 36.3%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in y0 around inf 39.7%

      \[\leadsto x \cdot \color{blue}{\left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 39.7%

         \[\leadsto x \cdot \left(y0 \cdot \left(c \cdot y2 - \color{blue}{j \cdot b}\right)\right) \]

   5. Simplified 39.7%

      \[\leadsto x \cdot \color{blue}{\left(y0 \cdot \left(c \cdot y2 - j \cdot b\right)\right)} \]

   if 1.9999999999999999e74 < y < 8.1999999999999996e152

   1. Initial program 14.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in x around inf 36.8%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in c around inf 65.4%

      \[\leadsto x \cdot \color{blue}{\left(c \cdot \left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 65.4%

         \[\leadsto x \cdot \left(c \cdot \color{blue}{\left(y0 \cdot y2 + -1 \cdot \left(i \cdot y\right)\right)}\right) \]

      2. mul-1-neg 65.4%

         \[\leadsto x \cdot \left(c \cdot \left(y0 \cdot y2 + \color{blue}{\left(-i \cdot y\right)}\right)\right) \]

      3. unsub-neg 65.4%

         \[\leadsto x \cdot \left(c \cdot \color{blue}{\left(y0 \cdot y2 - i \cdot y\right)}\right) \]

      4. *-commutative 65.4%

         \[\leadsto x \cdot \left(c \cdot \left(y0 \cdot y2 - \color{blue}{y \cdot i}\right)\right) \]

   5. Simplified 65.4%

      \[\leadsto x \cdot \color{blue}{\left(c \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)} \]

   if 8.1999999999999996e152 < y < 1.4e228

   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. Taylor expanded in b around inf 45.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in y4 around inf 63.9%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 63.9%

         \[\leadsto b \cdot \left(y4 \cdot \left(j \cdot t - \color{blue}{y \cdot k}\right)\right) \]

   5. Simplified 63.9%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - y \cdot k\right)\right)} \]

   if 1.4e228 < y

   1. Initial program 17.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around -inf 47.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 47.2%

         \[\leadsto \color{blue}{-a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. distribute-rgt-neg-in 47.2%

         \[\leadsto \color{blue}{a \cdot \left(-\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      3. +-commutative 47.2%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. mul-1-neg 47.2%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-b \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. unsub-neg 47.2%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 47.2%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. *-commutative 47.2%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative 47.2%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   4. Simplified 47.2%

      \[\leadsto \color{blue}{a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(y \cdot x - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   5. Taylor expanded in y around -inf 59.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 59.2%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)} \]

      2. neg-mul-1 59.2%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(y \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right) \]

      3. +-commutative 59.2%

         \[\leadsto \left(-a\right) \cdot \left(y \cdot \color{blue}{\left(y3 \cdot y5 + -1 \cdot \left(b \cdot x\right)\right)}\right) \]

      4. mul-1-neg 59.2%

         \[\leadsto \left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5 + \color{blue}{\left(-b \cdot x\right)}\right)\right) \]

      5. unsub-neg 59.2%

         \[\leadsto \left(-a\right) \cdot \left(y \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]

   7. Simplified 59.2%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)} \]

   8. Taylor expanded in y3 around inf 59.9%

      \[\leadsto \left(-a\right) \cdot \color{blue}{\left(y \cdot \left(y3 \cdot y5\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 60.0%

         \[\leadsto \left(-a\right) \cdot \color{blue}{\left(\left(y \cdot y3\right) \cdot y5\right)} \]

      2. *-commutative 60.0%

         \[\leadsto \left(-a\right) \cdot \left(\color{blue}{\left(y3 \cdot y\right)} \cdot y5\right) \]

      3. associate-*l* 71.3%

         \[\leadsto \left(-a\right) \cdot \color{blue}{\left(y3 \cdot \left(y \cdot y5\right)\right)} \]

   10. Simplified 71.3%

       \[\leadsto \left(-a\right) \cdot \color{blue}{\left(y3 \cdot \left(y \cdot y5\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{+54}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-54}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{-241}:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-306}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-212}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+152}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+228}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5\right)\right)\\ \end{array} \]

Alternative 19: 31.9% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y2 - z \cdot y3\\ \mathbf{if}\;y \leq -3.7 \cdot 10^{+54}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{-57}:\\ \;\;\;\;t_1 \cdot \left(c \cdot y0\right)\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-240}:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-306}:\\ \;\;\;\;c \cdot \left(y0 \cdot t_1\right)\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{-213}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+152}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+233}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* x y2) (* z y3))))
   (if (<= y -3.7e+54)
     (* b (* y (- (* x a) (* k y4))))
     (if (<= y -6.4e-57)
       (* t_1 (* c y0))
       (if (<= y -4.2e-240)
         (* y2 (* c (- (* x y0) (* t y4))))
         (if (<= y -2e-306)
           (* c (* y0 t_1))
           (if (<= y 1.06e-213)
             (* t (* c (- (* z i) (* y2 y4))))
             (if (<= y 1.8e+74)
               (* x (* y0 (- (* c y2) (* b j))))
               (if (<= y 4.4e+152)
                 (* x (* c (- (* y0 y2) (* y i))))
                 (if (<= y 2.7e+233)
                   (* b (* y4 (- (* t j) (* y k))))
                   (* (- a) (* y3 (* y y5)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (x * y2) - (z * y3);
	double tmp;
	if (y <= -3.7e+54) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (y <= -6.4e-57) {
		tmp = t_1 * (c * y0);
	} else if (y <= -4.2e-240) {
		tmp = y2 * (c * ((x * y0) - (t * y4)));
	} else if (y <= -2e-306) {
		tmp = c * (y0 * t_1);
	} else if (y <= 1.06e-213) {
		tmp = t * (c * ((z * i) - (y2 * y4)));
	} else if (y <= 1.8e+74) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (y <= 4.4e+152) {
		tmp = x * (c * ((y0 * y2) - (y * i)));
	} else if (y <= 2.7e+233) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else {
		tmp = -a * (y3 * (y * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y2) - (z * y3)
    if (y <= (-3.7d+54)) then
        tmp = b * (y * ((x * a) - (k * y4)))
    else if (y <= (-6.4d-57)) then
        tmp = t_1 * (c * y0)
    else if (y <= (-4.2d-240)) then
        tmp = y2 * (c * ((x * y0) - (t * y4)))
    else if (y <= (-2d-306)) then
        tmp = c * (y0 * t_1)
    else if (y <= 1.06d-213) then
        tmp = t * (c * ((z * i) - (y2 * y4)))
    else if (y <= 1.8d+74) then
        tmp = x * (y0 * ((c * y2) - (b * j)))
    else if (y <= 4.4d+152) then
        tmp = x * (c * ((y0 * y2) - (y * i)))
    else if (y <= 2.7d+233) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else
        tmp = -a * (y3 * (y * y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (x * y2) - (z * y3);
	double tmp;
	if (y <= -3.7e+54) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (y <= -6.4e-57) {
		tmp = t_1 * (c * y0);
	} else if (y <= -4.2e-240) {
		tmp = y2 * (c * ((x * y0) - (t * y4)));
	} else if (y <= -2e-306) {
		tmp = c * (y0 * t_1);
	} else if (y <= 1.06e-213) {
		tmp = t * (c * ((z * i) - (y2 * y4)));
	} else if (y <= 1.8e+74) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (y <= 4.4e+152) {
		tmp = x * (c * ((y0 * y2) - (y * i)));
	} else if (y <= 2.7e+233) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else {
		tmp = -a * (y3 * (y * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (x * y2) - (z * y3)
	tmp = 0
	if y <= -3.7e+54:
		tmp = b * (y * ((x * a) - (k * y4)))
	elif y <= -6.4e-57:
		tmp = t_1 * (c * y0)
	elif y <= -4.2e-240:
		tmp = y2 * (c * ((x * y0) - (t * y4)))
	elif y <= -2e-306:
		tmp = c * (y0 * t_1)
	elif y <= 1.06e-213:
		tmp = t * (c * ((z * i) - (y2 * y4)))
	elif y <= 1.8e+74:
		tmp = x * (y0 * ((c * y2) - (b * j)))
	elif y <= 4.4e+152:
		tmp = x * (c * ((y0 * y2) - (y * i)))
	elif y <= 2.7e+233:
		tmp = b * (y4 * ((t * j) - (y * k)))
	else:
		tmp = -a * (y3 * (y * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(x * y2) - Float64(z * y3))
	tmp = 0.0
	if (y <= -3.7e+54)
		tmp = Float64(b * Float64(y * Float64(Float64(x * a) - Float64(k * y4))));
	elseif (y <= -6.4e-57)
		tmp = Float64(t_1 * Float64(c * y0));
	elseif (y <= -4.2e-240)
		tmp = Float64(y2 * Float64(c * Float64(Float64(x * y0) - Float64(t * y4))));
	elseif (y <= -2e-306)
		tmp = Float64(c * Float64(y0 * t_1));
	elseif (y <= 1.06e-213)
		tmp = Float64(t * Float64(c * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (y <= 1.8e+74)
		tmp = Float64(x * Float64(y0 * Float64(Float64(c * y2) - Float64(b * j))));
	elseif (y <= 4.4e+152)
		tmp = Float64(x * Float64(c * Float64(Float64(y0 * y2) - Float64(y * i))));
	elseif (y <= 2.7e+233)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	else
		tmp = Float64(Float64(-a) * Float64(y3 * Float64(y * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (x * y2) - (z * y3);
	tmp = 0.0;
	if (y <= -3.7e+54)
		tmp = b * (y * ((x * a) - (k * y4)));
	elseif (y <= -6.4e-57)
		tmp = t_1 * (c * y0);
	elseif (y <= -4.2e-240)
		tmp = y2 * (c * ((x * y0) - (t * y4)));
	elseif (y <= -2e-306)
		tmp = c * (y0 * t_1);
	elseif (y <= 1.06e-213)
		tmp = t * (c * ((z * i) - (y2 * y4)));
	elseif (y <= 1.8e+74)
		tmp = x * (y0 * ((c * y2) - (b * j)));
	elseif (y <= 4.4e+152)
		tmp = x * (c * ((y0 * y2) - (y * i)));
	elseif (y <= 2.7e+233)
		tmp = b * (y4 * ((t * j) - (y * k)));
	else
		tmp = -a * (y3 * (y * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.7e+54], N[(b * N[(y * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.4e-57], N[(t$95$1 * N[(c * y0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.2e-240], N[(y2 * N[(c * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2e-306], N[(c * N[(y0 * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.06e-213], N[(t * N[(c * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e+74], N[(x * N[(y0 * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.4e+152], N[(x * N[(c * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e+233], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-a) * N[(y3 * N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y < -3.7000000000000002e54

   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. Taylor expanded in b around inf 48.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in y around inf 50.6%

      \[\leadsto b \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 50.6%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 50.6%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x + \color{blue}{\left(-k \cdot y4\right)}\right)\right) \]

      3. unsub-neg 50.6%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x - k \cdot y4\right)}\right) \]

      4. *-commutative 50.6%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x - \color{blue}{y4 \cdot k}\right)\right) \]

   5. Simplified 50.6%

      \[\leadsto b \cdot \color{blue}{\left(y \cdot \left(a \cdot x - y4 \cdot k\right)\right)} \]

   if -3.7000000000000002e54 < y < -6.4000000000000002e-57

   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. Taylor expanded in c around inf 46.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 46.1%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 46.1%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 46.1%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 46.1%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 46.1%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 46.1%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 46.1%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 46.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 56.4%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 56.5%

         \[\leadsto \color{blue}{\left(c \cdot y0\right) \cdot \left(x \cdot y2 - y3 \cdot z\right)} \]

      2. *-commutative 56.5%

         \[\leadsto \left(c \cdot y0\right) \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) \]

      3. *-commutative 56.5%

         \[\leadsto \left(c \cdot y0\right) \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) \]

      4. *-commutative 56.5%

         \[\leadsto \color{blue}{\left(y2 \cdot x - z \cdot y3\right) \cdot \left(c \cdot y0\right)} \]

      5. *-commutative 56.5%

         \[\leadsto \left(\color{blue}{x \cdot y2} - z \cdot y3\right) \cdot \left(c \cdot y0\right) \]

      6. *-commutative 56.5%

         \[\leadsto \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) \cdot \left(c \cdot y0\right) \]

   7. Simplified 56.5%

      \[\leadsto \color{blue}{\left(x \cdot y2 - y3 \cdot z\right) \cdot \left(c \cdot y0\right)} \]

   if -6.4000000000000002e-57 < y < -4.19999999999999987e-240

   1. Initial program 21.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 51.5%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 51.5%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 51.5%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 51.5%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 51.5%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 51.5%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 51.5%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 51.5%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 51.5%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y2 around inf 50.9%

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 50.9%

         \[\leadsto \color{blue}{\left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right) \cdot c} \]

      2. associate-*l* 48.3%

         \[\leadsto \color{blue}{y2 \cdot \left(\left(x \cdot y0 - t \cdot y4\right) \cdot c\right)} \]

      3. *-commutative 48.3%

         \[\leadsto y2 \cdot \left(\left(\color{blue}{y0 \cdot x} - t \cdot y4\right) \cdot c\right) \]

   7. Simplified 48.3%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(y0 \cdot x - t \cdot y4\right) \cdot c\right)} \]

   if -4.19999999999999987e-240 < y < -2.00000000000000006e-306

   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. Taylor expanded in c around inf 44.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 44.1%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 44.1%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 44.1%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 44.1%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 44.1%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 44.1%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 44.1%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 44.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 51.0%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   if -2.00000000000000006e-306 < y < 1.06000000000000001e-213

   1. Initial program 61.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 50.5%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 50.5%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 50.5%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 50.5%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 50.5%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 50.5%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 50.5%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 50.5%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 50.5%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in t around -inf 61.9%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(-1 \cdot \left(y2 \cdot y4\right) + i \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 61.9%

         \[\leadsto \color{blue}{\left(t \cdot \left(-1 \cdot \left(y2 \cdot y4\right) + i \cdot z\right)\right) \cdot c} \]

      2. associate-*l* 61.9%

         \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(y2 \cdot y4\right) + i \cdot z\right) \cdot c\right)} \]

      3. +-commutative 61.9%

         \[\leadsto t \cdot \left(\color{blue}{\left(i \cdot z + -1 \cdot \left(y2 \cdot y4\right)\right)} \cdot c\right) \]

      4. mul-1-neg 61.9%

         \[\leadsto t \cdot \left(\left(i \cdot z + \color{blue}{\left(-y2 \cdot y4\right)}\right) \cdot c\right) \]

      5. unsub-neg 61.9%

         \[\leadsto t \cdot \left(\color{blue}{\left(i \cdot z - y2 \cdot y4\right)} \cdot c\right) \]

      6. *-commutative 61.9%

         \[\leadsto t \cdot \left(\left(\color{blue}{z \cdot i} - y2 \cdot y4\right) \cdot c\right) \]

   7. Simplified 61.9%

      \[\leadsto \color{blue}{t \cdot \left(\left(z \cdot i - y2 \cdot y4\right) \cdot c\right)} \]

   if 1.06000000000000001e-213 < y < 1.79999999999999994e74

   1. Initial program 38.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in x around inf 36.3%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in y0 around inf 39.7%

      \[\leadsto x \cdot \color{blue}{\left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 39.7%

         \[\leadsto x \cdot \left(y0 \cdot \left(c \cdot y2 - \color{blue}{j \cdot b}\right)\right) \]

   5. Simplified 39.7%

      \[\leadsto x \cdot \color{blue}{\left(y0 \cdot \left(c \cdot y2 - j \cdot b\right)\right)} \]

   if 1.79999999999999994e74 < y < 4.3999999999999996e152

   1. Initial program 14.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in x around inf 36.8%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in c around inf 65.4%

      \[\leadsto x \cdot \color{blue}{\left(c \cdot \left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 65.4%

         \[\leadsto x \cdot \left(c \cdot \color{blue}{\left(y0 \cdot y2 + -1 \cdot \left(i \cdot y\right)\right)}\right) \]

      2. mul-1-neg 65.4%

         \[\leadsto x \cdot \left(c \cdot \left(y0 \cdot y2 + \color{blue}{\left(-i \cdot y\right)}\right)\right) \]

      3. unsub-neg 65.4%

         \[\leadsto x \cdot \left(c \cdot \color{blue}{\left(y0 \cdot y2 - i \cdot y\right)}\right) \]

      4. *-commutative 65.4%

         \[\leadsto x \cdot \left(c \cdot \left(y0 \cdot y2 - \color{blue}{y \cdot i}\right)\right) \]

   5. Simplified 65.4%

      \[\leadsto x \cdot \color{blue}{\left(c \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)} \]

   if 4.3999999999999996e152 < y < 2.70000000000000008e233

   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. Taylor expanded in b around inf 45.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in y4 around inf 63.9%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 63.9%

         \[\leadsto b \cdot \left(y4 \cdot \left(j \cdot t - \color{blue}{y \cdot k}\right)\right) \]

   5. Simplified 63.9%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - y \cdot k\right)\right)} \]

   if 2.70000000000000008e233 < y

   1. Initial program 17.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around -inf 47.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 47.2%

         \[\leadsto \color{blue}{-a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. distribute-rgt-neg-in 47.2%

         \[\leadsto \color{blue}{a \cdot \left(-\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      3. +-commutative 47.2%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. mul-1-neg 47.2%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-b \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. unsub-neg 47.2%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 47.2%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. *-commutative 47.2%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative 47.2%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   4. Simplified 47.2%

      \[\leadsto \color{blue}{a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(y \cdot x - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   5. Taylor expanded in y around -inf 59.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 59.2%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)} \]

      2. neg-mul-1 59.2%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(y \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right) \]

      3. +-commutative 59.2%

         \[\leadsto \left(-a\right) \cdot \left(y \cdot \color{blue}{\left(y3 \cdot y5 + -1 \cdot \left(b \cdot x\right)\right)}\right) \]

      4. mul-1-neg 59.2%

         \[\leadsto \left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5 + \color{blue}{\left(-b \cdot x\right)}\right)\right) \]

      5. unsub-neg 59.2%

         \[\leadsto \left(-a\right) \cdot \left(y \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]

   7. Simplified 59.2%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)} \]

   8. Taylor expanded in y3 around inf 59.9%

      \[\leadsto \left(-a\right) \cdot \color{blue}{\left(y \cdot \left(y3 \cdot y5\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 60.0%

         \[\leadsto \left(-a\right) \cdot \color{blue}{\left(\left(y \cdot y3\right) \cdot y5\right)} \]

      2. *-commutative 60.0%

         \[\leadsto \left(-a\right) \cdot \left(\color{blue}{\left(y3 \cdot y\right)} \cdot y5\right) \]

      3. associate-*l* 71.3%

         \[\leadsto \left(-a\right) \cdot \color{blue}{\left(y3 \cdot \left(y \cdot y5\right)\right)} \]

   10. Simplified 71.3%

       \[\leadsto \left(-a\right) \cdot \color{blue}{\left(y3 \cdot \left(y \cdot y5\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+54}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{-57}:\\ \;\;\;\;\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0\right)\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-240}:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-306}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{-213}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+152}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+233}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5\right)\right)\\ \end{array} \]

Alternative 20: 31.9% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y2 - z \cdot y3\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+54}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-56}:\\ \;\;\;\;t_1 \cdot \left(c \cdot y0\right)\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-238}:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-306}:\\ \;\;\;\;c \cdot \left(y0 \cdot t_1\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-216}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 10^{+74}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+151}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+221}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* x y2) (* z y3))))
   (if (<= y -5.8e+54)
     (* b (* y (- (* x a) (* k y4))))
     (if (<= y -1.35e-56)
       (* t_1 (* c y0))
       (if (<= y -3.2e-238)
         (* y2 (* c (- (* x y0) (* t y4))))
         (if (<= y -1.6e-306)
           (* c (* y0 t_1))
           (if (<= y 6.5e-216)
             (* t (* c (- (* z i) (* y2 y4))))
             (if (<= y 1e+74)
               (* x (* y0 (- (* c y2) (* b j))))
               (if (<= y 6.5e+151)
                 (* x (* c (- (* y0 y2) (* y i))))
                 (if (<= y 1.45e+221)
                   (* b (* y4 (- (* t j) (* y k))))
                   (* a (* y3 (- (* z y1) (* y y5))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (x * y2) - (z * y3);
	double tmp;
	if (y <= -5.8e+54) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (y <= -1.35e-56) {
		tmp = t_1 * (c * y0);
	} else if (y <= -3.2e-238) {
		tmp = y2 * (c * ((x * y0) - (t * y4)));
	} else if (y <= -1.6e-306) {
		tmp = c * (y0 * t_1);
	} else if (y <= 6.5e-216) {
		tmp = t * (c * ((z * i) - (y2 * y4)));
	} else if (y <= 1e+74) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (y <= 6.5e+151) {
		tmp = x * (c * ((y0 * y2) - (y * i)));
	} else if (y <= 1.45e+221) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y2) - (z * y3)
    if (y <= (-5.8d+54)) then
        tmp = b * (y * ((x * a) - (k * y4)))
    else if (y <= (-1.35d-56)) then
        tmp = t_1 * (c * y0)
    else if (y <= (-3.2d-238)) then
        tmp = y2 * (c * ((x * y0) - (t * y4)))
    else if (y <= (-1.6d-306)) then
        tmp = c * (y0 * t_1)
    else if (y <= 6.5d-216) then
        tmp = t * (c * ((z * i) - (y2 * y4)))
    else if (y <= 1d+74) then
        tmp = x * (y0 * ((c * y2) - (b * j)))
    else if (y <= 6.5d+151) then
        tmp = x * (c * ((y0 * y2) - (y * i)))
    else if (y <= 1.45d+221) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else
        tmp = a * (y3 * ((z * y1) - (y * y5)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (x * y2) - (z * y3);
	double tmp;
	if (y <= -5.8e+54) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (y <= -1.35e-56) {
		tmp = t_1 * (c * y0);
	} else if (y <= -3.2e-238) {
		tmp = y2 * (c * ((x * y0) - (t * y4)));
	} else if (y <= -1.6e-306) {
		tmp = c * (y0 * t_1);
	} else if (y <= 6.5e-216) {
		tmp = t * (c * ((z * i) - (y2 * y4)));
	} else if (y <= 1e+74) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (y <= 6.5e+151) {
		tmp = x * (c * ((y0 * y2) - (y * i)));
	} else if (y <= 1.45e+221) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (x * y2) - (z * y3)
	tmp = 0
	if y <= -5.8e+54:
		tmp = b * (y * ((x * a) - (k * y4)))
	elif y <= -1.35e-56:
		tmp = t_1 * (c * y0)
	elif y <= -3.2e-238:
		tmp = y2 * (c * ((x * y0) - (t * y4)))
	elif y <= -1.6e-306:
		tmp = c * (y0 * t_1)
	elif y <= 6.5e-216:
		tmp = t * (c * ((z * i) - (y2 * y4)))
	elif y <= 1e+74:
		tmp = x * (y0 * ((c * y2) - (b * j)))
	elif y <= 6.5e+151:
		tmp = x * (c * ((y0 * y2) - (y * i)))
	elif y <= 1.45e+221:
		tmp = b * (y4 * ((t * j) - (y * k)))
	else:
		tmp = a * (y3 * ((z * y1) - (y * y5)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(x * y2) - Float64(z * y3))
	tmp = 0.0
	if (y <= -5.8e+54)
		tmp = Float64(b * Float64(y * Float64(Float64(x * a) - Float64(k * y4))));
	elseif (y <= -1.35e-56)
		tmp = Float64(t_1 * Float64(c * y0));
	elseif (y <= -3.2e-238)
		tmp = Float64(y2 * Float64(c * Float64(Float64(x * y0) - Float64(t * y4))));
	elseif (y <= -1.6e-306)
		tmp = Float64(c * Float64(y0 * t_1));
	elseif (y <= 6.5e-216)
		tmp = Float64(t * Float64(c * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (y <= 1e+74)
		tmp = Float64(x * Float64(y0 * Float64(Float64(c * y2) - Float64(b * j))));
	elseif (y <= 6.5e+151)
		tmp = Float64(x * Float64(c * Float64(Float64(y0 * y2) - Float64(y * i))));
	elseif (y <= 1.45e+221)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	else
		tmp = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (x * y2) - (z * y3);
	tmp = 0.0;
	if (y <= -5.8e+54)
		tmp = b * (y * ((x * a) - (k * y4)));
	elseif (y <= -1.35e-56)
		tmp = t_1 * (c * y0);
	elseif (y <= -3.2e-238)
		tmp = y2 * (c * ((x * y0) - (t * y4)));
	elseif (y <= -1.6e-306)
		tmp = c * (y0 * t_1);
	elseif (y <= 6.5e-216)
		tmp = t * (c * ((z * i) - (y2 * y4)));
	elseif (y <= 1e+74)
		tmp = x * (y0 * ((c * y2) - (b * j)));
	elseif (y <= 6.5e+151)
		tmp = x * (c * ((y0 * y2) - (y * i)));
	elseif (y <= 1.45e+221)
		tmp = b * (y4 * ((t * j) - (y * k)));
	else
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.8e+54], N[(b * N[(y * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.35e-56], N[(t$95$1 * N[(c * y0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.2e-238], N[(y2 * N[(c * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.6e-306], N[(c * N[(y0 * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e-216], N[(t * N[(c * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e+74], N[(x * N[(y0 * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e+151], N[(x * N[(c * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.45e+221], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y < -5.7999999999999997e54

   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. Taylor expanded in b around inf 48.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in y around inf 50.6%

      \[\leadsto b \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 50.6%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 50.6%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x + \color{blue}{\left(-k \cdot y4\right)}\right)\right) \]

      3. unsub-neg 50.6%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x - k \cdot y4\right)}\right) \]

      4. *-commutative 50.6%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x - \color{blue}{y4 \cdot k}\right)\right) \]

   5. Simplified 50.6%

      \[\leadsto b \cdot \color{blue}{\left(y \cdot \left(a \cdot x - y4 \cdot k\right)\right)} \]

   if -5.7999999999999997e54 < y < -1.34999999999999997e-56

   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. Taylor expanded in c around inf 46.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 46.1%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 46.1%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 46.1%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 46.1%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 46.1%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 46.1%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 46.1%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 46.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 56.4%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 56.5%

         \[\leadsto \color{blue}{\left(c \cdot y0\right) \cdot \left(x \cdot y2 - y3 \cdot z\right)} \]

      2. *-commutative 56.5%

         \[\leadsto \left(c \cdot y0\right) \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) \]

      3. *-commutative 56.5%

         \[\leadsto \left(c \cdot y0\right) \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) \]

      4. *-commutative 56.5%

         \[\leadsto \color{blue}{\left(y2 \cdot x - z \cdot y3\right) \cdot \left(c \cdot y0\right)} \]

      5. *-commutative 56.5%

         \[\leadsto \left(\color{blue}{x \cdot y2} - z \cdot y3\right) \cdot \left(c \cdot y0\right) \]

      6. *-commutative 56.5%

         \[\leadsto \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) \cdot \left(c \cdot y0\right) \]

   7. Simplified 56.5%

      \[\leadsto \color{blue}{\left(x \cdot y2 - y3 \cdot z\right) \cdot \left(c \cdot y0\right)} \]

   if -1.34999999999999997e-56 < y < -3.2000000000000002e-238

   1. Initial program 21.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 51.5%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 51.5%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 51.5%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 51.5%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 51.5%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 51.5%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 51.5%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 51.5%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 51.5%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y2 around inf 50.9%

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 50.9%

         \[\leadsto \color{blue}{\left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right) \cdot c} \]

      2. associate-*l* 48.3%

         \[\leadsto \color{blue}{y2 \cdot \left(\left(x \cdot y0 - t \cdot y4\right) \cdot c\right)} \]

      3. *-commutative 48.3%

         \[\leadsto y2 \cdot \left(\left(\color{blue}{y0 \cdot x} - t \cdot y4\right) \cdot c\right) \]

   7. Simplified 48.3%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(y0 \cdot x - t \cdot y4\right) \cdot c\right)} \]

   if -3.2000000000000002e-238 < y < -1.59999999999999985e-306

   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. Taylor expanded in c around inf 44.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 44.1%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 44.1%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 44.1%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 44.1%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 44.1%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 44.1%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 44.1%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 44.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 51.0%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   if -1.59999999999999985e-306 < y < 6.4999999999999999e-216

   1. Initial program 61.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 50.5%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 50.5%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 50.5%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 50.5%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 50.5%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 50.5%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 50.5%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 50.5%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 50.5%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in t around -inf 61.9%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(-1 \cdot \left(y2 \cdot y4\right) + i \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 61.9%

         \[\leadsto \color{blue}{\left(t \cdot \left(-1 \cdot \left(y2 \cdot y4\right) + i \cdot z\right)\right) \cdot c} \]

      2. associate-*l* 61.9%

         \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(y2 \cdot y4\right) + i \cdot z\right) \cdot c\right)} \]

      3. +-commutative 61.9%

         \[\leadsto t \cdot \left(\color{blue}{\left(i \cdot z + -1 \cdot \left(y2 \cdot y4\right)\right)} \cdot c\right) \]

      4. mul-1-neg 61.9%

         \[\leadsto t \cdot \left(\left(i \cdot z + \color{blue}{\left(-y2 \cdot y4\right)}\right) \cdot c\right) \]

      5. unsub-neg 61.9%

         \[\leadsto t \cdot \left(\color{blue}{\left(i \cdot z - y2 \cdot y4\right)} \cdot c\right) \]

      6. *-commutative 61.9%

         \[\leadsto t \cdot \left(\left(\color{blue}{z \cdot i} - y2 \cdot y4\right) \cdot c\right) \]

   7. Simplified 61.9%

      \[\leadsto \color{blue}{t \cdot \left(\left(z \cdot i - y2 \cdot y4\right) \cdot c\right)} \]

   if 6.4999999999999999e-216 < y < 9.99999999999999952e73

   1. Initial program 38.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in x around inf 36.3%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in y0 around inf 39.7%

      \[\leadsto x \cdot \color{blue}{\left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 39.7%

         \[\leadsto x \cdot \left(y0 \cdot \left(c \cdot y2 - \color{blue}{j \cdot b}\right)\right) \]

   5. Simplified 39.7%

      \[\leadsto x \cdot \color{blue}{\left(y0 \cdot \left(c \cdot y2 - j \cdot b\right)\right)} \]

   if 9.99999999999999952e73 < y < 6.5000000000000002e151

   1. Initial program 14.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in x around inf 36.8%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in c around inf 65.4%

      \[\leadsto x \cdot \color{blue}{\left(c \cdot \left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 65.4%

         \[\leadsto x \cdot \left(c \cdot \color{blue}{\left(y0 \cdot y2 + -1 \cdot \left(i \cdot y\right)\right)}\right) \]

      2. mul-1-neg 65.4%

         \[\leadsto x \cdot \left(c \cdot \left(y0 \cdot y2 + \color{blue}{\left(-i \cdot y\right)}\right)\right) \]

      3. unsub-neg 65.4%

         \[\leadsto x \cdot \left(c \cdot \color{blue}{\left(y0 \cdot y2 - i \cdot y\right)}\right) \]

      4. *-commutative 65.4%

         \[\leadsto x \cdot \left(c \cdot \left(y0 \cdot y2 - \color{blue}{y \cdot i}\right)\right) \]

   5. Simplified 65.4%

      \[\leadsto x \cdot \color{blue}{\left(c \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)} \]

   if 6.5000000000000002e151 < y < 1.4499999999999999e221

   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. Taylor expanded in b around inf 45.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in y4 around inf 63.9%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 63.9%

         \[\leadsto b \cdot \left(y4 \cdot \left(j \cdot t - \color{blue}{y \cdot k}\right)\right) \]

   5. Simplified 63.9%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - y \cdot k\right)\right)} \]

   if 1.4499999999999999e221 < y

   1. Initial program 17.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around -inf 47.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 47.2%

         \[\leadsto \color{blue}{-a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. distribute-rgt-neg-in 47.2%

         \[\leadsto \color{blue}{a \cdot \left(-\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      3. +-commutative 47.2%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. mul-1-neg 47.2%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-b \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. unsub-neg 47.2%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 47.2%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. *-commutative 47.2%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative 47.2%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   4. Simplified 47.2%

      \[\leadsto \color{blue}{a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(y \cdot x - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   5. Taylor expanded in y3 around -inf 71.3%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 71.3%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]

      2. neg-mul-1 71.3%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right) \]

      3. *-commutative 71.3%

         \[\leadsto \left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - \color{blue}{z \cdot y1}\right)\right) \]

   7. Simplified 71.3%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - z \cdot y1\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+54}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-56}:\\ \;\;\;\;\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0\right)\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-238}:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-306}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-216}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 10^{+74}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+151}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+221}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \end{array} \]

Alternative 21: 29.3% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{if}\;t \leq -9.6 \cdot 10^{+96}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;t \leq -5.4:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-35}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-100}:\\ \;\;\;\;\left(j \cdot y3\right) \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-119}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+145}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+222}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y5 (- (* t y2) (* y y3))))))
   (if (<= t -9.6e+96)
     (* a (* b (- (* x y) (* z t))))
     (if (<= t -3.7e+28)
       (* x (* j (- (* i y1) (* b y0))))
       (if (<= t -5.4)
         t_1
         (if (<= t -6.2e-35)
           (* t (* c (- (* z i) (* y2 y4))))
           (if (<= t -4.2e-100)
             (* (* j y3) (- (* y0 y5) (* y1 y4)))
             (if (<= t 2.6e-119)
               (* c (* y0 (- (* x y2) (* z y3))))
               (if (<= t 6e+145)
                 (* b (* y (- (* x a) (* k y4))))
                 (if (<= t 1.1e+222)
                   (* x (* c (- (* y0 y2) (* y i))))
                   t_1))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y5 * ((t * y2) - (y * y3)));
	double tmp;
	if (t <= -9.6e+96) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (t <= -3.7e+28) {
		tmp = x * (j * ((i * y1) - (b * y0)));
	} else if (t <= -5.4) {
		tmp = t_1;
	} else if (t <= -6.2e-35) {
		tmp = t * (c * ((z * i) - (y2 * y4)));
	} else if (t <= -4.2e-100) {
		tmp = (j * y3) * ((y0 * y5) - (y1 * y4));
	} else if (t <= 2.6e-119) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (t <= 6e+145) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (t <= 1.1e+222) {
		tmp = x * (c * ((y0 * y2) - (y * i)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (y5 * ((t * y2) - (y * y3)))
    if (t <= (-9.6d+96)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (t <= (-3.7d+28)) then
        tmp = x * (j * ((i * y1) - (b * y0)))
    else if (t <= (-5.4d0)) then
        tmp = t_1
    else if (t <= (-6.2d-35)) then
        tmp = t * (c * ((z * i) - (y2 * y4)))
    else if (t <= (-4.2d-100)) then
        tmp = (j * y3) * ((y0 * y5) - (y1 * y4))
    else if (t <= 2.6d-119) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else if (t <= 6d+145) then
        tmp = b * (y * ((x * a) - (k * y4)))
    else if (t <= 1.1d+222) then
        tmp = x * (c * ((y0 * y2) - (y * i)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y5 * ((t * y2) - (y * y3)));
	double tmp;
	if (t <= -9.6e+96) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (t <= -3.7e+28) {
		tmp = x * (j * ((i * y1) - (b * y0)));
	} else if (t <= -5.4) {
		tmp = t_1;
	} else if (t <= -6.2e-35) {
		tmp = t * (c * ((z * i) - (y2 * y4)));
	} else if (t <= -4.2e-100) {
		tmp = (j * y3) * ((y0 * y5) - (y1 * y4));
	} else if (t <= 2.6e-119) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (t <= 6e+145) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (t <= 1.1e+222) {
		tmp = x * (c * ((y0 * y2) - (y * i)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y5 * ((t * y2) - (y * y3)))
	tmp = 0
	if t <= -9.6e+96:
		tmp = a * (b * ((x * y) - (z * t)))
	elif t <= -3.7e+28:
		tmp = x * (j * ((i * y1) - (b * y0)))
	elif t <= -5.4:
		tmp = t_1
	elif t <= -6.2e-35:
		tmp = t * (c * ((z * i) - (y2 * y4)))
	elif t <= -4.2e-100:
		tmp = (j * y3) * ((y0 * y5) - (y1 * y4))
	elif t <= 2.6e-119:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	elif t <= 6e+145:
		tmp = b * (y * ((x * a) - (k * y4)))
	elif t <= 1.1e+222:
		tmp = x * (c * ((y0 * y2) - (y * i)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))
	tmp = 0.0
	if (t <= -9.6e+96)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (t <= -3.7e+28)
		tmp = Float64(x * Float64(j * Float64(Float64(i * y1) - Float64(b * y0))));
	elseif (t <= -5.4)
		tmp = t_1;
	elseif (t <= -6.2e-35)
		tmp = Float64(t * Float64(c * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (t <= -4.2e-100)
		tmp = Float64(Float64(j * y3) * Float64(Float64(y0 * y5) - Float64(y1 * y4)));
	elseif (t <= 2.6e-119)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (t <= 6e+145)
		tmp = Float64(b * Float64(y * Float64(Float64(x * a) - Float64(k * y4))));
	elseif (t <= 1.1e+222)
		tmp = Float64(x * Float64(c * Float64(Float64(y0 * y2) - Float64(y * i))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y5 * ((t * y2) - (y * y3)));
	tmp = 0.0;
	if (t <= -9.6e+96)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (t <= -3.7e+28)
		tmp = x * (j * ((i * y1) - (b * y0)));
	elseif (t <= -5.4)
		tmp = t_1;
	elseif (t <= -6.2e-35)
		tmp = t * (c * ((z * i) - (y2 * y4)));
	elseif (t <= -4.2e-100)
		tmp = (j * y3) * ((y0 * y5) - (y1 * y4));
	elseif (t <= 2.6e-119)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	elseif (t <= 6e+145)
		tmp = b * (y * ((x * a) - (k * y4)));
	elseif (t <= 1.1e+222)
		tmp = x * (c * ((y0 * y2) - (y * i)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.6e+96], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.7e+28], N[(x * N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.4], t$95$1, If[LessEqual[t, -6.2e-35], N[(t * N[(c * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.2e-100], N[(N[(j * y3), $MachinePrecision] * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.6e-119], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e+145], N[(b * N[(y * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.1e+222], N[(x * N[(c * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if t < -9.59999999999999972e96

   1. Initial program 25.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf 37.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in a around inf 45.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if -9.59999999999999972e96 < t < -3.6999999999999999e28

   1. Initial program 14.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in x around inf 38.4%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in j around inf 62.5%

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 62.5%

         \[\leadsto x \cdot \left(j \cdot \left(\color{blue}{y1 \cdot i} - b \cdot y0\right)\right) \]

      2. *-commutative 62.5%

         \[\leadsto x \cdot \left(j \cdot \left(y1 \cdot i - \color{blue}{y0 \cdot b}\right)\right) \]

   5. Simplified 62.5%

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(y1 \cdot i - y0 \cdot b\right)\right)} \]

   if -3.6999999999999999e28 < t < -5.4000000000000004 or 1.1000000000000001e222 < t

   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. Taylor expanded in a around -inf 59.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 59.9%

         \[\leadsto \color{blue}{-a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. distribute-rgt-neg-in 59.9%

         \[\leadsto \color{blue}{a \cdot \left(-\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      3. +-commutative 59.9%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. mul-1-neg 59.9%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-b \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. unsub-neg 59.9%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 59.9%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. *-commutative 59.9%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative 59.9%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   4. Simplified 59.9%

      \[\leadsto \color{blue}{a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(y \cdot x - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   5. Taylor expanded in y5 around inf 64.1%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   if -5.4000000000000004 < t < -6.20000000000000024e-35

   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. Taylor expanded in c around inf 0.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 0.2%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 0.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 0.2%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 0.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 0.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 0.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 0.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 0.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in t around -inf 61.4%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(-1 \cdot \left(y2 \cdot y4\right) + i \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 61.4%

         \[\leadsto \color{blue}{\left(t \cdot \left(-1 \cdot \left(y2 \cdot y4\right) + i \cdot z\right)\right) \cdot c} \]

      2. associate-*l* 61.4%

         \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(y2 \cdot y4\right) + i \cdot z\right) \cdot c\right)} \]

      3. +-commutative 61.4%

         \[\leadsto t \cdot \left(\color{blue}{\left(i \cdot z + -1 \cdot \left(y2 \cdot y4\right)\right)} \cdot c\right) \]

      4. mul-1-neg 61.4%

         \[\leadsto t \cdot \left(\left(i \cdot z + \color{blue}{\left(-y2 \cdot y4\right)}\right) \cdot c\right) \]

      5. unsub-neg 61.4%

         \[\leadsto t \cdot \left(\color{blue}{\left(i \cdot z - y2 \cdot y4\right)} \cdot c\right) \]

      6. *-commutative 61.4%

         \[\leadsto t \cdot \left(\left(\color{blue}{z \cdot i} - y2 \cdot y4\right) \cdot c\right) \]

   7. Simplified 61.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(z \cdot i - y2 \cdot y4\right) \cdot c\right)} \]

   if -6.20000000000000024e-35 < t < -4.20000000000000019e-100

   1. Initial program 49.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y3 around -inf 70.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   3. Taylor expanded in j around inf 60.8%

      \[\leadsto -1 \cdot \color{blue}{\left(j \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 65.5%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

      2. *-commutative 65.5%

         \[\leadsto -1 \cdot \left(\color{blue}{\left(y3 \cdot j\right)} \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) \]

   5. Simplified 65.5%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(y3 \cdot j\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   if -4.20000000000000019e-100 < t < 2.60000000000000012e-119

   1. Initial program 37.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 50.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 50.6%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 50.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 50.6%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 50.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 50.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 50.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 50.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 50.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 47.2%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   if 2.60000000000000012e-119 < t < 6.0000000000000005e145

   1. Initial program 47.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf 46.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in y around inf 46.2%

      \[\leadsto b \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 46.2%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 46.2%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x + \color{blue}{\left(-k \cdot y4\right)}\right)\right) \]

      3. unsub-neg 46.2%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x - k \cdot y4\right)}\right) \]

      4. *-commutative 46.2%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x - \color{blue}{y4 \cdot k}\right)\right) \]

   5. Simplified 46.2%

      \[\leadsto b \cdot \color{blue}{\left(y \cdot \left(a \cdot x - y4 \cdot k\right)\right)} \]

   if 6.0000000000000005e145 < t < 1.1000000000000001e222

   1. Initial program 31.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in x around inf 47.7%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in c around inf 53.5%

      \[\leadsto x \cdot \color{blue}{\left(c \cdot \left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 53.5%

         \[\leadsto x \cdot \left(c \cdot \color{blue}{\left(y0 \cdot y2 + -1 \cdot \left(i \cdot y\right)\right)}\right) \]

      2. mul-1-neg 53.5%

         \[\leadsto x \cdot \left(c \cdot \left(y0 \cdot y2 + \color{blue}{\left(-i \cdot y\right)}\right)\right) \]

      3. unsub-neg 53.5%

         \[\leadsto x \cdot \left(c \cdot \color{blue}{\left(y0 \cdot y2 - i \cdot y\right)}\right) \]

      4. *-commutative 53.5%

         \[\leadsto x \cdot \left(c \cdot \left(y0 \cdot y2 - \color{blue}{y \cdot i}\right)\right) \]

   5. Simplified 53.5%

      \[\leadsto x \cdot \color{blue}{\left(c \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.6 \cdot 10^{+96}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;t \leq -5.4:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-35}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-100}:\\ \;\;\;\;\left(j \cdot y3\right) \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-119}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+145}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+222}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \end{array} \]

Alternative 22: 26.0% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{if}\;t \leq -1.9 \cdot 10^{+77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \left(\left(j \cdot y0\right) \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{-78}:\\ \;\;\;\;\left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-162}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-132}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;t \leq 24000:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+196}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* b (- (* x y) (* z t))))))
   (if (<= t -1.9e+77)
     t_1
     (if (<= t -2.7e+19)
       (* x (* (* j y0) (- b)))
       (if (<= t -3.9e-78)
         (* (- a) (* y (* y3 y5)))
         (if (<= t -6.2e-162)
           (* a (* y3 (* z y1)))
           (if (<= t 3.4e-132)
             (* x (* c (* y0 y2)))
             (if (<= t 24000.0)
               (* a (* y1 (- (* z y3) (* x y2))))
               (if (<= t 4.5e+196)
                 t_1
                 (* a (* y5 (- (* t y2) (* y y3)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (b * ((x * y) - (z * t)));
	double tmp;
	if (t <= -1.9e+77) {
		tmp = t_1;
	} else if (t <= -2.7e+19) {
		tmp = x * ((j * y0) * -b);
	} else if (t <= -3.9e-78) {
		tmp = -a * (y * (y3 * y5));
	} else if (t <= -6.2e-162) {
		tmp = a * (y3 * (z * y1));
	} else if (t <= 3.4e-132) {
		tmp = x * (c * (y0 * y2));
	} else if (t <= 24000.0) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (t <= 4.5e+196) {
		tmp = t_1;
	} else {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (b * ((x * y) - (z * t)))
    if (t <= (-1.9d+77)) then
        tmp = t_1
    else if (t <= (-2.7d+19)) then
        tmp = x * ((j * y0) * -b)
    else if (t <= (-3.9d-78)) then
        tmp = -a * (y * (y3 * y5))
    else if (t <= (-6.2d-162)) then
        tmp = a * (y3 * (z * y1))
    else if (t <= 3.4d-132) then
        tmp = x * (c * (y0 * y2))
    else if (t <= 24000.0d0) then
        tmp = a * (y1 * ((z * y3) - (x * y2)))
    else if (t <= 4.5d+196) then
        tmp = t_1
    else
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (b * ((x * y) - (z * t)));
	double tmp;
	if (t <= -1.9e+77) {
		tmp = t_1;
	} else if (t <= -2.7e+19) {
		tmp = x * ((j * y0) * -b);
	} else if (t <= -3.9e-78) {
		tmp = -a * (y * (y3 * y5));
	} else if (t <= -6.2e-162) {
		tmp = a * (y3 * (z * y1));
	} else if (t <= 3.4e-132) {
		tmp = x * (c * (y0 * y2));
	} else if (t <= 24000.0) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (t <= 4.5e+196) {
		tmp = t_1;
	} else {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (b * ((x * y) - (z * t)))
	tmp = 0
	if t <= -1.9e+77:
		tmp = t_1
	elif t <= -2.7e+19:
		tmp = x * ((j * y0) * -b)
	elif t <= -3.9e-78:
		tmp = -a * (y * (y3 * y5))
	elif t <= -6.2e-162:
		tmp = a * (y3 * (z * y1))
	elif t <= 3.4e-132:
		tmp = x * (c * (y0 * y2))
	elif t <= 24000.0:
		tmp = a * (y1 * ((z * y3) - (x * y2)))
	elif t <= 4.5e+196:
		tmp = t_1
	else:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))))
	tmp = 0.0
	if (t <= -1.9e+77)
		tmp = t_1;
	elseif (t <= -2.7e+19)
		tmp = Float64(x * Float64(Float64(j * y0) * Float64(-b)));
	elseif (t <= -3.9e-78)
		tmp = Float64(Float64(-a) * Float64(y * Float64(y3 * y5)));
	elseif (t <= -6.2e-162)
		tmp = Float64(a * Float64(y3 * Float64(z * y1)));
	elseif (t <= 3.4e-132)
		tmp = Float64(x * Float64(c * Float64(y0 * y2)));
	elseif (t <= 24000.0)
		tmp = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))));
	elseif (t <= 4.5e+196)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (b * ((x * y) - (z * t)));
	tmp = 0.0;
	if (t <= -1.9e+77)
		tmp = t_1;
	elseif (t <= -2.7e+19)
		tmp = x * ((j * y0) * -b);
	elseif (t <= -3.9e-78)
		tmp = -a * (y * (y3 * y5));
	elseif (t <= -6.2e-162)
		tmp = a * (y3 * (z * y1));
	elseif (t <= 3.4e-132)
		tmp = x * (c * (y0 * y2));
	elseif (t <= 24000.0)
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	elseif (t <= 4.5e+196)
		tmp = t_1;
	else
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.9e+77], t$95$1, If[LessEqual[t, -2.7e+19], N[(x * N[(N[(j * y0), $MachinePrecision] * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.9e-78], N[((-a) * N[(y * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.2e-162], N[(a * N[(y3 * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.4e-132], N[(x * N[(c * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 24000.0], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e+196], t$95$1, N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -1.9000000000000001e77 or 24000 < t < 4.49999999999999978e196

   1. Initial program 30.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf 43.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in a around inf 41.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if -1.9000000000000001e77 < t < -2.7e19

   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. Taylor expanded in x around inf 39.2%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in j around inf 56.3%

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 56.3%

         \[\leadsto x \cdot \left(j \cdot \left(\color{blue}{y1 \cdot i} - b \cdot y0\right)\right) \]

      2. *-commutative 56.3%

         \[\leadsto x \cdot \left(j \cdot \left(y1 \cdot i - \color{blue}{y0 \cdot b}\right)\right) \]

   5. Simplified 56.3%

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(y1 \cdot i - y0 \cdot b\right)\right)} \]

   6. Taylor expanded in y1 around 0 40.8%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(b \cdot \left(j \cdot y0\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 40.8%

         \[\leadsto x \cdot \color{blue}{\left(\left(-1 \cdot b\right) \cdot \left(j \cdot y0\right)\right)} \]

      2. neg-mul-1 40.8%

         \[\leadsto x \cdot \left(\color{blue}{\left(-b\right)} \cdot \left(j \cdot y0\right)\right) \]

      3. *-commutative 40.8%

         \[\leadsto x \cdot \left(\left(-b\right) \cdot \color{blue}{\left(y0 \cdot j\right)}\right) \]

   8. Simplified 40.8%

      \[\leadsto x \cdot \color{blue}{\left(\left(-b\right) \cdot \left(y0 \cdot j\right)\right)} \]

   if -2.7e19 < t < -3.9000000000000002e-78

   1. Initial program 37.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around -inf 30.5%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 30.5%

         \[\leadsto \color{blue}{-a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. distribute-rgt-neg-in 30.5%

         \[\leadsto \color{blue}{a \cdot \left(-\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      3. +-commutative 30.5%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. mul-1-neg 30.5%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-b \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. unsub-neg 30.5%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 30.5%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. *-commutative 30.5%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative 30.5%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   4. Simplified 30.5%

      \[\leadsto \color{blue}{a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(y \cdot x - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   5. Taylor expanded in y around -inf 35.4%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 35.4%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)} \]

      2. neg-mul-1 35.4%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(y \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right) \]

      3. +-commutative 35.4%

         \[\leadsto \left(-a\right) \cdot \left(y \cdot \color{blue}{\left(y3 \cdot y5 + -1 \cdot \left(b \cdot x\right)\right)}\right) \]

      4. mul-1-neg 35.4%

         \[\leadsto \left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5 + \color{blue}{\left(-b \cdot x\right)}\right)\right) \]

      5. unsub-neg 35.4%

         \[\leadsto \left(-a\right) \cdot \left(y \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]

   7. Simplified 35.4%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)} \]

   8. Taylor expanded in y3 around inf 35.1%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 35.1%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)} \]

      2. neg-mul-1 35.1%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(y \cdot \left(y3 \cdot y5\right)\right) \]

   10. Simplified 35.1%

       \[\leadsto \color{blue}{\left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)} \]

   if -3.9000000000000002e-78 < t < -6.1999999999999997e-162

   1. Initial program 41.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around -inf 41.8%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 41.8%

         \[\leadsto \color{blue}{-a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. distribute-rgt-neg-in 41.8%

         \[\leadsto \color{blue}{a \cdot \left(-\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      3. +-commutative 41.8%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. mul-1-neg 41.8%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-b \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. unsub-neg 41.8%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 41.8%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. *-commutative 41.8%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative 41.8%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   4. Simplified 41.8%

      \[\leadsto \color{blue}{a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(y \cdot x - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   5. Taylor expanded in y3 around -inf 53.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 53.2%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]

      2. neg-mul-1 53.2%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right) \]

      3. *-commutative 53.2%

         \[\leadsto \left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - \color{blue}{z \cdot y1}\right)\right) \]

   7. Simplified 53.2%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - z \cdot y1\right)\right)} \]

   8. Taylor expanded in y around 0 36.6%

      \[\leadsto \left(-a\right) \cdot \left(y3 \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot z\right)\right)}\right) \]
   9. Step-by-step derivation

      1. mul-1-neg 36.6%

         \[\leadsto \left(-a\right) \cdot \left(y3 \cdot \color{blue}{\left(-y1 \cdot z\right)}\right) \]

      2. *-commutative 36.6%

         \[\leadsto \left(-a\right) \cdot \left(y3 \cdot \left(-\color{blue}{z \cdot y1}\right)\right) \]

      3. distribute-rgt-neg-in 36.6%

         \[\leadsto \left(-a\right) \cdot \left(y3 \cdot \color{blue}{\left(z \cdot \left(-y1\right)\right)}\right) \]

   10. Simplified 36.6%

       \[\leadsto \left(-a\right) \cdot \left(y3 \cdot \color{blue}{\left(z \cdot \left(-y1\right)\right)}\right) \]

   if -6.1999999999999997e-162 < t < 3.39999999999999983e-132

   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. Taylor expanded in c around inf 51.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 51.4%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 51.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 51.4%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 51.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 51.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 51.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 51.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 51.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 49.2%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 37.2%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 37.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y0 \cdot y2\right)\right) \cdot c} \]

      2. associate-*l* 39.1%

         \[\leadsto \color{blue}{x \cdot \left(\left(y0 \cdot y2\right) \cdot c\right)} \]

   8. Simplified 39.1%

      \[\leadsto \color{blue}{x \cdot \left(\left(y0 \cdot y2\right) \cdot c\right)} \]

   if 3.39999999999999983e-132 < t < 24000

   1. Initial program 54.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around -inf 28.7%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 28.7%

         \[\leadsto \color{blue}{-a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. distribute-rgt-neg-in 28.7%

         \[\leadsto \color{blue}{a \cdot \left(-\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      3. +-commutative 28.7%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. mul-1-neg 28.7%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-b \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. unsub-neg 28.7%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 28.7%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. *-commutative 28.7%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative 28.7%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   4. Simplified 28.7%

      \[\leadsto \color{blue}{a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(y \cdot x - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   5. Taylor expanded in y1 around inf 37.4%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

   if 4.49999999999999978e196 < t

   1. Initial program 34.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around -inf 50.4%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 50.4%

         \[\leadsto \color{blue}{-a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. distribute-rgt-neg-in 50.4%

         \[\leadsto \color{blue}{a \cdot \left(-\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      3. +-commutative 50.4%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. mul-1-neg 50.4%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-b \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. unsub-neg 50.4%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 50.4%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. *-commutative 50.4%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative 50.4%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   4. Simplified 50.4%

      \[\leadsto \color{blue}{a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(y \cdot x - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   5. Taylor expanded in y5 around inf 54.8%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+77}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \left(\left(j \cdot y0\right) \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{-78}:\\ \;\;\;\;\left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-162}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-132}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;t \leq 24000:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+196}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \end{array} \]

Alternative 23: 27.4% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ t_2 := b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ t_3 := a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{if}\;y2 \leq -4.5 \cdot 10^{+127}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq -1.15 \cdot 10^{-47}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y2 \leq -1.65 \cdot 10^{-81}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y2 \leq 4.2 \cdot 10^{-288}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y2 \leq 1.55 \cdot 10^{+91}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y2 \leq 1.05 \cdot 10^{+128}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq 2.15 \cdot 10^{+275}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* x (* c (* y0 y2))))
        (t_2 (* b (* y (- (* x a) (* k y4)))))
        (t_3 (* a (* y5 (- (* t y2) (* y y3))))))
   (if (<= y2 -4.5e+127)
     t_1
     (if (<= y2 -1.15e-47)
       t_3
       (if (<= y2 -1.65e-81)
         t_2
         (if (<= y2 4.2e-288)
           t_3
           (if (<= y2 1.55e+91)
             t_2
             (if (<= y2 1.05e+128)
               t_1
               (if (<= y2 2.15e+275)
                 (* a (* y1 (- (* z y3) (* x y2))))
                 (* c (* x (* y0 y2))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = x * (c * (y0 * y2));
	double t_2 = b * (y * ((x * a) - (k * y4)));
	double t_3 = a * (y5 * ((t * y2) - (y * y3)));
	double tmp;
	if (y2 <= -4.5e+127) {
		tmp = t_1;
	} else if (y2 <= -1.15e-47) {
		tmp = t_3;
	} else if (y2 <= -1.65e-81) {
		tmp = t_2;
	} else if (y2 <= 4.2e-288) {
		tmp = t_3;
	} else if (y2 <= 1.55e+91) {
		tmp = t_2;
	} else if (y2 <= 1.05e+128) {
		tmp = t_1;
	} else if (y2 <= 2.15e+275) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else {
		tmp = c * (x * (y0 * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * (c * (y0 * y2))
    t_2 = b * (y * ((x * a) - (k * y4)))
    t_3 = a * (y5 * ((t * y2) - (y * y3)))
    if (y2 <= (-4.5d+127)) then
        tmp = t_1
    else if (y2 <= (-1.15d-47)) then
        tmp = t_3
    else if (y2 <= (-1.65d-81)) then
        tmp = t_2
    else if (y2 <= 4.2d-288) then
        tmp = t_3
    else if (y2 <= 1.55d+91) then
        tmp = t_2
    else if (y2 <= 1.05d+128) then
        tmp = t_1
    else if (y2 <= 2.15d+275) then
        tmp = a * (y1 * ((z * y3) - (x * y2)))
    else
        tmp = c * (x * (y0 * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = x * (c * (y0 * y2));
	double t_2 = b * (y * ((x * a) - (k * y4)));
	double t_3 = a * (y5 * ((t * y2) - (y * y3)));
	double tmp;
	if (y2 <= -4.5e+127) {
		tmp = t_1;
	} else if (y2 <= -1.15e-47) {
		tmp = t_3;
	} else if (y2 <= -1.65e-81) {
		tmp = t_2;
	} else if (y2 <= 4.2e-288) {
		tmp = t_3;
	} else if (y2 <= 1.55e+91) {
		tmp = t_2;
	} else if (y2 <= 1.05e+128) {
		tmp = t_1;
	} else if (y2 <= 2.15e+275) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else {
		tmp = c * (x * (y0 * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = x * (c * (y0 * y2))
	t_2 = b * (y * ((x * a) - (k * y4)))
	t_3 = a * (y5 * ((t * y2) - (y * y3)))
	tmp = 0
	if y2 <= -4.5e+127:
		tmp = t_1
	elif y2 <= -1.15e-47:
		tmp = t_3
	elif y2 <= -1.65e-81:
		tmp = t_2
	elif y2 <= 4.2e-288:
		tmp = t_3
	elif y2 <= 1.55e+91:
		tmp = t_2
	elif y2 <= 1.05e+128:
		tmp = t_1
	elif y2 <= 2.15e+275:
		tmp = a * (y1 * ((z * y3) - (x * y2)))
	else:
		tmp = c * (x * (y0 * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(x * Float64(c * Float64(y0 * y2)))
	t_2 = Float64(b * Float64(y * Float64(Float64(x * a) - Float64(k * y4))))
	t_3 = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))
	tmp = 0.0
	if (y2 <= -4.5e+127)
		tmp = t_1;
	elseif (y2 <= -1.15e-47)
		tmp = t_3;
	elseif (y2 <= -1.65e-81)
		tmp = t_2;
	elseif (y2 <= 4.2e-288)
		tmp = t_3;
	elseif (y2 <= 1.55e+91)
		tmp = t_2;
	elseif (y2 <= 1.05e+128)
		tmp = t_1;
	elseif (y2 <= 2.15e+275)
		tmp = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))));
	else
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = x * (c * (y0 * y2));
	t_2 = b * (y * ((x * a) - (k * y4)));
	t_3 = a * (y5 * ((t * y2) - (y * y3)));
	tmp = 0.0;
	if (y2 <= -4.5e+127)
		tmp = t_1;
	elseif (y2 <= -1.15e-47)
		tmp = t_3;
	elseif (y2 <= -1.65e-81)
		tmp = t_2;
	elseif (y2 <= 4.2e-288)
		tmp = t_3;
	elseif (y2 <= 1.55e+91)
		tmp = t_2;
	elseif (y2 <= 1.05e+128)
		tmp = t_1;
	elseif (y2 <= 2.15e+275)
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	else
		tmp = c * (x * (y0 * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(x * N[(c * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(y * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -4.5e+127], t$95$1, If[LessEqual[y2, -1.15e-47], t$95$3, If[LessEqual[y2, -1.65e-81], t$95$2, If[LessEqual[y2, 4.2e-288], t$95$3, If[LessEqual[y2, 1.55e+91], t$95$2, If[LessEqual[y2, 1.05e+128], t$95$1, If[LessEqual[y2, 2.15e+275], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y2 < -4.50000000000000034e127 or 1.54999999999999999e91 < y2 < 1.05e128

   1. Initial program 22.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 50.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 50.8%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 50.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 50.8%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 50.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 50.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 50.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 50.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 50.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 51.4%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 53.2%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 53.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y0 \cdot y2\right)\right) \cdot c} \]

      2. associate-*l* 57.9%

         \[\leadsto \color{blue}{x \cdot \left(\left(y0 \cdot y2\right) \cdot c\right)} \]

   8. Simplified 57.9%

      \[\leadsto \color{blue}{x \cdot \left(\left(y0 \cdot y2\right) \cdot c\right)} \]

   if -4.50000000000000034e127 < y2 < -1.14999999999999991e-47 or -1.64999999999999994e-81 < y2 < 4.19999999999999991e-288

   1. Initial program 41.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around -inf 40.4%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 40.4%

         \[\leadsto \color{blue}{-a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. distribute-rgt-neg-in 40.4%

         \[\leadsto \color{blue}{a \cdot \left(-\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      3. +-commutative 40.4%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. mul-1-neg 40.4%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-b \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. unsub-neg 40.4%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 40.4%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. *-commutative 40.4%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative 40.4%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   4. Simplified 40.4%

      \[\leadsto \color{blue}{a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(y \cdot x - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   5. Taylor expanded in y5 around inf 36.6%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   if -1.14999999999999991e-47 < y2 < -1.64999999999999994e-81 or 4.19999999999999991e-288 < y2 < 1.54999999999999999e91

   1. Initial program 36.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf 38.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in y around inf 36.3%

      \[\leadsto b \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 36.3%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 36.3%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x + \color{blue}{\left(-k \cdot y4\right)}\right)\right) \]

      3. unsub-neg 36.3%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x - k \cdot y4\right)}\right) \]

      4. *-commutative 36.3%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x - \color{blue}{y4 \cdot k}\right)\right) \]

   5. Simplified 36.3%

      \[\leadsto b \cdot \color{blue}{\left(y \cdot \left(a \cdot x - y4 \cdot k\right)\right)} \]

   if 1.05e128 < y2 < 2.15000000000000001e275

   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. Taylor expanded in a around -inf 43.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 43.9%

         \[\leadsto \color{blue}{-a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. distribute-rgt-neg-in 43.9%

         \[\leadsto \color{blue}{a \cdot \left(-\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      3. +-commutative 43.9%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. mul-1-neg 43.9%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-b \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. unsub-neg 43.9%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 43.9%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. *-commutative 43.9%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative 43.9%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   4. Simplified 43.9%

      \[\leadsto \color{blue}{a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(y \cdot x - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   5. Taylor expanded in y1 around inf 48.2%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

   if 2.15000000000000001e275 < y2

   1. Initial program 7.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 53.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 53.8%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 53.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 53.8%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 53.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 53.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 53.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 53.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 53.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 84.7%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 77.4%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 43.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -4.5 \cdot 10^{+127}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -1.15 \cdot 10^{-47}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq -1.65 \cdot 10^{-81}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 4.2 \cdot 10^{-288}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 1.55 \cdot 10^{+91}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 1.05 \cdot 10^{+128}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 2.15 \cdot 10^{+275}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \end{array} \]

Alternative 24: 21.4% accurate, 3.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(z \cdot y3\right) \cdot \left(-y0\right)\right)\\ t_2 := x \cdot \left(j \cdot \left(b \cdot \left(-y0\right)\right)\right)\\ \mathbf{if}\;y3 \leq -1.22 \cdot 10^{+253}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y3 \leq -1.05 \cdot 10^{+93}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{elif}\;y3 \leq -1.28 \cdot 10^{-138}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y3 \leq 6.6 \cdot 10^{-245}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 1.5 \cdot 10^{-107}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y3 \leq 1.9 \cdot 10^{+61}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 1.1 \cdot 10^{+98}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;y3 \leq 4.3 \cdot 10^{+212}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* (* z y3) (- y0)))) (t_2 (* x (* j (* b (- y0))))))
   (if (<= y3 -1.22e+253)
     t_1
     (if (<= y3 -1.05e+93)
       (* a (* y1 (* z y3)))
       (if (<= y3 -1.28e-138)
         t_2
         (if (<= y3 6.6e-245)
           (* c (* x (* y0 y2)))
           (if (<= y3 1.5e-107)
             t_2
             (if (<= y3 1.9e+61)
               (* c (* y0 (* x y2)))
               (if (<= y3 1.1e+98)
                 (* a (* y (* x b)))
                 (if (<= y3 4.3e+212) (* x (* c (* y0 y2))) t_1))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * ((z * y3) * -y0);
	double t_2 = x * (j * (b * -y0));
	double tmp;
	if (y3 <= -1.22e+253) {
		tmp = t_1;
	} else if (y3 <= -1.05e+93) {
		tmp = a * (y1 * (z * y3));
	} else if (y3 <= -1.28e-138) {
		tmp = t_2;
	} else if (y3 <= 6.6e-245) {
		tmp = c * (x * (y0 * y2));
	} else if (y3 <= 1.5e-107) {
		tmp = t_2;
	} else if (y3 <= 1.9e+61) {
		tmp = c * (y0 * (x * y2));
	} else if (y3 <= 1.1e+98) {
		tmp = a * (y * (x * b));
	} else if (y3 <= 4.3e+212) {
		tmp = x * (c * (y0 * y2));
	} 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 = c * ((z * y3) * -y0)
    t_2 = x * (j * (b * -y0))
    if (y3 <= (-1.22d+253)) then
        tmp = t_1
    else if (y3 <= (-1.05d+93)) then
        tmp = a * (y1 * (z * y3))
    else if (y3 <= (-1.28d-138)) then
        tmp = t_2
    else if (y3 <= 6.6d-245) then
        tmp = c * (x * (y0 * y2))
    else if (y3 <= 1.5d-107) then
        tmp = t_2
    else if (y3 <= 1.9d+61) then
        tmp = c * (y0 * (x * y2))
    else if (y3 <= 1.1d+98) then
        tmp = a * (y * (x * b))
    else if (y3 <= 4.3d+212) then
        tmp = x * (c * (y0 * y2))
    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 = c * ((z * y3) * -y0);
	double t_2 = x * (j * (b * -y0));
	double tmp;
	if (y3 <= -1.22e+253) {
		tmp = t_1;
	} else if (y3 <= -1.05e+93) {
		tmp = a * (y1 * (z * y3));
	} else if (y3 <= -1.28e-138) {
		tmp = t_2;
	} else if (y3 <= 6.6e-245) {
		tmp = c * (x * (y0 * y2));
	} else if (y3 <= 1.5e-107) {
		tmp = t_2;
	} else if (y3 <= 1.9e+61) {
		tmp = c * (y0 * (x * y2));
	} else if (y3 <= 1.1e+98) {
		tmp = a * (y * (x * b));
	} else if (y3 <= 4.3e+212) {
		tmp = x * (c * (y0 * y2));
	} 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 = c * ((z * y3) * -y0)
	t_2 = x * (j * (b * -y0))
	tmp = 0
	if y3 <= -1.22e+253:
		tmp = t_1
	elif y3 <= -1.05e+93:
		tmp = a * (y1 * (z * y3))
	elif y3 <= -1.28e-138:
		tmp = t_2
	elif y3 <= 6.6e-245:
		tmp = c * (x * (y0 * y2))
	elif y3 <= 1.5e-107:
		tmp = t_2
	elif y3 <= 1.9e+61:
		tmp = c * (y0 * (x * y2))
	elif y3 <= 1.1e+98:
		tmp = a * (y * (x * b))
	elif y3 <= 4.3e+212:
		tmp = x * (c * (y0 * y2))
	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(c * Float64(Float64(z * y3) * Float64(-y0)))
	t_2 = Float64(x * Float64(j * Float64(b * Float64(-y0))))
	tmp = 0.0
	if (y3 <= -1.22e+253)
		tmp = t_1;
	elseif (y3 <= -1.05e+93)
		tmp = Float64(a * Float64(y1 * Float64(z * y3)));
	elseif (y3 <= -1.28e-138)
		tmp = t_2;
	elseif (y3 <= 6.6e-245)
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	elseif (y3 <= 1.5e-107)
		tmp = t_2;
	elseif (y3 <= 1.9e+61)
		tmp = Float64(c * Float64(y0 * Float64(x * y2)));
	elseif (y3 <= 1.1e+98)
		tmp = Float64(a * Float64(y * Float64(x * b)));
	elseif (y3 <= 4.3e+212)
		tmp = Float64(x * Float64(c * Float64(y0 * y2)));
	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 = c * ((z * y3) * -y0);
	t_2 = x * (j * (b * -y0));
	tmp = 0.0;
	if (y3 <= -1.22e+253)
		tmp = t_1;
	elseif (y3 <= -1.05e+93)
		tmp = a * (y1 * (z * y3));
	elseif (y3 <= -1.28e-138)
		tmp = t_2;
	elseif (y3 <= 6.6e-245)
		tmp = c * (x * (y0 * y2));
	elseif (y3 <= 1.5e-107)
		tmp = t_2;
	elseif (y3 <= 1.9e+61)
		tmp = c * (y0 * (x * y2));
	elseif (y3 <= 1.1e+98)
		tmp = a * (y * (x * b));
	elseif (y3 <= 4.3e+212)
		tmp = x * (c * (y0 * y2));
	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[(c * N[(N[(z * y3), $MachinePrecision] * (-y0)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(j * N[(b * (-y0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -1.22e+253], t$95$1, If[LessEqual[y3, -1.05e+93], N[(a * N[(y1 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -1.28e-138], t$95$2, If[LessEqual[y3, 6.6e-245], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.5e-107], t$95$2, If[LessEqual[y3, 1.9e+61], N[(c * N[(y0 * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.1e+98], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 4.3e+212], N[(x * N[(c * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y3 < -1.21999999999999994e253 or 4.2999999999999996e212 < y3

   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. Taylor expanded in c around inf 46.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 46.8%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 46.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 46.8%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 46.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 46.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 46.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 46.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 46.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 54.2%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   6. Taylor expanded in x around 0 54.4%

      \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 54.4%

         \[\leadsto c \cdot \color{blue}{\left(-y0 \cdot \left(y3 \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 54.4%

         \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(-y3 \cdot z\right)\right)} \]

      3. distribute-lft-neg-in 54.4%

         \[\leadsto c \cdot \left(y0 \cdot \color{blue}{\left(\left(-y3\right) \cdot z\right)}\right) \]

      4. *-commutative 54.4%

         \[\leadsto c \cdot \left(y0 \cdot \color{blue}{\left(z \cdot \left(-y3\right)\right)}\right) \]

   8. Simplified 54.4%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(z \cdot \left(-y3\right)\right)\right)} \]

   if -1.21999999999999994e253 < y3 < -1.0499999999999999e93

   1. Initial program 28.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around -inf 33.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 33.9%

         \[\leadsto \color{blue}{-a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. distribute-rgt-neg-in 33.9%

         \[\leadsto \color{blue}{a \cdot \left(-\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      3. +-commutative 33.9%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. mul-1-neg 33.9%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-b \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. unsub-neg 33.9%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 33.9%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. *-commutative 33.9%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative 33.9%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   4. Simplified 33.9%

      \[\leadsto \color{blue}{a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(y \cdot x - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   5. Taylor expanded in y3 around -inf 43.0%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 43.0%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]

      2. neg-mul-1 43.0%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right) \]

      3. *-commutative 43.0%

         \[\leadsto \left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - \color{blue}{z \cdot y1}\right)\right) \]

   7. Simplified 43.0%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - z \cdot y1\right)\right)} \]

   8. Taylor expanded in y around 0 40.7%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]

   if -1.0499999999999999e93 < y3 < -1.28e-138 or 6.6000000000000002e-245 < y3 < 1.4999999999999999e-107

   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. Taylor expanded in x around inf 42.9%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in j around inf 40.3%

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 40.3%

         \[\leadsto x \cdot \left(j \cdot \left(\color{blue}{y1 \cdot i} - b \cdot y0\right)\right) \]

      2. *-commutative 40.3%

         \[\leadsto x \cdot \left(j \cdot \left(y1 \cdot i - \color{blue}{y0 \cdot b}\right)\right) \]

   5. Simplified 40.3%

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(y1 \cdot i - y0 \cdot b\right)\right)} \]

   6. Taylor expanded in y1 around 0 39.1%

      \[\leadsto x \cdot \left(j \cdot \color{blue}{\left(-1 \cdot \left(b \cdot y0\right)\right)}\right) \]
   7. Step-by-step derivation

      1. mul-1-neg 39.1%

         \[\leadsto x \cdot \left(j \cdot \color{blue}{\left(-b \cdot y0\right)}\right) \]

      2. *-commutative 39.1%

         \[\leadsto x \cdot \left(j \cdot \left(-\color{blue}{y0 \cdot b}\right)\right) \]

      3. distribute-rgt-neg-in 39.1%

         \[\leadsto x \cdot \left(j \cdot \color{blue}{\left(y0 \cdot \left(-b\right)\right)}\right) \]

   8. Simplified 39.1%

      \[\leadsto x \cdot \left(j \cdot \color{blue}{\left(y0 \cdot \left(-b\right)\right)}\right) \]

   if -1.28e-138 < y3 < 6.6000000000000002e-245

   1. Initial program 43.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 41.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 41.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 41.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 41.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 41.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 41.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 41.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 41.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 41.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 25.4%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 25.2%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]

   if 1.4999999999999999e-107 < y3 < 1.89999999999999998e61

   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. Taylor expanded in c around inf 52.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 52.7%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 52.7%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 52.7%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 52.7%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 52.7%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 52.7%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 52.7%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 52.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 48.9%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 39.4%

      \[\leadsto c \cdot \color{blue}{\left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 41.8%

         \[\leadsto c \cdot \color{blue}{\left(\left(x \cdot y0\right) \cdot y2\right)} \]

      2. *-commutative 41.8%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot x\right)} \cdot y2\right) \]

      3. associate-*r* 39.4%

         \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2\right)\right)} \]

   8. Simplified 39.4%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2\right)\right)} \]

   if 1.89999999999999998e61 < y3 < 1.10000000000000004e98

   1. Initial program 54.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf 73.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in a around inf 47.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   4. Taylor expanded in x around inf 38.2%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 55.6%

         \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot x\right) \cdot y\right)} \]

      2. *-commutative 55.6%

         \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot b\right)} \cdot y\right) \]

      3. associate-*l* 38.1%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

   6. Simplified 38.1%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

   7. Taylor expanded in x around 0 38.2%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 38.2%

         \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot b\right)} \]

      2. *-commutative 38.2%

         \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot b\right) \]

      3. associate-*l* 55.6%

         \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(x \cdot b\right)\right)} \]

   9. Simplified 55.6%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(x \cdot b\right)\right)} \]

   if 1.10000000000000004e98 < y3 < 4.2999999999999996e212

   1. Initial program 35.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 31.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 31.0%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 31.0%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 31.0%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 31.0%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 31.0%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 31.0%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 31.0%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 31.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 27.5%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 27.5%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 27.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y0 \cdot y2\right)\right) \cdot c} \]

      2. associate-*l* 31.7%

         \[\leadsto \color{blue}{x \cdot \left(\left(y0 \cdot y2\right) \cdot c\right)} \]

   8. Simplified 31.7%

      \[\leadsto \color{blue}{x \cdot \left(\left(y0 \cdot y2\right) \cdot c\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -1.22 \cdot 10^{+253}:\\ \;\;\;\;c \cdot \left(\left(z \cdot y3\right) \cdot \left(-y0\right)\right)\\ \mathbf{elif}\;y3 \leq -1.05 \cdot 10^{+93}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{elif}\;y3 \leq -1.28 \cdot 10^{-138}:\\ \;\;\;\;x \cdot \left(j \cdot \left(b \cdot \left(-y0\right)\right)\right)\\ \mathbf{elif}\;y3 \leq 6.6 \cdot 10^{-245}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 1.5 \cdot 10^{-107}:\\ \;\;\;\;x \cdot \left(j \cdot \left(b \cdot \left(-y0\right)\right)\right)\\ \mathbf{elif}\;y3 \leq 1.9 \cdot 10^{+61}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 1.1 \cdot 10^{+98}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;y3 \leq 4.3 \cdot 10^{+212}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(z \cdot y3\right) \cdot \left(-y0\right)\right)\\ \end{array} \]

Alternative 25: 21.4% accurate, 3.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(z \cdot y3\right) \cdot \left(-y0\right)\right)\\ \mathbf{if}\;y3 \leq -2.3 \cdot 10^{+253}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y3 \leq -9.8 \cdot 10^{+92}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{elif}\;y3 \leq -7.2 \cdot 10^{-135}:\\ \;\;\;\;x \cdot \left(j \cdot \left(b \cdot \left(-y0\right)\right)\right)\\ \mathbf{elif}\;y3 \leq 1.55 \cdot 10^{-252}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 2.4 \cdot 10^{-107}:\\ \;\;\;\;x \cdot \left(\left(j \cdot y0\right) \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y3 \leq 4 \cdot 10^{+61}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 2.25 \cdot 10^{+98}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;y3 \leq 5.1 \cdot 10^{+212}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* (* z y3) (- y0)))))
   (if (<= y3 -2.3e+253)
     t_1
     (if (<= y3 -9.8e+92)
       (* a (* y1 (* z y3)))
       (if (<= y3 -7.2e-135)
         (* x (* j (* b (- y0))))
         (if (<= y3 1.55e-252)
           (* c (* x (* y0 y2)))
           (if (<= y3 2.4e-107)
             (* x (* (* j y0) (- b)))
             (if (<= y3 4e+61)
               (* c (* y0 (* x y2)))
               (if (<= y3 2.25e+98)
                 (* a (* y (* x b)))
                 (if (<= y3 5.1e+212) (* x (* c (* y0 y2))) t_1))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * ((z * y3) * -y0);
	double tmp;
	if (y3 <= -2.3e+253) {
		tmp = t_1;
	} else if (y3 <= -9.8e+92) {
		tmp = a * (y1 * (z * y3));
	} else if (y3 <= -7.2e-135) {
		tmp = x * (j * (b * -y0));
	} else if (y3 <= 1.55e-252) {
		tmp = c * (x * (y0 * y2));
	} else if (y3 <= 2.4e-107) {
		tmp = x * ((j * y0) * -b);
	} else if (y3 <= 4e+61) {
		tmp = c * (y0 * (x * y2));
	} else if (y3 <= 2.25e+98) {
		tmp = a * (y * (x * b));
	} else if (y3 <= 5.1e+212) {
		tmp = x * (c * (y0 * y2));
	} 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 = c * ((z * y3) * -y0)
    if (y3 <= (-2.3d+253)) then
        tmp = t_1
    else if (y3 <= (-9.8d+92)) then
        tmp = a * (y1 * (z * y3))
    else if (y3 <= (-7.2d-135)) then
        tmp = x * (j * (b * -y0))
    else if (y3 <= 1.55d-252) then
        tmp = c * (x * (y0 * y2))
    else if (y3 <= 2.4d-107) then
        tmp = x * ((j * y0) * -b)
    else if (y3 <= 4d+61) then
        tmp = c * (y0 * (x * y2))
    else if (y3 <= 2.25d+98) then
        tmp = a * (y * (x * b))
    else if (y3 <= 5.1d+212) then
        tmp = x * (c * (y0 * y2))
    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 = c * ((z * y3) * -y0);
	double tmp;
	if (y3 <= -2.3e+253) {
		tmp = t_1;
	} else if (y3 <= -9.8e+92) {
		tmp = a * (y1 * (z * y3));
	} else if (y3 <= -7.2e-135) {
		tmp = x * (j * (b * -y0));
	} else if (y3 <= 1.55e-252) {
		tmp = c * (x * (y0 * y2));
	} else if (y3 <= 2.4e-107) {
		tmp = x * ((j * y0) * -b);
	} else if (y3 <= 4e+61) {
		tmp = c * (y0 * (x * y2));
	} else if (y3 <= 2.25e+98) {
		tmp = a * (y * (x * b));
	} else if (y3 <= 5.1e+212) {
		tmp = x * (c * (y0 * y2));
	} 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 = c * ((z * y3) * -y0)
	tmp = 0
	if y3 <= -2.3e+253:
		tmp = t_1
	elif y3 <= -9.8e+92:
		tmp = a * (y1 * (z * y3))
	elif y3 <= -7.2e-135:
		tmp = x * (j * (b * -y0))
	elif y3 <= 1.55e-252:
		tmp = c * (x * (y0 * y2))
	elif y3 <= 2.4e-107:
		tmp = x * ((j * y0) * -b)
	elif y3 <= 4e+61:
		tmp = c * (y0 * (x * y2))
	elif y3 <= 2.25e+98:
		tmp = a * (y * (x * b))
	elif y3 <= 5.1e+212:
		tmp = x * (c * (y0 * y2))
	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(c * Float64(Float64(z * y3) * Float64(-y0)))
	tmp = 0.0
	if (y3 <= -2.3e+253)
		tmp = t_1;
	elseif (y3 <= -9.8e+92)
		tmp = Float64(a * Float64(y1 * Float64(z * y3)));
	elseif (y3 <= -7.2e-135)
		tmp = Float64(x * Float64(j * Float64(b * Float64(-y0))));
	elseif (y3 <= 1.55e-252)
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	elseif (y3 <= 2.4e-107)
		tmp = Float64(x * Float64(Float64(j * y0) * Float64(-b)));
	elseif (y3 <= 4e+61)
		tmp = Float64(c * Float64(y0 * Float64(x * y2)));
	elseif (y3 <= 2.25e+98)
		tmp = Float64(a * Float64(y * Float64(x * b)));
	elseif (y3 <= 5.1e+212)
		tmp = Float64(x * Float64(c * Float64(y0 * y2)));
	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 = c * ((z * y3) * -y0);
	tmp = 0.0;
	if (y3 <= -2.3e+253)
		tmp = t_1;
	elseif (y3 <= -9.8e+92)
		tmp = a * (y1 * (z * y3));
	elseif (y3 <= -7.2e-135)
		tmp = x * (j * (b * -y0));
	elseif (y3 <= 1.55e-252)
		tmp = c * (x * (y0 * y2));
	elseif (y3 <= 2.4e-107)
		tmp = x * ((j * y0) * -b);
	elseif (y3 <= 4e+61)
		tmp = c * (y0 * (x * y2));
	elseif (y3 <= 2.25e+98)
		tmp = a * (y * (x * b));
	elseif (y3 <= 5.1e+212)
		tmp = x * (c * (y0 * y2));
	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[(c * N[(N[(z * y3), $MachinePrecision] * (-y0)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -2.3e+253], t$95$1, If[LessEqual[y3, -9.8e+92], N[(a * N[(y1 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -7.2e-135], N[(x * N[(j * N[(b * (-y0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.55e-252], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 2.4e-107], N[(x * N[(N[(j * y0), $MachinePrecision] * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 4e+61], N[(c * N[(y0 * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 2.25e+98], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 5.1e+212], N[(x * N[(c * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y3 < -2.3e253 or 5.1000000000000002e212 < y3

   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. Taylor expanded in c around inf 46.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 46.8%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 46.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 46.8%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 46.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 46.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 46.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 46.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 46.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 54.2%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   6. Taylor expanded in x around 0 54.4%

      \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 54.4%

         \[\leadsto c \cdot \color{blue}{\left(-y0 \cdot \left(y3 \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 54.4%

         \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(-y3 \cdot z\right)\right)} \]

      3. distribute-lft-neg-in 54.4%

         \[\leadsto c \cdot \left(y0 \cdot \color{blue}{\left(\left(-y3\right) \cdot z\right)}\right) \]

      4. *-commutative 54.4%

         \[\leadsto c \cdot \left(y0 \cdot \color{blue}{\left(z \cdot \left(-y3\right)\right)}\right) \]

   8. Simplified 54.4%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(z \cdot \left(-y3\right)\right)\right)} \]

   if -2.3e253 < y3 < -9.8000000000000003e92

   1. Initial program 28.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around -inf 33.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 33.9%

         \[\leadsto \color{blue}{-a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. distribute-rgt-neg-in 33.9%

         \[\leadsto \color{blue}{a \cdot \left(-\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      3. +-commutative 33.9%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. mul-1-neg 33.9%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-b \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. unsub-neg 33.9%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 33.9%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. *-commutative 33.9%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative 33.9%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   4. Simplified 33.9%

      \[\leadsto \color{blue}{a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(y \cdot x - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   5. Taylor expanded in y3 around -inf 43.0%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 43.0%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]

      2. neg-mul-1 43.0%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right) \]

      3. *-commutative 43.0%

         \[\leadsto \left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - \color{blue}{z \cdot y1}\right)\right) \]

   7. Simplified 43.0%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - z \cdot y1\right)\right)} \]

   8. Taylor expanded in y around 0 40.7%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]

   if -9.8000000000000003e92 < y3 < -7.19999999999999955e-135

   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. Taylor expanded in x around inf 52.8%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in j around inf 43.5%

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 43.5%

         \[\leadsto x \cdot \left(j \cdot \left(\color{blue}{y1 \cdot i} - b \cdot y0\right)\right) \]

      2. *-commutative 43.5%

         \[\leadsto x \cdot \left(j \cdot \left(y1 \cdot i - \color{blue}{y0 \cdot b}\right)\right) \]

   5. Simplified 43.5%

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(y1 \cdot i - y0 \cdot b\right)\right)} \]

   6. Taylor expanded in y1 around 0 41.1%

      \[\leadsto x \cdot \left(j \cdot \color{blue}{\left(-1 \cdot \left(b \cdot y0\right)\right)}\right) \]
   7. Step-by-step derivation

      1. mul-1-neg 41.1%

         \[\leadsto x \cdot \left(j \cdot \color{blue}{\left(-b \cdot y0\right)}\right) \]

      2. *-commutative 41.1%

         \[\leadsto x \cdot \left(j \cdot \left(-\color{blue}{y0 \cdot b}\right)\right) \]

      3. distribute-rgt-neg-in 41.1%

         \[\leadsto x \cdot \left(j \cdot \color{blue}{\left(y0 \cdot \left(-b\right)\right)}\right) \]

   8. Simplified 41.1%

      \[\leadsto x \cdot \left(j \cdot \color{blue}{\left(y0 \cdot \left(-b\right)\right)}\right) \]

   if -7.19999999999999955e-135 < y3 < 1.5499999999999999e-252

   1. Initial program 43.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 41.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 41.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 41.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 41.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 41.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 41.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 41.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 41.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 41.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 25.4%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 25.2%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]

   if 1.5499999999999999e-252 < y3 < 2.39999999999999994e-107

   1. Initial program 19.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in x around inf 27.6%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in j around inf 35.4%

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 35.4%

         \[\leadsto x \cdot \left(j \cdot \left(\color{blue}{y1 \cdot i} - b \cdot y0\right)\right) \]

      2. *-commutative 35.4%

         \[\leadsto x \cdot \left(j \cdot \left(y1 \cdot i - \color{blue}{y0 \cdot b}\right)\right) \]

   5. Simplified 35.4%

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(y1 \cdot i - y0 \cdot b\right)\right)} \]

   6. Taylor expanded in y1 around 0 39.6%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(b \cdot \left(j \cdot y0\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 39.6%

         \[\leadsto x \cdot \color{blue}{\left(\left(-1 \cdot b\right) \cdot \left(j \cdot y0\right)\right)} \]

      2. neg-mul-1 39.6%

         \[\leadsto x \cdot \left(\color{blue}{\left(-b\right)} \cdot \left(j \cdot y0\right)\right) \]

      3. *-commutative 39.6%

         \[\leadsto x \cdot \left(\left(-b\right) \cdot \color{blue}{\left(y0 \cdot j\right)}\right) \]

   8. Simplified 39.6%

      \[\leadsto x \cdot \color{blue}{\left(\left(-b\right) \cdot \left(y0 \cdot j\right)\right)} \]

   if 2.39999999999999994e-107 < y3 < 3.9999999999999998e61

   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. Taylor expanded in c around inf 52.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 52.7%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 52.7%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 52.7%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 52.7%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 52.7%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 52.7%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 52.7%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 52.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 48.9%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 39.4%

      \[\leadsto c \cdot \color{blue}{\left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 41.8%

         \[\leadsto c \cdot \color{blue}{\left(\left(x \cdot y0\right) \cdot y2\right)} \]

      2. *-commutative 41.8%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot x\right)} \cdot y2\right) \]

      3. associate-*r* 39.4%

         \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2\right)\right)} \]

   8. Simplified 39.4%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2\right)\right)} \]

   if 3.9999999999999998e61 < y3 < 2.2500000000000001e98

   1. Initial program 54.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf 73.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in a around inf 47.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   4. Taylor expanded in x around inf 38.2%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 55.6%

         \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot x\right) \cdot y\right)} \]

      2. *-commutative 55.6%

         \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot b\right)} \cdot y\right) \]

      3. associate-*l* 38.1%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

   6. Simplified 38.1%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

   7. Taylor expanded in x around 0 38.2%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 38.2%

         \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot b\right)} \]

      2. *-commutative 38.2%

         \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot b\right) \]

      3. associate-*l* 55.6%

         \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(x \cdot b\right)\right)} \]

   9. Simplified 55.6%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(x \cdot b\right)\right)} \]

   if 2.2500000000000001e98 < y3 < 5.1000000000000002e212

   1. Initial program 35.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 31.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 31.0%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 31.0%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 31.0%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 31.0%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 31.0%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 31.0%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 31.0%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 31.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 27.5%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 27.5%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 27.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y0 \cdot y2\right)\right) \cdot c} \]

      2. associate-*l* 31.7%

         \[\leadsto \color{blue}{x \cdot \left(\left(y0 \cdot y2\right) \cdot c\right)} \]

   8. Simplified 31.7%

      \[\leadsto \color{blue}{x \cdot \left(\left(y0 \cdot y2\right) \cdot c\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 39.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -2.3 \cdot 10^{+253}:\\ \;\;\;\;c \cdot \left(\left(z \cdot y3\right) \cdot \left(-y0\right)\right)\\ \mathbf{elif}\;y3 \leq -9.8 \cdot 10^{+92}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{elif}\;y3 \leq -7.2 \cdot 10^{-135}:\\ \;\;\;\;x \cdot \left(j \cdot \left(b \cdot \left(-y0\right)\right)\right)\\ \mathbf{elif}\;y3 \leq 1.55 \cdot 10^{-252}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 2.4 \cdot 10^{-107}:\\ \;\;\;\;x \cdot \left(\left(j \cdot y0\right) \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y3 \leq 4 \cdot 10^{+61}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 2.25 \cdot 10^{+98}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;y3 \leq 5.1 \cdot 10^{+212}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(z \cdot y3\right) \cdot \left(-y0\right)\right)\\ \end{array} \]

Alternative 26: 30.3% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+55}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-288}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-182}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+38}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+125}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y0 (- (* x y2) (* z y3))))))
   (if (<= y -4.2e+55)
     (* b (* y (- (* x a) (* k y4))))
     (if (<= y 1.05e-288)
       t_1
       (if (<= y 4.8e-182)
         (* b (* y4 (- (* t j) (* y k))))
         (if (<= y 1.65e-19)
           t_1
           (if (<= y 3.3e+38)
             (* c (* y (* y3 y4)))
             (if (<= y 2.2e+125) t_1 (* a (* y5 (- (* t y2) (* y y3))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y0 * ((x * y2) - (z * y3)));
	double tmp;
	if (y <= -4.2e+55) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (y <= 1.05e-288) {
		tmp = t_1;
	} else if (y <= 4.8e-182) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y <= 1.65e-19) {
		tmp = t_1;
	} else if (y <= 3.3e+38) {
		tmp = c * (y * (y3 * y4));
	} else if (y <= 2.2e+125) {
		tmp = t_1;
	} else {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (y0 * ((x * y2) - (z * y3)))
    if (y <= (-4.2d+55)) then
        tmp = b * (y * ((x * a) - (k * y4)))
    else if (y <= 1.05d-288) then
        tmp = t_1
    else if (y <= 4.8d-182) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (y <= 1.65d-19) then
        tmp = t_1
    else if (y <= 3.3d+38) then
        tmp = c * (y * (y3 * y4))
    else if (y <= 2.2d+125) then
        tmp = t_1
    else
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y0 * ((x * y2) - (z * y3)));
	double tmp;
	if (y <= -4.2e+55) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (y <= 1.05e-288) {
		tmp = t_1;
	} else if (y <= 4.8e-182) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y <= 1.65e-19) {
		tmp = t_1;
	} else if (y <= 3.3e+38) {
		tmp = c * (y * (y3 * y4));
	} else if (y <= 2.2e+125) {
		tmp = t_1;
	} else {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (y0 * ((x * y2) - (z * y3)))
	tmp = 0
	if y <= -4.2e+55:
		tmp = b * (y * ((x * a) - (k * y4)))
	elif y <= 1.05e-288:
		tmp = t_1
	elif y <= 4.8e-182:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif y <= 1.65e-19:
		tmp = t_1
	elif y <= 3.3e+38:
		tmp = c * (y * (y3 * y4))
	elif y <= 2.2e+125:
		tmp = t_1
	else:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))))
	tmp = 0.0
	if (y <= -4.2e+55)
		tmp = Float64(b * Float64(y * Float64(Float64(x * a) - Float64(k * y4))));
	elseif (y <= 1.05e-288)
		tmp = t_1;
	elseif (y <= 4.8e-182)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (y <= 1.65e-19)
		tmp = t_1;
	elseif (y <= 3.3e+38)
		tmp = Float64(c * Float64(y * Float64(y3 * y4)));
	elseif (y <= 2.2e+125)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (y0 * ((x * y2) - (z * y3)));
	tmp = 0.0;
	if (y <= -4.2e+55)
		tmp = b * (y * ((x * a) - (k * y4)));
	elseif (y <= 1.05e-288)
		tmp = t_1;
	elseif (y <= 4.8e-182)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (y <= 1.65e-19)
		tmp = t_1;
	elseif (y <= 3.3e+38)
		tmp = c * (y * (y3 * y4));
	elseif (y <= 2.2e+125)
		tmp = t_1;
	else
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.2e+55], N[(b * N[(y * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05e-288], t$95$1, If[LessEqual[y, 4.8e-182], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e-19], t$95$1, If[LessEqual[y, 3.3e+38], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.2e+125], t$95$1, N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -4.2000000000000001e55

   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. Taylor expanded in b around inf 48.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in y around inf 50.6%

      \[\leadsto b \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 50.6%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 50.6%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x + \color{blue}{\left(-k \cdot y4\right)}\right)\right) \]

      3. unsub-neg 50.6%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x - k \cdot y4\right)}\right) \]

      4. *-commutative 50.6%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x - \color{blue}{y4 \cdot k}\right)\right) \]

   5. Simplified 50.6%

      \[\leadsto b \cdot \color{blue}{\left(y \cdot \left(a \cdot x - y4 \cdot k\right)\right)} \]

   if -4.2000000000000001e55 < y < 1.04999999999999998e-288 or 4.7999999999999997e-182 < y < 1.6499999999999999e-19 or 3.2999999999999999e38 < y < 2.19999999999999991e125

   1. Initial program 32.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 44.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 44.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 44.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 44.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 44.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 44.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 44.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 44.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 44.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 43.2%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   if 1.04999999999999998e-288 < y < 4.7999999999999997e-182

   1. Initial program 55.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf 56.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in y4 around inf 45.6%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 45.6%

         \[\leadsto b \cdot \left(y4 \cdot \left(j \cdot t - \color{blue}{y \cdot k}\right)\right) \]

   5. Simplified 45.6%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - y \cdot k\right)\right)} \]

   if 1.6499999999999999e-19 < y < 3.2999999999999999e38

   1. Initial program 47.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y3 around -inf 37.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   3. Taylor expanded in y4 around inf 26.6%

      \[\leadsto -1 \cdot \color{blue}{\left(y3 \cdot \left(y4 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 26.6%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(y3 \cdot y4\right) \cdot \left(j \cdot y1 - c \cdot y\right)\right)} \]

      2. *-commutative 26.6%

         \[\leadsto -1 \cdot \left(\left(y3 \cdot y4\right) \cdot \left(\color{blue}{y1 \cdot j} - c \cdot y\right)\right) \]

   5. Simplified 26.6%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(y3 \cdot y4\right) \cdot \left(y1 \cdot j - c \cdot y\right)\right)} \]

   6. Taylor expanded in y1 around 0 33.3%

      \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 33.3%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(-1 \cdot c\right) \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\right)} \]

      2. neg-mul-1 33.3%

         \[\leadsto -1 \cdot \left(\color{blue}{\left(-c\right)} \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\right) \]

   8. Simplified 33.3%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(-c\right) \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\right)} \]

   if 2.19999999999999991e125 < y

   1. Initial program 17.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around -inf 44.4%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 44.4%

         \[\leadsto \color{blue}{-a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. distribute-rgt-neg-in 44.4%

         \[\leadsto \color{blue}{a \cdot \left(-\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      3. +-commutative 44.4%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. mul-1-neg 44.4%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-b \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. unsub-neg 44.4%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 44.4%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. *-commutative 44.4%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative 44.4%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   4. Simplified 44.4%

      \[\leadsto \color{blue}{a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(y \cdot x - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   5. Taylor expanded in y5 around inf 56.5%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 45.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+55}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-288}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-182}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-19}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+38}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+125}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \end{array} \]

Alternative 27: 31.7% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ t_2 := t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{if}\;y \leq -2 \cdot 10^{+55}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-306}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-179}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{-30}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+126}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y0 (- (* x y2) (* z y3)))))
        (t_2 (* t (* c (- (* z i) (* y2 y4))))))
   (if (<= y -2e+55)
     (* b (* y (- (* x a) (* k y4))))
     (if (<= y -1.45e-306)
       t_1
       (if (<= y 1.1e-179)
         t_2
         (if (<= y 2.55e-30)
           (* b (* y0 (- (* z k) (* x j))))
           (if (<= y 7.5e+40)
             t_2
             (if (<= y 2.9e+126) t_1 (* a (* y5 (- (* t y2) (* y y3))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y0 * ((x * y2) - (z * y3)));
	double t_2 = t * (c * ((z * i) - (y2 * y4)));
	double tmp;
	if (y <= -2e+55) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (y <= -1.45e-306) {
		tmp = t_1;
	} else if (y <= 1.1e-179) {
		tmp = t_2;
	} else if (y <= 2.55e-30) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y <= 7.5e+40) {
		tmp = t_2;
	} else if (y <= 2.9e+126) {
		tmp = t_1;
	} else {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * (y0 * ((x * y2) - (z * y3)))
    t_2 = t * (c * ((z * i) - (y2 * y4)))
    if (y <= (-2d+55)) then
        tmp = b * (y * ((x * a) - (k * y4)))
    else if (y <= (-1.45d-306)) then
        tmp = t_1
    else if (y <= 1.1d-179) then
        tmp = t_2
    else if (y <= 2.55d-30) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (y <= 7.5d+40) then
        tmp = t_2
    else if (y <= 2.9d+126) then
        tmp = t_1
    else
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y0 * ((x * y2) - (z * y3)));
	double t_2 = t * (c * ((z * i) - (y2 * y4)));
	double tmp;
	if (y <= -2e+55) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (y <= -1.45e-306) {
		tmp = t_1;
	} else if (y <= 1.1e-179) {
		tmp = t_2;
	} else if (y <= 2.55e-30) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y <= 7.5e+40) {
		tmp = t_2;
	} else if (y <= 2.9e+126) {
		tmp = t_1;
	} else {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (y0 * ((x * y2) - (z * y3)))
	t_2 = t * (c * ((z * i) - (y2 * y4)))
	tmp = 0
	if y <= -2e+55:
		tmp = b * (y * ((x * a) - (k * y4)))
	elif y <= -1.45e-306:
		tmp = t_1
	elif y <= 1.1e-179:
		tmp = t_2
	elif y <= 2.55e-30:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif y <= 7.5e+40:
		tmp = t_2
	elif y <= 2.9e+126:
		tmp = t_1
	else:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))))
	t_2 = Float64(t * Float64(c * Float64(Float64(z * i) - Float64(y2 * y4))))
	tmp = 0.0
	if (y <= -2e+55)
		tmp = Float64(b * Float64(y * Float64(Float64(x * a) - Float64(k * y4))));
	elseif (y <= -1.45e-306)
		tmp = t_1;
	elseif (y <= 1.1e-179)
		tmp = t_2;
	elseif (y <= 2.55e-30)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (y <= 7.5e+40)
		tmp = t_2;
	elseif (y <= 2.9e+126)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (y0 * ((x * y2) - (z * y3)));
	t_2 = t * (c * ((z * i) - (y2 * y4)));
	tmp = 0.0;
	if (y <= -2e+55)
		tmp = b * (y * ((x * a) - (k * y4)));
	elseif (y <= -1.45e-306)
		tmp = t_1;
	elseif (y <= 1.1e-179)
		tmp = t_2;
	elseif (y <= 2.55e-30)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (y <= 7.5e+40)
		tmp = t_2;
	elseif (y <= 2.9e+126)
		tmp = t_1;
	else
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(c * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2e+55], N[(b * N[(y * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.45e-306], t$95$1, If[LessEqual[y, 1.1e-179], t$95$2, If[LessEqual[y, 2.55e-30], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e+40], t$95$2, If[LessEqual[y, 2.9e+126], t$95$1, N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.00000000000000002e55

   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. Taylor expanded in b around inf 48.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in y around inf 50.6%

      \[\leadsto b \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 50.6%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 50.6%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x + \color{blue}{\left(-k \cdot y4\right)}\right)\right) \]

      3. unsub-neg 50.6%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x - k \cdot y4\right)}\right) \]

      4. *-commutative 50.6%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x - \color{blue}{y4 \cdot k}\right)\right) \]

   5. Simplified 50.6%

      \[\leadsto b \cdot \color{blue}{\left(y \cdot \left(a \cdot x - y4 \cdot k\right)\right)} \]

   if -2.00000000000000002e55 < y < -1.4499999999999999e-306 or 7.4999999999999996e40 < y < 2.89999999999999986e126

   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. Taylor expanded in c around inf 46.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 46.7%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 46.7%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 46.7%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 46.7%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 46.7%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 46.7%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 46.7%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 46.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 47.1%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   if -1.4499999999999999e-306 < y < 1.10000000000000002e-179 or 2.54999999999999986e-30 < y < 7.4999999999999996e40

   1. Initial program 50.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 42.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 42.2%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 42.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 42.2%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 42.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 42.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 42.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 42.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 42.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in t around -inf 48.7%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(-1 \cdot \left(y2 \cdot y4\right) + i \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 48.7%

         \[\leadsto \color{blue}{\left(t \cdot \left(-1 \cdot \left(y2 \cdot y4\right) + i \cdot z\right)\right) \cdot c} \]

      2. associate-*l* 48.7%

         \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(y2 \cdot y4\right) + i \cdot z\right) \cdot c\right)} \]

      3. +-commutative 48.7%

         \[\leadsto t \cdot \left(\color{blue}{\left(i \cdot z + -1 \cdot \left(y2 \cdot y4\right)\right)} \cdot c\right) \]

      4. mul-1-neg 48.7%

         \[\leadsto t \cdot \left(\left(i \cdot z + \color{blue}{\left(-y2 \cdot y4\right)}\right) \cdot c\right) \]

      5. unsub-neg 48.7%

         \[\leadsto t \cdot \left(\color{blue}{\left(i \cdot z - y2 \cdot y4\right)} \cdot c\right) \]

      6. *-commutative 48.7%

         \[\leadsto t \cdot \left(\left(\color{blue}{z \cdot i} - y2 \cdot y4\right) \cdot c\right) \]

   7. Simplified 48.7%

      \[\leadsto \color{blue}{t \cdot \left(\left(z \cdot i - y2 \cdot y4\right) \cdot c\right)} \]

   if 1.10000000000000002e-179 < y < 2.54999999999999986e-30

   1. Initial program 39.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf 47.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in y0 around inf 41.8%

      \[\leadsto b \cdot \color{blue}{\left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 41.8%

         \[\leadsto b \cdot \left(y0 \cdot \left(\color{blue}{z \cdot k} - j \cdot x\right)\right) \]

   5. Simplified 41.8%

      \[\leadsto b \cdot \color{blue}{\left(y0 \cdot \left(z \cdot k - j \cdot x\right)\right)} \]

   if 2.89999999999999986e126 < y

   1. Initial program 17.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around -inf 44.4%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 44.4%

         \[\leadsto \color{blue}{-a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. distribute-rgt-neg-in 44.4%

         \[\leadsto \color{blue}{a \cdot \left(-\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      3. +-commutative 44.4%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. mul-1-neg 44.4%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-b \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. unsub-neg 44.4%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 44.4%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. *-commutative 44.4%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative 44.4%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   4. Simplified 44.4%

      \[\leadsto \color{blue}{a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(y \cdot x - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   5. Taylor expanded in y5 around inf 56.5%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+55}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-306}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-179}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{-30}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+40}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+126}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \end{array} \]

Alternative 28: 31.8% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+53}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-306}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-213}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+149}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+229}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y -1.7e+53)
   (* b (* y (- (* x a) (* k y4))))
   (if (<= y -2.1e-306)
     (* c (* y0 (- (* x y2) (* z y3))))
     (if (<= y 1.6e-213)
       (* t (* c (- (* z i) (* y2 y4))))
       (if (<= y 2.1e+74)
         (* x (* y0 (- (* c y2) (* b j))))
         (if (<= y 3.6e+149)
           (* x (* c (- (* y0 y2) (* y i))))
           (if (<= y 7.2e+229)
             (* b (* y4 (- (* t j) (* y k))))
             (* (- a) (* y3 (* y y5))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -1.7e+53) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (y <= -2.1e-306) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (y <= 1.6e-213) {
		tmp = t * (c * ((z * i) - (y2 * y4)));
	} else if (y <= 2.1e+74) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (y <= 3.6e+149) {
		tmp = x * (c * ((y0 * y2) - (y * i)));
	} else if (y <= 7.2e+229) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else {
		tmp = -a * (y3 * (y * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y <= (-1.7d+53)) then
        tmp = b * (y * ((x * a) - (k * y4)))
    else if (y <= (-2.1d-306)) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else if (y <= 1.6d-213) then
        tmp = t * (c * ((z * i) - (y2 * y4)))
    else if (y <= 2.1d+74) then
        tmp = x * (y0 * ((c * y2) - (b * j)))
    else if (y <= 3.6d+149) then
        tmp = x * (c * ((y0 * y2) - (y * i)))
    else if (y <= 7.2d+229) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else
        tmp = -a * (y3 * (y * y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -1.7e+53) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (y <= -2.1e-306) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (y <= 1.6e-213) {
		tmp = t * (c * ((z * i) - (y2 * y4)));
	} else if (y <= 2.1e+74) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (y <= 3.6e+149) {
		tmp = x * (c * ((y0 * y2) - (y * i)));
	} else if (y <= 7.2e+229) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else {
		tmp = -a * (y3 * (y * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y <= -1.7e+53:
		tmp = b * (y * ((x * a) - (k * y4)))
	elif y <= -2.1e-306:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	elif y <= 1.6e-213:
		tmp = t * (c * ((z * i) - (y2 * y4)))
	elif y <= 2.1e+74:
		tmp = x * (y0 * ((c * y2) - (b * j)))
	elif y <= 3.6e+149:
		tmp = x * (c * ((y0 * y2) - (y * i)))
	elif y <= 7.2e+229:
		tmp = b * (y4 * ((t * j) - (y * k)))
	else:
		tmp = -a * (y3 * (y * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y <= -1.7e+53)
		tmp = Float64(b * Float64(y * Float64(Float64(x * a) - Float64(k * y4))));
	elseif (y <= -2.1e-306)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (y <= 1.6e-213)
		tmp = Float64(t * Float64(c * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (y <= 2.1e+74)
		tmp = Float64(x * Float64(y0 * Float64(Float64(c * y2) - Float64(b * j))));
	elseif (y <= 3.6e+149)
		tmp = Float64(x * Float64(c * Float64(Float64(y0 * y2) - Float64(y * i))));
	elseif (y <= 7.2e+229)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	else
		tmp = Float64(Float64(-a) * Float64(y3 * Float64(y * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y <= -1.7e+53)
		tmp = b * (y * ((x * a) - (k * y4)));
	elseif (y <= -2.1e-306)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	elseif (y <= 1.6e-213)
		tmp = t * (c * ((z * i) - (y2 * y4)));
	elseif (y <= 2.1e+74)
		tmp = x * (y0 * ((c * y2) - (b * j)));
	elseif (y <= 3.6e+149)
		tmp = x * (c * ((y0 * y2) - (y * i)));
	elseif (y <= 7.2e+229)
		tmp = b * (y4 * ((t * j) - (y * k)));
	else
		tmp = -a * (y3 * (y * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y, -1.7e+53], N[(b * N[(y * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.1e-306], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e-213], N[(t * N[(c * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e+74], N[(x * N[(y0 * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e+149], N[(x * N[(c * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e+229], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-a) * N[(y3 * N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -1.69999999999999999e53

   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. Taylor expanded in b around inf 48.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in y around inf 50.6%

      \[\leadsto b \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 50.6%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 50.6%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x + \color{blue}{\left(-k \cdot y4\right)}\right)\right) \]

      3. unsub-neg 50.6%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x - k \cdot y4\right)}\right) \]

      4. *-commutative 50.6%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x - \color{blue}{y4 \cdot k}\right)\right) \]

   5. Simplified 50.6%

      \[\leadsto b \cdot \color{blue}{\left(y \cdot \left(a \cdot x - y4 \cdot k\right)\right)} \]

   if -1.69999999999999999e53 < y < -2.1000000000000001e-306

   1. Initial program 28.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 48.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 48.6%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 48.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 48.6%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 48.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 48.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 48.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 48.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 48.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 44.6%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   if -2.1000000000000001e-306 < y < 1.59999999999999986e-213

   1. Initial program 61.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 50.5%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 50.5%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 50.5%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 50.5%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 50.5%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 50.5%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 50.5%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 50.5%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 50.5%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in t around -inf 61.9%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(-1 \cdot \left(y2 \cdot y4\right) + i \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 61.9%

         \[\leadsto \color{blue}{\left(t \cdot \left(-1 \cdot \left(y2 \cdot y4\right) + i \cdot z\right)\right) \cdot c} \]

      2. associate-*l* 61.9%

         \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(y2 \cdot y4\right) + i \cdot z\right) \cdot c\right)} \]

      3. +-commutative 61.9%

         \[\leadsto t \cdot \left(\color{blue}{\left(i \cdot z + -1 \cdot \left(y2 \cdot y4\right)\right)} \cdot c\right) \]

      4. mul-1-neg 61.9%

         \[\leadsto t \cdot \left(\left(i \cdot z + \color{blue}{\left(-y2 \cdot y4\right)}\right) \cdot c\right) \]

      5. unsub-neg 61.9%

         \[\leadsto t \cdot \left(\color{blue}{\left(i \cdot z - y2 \cdot y4\right)} \cdot c\right) \]

      6. *-commutative 61.9%

         \[\leadsto t \cdot \left(\left(\color{blue}{z \cdot i} - y2 \cdot y4\right) \cdot c\right) \]

   7. Simplified 61.9%

      \[\leadsto \color{blue}{t \cdot \left(\left(z \cdot i - y2 \cdot y4\right) \cdot c\right)} \]

   if 1.59999999999999986e-213 < y < 2.0999999999999999e74

   1. Initial program 38.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in x around inf 36.3%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in y0 around inf 39.7%

      \[\leadsto x \cdot \color{blue}{\left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 39.7%

         \[\leadsto x \cdot \left(y0 \cdot \left(c \cdot y2 - \color{blue}{j \cdot b}\right)\right) \]

   5. Simplified 39.7%

      \[\leadsto x \cdot \color{blue}{\left(y0 \cdot \left(c \cdot y2 - j \cdot b\right)\right)} \]

   if 2.0999999999999999e74 < y < 3.59999999999999995e149

   1. Initial program 14.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in x around inf 36.8%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in c around inf 65.4%

      \[\leadsto x \cdot \color{blue}{\left(c \cdot \left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 65.4%

         \[\leadsto x \cdot \left(c \cdot \color{blue}{\left(y0 \cdot y2 + -1 \cdot \left(i \cdot y\right)\right)}\right) \]

      2. mul-1-neg 65.4%

         \[\leadsto x \cdot \left(c \cdot \left(y0 \cdot y2 + \color{blue}{\left(-i \cdot y\right)}\right)\right) \]

      3. unsub-neg 65.4%

         \[\leadsto x \cdot \left(c \cdot \color{blue}{\left(y0 \cdot y2 - i \cdot y\right)}\right) \]

      4. *-commutative 65.4%

         \[\leadsto x \cdot \left(c \cdot \left(y0 \cdot y2 - \color{blue}{y \cdot i}\right)\right) \]

   5. Simplified 65.4%

      \[\leadsto x \cdot \color{blue}{\left(c \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)} \]

   if 3.59999999999999995e149 < y < 7.19999999999999973e229

   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. Taylor expanded in b around inf 45.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in y4 around inf 63.9%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 63.9%

         \[\leadsto b \cdot \left(y4 \cdot \left(j \cdot t - \color{blue}{y \cdot k}\right)\right) \]

   5. Simplified 63.9%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - y \cdot k\right)\right)} \]

   if 7.19999999999999973e229 < y

   1. Initial program 17.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around -inf 47.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 47.2%

         \[\leadsto \color{blue}{-a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. distribute-rgt-neg-in 47.2%

         \[\leadsto \color{blue}{a \cdot \left(-\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      3. +-commutative 47.2%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. mul-1-neg 47.2%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-b \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. unsub-neg 47.2%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 47.2%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. *-commutative 47.2%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative 47.2%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   4. Simplified 47.2%

      \[\leadsto \color{blue}{a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(y \cdot x - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   5. Taylor expanded in y around -inf 59.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 59.2%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)} \]

      2. neg-mul-1 59.2%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(y \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right) \]

      3. +-commutative 59.2%

         \[\leadsto \left(-a\right) \cdot \left(y \cdot \color{blue}{\left(y3 \cdot y5 + -1 \cdot \left(b \cdot x\right)\right)}\right) \]

      4. mul-1-neg 59.2%

         \[\leadsto \left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5 + \color{blue}{\left(-b \cdot x\right)}\right)\right) \]

      5. unsub-neg 59.2%

         \[\leadsto \left(-a\right) \cdot \left(y \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]

   7. Simplified 59.2%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)} \]

   8. Taylor expanded in y3 around inf 59.9%

      \[\leadsto \left(-a\right) \cdot \color{blue}{\left(y \cdot \left(y3 \cdot y5\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 60.0%

         \[\leadsto \left(-a\right) \cdot \color{blue}{\left(\left(y \cdot y3\right) \cdot y5\right)} \]

      2. *-commutative 60.0%

         \[\leadsto \left(-a\right) \cdot \left(\color{blue}{\left(y3 \cdot y\right)} \cdot y5\right) \]

      3. associate-*l* 71.3%

         \[\leadsto \left(-a\right) \cdot \color{blue}{\left(y3 \cdot \left(y \cdot y5\right)\right)} \]

   10. Simplified 71.3%

       \[\leadsto \left(-a\right) \cdot \color{blue}{\left(y3 \cdot \left(y \cdot y5\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+53}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-306}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-213}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+149}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+229}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5\right)\right)\\ \end{array} \]

Alternative 29: 25.7% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{if}\;y0 \leq -3.8 \cdot 10^{+153}:\\ \;\;\;\;x \cdot \left(j \cdot \left(b \cdot \left(-y0\right)\right)\right)\\ \mathbf{elif}\;y0 \leq -1.1 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y0 \leq -1550000000:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(y4 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 5.8 \cdot 10^{-170}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y0 \leq 1.25 \cdot 10^{-8}:\\ \;\;\;\;\left(y3 \cdot y4\right) \cdot \left(y \cdot c\right)\\ \mathbf{elif}\;y0 \leq 1.85 \cdot 10^{+125} \lor \neg \left(y0 \leq 7.5 \cdot 10^{+230}\right):\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y3\right) \cdot \left(c \cdot \left(-y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* b (- (* x y) (* z t))))))
   (if (<= y0 -3.8e+153)
     (* x (* j (* b (- y0))))
     (if (<= y0 -1.1e+55)
       t_1
       (if (<= y0 -1550000000.0)
         (* j (* y1 (* y4 (- y3))))
         (if (<= y0 5.8e-170)
           t_1
           (if (<= y0 1.25e-8)
             (* (* y3 y4) (* y c))
             (if (or (<= y0 1.85e+125) (not (<= y0 7.5e+230)))
               (* c (* x (* y0 y2)))
               (* (* z y3) (* c (- y0)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (b * ((x * y) - (z * t)));
	double tmp;
	if (y0 <= -3.8e+153) {
		tmp = x * (j * (b * -y0));
	} else if (y0 <= -1.1e+55) {
		tmp = t_1;
	} else if (y0 <= -1550000000.0) {
		tmp = j * (y1 * (y4 * -y3));
	} else if (y0 <= 5.8e-170) {
		tmp = t_1;
	} else if (y0 <= 1.25e-8) {
		tmp = (y3 * y4) * (y * c);
	} else if ((y0 <= 1.85e+125) || !(y0 <= 7.5e+230)) {
		tmp = c * (x * (y0 * y2));
	} else {
		tmp = (z * y3) * (c * -y0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (b * ((x * y) - (z * t)))
    if (y0 <= (-3.8d+153)) then
        tmp = x * (j * (b * -y0))
    else if (y0 <= (-1.1d+55)) then
        tmp = t_1
    else if (y0 <= (-1550000000.0d0)) then
        tmp = j * (y1 * (y4 * -y3))
    else if (y0 <= 5.8d-170) then
        tmp = t_1
    else if (y0 <= 1.25d-8) then
        tmp = (y3 * y4) * (y * c)
    else if ((y0 <= 1.85d+125) .or. (.not. (y0 <= 7.5d+230))) then
        tmp = c * (x * (y0 * y2))
    else
        tmp = (z * y3) * (c * -y0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (b * ((x * y) - (z * t)));
	double tmp;
	if (y0 <= -3.8e+153) {
		tmp = x * (j * (b * -y0));
	} else if (y0 <= -1.1e+55) {
		tmp = t_1;
	} else if (y0 <= -1550000000.0) {
		tmp = j * (y1 * (y4 * -y3));
	} else if (y0 <= 5.8e-170) {
		tmp = t_1;
	} else if (y0 <= 1.25e-8) {
		tmp = (y3 * y4) * (y * c);
	} else if ((y0 <= 1.85e+125) || !(y0 <= 7.5e+230)) {
		tmp = c * (x * (y0 * y2));
	} else {
		tmp = (z * y3) * (c * -y0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (b * ((x * y) - (z * t)))
	tmp = 0
	if y0 <= -3.8e+153:
		tmp = x * (j * (b * -y0))
	elif y0 <= -1.1e+55:
		tmp = t_1
	elif y0 <= -1550000000.0:
		tmp = j * (y1 * (y4 * -y3))
	elif y0 <= 5.8e-170:
		tmp = t_1
	elif y0 <= 1.25e-8:
		tmp = (y3 * y4) * (y * c)
	elif (y0 <= 1.85e+125) or not (y0 <= 7.5e+230):
		tmp = c * (x * (y0 * y2))
	else:
		tmp = (z * y3) * (c * -y0)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))))
	tmp = 0.0
	if (y0 <= -3.8e+153)
		tmp = Float64(x * Float64(j * Float64(b * Float64(-y0))));
	elseif (y0 <= -1.1e+55)
		tmp = t_1;
	elseif (y0 <= -1550000000.0)
		tmp = Float64(j * Float64(y1 * Float64(y4 * Float64(-y3))));
	elseif (y0 <= 5.8e-170)
		tmp = t_1;
	elseif (y0 <= 1.25e-8)
		tmp = Float64(Float64(y3 * y4) * Float64(y * c));
	elseif ((y0 <= 1.85e+125) || !(y0 <= 7.5e+230))
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	else
		tmp = Float64(Float64(z * y3) * Float64(c * Float64(-y0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (b * ((x * y) - (z * t)));
	tmp = 0.0;
	if (y0 <= -3.8e+153)
		tmp = x * (j * (b * -y0));
	elseif (y0 <= -1.1e+55)
		tmp = t_1;
	elseif (y0 <= -1550000000.0)
		tmp = j * (y1 * (y4 * -y3));
	elseif (y0 <= 5.8e-170)
		tmp = t_1;
	elseif (y0 <= 1.25e-8)
		tmp = (y3 * y4) * (y * c);
	elseif ((y0 <= 1.85e+125) || ~((y0 <= 7.5e+230)))
		tmp = c * (x * (y0 * y2));
	else
		tmp = (z * y3) * (c * -y0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -3.8e+153], N[(x * N[(j * N[(b * (-y0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1.1e+55], t$95$1, If[LessEqual[y0, -1550000000.0], N[(j * N[(y1 * N[(y4 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 5.8e-170], t$95$1, If[LessEqual[y0, 1.25e-8], N[(N[(y3 * y4), $MachinePrecision] * N[(y * c), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y0, 1.85e+125], N[Not[LessEqual[y0, 7.5e+230]], $MachinePrecision]], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * y3), $MachinePrecision] * N[(c * (-y0)), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y0 < -3.79999999999999966e153

   1. Initial program 14.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in x around inf 37.8%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in j around inf 46.6%

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 46.6%

         \[\leadsto x \cdot \left(j \cdot \left(\color{blue}{y1 \cdot i} - b \cdot y0\right)\right) \]

      2. *-commutative 46.6%

         \[\leadsto x \cdot \left(j \cdot \left(y1 \cdot i - \color{blue}{y0 \cdot b}\right)\right) \]

   5. Simplified 46.6%

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(y1 \cdot i - y0 \cdot b\right)\right)} \]

   6. Taylor expanded in y1 around 0 49.5%

      \[\leadsto x \cdot \left(j \cdot \color{blue}{\left(-1 \cdot \left(b \cdot y0\right)\right)}\right) \]
   7. Step-by-step derivation

      1. mul-1-neg 49.5%

         \[\leadsto x \cdot \left(j \cdot \color{blue}{\left(-b \cdot y0\right)}\right) \]

      2. *-commutative 49.5%

         \[\leadsto x \cdot \left(j \cdot \left(-\color{blue}{y0 \cdot b}\right)\right) \]

      3. distribute-rgt-neg-in 49.5%

         \[\leadsto x \cdot \left(j \cdot \color{blue}{\left(y0 \cdot \left(-b\right)\right)}\right) \]

   8. Simplified 49.5%

      \[\leadsto x \cdot \left(j \cdot \color{blue}{\left(y0 \cdot \left(-b\right)\right)}\right) \]

   if -3.79999999999999966e153 < y0 < -1.10000000000000005e55 or -1.55e9 < y0 < 5.8000000000000001e-170

   1. Initial program 41.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf 40.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in a around inf 32.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if -1.10000000000000005e55 < y0 < -1.55e9

   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. Taylor expanded in y3 around -inf 50.3%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   3. Taylor expanded in y4 around inf 60.5%

      \[\leadsto -1 \cdot \color{blue}{\left(y3 \cdot \left(y4 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 60.5%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(y3 \cdot y4\right) \cdot \left(j \cdot y1 - c \cdot y\right)\right)} \]

      2. *-commutative 60.5%

         \[\leadsto -1 \cdot \left(\left(y3 \cdot y4\right) \cdot \left(\color{blue}{y1 \cdot j} - c \cdot y\right)\right) \]

   5. Simplified 60.5%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(y3 \cdot y4\right) \cdot \left(y1 \cdot j - c \cdot y\right)\right)} \]

   6. Taylor expanded in y1 around inf 60.6%

      \[\leadsto -1 \cdot \color{blue}{\left(j \cdot \left(y1 \cdot \left(y3 \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 60.6%

         \[\leadsto -1 \cdot \left(j \cdot \color{blue}{\left(\left(y3 \cdot y4\right) \cdot y1\right)}\right) \]

   8. Simplified 60.6%

      \[\leadsto -1 \cdot \color{blue}{\left(j \cdot \left(\left(y3 \cdot y4\right) \cdot y1\right)\right)} \]

   if 5.8000000000000001e-170 < y0 < 1.2499999999999999e-8

   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. Taylor expanded in y3 around -inf 33.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   3. Taylor expanded in y4 around inf 27.5%

      \[\leadsto -1 \cdot \color{blue}{\left(y3 \cdot \left(y4 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 24.6%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(y3 \cdot y4\right) \cdot \left(j \cdot y1 - c \cdot y\right)\right)} \]

      2. *-commutative 24.6%

         \[\leadsto -1 \cdot \left(\left(y3 \cdot y4\right) \cdot \left(\color{blue}{y1 \cdot j} - c \cdot y\right)\right) \]

   5. Simplified 24.6%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(y3 \cdot y4\right) \cdot \left(y1 \cdot j - c \cdot y\right)\right)} \]

   6. Taylor expanded in y1 around 0 30.5%

      \[\leadsto -1 \cdot \left(\left(y3 \cdot y4\right) \cdot \color{blue}{\left(-1 \cdot \left(c \cdot y\right)\right)}\right) \]
   7. Step-by-step derivation

      1. neg-mul-1 30.5%

         \[\leadsto -1 \cdot \left(\left(y3 \cdot y4\right) \cdot \color{blue}{\left(-c \cdot y\right)}\right) \]

      2. distribute-rgt-neg-in 30.5%

         \[\leadsto -1 \cdot \left(\left(y3 \cdot y4\right) \cdot \color{blue}{\left(c \cdot \left(-y\right)\right)}\right) \]

   8. Simplified 30.5%

      \[\leadsto -1 \cdot \left(\left(y3 \cdot y4\right) \cdot \color{blue}{\left(c \cdot \left(-y\right)\right)}\right) \]

   if 1.2499999999999999e-8 < y0 < 1.8499999999999999e125 or 7.5000000000000004e230 < y0

   1. Initial program 30.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 44.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 44.6%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 44.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 44.6%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 44.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 44.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 44.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 44.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 44.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 54.1%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 49.6%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]

   if 1.8499999999999999e125 < y0 < 7.5000000000000004e230

   1. Initial program 35.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 29.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 29.1%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 29.1%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 29.1%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 29.1%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 29.1%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 29.1%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 29.1%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 29.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 45.7%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   6. Taylor expanded in x around 0 45.6%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 45.6%

         \[\leadsto \color{blue}{-c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)} \]

      2. associate-*r* 53.0%

         \[\leadsto -\color{blue}{\left(c \cdot y0\right) \cdot \left(y3 \cdot z\right)} \]

      3. distribute-rgt-neg-in 53.0%

         \[\leadsto \color{blue}{\left(c \cdot y0\right) \cdot \left(-y3 \cdot z\right)} \]

      4. distribute-lft-neg-in 53.0%

         \[\leadsto \left(c \cdot y0\right) \cdot \color{blue}{\left(\left(-y3\right) \cdot z\right)} \]

      5. *-commutative 53.0%

         \[\leadsto \left(c \cdot y0\right) \cdot \color{blue}{\left(z \cdot \left(-y3\right)\right)} \]

   8. Simplified 53.0%

      \[\leadsto \color{blue}{\left(c \cdot y0\right) \cdot \left(z \cdot \left(-y3\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -3.8 \cdot 10^{+153}:\\ \;\;\;\;x \cdot \left(j \cdot \left(b \cdot \left(-y0\right)\right)\right)\\ \mathbf{elif}\;y0 \leq -1.1 \cdot 10^{+55}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y0 \leq -1550000000:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(y4 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 5.8 \cdot 10^{-170}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y0 \leq 1.25 \cdot 10^{-8}:\\ \;\;\;\;\left(y3 \cdot y4\right) \cdot \left(y \cdot c\right)\\ \mathbf{elif}\;y0 \leq 1.85 \cdot 10^{+125} \lor \neg \left(y0 \leq 7.5 \cdot 10^{+230}\right):\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y3\right) \cdot \left(c \cdot \left(-y0\right)\right)\\ \end{array} \]

Alternative 30: 21.0% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{if}\;y4 \leq -2.4 \cdot 10^{+184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y4 \leq -4.3 \cdot 10^{-209}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq 7 \cdot 10^{-163}:\\ \;\;\;\;\left(z \cdot y3\right) \cdot \left(c \cdot \left(-y0\right)\right)\\ \mathbf{elif}\;y4 \leq 2.3 \cdot 10^{-31}:\\ \;\;\;\;\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq 3.8 \cdot 10^{+120}:\\ \;\;\;\;\left(z \cdot y3\right) \cdot \left(a \cdot y1\right)\\ \mathbf{elif}\;y4 \leq 8.5 \cdot 10^{+241}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(y4 \cdot \left(-y3\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y (* y3 y4)))))
   (if (<= y4 -2.4e+184)
     t_1
     (if (<= y4 -4.3e-209)
       (* x (* c (* y0 y2)))
       (if (<= y4 7e-163)
         (* (* z y3) (* c (- y0)))
         (if (<= y4 2.3e-31)
           (* (- a) (* y3 (* y y5)))
           (if (<= y4 3.8e+120)
             (* (* z y3) (* a y1))
             (if (<= y4 8.5e+241) t_1 (* j (* y1 (* y4 (- y3))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y * (y3 * y4));
	double tmp;
	if (y4 <= -2.4e+184) {
		tmp = t_1;
	} else if (y4 <= -4.3e-209) {
		tmp = x * (c * (y0 * y2));
	} else if (y4 <= 7e-163) {
		tmp = (z * y3) * (c * -y0);
	} else if (y4 <= 2.3e-31) {
		tmp = -a * (y3 * (y * y5));
	} else if (y4 <= 3.8e+120) {
		tmp = (z * y3) * (a * y1);
	} else if (y4 <= 8.5e+241) {
		tmp = t_1;
	} else {
		tmp = j * (y1 * (y4 * -y3));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (y * (y3 * y4))
    if (y4 <= (-2.4d+184)) then
        tmp = t_1
    else if (y4 <= (-4.3d-209)) then
        tmp = x * (c * (y0 * y2))
    else if (y4 <= 7d-163) then
        tmp = (z * y3) * (c * -y0)
    else if (y4 <= 2.3d-31) then
        tmp = -a * (y3 * (y * y5))
    else if (y4 <= 3.8d+120) then
        tmp = (z * y3) * (a * y1)
    else if (y4 <= 8.5d+241) then
        tmp = t_1
    else
        tmp = j * (y1 * (y4 * -y3))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y * (y3 * y4));
	double tmp;
	if (y4 <= -2.4e+184) {
		tmp = t_1;
	} else if (y4 <= -4.3e-209) {
		tmp = x * (c * (y0 * y2));
	} else if (y4 <= 7e-163) {
		tmp = (z * y3) * (c * -y0);
	} else if (y4 <= 2.3e-31) {
		tmp = -a * (y3 * (y * y5));
	} else if (y4 <= 3.8e+120) {
		tmp = (z * y3) * (a * y1);
	} else if (y4 <= 8.5e+241) {
		tmp = t_1;
	} else {
		tmp = j * (y1 * (y4 * -y3));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (y * (y3 * y4))
	tmp = 0
	if y4 <= -2.4e+184:
		tmp = t_1
	elif y4 <= -4.3e-209:
		tmp = x * (c * (y0 * y2))
	elif y4 <= 7e-163:
		tmp = (z * y3) * (c * -y0)
	elif y4 <= 2.3e-31:
		tmp = -a * (y3 * (y * y5))
	elif y4 <= 3.8e+120:
		tmp = (z * y3) * (a * y1)
	elif y4 <= 8.5e+241:
		tmp = t_1
	else:
		tmp = j * (y1 * (y4 * -y3))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(y * Float64(y3 * y4)))
	tmp = 0.0
	if (y4 <= -2.4e+184)
		tmp = t_1;
	elseif (y4 <= -4.3e-209)
		tmp = Float64(x * Float64(c * Float64(y0 * y2)));
	elseif (y4 <= 7e-163)
		tmp = Float64(Float64(z * y3) * Float64(c * Float64(-y0)));
	elseif (y4 <= 2.3e-31)
		tmp = Float64(Float64(-a) * Float64(y3 * Float64(y * y5)));
	elseif (y4 <= 3.8e+120)
		tmp = Float64(Float64(z * y3) * Float64(a * y1));
	elseif (y4 <= 8.5e+241)
		tmp = t_1;
	else
		tmp = Float64(j * Float64(y1 * Float64(y4 * Float64(-y3))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (y * (y3 * y4));
	tmp = 0.0;
	if (y4 <= -2.4e+184)
		tmp = t_1;
	elseif (y4 <= -4.3e-209)
		tmp = x * (c * (y0 * y2));
	elseif (y4 <= 7e-163)
		tmp = (z * y3) * (c * -y0);
	elseif (y4 <= 2.3e-31)
		tmp = -a * (y3 * (y * y5));
	elseif (y4 <= 3.8e+120)
		tmp = (z * y3) * (a * y1);
	elseif (y4 <= 8.5e+241)
		tmp = t_1;
	else
		tmp = j * (y1 * (y4 * -y3));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -2.4e+184], t$95$1, If[LessEqual[y4, -4.3e-209], N[(x * N[(c * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 7e-163], N[(N[(z * y3), $MachinePrecision] * N[(c * (-y0)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 2.3e-31], N[((-a) * N[(y3 * N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 3.8e+120], N[(N[(z * y3), $MachinePrecision] * N[(a * y1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 8.5e+241], t$95$1, N[(j * N[(y1 * N[(y4 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y4 < -2.39999999999999997e184 or 3.7999999999999998e120 < y4 < 8.49999999999999954e241

   1. Initial program 13.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y3 around -inf 41.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   3. Taylor expanded in y4 around inf 48.1%

      \[\leadsto -1 \cdot \color{blue}{\left(y3 \cdot \left(y4 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 46.4%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(y3 \cdot y4\right) \cdot \left(j \cdot y1 - c \cdot y\right)\right)} \]

      2. *-commutative 46.4%

         \[\leadsto -1 \cdot \left(\left(y3 \cdot y4\right) \cdot \left(\color{blue}{y1 \cdot j} - c \cdot y\right)\right) \]

   5. Simplified 46.4%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(y3 \cdot y4\right) \cdot \left(y1 \cdot j - c \cdot y\right)\right)} \]

   6. Taylor expanded in y1 around 0 42.5%

      \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 42.5%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(-1 \cdot c\right) \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\right)} \]

      2. neg-mul-1 42.5%

         \[\leadsto -1 \cdot \left(\color{blue}{\left(-c\right)} \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\right) \]

   8. Simplified 42.5%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(-c\right) \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\right)} \]

   if -2.39999999999999997e184 < y4 < -4.30000000000000005e-209

   1. Initial program 41.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 40.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 40.1%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 40.1%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 40.1%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 40.1%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 40.1%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 40.1%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 40.1%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 40.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 31.8%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 28.0%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 28.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y0 \cdot y2\right)\right) \cdot c} \]

      2. associate-*l* 30.2%

         \[\leadsto \color{blue}{x \cdot \left(\left(y0 \cdot y2\right) \cdot c\right)} \]

   8. Simplified 30.2%

      \[\leadsto \color{blue}{x \cdot \left(\left(y0 \cdot y2\right) \cdot c\right)} \]

   if -4.30000000000000005e-209 < y4 < 7.00000000000000054e-163

   1. Initial program 35.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 38.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 38.8%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 38.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 38.8%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 38.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 38.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 38.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 38.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 38.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 48.1%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   6. Taylor expanded in x around 0 39.2%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 39.2%

         \[\leadsto \color{blue}{-c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)} \]

      2. associate-*r* 45.5%

         \[\leadsto -\color{blue}{\left(c \cdot y0\right) \cdot \left(y3 \cdot z\right)} \]

      3. distribute-rgt-neg-in 45.5%

         \[\leadsto \color{blue}{\left(c \cdot y0\right) \cdot \left(-y3 \cdot z\right)} \]

      4. distribute-lft-neg-in 45.5%

         \[\leadsto \left(c \cdot y0\right) \cdot \color{blue}{\left(\left(-y3\right) \cdot z\right)} \]

      5. *-commutative 45.5%

         \[\leadsto \left(c \cdot y0\right) \cdot \color{blue}{\left(z \cdot \left(-y3\right)\right)} \]

   8. Simplified 45.5%

      \[\leadsto \color{blue}{\left(c \cdot y0\right) \cdot \left(z \cdot \left(-y3\right)\right)} \]

   if 7.00000000000000054e-163 < y4 < 2.2999999999999998e-31

   1. Initial program 48.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around -inf 31.6%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 31.6%

         \[\leadsto \color{blue}{-a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. distribute-rgt-neg-in 31.6%

         \[\leadsto \color{blue}{a \cdot \left(-\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      3. +-commutative 31.6%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. mul-1-neg 31.6%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-b \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. unsub-neg 31.6%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 31.6%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. *-commutative 31.6%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative 31.6%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   4. Simplified 31.6%

      \[\leadsto \color{blue}{a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(y \cdot x - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   5. Taylor expanded in y around -inf 34.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 34.9%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)} \]

      2. neg-mul-1 34.9%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(y \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right) \]

      3. +-commutative 34.9%

         \[\leadsto \left(-a\right) \cdot \left(y \cdot \color{blue}{\left(y3 \cdot y5 + -1 \cdot \left(b \cdot x\right)\right)}\right) \]

      4. mul-1-neg 34.9%

         \[\leadsto \left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5 + \color{blue}{\left(-b \cdot x\right)}\right)\right) \]

      5. unsub-neg 34.9%

         \[\leadsto \left(-a\right) \cdot \left(y \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]

   7. Simplified 34.9%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)} \]

   8. Taylor expanded in y3 around inf 35.8%

      \[\leadsto \left(-a\right) \cdot \color{blue}{\left(y \cdot \left(y3 \cdot y5\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 35.8%

         \[\leadsto \left(-a\right) \cdot \color{blue}{\left(\left(y \cdot y3\right) \cdot y5\right)} \]

      2. *-commutative 35.8%

         \[\leadsto \left(-a\right) \cdot \left(\color{blue}{\left(y3 \cdot y\right)} \cdot y5\right) \]

      3. associate-*l* 39.0%

         \[\leadsto \left(-a\right) \cdot \color{blue}{\left(y3 \cdot \left(y \cdot y5\right)\right)} \]

   10. Simplified 39.0%

       \[\leadsto \left(-a\right) \cdot \color{blue}{\left(y3 \cdot \left(y \cdot y5\right)\right)} \]

   if 2.2999999999999998e-31 < y4 < 3.7999999999999998e120

   1. Initial program 22.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around -inf 52.7%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 52.7%

         \[\leadsto \color{blue}{-a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. distribute-rgt-neg-in 52.7%

         \[\leadsto \color{blue}{a \cdot \left(-\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      3. +-commutative 52.7%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. mul-1-neg 52.7%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-b \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. unsub-neg 52.7%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 52.7%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. *-commutative 52.7%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative 52.7%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   4. Simplified 52.7%

      \[\leadsto \color{blue}{a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(y \cdot x - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   5. Taylor expanded in y3 around -inf 27.3%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 27.3%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]

      2. neg-mul-1 27.3%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right) \]

      3. *-commutative 27.3%

         \[\leadsto \left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - \color{blue}{z \cdot y1}\right)\right) \]

   7. Simplified 27.3%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - z \cdot y1\right)\right)} \]

   8. Taylor expanded in y around 0 27.3%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 31.4%

         \[\leadsto \color{blue}{\left(a \cdot y1\right) \cdot \left(y3 \cdot z\right)} \]

   10. Simplified 31.4%

       \[\leadsto \color{blue}{\left(a \cdot y1\right) \cdot \left(y3 \cdot z\right)} \]

   if 8.49999999999999954e241 < y4

   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. Taylor expanded in y3 around -inf 38.1%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   3. Taylor expanded in y4 around inf 52.8%

      \[\leadsto -1 \cdot \color{blue}{\left(y3 \cdot \left(y4 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 43.8%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(y3 \cdot y4\right) \cdot \left(j \cdot y1 - c \cdot y\right)\right)} \]

      2. *-commutative 43.8%

         \[\leadsto -1 \cdot \left(\left(y3 \cdot y4\right) \cdot \left(\color{blue}{y1 \cdot j} - c \cdot y\right)\right) \]

   5. Simplified 43.8%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(y3 \cdot y4\right) \cdot \left(y1 \cdot j - c \cdot y\right)\right)} \]

   6. Taylor expanded in y1 around inf 39.9%

      \[\leadsto -1 \cdot \color{blue}{\left(j \cdot \left(y1 \cdot \left(y3 \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 39.9%

         \[\leadsto -1 \cdot \left(j \cdot \color{blue}{\left(\left(y3 \cdot y4\right) \cdot y1\right)}\right) \]

   8. Simplified 39.9%

      \[\leadsto -1 \cdot \color{blue}{\left(j \cdot \left(\left(y3 \cdot y4\right) \cdot y1\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 37.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -2.4 \cdot 10^{+184}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -4.3 \cdot 10^{-209}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq 7 \cdot 10^{-163}:\\ \;\;\;\;\left(z \cdot y3\right) \cdot \left(c \cdot \left(-y0\right)\right)\\ \mathbf{elif}\;y4 \leq 2.3 \cdot 10^{-31}:\\ \;\;\;\;\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq 3.8 \cdot 10^{+120}:\\ \;\;\;\;\left(z \cdot y3\right) \cdot \left(a \cdot y1\right)\\ \mathbf{elif}\;y4 \leq 8.5 \cdot 10^{+241}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(y4 \cdot \left(-y3\right)\right)\right)\\ \end{array} \]

Alternative 31: 20.1% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(z \cdot y3\right) \cdot \left(-y0\right)\right)\\ \mathbf{if}\;y3 \leq -1.32 \cdot 10^{+253}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y3 \leq -3.2 \cdot 10^{-64}:\\ \;\;\;\;\left(z \cdot y3\right) \cdot \left(a \cdot y1\right)\\ \mathbf{elif}\;y3 \leq 4.3 \cdot 10^{+61}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 1.28 \cdot 10^{+98}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;y3 \leq 4.5 \cdot 10^{+212}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* (* z y3) (- y0)))))
   (if (<= y3 -1.32e+253)
     t_1
     (if (<= y3 -3.2e-64)
       (* (* z y3) (* a y1))
       (if (<= y3 4.3e+61)
         (* c (* x (* y0 y2)))
         (if (<= y3 1.28e+98)
           (* a (* y (* x b)))
           (if (<= y3 4.5e+212) (* x (* c (* y0 y2))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * ((z * y3) * -y0);
	double tmp;
	if (y3 <= -1.32e+253) {
		tmp = t_1;
	} else if (y3 <= -3.2e-64) {
		tmp = (z * y3) * (a * y1);
	} else if (y3 <= 4.3e+61) {
		tmp = c * (x * (y0 * y2));
	} else if (y3 <= 1.28e+98) {
		tmp = a * (y * (x * b));
	} else if (y3 <= 4.5e+212) {
		tmp = x * (c * (y0 * y2));
	} 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 = c * ((z * y3) * -y0)
    if (y3 <= (-1.32d+253)) then
        tmp = t_1
    else if (y3 <= (-3.2d-64)) then
        tmp = (z * y3) * (a * y1)
    else if (y3 <= 4.3d+61) then
        tmp = c * (x * (y0 * y2))
    else if (y3 <= 1.28d+98) then
        tmp = a * (y * (x * b))
    else if (y3 <= 4.5d+212) then
        tmp = x * (c * (y0 * y2))
    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 = c * ((z * y3) * -y0);
	double tmp;
	if (y3 <= -1.32e+253) {
		tmp = t_1;
	} else if (y3 <= -3.2e-64) {
		tmp = (z * y3) * (a * y1);
	} else if (y3 <= 4.3e+61) {
		tmp = c * (x * (y0 * y2));
	} else if (y3 <= 1.28e+98) {
		tmp = a * (y * (x * b));
	} else if (y3 <= 4.5e+212) {
		tmp = x * (c * (y0 * y2));
	} 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 = c * ((z * y3) * -y0)
	tmp = 0
	if y3 <= -1.32e+253:
		tmp = t_1
	elif y3 <= -3.2e-64:
		tmp = (z * y3) * (a * y1)
	elif y3 <= 4.3e+61:
		tmp = c * (x * (y0 * y2))
	elif y3 <= 1.28e+98:
		tmp = a * (y * (x * b))
	elif y3 <= 4.5e+212:
		tmp = x * (c * (y0 * y2))
	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(c * Float64(Float64(z * y3) * Float64(-y0)))
	tmp = 0.0
	if (y3 <= -1.32e+253)
		tmp = t_1;
	elseif (y3 <= -3.2e-64)
		tmp = Float64(Float64(z * y3) * Float64(a * y1));
	elseif (y3 <= 4.3e+61)
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	elseif (y3 <= 1.28e+98)
		tmp = Float64(a * Float64(y * Float64(x * b)));
	elseif (y3 <= 4.5e+212)
		tmp = Float64(x * Float64(c * Float64(y0 * y2)));
	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 = c * ((z * y3) * -y0);
	tmp = 0.0;
	if (y3 <= -1.32e+253)
		tmp = t_1;
	elseif (y3 <= -3.2e-64)
		tmp = (z * y3) * (a * y1);
	elseif (y3 <= 4.3e+61)
		tmp = c * (x * (y0 * y2));
	elseif (y3 <= 1.28e+98)
		tmp = a * (y * (x * b));
	elseif (y3 <= 4.5e+212)
		tmp = x * (c * (y0 * y2));
	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[(c * N[(N[(z * y3), $MachinePrecision] * (-y0)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -1.32e+253], t$95$1, If[LessEqual[y3, -3.2e-64], N[(N[(z * y3), $MachinePrecision] * N[(a * y1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 4.3e+61], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.28e+98], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 4.5e+212], N[(x * N[(c * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y3 < -1.32e253 or 4.5000000000000002e212 < y3

   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. Taylor expanded in c around inf 46.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 46.8%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 46.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 46.8%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 46.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 46.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 46.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 46.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 46.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 54.2%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   6. Taylor expanded in x around 0 54.4%

      \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 54.4%

         \[\leadsto c \cdot \color{blue}{\left(-y0 \cdot \left(y3 \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 54.4%

         \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(-y3 \cdot z\right)\right)} \]

      3. distribute-lft-neg-in 54.4%

         \[\leadsto c \cdot \left(y0 \cdot \color{blue}{\left(\left(-y3\right) \cdot z\right)}\right) \]

      4. *-commutative 54.4%

         \[\leadsto c \cdot \left(y0 \cdot \color{blue}{\left(z \cdot \left(-y3\right)\right)}\right) \]

   8. Simplified 54.4%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(z \cdot \left(-y3\right)\right)\right)} \]

   if -1.32e253 < y3 < -3.19999999999999975e-64

   1. Initial program 31.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around -inf 40.0%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 40.0%

         \[\leadsto \color{blue}{-a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. distribute-rgt-neg-in 40.0%

         \[\leadsto \color{blue}{a \cdot \left(-\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      3. +-commutative 40.0%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. mul-1-neg 40.0%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-b \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. unsub-neg 40.0%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 40.0%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. *-commutative 40.0%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative 40.0%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   4. Simplified 40.0%

      \[\leadsto \color{blue}{a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(y \cdot x - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   5. Taylor expanded in y3 around -inf 36.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 36.2%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]

      2. neg-mul-1 36.2%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right) \]

      3. *-commutative 36.2%

         \[\leadsto \left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - \color{blue}{z \cdot y1}\right)\right) \]

   7. Simplified 36.2%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - z \cdot y1\right)\right)} \]

   8. Taylor expanded in y around 0 29.2%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 31.8%

         \[\leadsto \color{blue}{\left(a \cdot y1\right) \cdot \left(y3 \cdot z\right)} \]

   10. Simplified 31.8%

       \[\leadsto \color{blue}{\left(a \cdot y1\right) \cdot \left(y3 \cdot z\right)} \]

   if -3.19999999999999975e-64 < y3 < 4.3000000000000001e61

   1. Initial program 35.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 42.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 42.7%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 42.7%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 42.7%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 42.7%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 42.7%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 42.7%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 42.7%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 42.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 33.6%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 29.4%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]

   if 4.3000000000000001e61 < y3 < 1.28000000000000006e98

   1. Initial program 54.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf 73.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in a around inf 47.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   4. Taylor expanded in x around inf 38.2%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 55.6%

         \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot x\right) \cdot y\right)} \]

      2. *-commutative 55.6%

         \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot b\right)} \cdot y\right) \]

      3. associate-*l* 38.1%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

   6. Simplified 38.1%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

   7. Taylor expanded in x around 0 38.2%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 38.2%

         \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot b\right)} \]

      2. *-commutative 38.2%

         \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot b\right) \]

      3. associate-*l* 55.6%

         \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(x \cdot b\right)\right)} \]

   9. Simplified 55.6%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(x \cdot b\right)\right)} \]

   if 1.28000000000000006e98 < y3 < 4.5000000000000002e212

   1. Initial program 35.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 31.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 31.0%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 31.0%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 31.0%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 31.0%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 31.0%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 31.0%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 31.0%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 31.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 27.5%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 27.5%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 27.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y0 \cdot y2\right)\right) \cdot c} \]

      2. associate-*l* 31.7%

         \[\leadsto \color{blue}{x \cdot \left(\left(y0 \cdot y2\right) \cdot c\right)} \]

   8. Simplified 31.7%

      \[\leadsto \color{blue}{x \cdot \left(\left(y0 \cdot y2\right) \cdot c\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 34.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -1.32 \cdot 10^{+253}:\\ \;\;\;\;c \cdot \left(\left(z \cdot y3\right) \cdot \left(-y0\right)\right)\\ \mathbf{elif}\;y3 \leq -3.2 \cdot 10^{-64}:\\ \;\;\;\;\left(z \cdot y3\right) \cdot \left(a \cdot y1\right)\\ \mathbf{elif}\;y3 \leq 4.3 \cdot 10^{+61}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 1.28 \cdot 10^{+98}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;y3 \leq 4.5 \cdot 10^{+212}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(z \cdot y3\right) \cdot \left(-y0\right)\right)\\ \end{array} \]

Alternative 32: 21.2% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y0 \leq -3.2 \cdot 10^{+224}:\\ \;\;\;\;x \cdot \left(\left(j \cdot y0\right) \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y0 \leq -1.65 \cdot 10^{+109}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq 2.7 \cdot 10^{-298}:\\ \;\;\;\;z \cdot \left(\left(-a\right) \cdot \left(t \cdot b\right)\right)\\ \mathbf{elif}\;y0 \leq 9 \cdot 10^{+147}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq 4.2 \cdot 10^{+225}:\\ \;\;\;\;c \cdot \left(\left(z \cdot y3\right) \cdot \left(-y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y0 -3.2e+224)
   (* x (* (* j y0) (- b)))
   (if (<= y0 -1.65e+109)
     (* x (* c (* y0 y2)))
     (if (<= y0 2.7e-298)
       (* z (* (- a) (* t b)))
       (if (<= y0 9e+147)
         (* i (* y1 (* x j)))
         (if (<= y0 4.2e+225)
           (* c (* (* z y3) (- y0)))
           (* c (* x (* y0 y2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y0 <= -3.2e+224) {
		tmp = x * ((j * y0) * -b);
	} else if (y0 <= -1.65e+109) {
		tmp = x * (c * (y0 * y2));
	} else if (y0 <= 2.7e-298) {
		tmp = z * (-a * (t * b));
	} else if (y0 <= 9e+147) {
		tmp = i * (y1 * (x * j));
	} else if (y0 <= 4.2e+225) {
		tmp = c * ((z * y3) * -y0);
	} else {
		tmp = c * (x * (y0 * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y0 <= (-3.2d+224)) then
        tmp = x * ((j * y0) * -b)
    else if (y0 <= (-1.65d+109)) then
        tmp = x * (c * (y0 * y2))
    else if (y0 <= 2.7d-298) then
        tmp = z * (-a * (t * b))
    else if (y0 <= 9d+147) then
        tmp = i * (y1 * (x * j))
    else if (y0 <= 4.2d+225) then
        tmp = c * ((z * y3) * -y0)
    else
        tmp = c * (x * (y0 * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y0 <= -3.2e+224) {
		tmp = x * ((j * y0) * -b);
	} else if (y0 <= -1.65e+109) {
		tmp = x * (c * (y0 * y2));
	} else if (y0 <= 2.7e-298) {
		tmp = z * (-a * (t * b));
	} else if (y0 <= 9e+147) {
		tmp = i * (y1 * (x * j));
	} else if (y0 <= 4.2e+225) {
		tmp = c * ((z * y3) * -y0);
	} else {
		tmp = c * (x * (y0 * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y0 <= -3.2e+224:
		tmp = x * ((j * y0) * -b)
	elif y0 <= -1.65e+109:
		tmp = x * (c * (y0 * y2))
	elif y0 <= 2.7e-298:
		tmp = z * (-a * (t * b))
	elif y0 <= 9e+147:
		tmp = i * (y1 * (x * j))
	elif y0 <= 4.2e+225:
		tmp = c * ((z * y3) * -y0)
	else:
		tmp = c * (x * (y0 * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y0 <= -3.2e+224)
		tmp = Float64(x * Float64(Float64(j * y0) * Float64(-b)));
	elseif (y0 <= -1.65e+109)
		tmp = Float64(x * Float64(c * Float64(y0 * y2)));
	elseif (y0 <= 2.7e-298)
		tmp = Float64(z * Float64(Float64(-a) * Float64(t * b)));
	elseif (y0 <= 9e+147)
		tmp = Float64(i * Float64(y1 * Float64(x * j)));
	elseif (y0 <= 4.2e+225)
		tmp = Float64(c * Float64(Float64(z * y3) * Float64(-y0)));
	else
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y0 <= -3.2e+224)
		tmp = x * ((j * y0) * -b);
	elseif (y0 <= -1.65e+109)
		tmp = x * (c * (y0 * y2));
	elseif (y0 <= 2.7e-298)
		tmp = z * (-a * (t * b));
	elseif (y0 <= 9e+147)
		tmp = i * (y1 * (x * j));
	elseif (y0 <= 4.2e+225)
		tmp = c * ((z * y3) * -y0);
	else
		tmp = c * (x * (y0 * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y0, -3.2e+224], N[(x * N[(N[(j * y0), $MachinePrecision] * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1.65e+109], N[(x * N[(c * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 2.7e-298], N[(z * N[((-a) * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 9e+147], N[(i * N[(y1 * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 4.2e+225], N[(c * N[(N[(z * y3), $MachinePrecision] * (-y0)), $MachinePrecision]), $MachinePrecision], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y0 < -3.20000000000000015e224

   1. Initial program 15.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in x around inf 47.9%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in j around inf 58.7%

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 58.7%

         \[\leadsto x \cdot \left(j \cdot \left(\color{blue}{y1 \cdot i} - b \cdot y0\right)\right) \]

      2. *-commutative 58.7%

         \[\leadsto x \cdot \left(j \cdot \left(y1 \cdot i - \color{blue}{y0 \cdot b}\right)\right) \]

   5. Simplified 58.7%

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(y1 \cdot i - y0 \cdot b\right)\right)} \]

   6. Taylor expanded in y1 around 0 64.3%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(b \cdot \left(j \cdot y0\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 64.3%

         \[\leadsto x \cdot \color{blue}{\left(\left(-1 \cdot b\right) \cdot \left(j \cdot y0\right)\right)} \]

      2. neg-mul-1 64.3%

         \[\leadsto x \cdot \left(\color{blue}{\left(-b\right)} \cdot \left(j \cdot y0\right)\right) \]

      3. *-commutative 64.3%

         \[\leadsto x \cdot \left(\left(-b\right) \cdot \color{blue}{\left(y0 \cdot j\right)}\right) \]

   8. Simplified 64.3%

      \[\leadsto x \cdot \color{blue}{\left(\left(-b\right) \cdot \left(y0 \cdot j\right)\right)} \]

   if -3.20000000000000015e224 < y0 < -1.6499999999999999e109

   1. Initial program 18.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 43.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 43.6%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 43.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 43.6%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 43.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 43.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 43.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 43.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 43.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 51.3%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 37.4%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 37.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y0 \cdot y2\right)\right) \cdot c} \]

      2. associate-*l* 40.7%

         \[\leadsto \color{blue}{x \cdot \left(\left(y0 \cdot y2\right) \cdot c\right)} \]

   8. Simplified 40.7%

      \[\leadsto \color{blue}{x \cdot \left(\left(y0 \cdot y2\right) \cdot c\right)} \]

   if -1.6499999999999999e109 < y0 < 2.7000000000000001e-298

   1. Initial program 45.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf 36.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in a around inf 32.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   4. Taylor expanded in x around 0 24.6%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 24.6%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(b \cdot \left(t \cdot z\right)\right)} \]

      2. neg-mul-1 24.6%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(b \cdot \left(t \cdot z\right)\right) \]

      3. *-commutative 24.6%

         \[\leadsto \left(-a\right) \cdot \left(b \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

   6. Simplified 24.6%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(b \cdot \left(z \cdot t\right)\right)} \]

   7. Taylor expanded in a around 0 24.6%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 24.6%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(b \cdot \left(t \cdot z\right)\right)} \]

      2. *-commutative 24.6%

         \[\leadsto \left(-1 \cdot a\right) \cdot \left(b \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

      3. *-commutative 24.6%

         \[\leadsto \left(-1 \cdot a\right) \cdot \color{blue}{\left(\left(z \cdot t\right) \cdot b\right)} \]

      4. neg-mul-1 24.6%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(\left(z \cdot t\right) \cdot b\right) \]

      5. *-commutative 24.6%

         \[\leadsto \color{blue}{\left(\left(z \cdot t\right) \cdot b\right) \cdot \left(-a\right)} \]

      6. associate-*l* 26.9%

         \[\leadsto \color{blue}{\left(z \cdot \left(t \cdot b\right)\right)} \cdot \left(-a\right) \]

      7. associate-*l* 27.9%

         \[\leadsto \color{blue}{z \cdot \left(\left(t \cdot b\right) \cdot \left(-a\right)\right)} \]

   9. Simplified 27.9%

      \[\leadsto \color{blue}{z \cdot \left(\left(t \cdot b\right) \cdot \left(-a\right)\right)} \]

   if 2.7000000000000001e-298 < y0 < 9.00000000000000016e147

   1. Initial program 35.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in x around inf 31.4%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in j around inf 23.5%

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 23.5%

         \[\leadsto x \cdot \left(j \cdot \left(\color{blue}{y1 \cdot i} - b \cdot y0\right)\right) \]

      2. *-commutative 23.5%

         \[\leadsto x \cdot \left(j \cdot \left(y1 \cdot i - \color{blue}{y0 \cdot b}\right)\right) \]

   5. Simplified 23.5%

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(y1 \cdot i - y0 \cdot b\right)\right)} \]

   6. Taylor expanded in y1 around inf 21.2%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 23.4%

         \[\leadsto i \cdot \color{blue}{\left(\left(j \cdot x\right) \cdot y1\right)} \]

   8. Simplified 23.4%

      \[\leadsto \color{blue}{i \cdot \left(\left(j \cdot x\right) \cdot y1\right)} \]

   if 9.00000000000000016e147 < y0 < 4.2e225

   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. Taylor expanded in c around inf 37.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 37.8%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 37.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 37.8%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 37.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 37.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 37.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 37.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 37.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 54.2%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   6. Taylor expanded in x around 0 54.1%

      \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 54.1%

         \[\leadsto c \cdot \color{blue}{\left(-y0 \cdot \left(y3 \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 54.1%

         \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(-y3 \cdot z\right)\right)} \]

      3. distribute-lft-neg-in 54.1%

         \[\leadsto c \cdot \left(y0 \cdot \color{blue}{\left(\left(-y3\right) \cdot z\right)}\right) \]

      4. *-commutative 54.1%

         \[\leadsto c \cdot \left(y0 \cdot \color{blue}{\left(z \cdot \left(-y3\right)\right)}\right) \]

   8. Simplified 54.1%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(z \cdot \left(-y3\right)\right)\right)} \]

   if 4.2e225 < y0

   1. Initial program 12.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 62.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 62.8%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 62.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 62.8%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 62.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 62.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 62.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 62.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 62.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 69.1%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 69.0%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 34.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -3.2 \cdot 10^{+224}:\\ \;\;\;\;x \cdot \left(\left(j \cdot y0\right) \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y0 \leq -1.65 \cdot 10^{+109}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq 2.7 \cdot 10^{-298}:\\ \;\;\;\;z \cdot \left(\left(-a\right) \cdot \left(t \cdot b\right)\right)\\ \mathbf{elif}\;y0 \leq 9 \cdot 10^{+147}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq 4.2 \cdot 10^{+225}:\\ \;\;\;\;c \cdot \left(\left(z \cdot y3\right) \cdot \left(-y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \end{array} \]

Alternative 33: 22.7% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+114}:\\ \;\;\;\;a \cdot \left(b \cdot \left(z \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \left(\left(j \cdot y0\right) \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-162}:\\ \;\;\;\;\left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+50}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(-a\right) \cdot \left(t \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= t -2e+114)
   (* a (* b (* z (- t))))
   (if (<= t -3.5e+19)
     (* x (* (* j y0) (- b)))
     (if (<= t -3e-162)
       (* (- a) (* y (* y3 y5)))
       (if (<= t 9.5e+50) (* c (* x (* y0 y2))) (* z (* (- a) (* t b))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (t <= -2e+114) {
		tmp = a * (b * (z * -t));
	} else if (t <= -3.5e+19) {
		tmp = x * ((j * y0) * -b);
	} else if (t <= -3e-162) {
		tmp = -a * (y * (y3 * y5));
	} else if (t <= 9.5e+50) {
		tmp = c * (x * (y0 * y2));
	} else {
		tmp = z * (-a * (t * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (t <= (-2d+114)) then
        tmp = a * (b * (z * -t))
    else if (t <= (-3.5d+19)) then
        tmp = x * ((j * y0) * -b)
    else if (t <= (-3d-162)) then
        tmp = -a * (y * (y3 * y5))
    else if (t <= 9.5d+50) then
        tmp = c * (x * (y0 * y2))
    else
        tmp = z * (-a * (t * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (t <= -2e+114) {
		tmp = a * (b * (z * -t));
	} else if (t <= -3.5e+19) {
		tmp = x * ((j * y0) * -b);
	} else if (t <= -3e-162) {
		tmp = -a * (y * (y3 * y5));
	} else if (t <= 9.5e+50) {
		tmp = c * (x * (y0 * y2));
	} else {
		tmp = z * (-a * (t * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if t <= -2e+114:
		tmp = a * (b * (z * -t))
	elif t <= -3.5e+19:
		tmp = x * ((j * y0) * -b)
	elif t <= -3e-162:
		tmp = -a * (y * (y3 * y5))
	elif t <= 9.5e+50:
		tmp = c * (x * (y0 * y2))
	else:
		tmp = z * (-a * (t * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (t <= -2e+114)
		tmp = Float64(a * Float64(b * Float64(z * Float64(-t))));
	elseif (t <= -3.5e+19)
		tmp = Float64(x * Float64(Float64(j * y0) * Float64(-b)));
	elseif (t <= -3e-162)
		tmp = Float64(Float64(-a) * Float64(y * Float64(y3 * y5)));
	elseif (t <= 9.5e+50)
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	else
		tmp = Float64(z * Float64(Float64(-a) * Float64(t * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (t <= -2e+114)
		tmp = a * (b * (z * -t));
	elseif (t <= -3.5e+19)
		tmp = x * ((j * y0) * -b);
	elseif (t <= -3e-162)
		tmp = -a * (y * (y3 * y5));
	elseif (t <= 9.5e+50)
		tmp = c * (x * (y0 * y2));
	else
		tmp = z * (-a * (t * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[t, -2e+114], N[(a * N[(b * N[(z * (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.5e+19], N[(x * N[(N[(j * y0), $MachinePrecision] * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3e-162], N[((-a) * N[(y * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e+50], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[((-a) * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2e114

   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. Taylor expanded in b around inf 33.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in a around inf 45.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   4. Taylor expanded in x around 0 36.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 36.2%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(b \cdot \left(t \cdot z\right)\right)} \]

      2. neg-mul-1 36.2%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(b \cdot \left(t \cdot z\right)\right) \]

      3. *-commutative 36.2%

         \[\leadsto \left(-a\right) \cdot \left(b \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

   6. Simplified 36.2%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(b \cdot \left(z \cdot t\right)\right)} \]

   if -2e114 < t < -3.5e19

   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. Taylor expanded in x around inf 37.3%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in j around inf 56.2%

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 56.2%

         \[\leadsto x \cdot \left(j \cdot \left(\color{blue}{y1 \cdot i} - b \cdot y0\right)\right) \]

      2. *-commutative 56.2%

         \[\leadsto x \cdot \left(j \cdot \left(y1 \cdot i - \color{blue}{y0 \cdot b}\right)\right) \]

   5. Simplified 56.2%

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(y1 \cdot i - y0 \cdot b\right)\right)} \]

   6. Taylor expanded in y1 around 0 38.6%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(b \cdot \left(j \cdot y0\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 38.6%

         \[\leadsto x \cdot \color{blue}{\left(\left(-1 \cdot b\right) \cdot \left(j \cdot y0\right)\right)} \]

      2. neg-mul-1 38.6%

         \[\leadsto x \cdot \left(\color{blue}{\left(-b\right)} \cdot \left(j \cdot y0\right)\right) \]

      3. *-commutative 38.6%

         \[\leadsto x \cdot \left(\left(-b\right) \cdot \color{blue}{\left(y0 \cdot j\right)}\right) \]

   8. Simplified 38.6%

      \[\leadsto x \cdot \color{blue}{\left(\left(-b\right) \cdot \left(y0 \cdot j\right)\right)} \]

   if -3.5e19 < t < -2.99999999999999999e-162

   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. Taylor expanded in a around -inf 34.5%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 34.5%

         \[\leadsto \color{blue}{-a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. distribute-rgt-neg-in 34.5%

         \[\leadsto \color{blue}{a \cdot \left(-\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      3. +-commutative 34.5%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. mul-1-neg 34.5%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-b \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. unsub-neg 34.5%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 34.5%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. *-commutative 34.5%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative 34.5%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   4. Simplified 34.5%

      \[\leadsto \color{blue}{a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(y \cdot x - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   5. Taylor expanded in y around -inf 30.1%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 30.1%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)} \]

      2. neg-mul-1 30.1%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(y \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right) \]

      3. +-commutative 30.1%

         \[\leadsto \left(-a\right) \cdot \left(y \cdot \color{blue}{\left(y3 \cdot y5 + -1 \cdot \left(b \cdot x\right)\right)}\right) \]

      4. mul-1-neg 30.1%

         \[\leadsto \left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5 + \color{blue}{\left(-b \cdot x\right)}\right)\right) \]

      5. unsub-neg 30.1%

         \[\leadsto \left(-a\right) \cdot \left(y \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]

   7. Simplified 30.1%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)} \]

   8. Taylor expanded in y3 around inf 29.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 29.9%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)} \]

      2. neg-mul-1 29.9%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(y \cdot \left(y3 \cdot y5\right)\right) \]

   10. Simplified 29.9%

       \[\leadsto \color{blue}{\left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)} \]

   if -2.99999999999999999e-162 < t < 9.4999999999999993e50

   1. Initial program 37.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 44.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 44.6%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 44.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 44.6%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 44.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 44.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 44.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 44.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 44.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 44.2%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 33.0%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]

   if 9.4999999999999993e50 < t

   1. Initial program 39.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf 41.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in a around inf 37.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   4. Taylor expanded in x around 0 29.0%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 29.0%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(b \cdot \left(t \cdot z\right)\right)} \]

      2. neg-mul-1 29.0%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(b \cdot \left(t \cdot z\right)\right) \]

      3. *-commutative 29.0%

         \[\leadsto \left(-a\right) \cdot \left(b \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

   6. Simplified 29.0%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(b \cdot \left(z \cdot t\right)\right)} \]

   7. Taylor expanded in a around 0 29.0%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 29.0%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(b \cdot \left(t \cdot z\right)\right)} \]

      2. *-commutative 29.0%

         \[\leadsto \left(-1 \cdot a\right) \cdot \left(b \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

      3. *-commutative 29.0%

         \[\leadsto \left(-1 \cdot a\right) \cdot \color{blue}{\left(\left(z \cdot t\right) \cdot b\right)} \]

      4. neg-mul-1 29.0%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(\left(z \cdot t\right) \cdot b\right) \]

      5. *-commutative 29.0%

         \[\leadsto \color{blue}{\left(\left(z \cdot t\right) \cdot b\right) \cdot \left(-a\right)} \]

      6. associate-*l* 30.6%

         \[\leadsto \color{blue}{\left(z \cdot \left(t \cdot b\right)\right)} \cdot \left(-a\right) \]

      7. associate-*l* 30.4%

         \[\leadsto \color{blue}{z \cdot \left(\left(t \cdot b\right) \cdot \left(-a\right)\right)} \]

   9. Simplified 30.4%

      \[\leadsto \color{blue}{z \cdot \left(\left(t \cdot b\right) \cdot \left(-a\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 33.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+114}:\\ \;\;\;\;a \cdot \left(b \cdot \left(z \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \left(\left(j \cdot y0\right) \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-162}:\\ \;\;\;\;\left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+50}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(-a\right) \cdot \left(t \cdot b\right)\right)\\ \end{array} \]

Alternative 34: 22.5% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.35 \cdot 10^{+111}:\\ \;\;\;\;a \cdot \left(b \cdot \left(z \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \left(\left(j \cdot y0\right) \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-162}:\\ \;\;\;\;\left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+51}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(t \cdot b\right) \cdot \left(-z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= t -2.35e+111)
   (* a (* b (* z (- t))))
   (if (<= t -1.2e+19)
     (* x (* (* j y0) (- b)))
     (if (<= t -1.75e-162)
       (* (- a) (* y (* y3 y5)))
       (if (<= t 3.5e+51) (* c (* x (* y0 y2))) (* a (* (* t b) (- z))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (t <= -2.35e+111) {
		tmp = a * (b * (z * -t));
	} else if (t <= -1.2e+19) {
		tmp = x * ((j * y0) * -b);
	} else if (t <= -1.75e-162) {
		tmp = -a * (y * (y3 * y5));
	} else if (t <= 3.5e+51) {
		tmp = c * (x * (y0 * y2));
	} else {
		tmp = a * ((t * b) * -z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (t <= (-2.35d+111)) then
        tmp = a * (b * (z * -t))
    else if (t <= (-1.2d+19)) then
        tmp = x * ((j * y0) * -b)
    else if (t <= (-1.75d-162)) then
        tmp = -a * (y * (y3 * y5))
    else if (t <= 3.5d+51) then
        tmp = c * (x * (y0 * y2))
    else
        tmp = a * ((t * b) * -z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (t <= -2.35e+111) {
		tmp = a * (b * (z * -t));
	} else if (t <= -1.2e+19) {
		tmp = x * ((j * y0) * -b);
	} else if (t <= -1.75e-162) {
		tmp = -a * (y * (y3 * y5));
	} else if (t <= 3.5e+51) {
		tmp = c * (x * (y0 * y2));
	} else {
		tmp = a * ((t * b) * -z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if t <= -2.35e+111:
		tmp = a * (b * (z * -t))
	elif t <= -1.2e+19:
		tmp = x * ((j * y0) * -b)
	elif t <= -1.75e-162:
		tmp = -a * (y * (y3 * y5))
	elif t <= 3.5e+51:
		tmp = c * (x * (y0 * y2))
	else:
		tmp = a * ((t * b) * -z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (t <= -2.35e+111)
		tmp = Float64(a * Float64(b * Float64(z * Float64(-t))));
	elseif (t <= -1.2e+19)
		tmp = Float64(x * Float64(Float64(j * y0) * Float64(-b)));
	elseif (t <= -1.75e-162)
		tmp = Float64(Float64(-a) * Float64(y * Float64(y3 * y5)));
	elseif (t <= 3.5e+51)
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	else
		tmp = Float64(a * Float64(Float64(t * b) * Float64(-z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (t <= -2.35e+111)
		tmp = a * (b * (z * -t));
	elseif (t <= -1.2e+19)
		tmp = x * ((j * y0) * -b);
	elseif (t <= -1.75e-162)
		tmp = -a * (y * (y3 * y5));
	elseif (t <= 3.5e+51)
		tmp = c * (x * (y0 * y2));
	else
		tmp = a * ((t * b) * -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[t, -2.35e+111], N[(a * N[(b * N[(z * (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.2e+19], N[(x * N[(N[(j * y0), $MachinePrecision] * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.75e-162], N[((-a) * N[(y * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e+51], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(t * b), $MachinePrecision] * (-z)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.35000000000000004e111

   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. Taylor expanded in b around inf 33.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in a around inf 45.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   4. Taylor expanded in x around 0 36.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 36.2%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(b \cdot \left(t \cdot z\right)\right)} \]

      2. neg-mul-1 36.2%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(b \cdot \left(t \cdot z\right)\right) \]

      3. *-commutative 36.2%

         \[\leadsto \left(-a\right) \cdot \left(b \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

   6. Simplified 36.2%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(b \cdot \left(z \cdot t\right)\right)} \]

   if -2.35000000000000004e111 < t < -1.2e19

   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. Taylor expanded in x around inf 37.3%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in j around inf 56.2%

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 56.2%

         \[\leadsto x \cdot \left(j \cdot \left(\color{blue}{y1 \cdot i} - b \cdot y0\right)\right) \]

      2. *-commutative 56.2%

         \[\leadsto x \cdot \left(j \cdot \left(y1 \cdot i - \color{blue}{y0 \cdot b}\right)\right) \]

   5. Simplified 56.2%

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(y1 \cdot i - y0 \cdot b\right)\right)} \]

   6. Taylor expanded in y1 around 0 38.6%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(b \cdot \left(j \cdot y0\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 38.6%

         \[\leadsto x \cdot \color{blue}{\left(\left(-1 \cdot b\right) \cdot \left(j \cdot y0\right)\right)} \]

      2. neg-mul-1 38.6%

         \[\leadsto x \cdot \left(\color{blue}{\left(-b\right)} \cdot \left(j \cdot y0\right)\right) \]

      3. *-commutative 38.6%

         \[\leadsto x \cdot \left(\left(-b\right) \cdot \color{blue}{\left(y0 \cdot j\right)}\right) \]

   8. Simplified 38.6%

      \[\leadsto x \cdot \color{blue}{\left(\left(-b\right) \cdot \left(y0 \cdot j\right)\right)} \]

   if -1.2e19 < t < -1.74999999999999995e-162

   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. Taylor expanded in a around -inf 34.5%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 34.5%

         \[\leadsto \color{blue}{-a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. distribute-rgt-neg-in 34.5%

         \[\leadsto \color{blue}{a \cdot \left(-\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      3. +-commutative 34.5%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. mul-1-neg 34.5%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-b \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. unsub-neg 34.5%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 34.5%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. *-commutative 34.5%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative 34.5%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   4. Simplified 34.5%

      \[\leadsto \color{blue}{a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(y \cdot x - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   5. Taylor expanded in y around -inf 30.1%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 30.1%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)} \]

      2. neg-mul-1 30.1%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(y \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right) \]

      3. +-commutative 30.1%

         \[\leadsto \left(-a\right) \cdot \left(y \cdot \color{blue}{\left(y3 \cdot y5 + -1 \cdot \left(b \cdot x\right)\right)}\right) \]

      4. mul-1-neg 30.1%

         \[\leadsto \left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5 + \color{blue}{\left(-b \cdot x\right)}\right)\right) \]

      5. unsub-neg 30.1%

         \[\leadsto \left(-a\right) \cdot \left(y \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]

   7. Simplified 30.1%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)} \]

   8. Taylor expanded in y3 around inf 29.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 29.9%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)} \]

      2. neg-mul-1 29.9%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(y \cdot \left(y3 \cdot y5\right)\right) \]

   10. Simplified 29.9%

       \[\leadsto \color{blue}{\left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)} \]

   if -1.74999999999999995e-162 < t < 3.5e51

   1. Initial program 37.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 44.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 44.6%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 44.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 44.6%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 44.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 44.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 44.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 44.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 44.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 44.2%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 33.0%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]

   if 3.5e51 < t

   1. Initial program 39.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf 41.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in a around inf 37.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   4. Taylor expanded in x around 0 29.0%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 29.0%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(b \cdot \left(t \cdot z\right)\right)} \]

      2. neg-mul-1 29.0%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(b \cdot \left(t \cdot z\right)\right) \]

      3. *-commutative 29.0%

         \[\leadsto \left(-a\right) \cdot \left(b \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

   6. Simplified 29.0%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(b \cdot \left(z \cdot t\right)\right)} \]

   7. Taylor expanded in b around 0 29.0%

      \[\leadsto \left(-a\right) \cdot \color{blue}{\left(b \cdot \left(t \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 29.0%

         \[\leadsto \left(-a\right) \cdot \left(b \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

      2. *-commutative 29.0%

         \[\leadsto \left(-a\right) \cdot \color{blue}{\left(\left(z \cdot t\right) \cdot b\right)} \]

      3. associate-*l* 30.6%

         \[\leadsto \left(-a\right) \cdot \color{blue}{\left(z \cdot \left(t \cdot b\right)\right)} \]

   9. Simplified 30.6%

      \[\leadsto \left(-a\right) \cdot \color{blue}{\left(z \cdot \left(t \cdot b\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 33.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.35 \cdot 10^{+111}:\\ \;\;\;\;a \cdot \left(b \cdot \left(z \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \left(\left(j \cdot y0\right) \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-162}:\\ \;\;\;\;\left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+51}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(t \cdot b\right) \cdot \left(-z\right)\right)\\ \end{array} \]

Alternative 35: 22.3% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y5 \leq -1.35 \cdot 10^{+81}:\\ \;\;\;\;\left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq -7.6 \cdot 10^{-262}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq -6.6 \cdot 10^{-307}:\\ \;\;\;\;\left(z \cdot y3\right) \cdot \left(c \cdot \left(-y0\right)\right)\\ \mathbf{elif}\;y5 \leq 1.38 \cdot 10^{+51}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y5 -1.35e+81)
   (* (- a) (* y (* y3 y5)))
   (if (<= y5 -7.6e-262)
     (* x (* c (* y0 y2)))
     (if (<= y5 -6.6e-307)
       (* (* z y3) (* c (- y0)))
       (if (<= y5 1.38e+51)
         (* c (* y0 (* x y2)))
         (* (- a) (* y3 (* y y5))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -1.35e+81) {
		tmp = -a * (y * (y3 * y5));
	} else if (y5 <= -7.6e-262) {
		tmp = x * (c * (y0 * y2));
	} else if (y5 <= -6.6e-307) {
		tmp = (z * y3) * (c * -y0);
	} else if (y5 <= 1.38e+51) {
		tmp = c * (y0 * (x * y2));
	} else {
		tmp = -a * (y3 * (y * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y5 <= (-1.35d+81)) then
        tmp = -a * (y * (y3 * y5))
    else if (y5 <= (-7.6d-262)) then
        tmp = x * (c * (y0 * y2))
    else if (y5 <= (-6.6d-307)) then
        tmp = (z * y3) * (c * -y0)
    else if (y5 <= 1.38d+51) then
        tmp = c * (y0 * (x * y2))
    else
        tmp = -a * (y3 * (y * y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -1.35e+81) {
		tmp = -a * (y * (y3 * y5));
	} else if (y5 <= -7.6e-262) {
		tmp = x * (c * (y0 * y2));
	} else if (y5 <= -6.6e-307) {
		tmp = (z * y3) * (c * -y0);
	} else if (y5 <= 1.38e+51) {
		tmp = c * (y0 * (x * y2));
	} else {
		tmp = -a * (y3 * (y * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y5 <= -1.35e+81:
		tmp = -a * (y * (y3 * y5))
	elif y5 <= -7.6e-262:
		tmp = x * (c * (y0 * y2))
	elif y5 <= -6.6e-307:
		tmp = (z * y3) * (c * -y0)
	elif y5 <= 1.38e+51:
		tmp = c * (y0 * (x * y2))
	else:
		tmp = -a * (y3 * (y * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y5 <= -1.35e+81)
		tmp = Float64(Float64(-a) * Float64(y * Float64(y3 * y5)));
	elseif (y5 <= -7.6e-262)
		tmp = Float64(x * Float64(c * Float64(y0 * y2)));
	elseif (y5 <= -6.6e-307)
		tmp = Float64(Float64(z * y3) * Float64(c * Float64(-y0)));
	elseif (y5 <= 1.38e+51)
		tmp = Float64(c * Float64(y0 * Float64(x * y2)));
	else
		tmp = Float64(Float64(-a) * Float64(y3 * Float64(y * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y5 <= -1.35e+81)
		tmp = -a * (y * (y3 * y5));
	elseif (y5 <= -7.6e-262)
		tmp = x * (c * (y0 * y2));
	elseif (y5 <= -6.6e-307)
		tmp = (z * y3) * (c * -y0);
	elseif (y5 <= 1.38e+51)
		tmp = c * (y0 * (x * y2));
	else
		tmp = -a * (y3 * (y * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y5, -1.35e+81], N[((-a) * N[(y * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -7.6e-262], N[(x * N[(c * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -6.6e-307], N[(N[(z * y3), $MachinePrecision] * N[(c * (-y0)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.38e+51], N[(c * N[(y0 * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-a) * N[(y3 * N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y5 < -1.35e81

   1. Initial program 31.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around -inf 36.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 36.2%

         \[\leadsto \color{blue}{-a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. distribute-rgt-neg-in 36.2%

         \[\leadsto \color{blue}{a \cdot \left(-\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      3. +-commutative 36.2%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. mul-1-neg 36.2%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-b \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. unsub-neg 36.2%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 36.2%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. *-commutative 36.2%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative 36.2%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   4. Simplified 36.2%

      \[\leadsto \color{blue}{a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(y \cdot x - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   5. Taylor expanded in y around -inf 41.5%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 41.5%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)} \]

      2. neg-mul-1 41.5%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(y \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right) \]

      3. +-commutative 41.5%

         \[\leadsto \left(-a\right) \cdot \left(y \cdot \color{blue}{\left(y3 \cdot y5 + -1 \cdot \left(b \cdot x\right)\right)}\right) \]

      4. mul-1-neg 41.5%

         \[\leadsto \left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5 + \color{blue}{\left(-b \cdot x\right)}\right)\right) \]

      5. unsub-neg 41.5%

         \[\leadsto \left(-a\right) \cdot \left(y \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]

   7. Simplified 41.5%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)} \]

   8. Taylor expanded in y3 around inf 39.3%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 39.3%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)} \]

      2. neg-mul-1 39.3%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(y \cdot \left(y3 \cdot y5\right)\right) \]

   10. Simplified 39.3%

       \[\leadsto \color{blue}{\left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)} \]

   if -1.35e81 < y5 < -7.6000000000000004e-262

   1. Initial program 26.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 45.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 45.6%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 45.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 45.6%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 45.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 45.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 45.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 45.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 45.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 38.4%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 30.5%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 30.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y0 \cdot y2\right)\right) \cdot c} \]

      2. associate-*l* 31.8%

         \[\leadsto \color{blue}{x \cdot \left(\left(y0 \cdot y2\right) \cdot c\right)} \]

   8. Simplified 31.8%

      \[\leadsto \color{blue}{x \cdot \left(\left(y0 \cdot y2\right) \cdot c\right)} \]

   if -7.6000000000000004e-262 < y5 < -6.59999999999999999e-307

   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. Taylor expanded in c around inf 45.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 45.8%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 45.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 45.8%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 45.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 45.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 45.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 45.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 45.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 37.0%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   6. Taylor expanded in x around 0 37.5%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 37.5%

         \[\leadsto \color{blue}{-c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)} \]

      2. associate-*r* 46.2%

         \[\leadsto -\color{blue}{\left(c \cdot y0\right) \cdot \left(y3 \cdot z\right)} \]

      3. distribute-rgt-neg-in 46.2%

         \[\leadsto \color{blue}{\left(c \cdot y0\right) \cdot \left(-y3 \cdot z\right)} \]

      4. distribute-lft-neg-in 46.2%

         \[\leadsto \left(c \cdot y0\right) \cdot \color{blue}{\left(\left(-y3\right) \cdot z\right)} \]

      5. *-commutative 46.2%

         \[\leadsto \left(c \cdot y0\right) \cdot \color{blue}{\left(z \cdot \left(-y3\right)\right)} \]

   8. Simplified 46.2%

      \[\leadsto \color{blue}{\left(c \cdot y0\right) \cdot \left(z \cdot \left(-y3\right)\right)} \]

   if -6.59999999999999999e-307 < y5 < 1.38000000000000006e51

   1. Initial program 48.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 43.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 43.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 43.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 43.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 43.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 43.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 43.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 43.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 43.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 45.1%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 32.4%

      \[\leadsto c \cdot \color{blue}{\left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 32.5%

         \[\leadsto c \cdot \color{blue}{\left(\left(x \cdot y0\right) \cdot y2\right)} \]

      2. *-commutative 32.5%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot x\right)} \cdot y2\right) \]

      3. associate-*r* 32.8%

         \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2\right)\right)} \]

   8. Simplified 32.8%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2\right)\right)} \]

   if 1.38000000000000006e51 < y5

   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. Taylor expanded in a around -inf 39.6%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 39.6%

         \[\leadsto \color{blue}{-a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. distribute-rgt-neg-in 39.6%

         \[\leadsto \color{blue}{a \cdot \left(-\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      3. +-commutative 39.6%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. mul-1-neg 39.6%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-b \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. unsub-neg 39.6%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 39.6%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. *-commutative 39.6%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative 39.6%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   4. Simplified 39.6%

      \[\leadsto \color{blue}{a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(y \cdot x - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   5. Taylor expanded in y around -inf 33.1%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 33.1%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)} \]

      2. neg-mul-1 33.1%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(y \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right) \]

      3. +-commutative 33.1%

         \[\leadsto \left(-a\right) \cdot \left(y \cdot \color{blue}{\left(y3 \cdot y5 + -1 \cdot \left(b \cdot x\right)\right)}\right) \]

      4. mul-1-neg 33.1%

         \[\leadsto \left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5 + \color{blue}{\left(-b \cdot x\right)}\right)\right) \]

      5. unsub-neg 33.1%

         \[\leadsto \left(-a\right) \cdot \left(y \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]

   7. Simplified 33.1%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)} \]

   8. Taylor expanded in y3 around inf 26.8%

      \[\leadsto \left(-a\right) \cdot \color{blue}{\left(y \cdot \left(y3 \cdot y5\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 25.3%

         \[\leadsto \left(-a\right) \cdot \color{blue}{\left(\left(y \cdot y3\right) \cdot y5\right)} \]

      2. *-commutative 25.3%

         \[\leadsto \left(-a\right) \cdot \left(\color{blue}{\left(y3 \cdot y\right)} \cdot y5\right) \]

      3. associate-*l* 29.9%

         \[\leadsto \left(-a\right) \cdot \color{blue}{\left(y3 \cdot \left(y \cdot y5\right)\right)} \]

   10. Simplified 29.9%

       \[\leadsto \left(-a\right) \cdot \color{blue}{\left(y3 \cdot \left(y \cdot y5\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 33.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -1.35 \cdot 10^{+81}:\\ \;\;\;\;\left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq -7.6 \cdot 10^{-262}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq -6.6 \cdot 10^{-307}:\\ \;\;\;\;\left(z \cdot y3\right) \cdot \left(c \cdot \left(-y0\right)\right)\\ \mathbf{elif}\;y5 \leq 1.38 \cdot 10^{+51}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5\right)\right)\\ \end{array} \]

Alternative 36: 22.2% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y5 \leq -5.3 \cdot 10^{+82}:\\ \;\;\;\;\left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq -2.1 \cdot 10^{-253}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq -3.6 \cdot 10^{-306}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;y5 \leq 5.5 \cdot 10^{+50}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y5 -5.3e+82)
   (* (- a) (* y (* y3 y5)))
   (if (<= y5 -2.1e-253)
     (* x (* c (* y0 y2)))
     (if (<= y5 -3.6e-306)
       (* a (* y3 (* z y1)))
       (if (<= y5 5.5e+50) (* c (* y0 (* x y2))) (* (- a) (* y3 (* y y5))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -5.3e+82) {
		tmp = -a * (y * (y3 * y5));
	} else if (y5 <= -2.1e-253) {
		tmp = x * (c * (y0 * y2));
	} else if (y5 <= -3.6e-306) {
		tmp = a * (y3 * (z * y1));
	} else if (y5 <= 5.5e+50) {
		tmp = c * (y0 * (x * y2));
	} else {
		tmp = -a * (y3 * (y * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y5 <= (-5.3d+82)) then
        tmp = -a * (y * (y3 * y5))
    else if (y5 <= (-2.1d-253)) then
        tmp = x * (c * (y0 * y2))
    else if (y5 <= (-3.6d-306)) then
        tmp = a * (y3 * (z * y1))
    else if (y5 <= 5.5d+50) then
        tmp = c * (y0 * (x * y2))
    else
        tmp = -a * (y3 * (y * y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -5.3e+82) {
		tmp = -a * (y * (y3 * y5));
	} else if (y5 <= -2.1e-253) {
		tmp = x * (c * (y0 * y2));
	} else if (y5 <= -3.6e-306) {
		tmp = a * (y3 * (z * y1));
	} else if (y5 <= 5.5e+50) {
		tmp = c * (y0 * (x * y2));
	} else {
		tmp = -a * (y3 * (y * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y5 <= -5.3e+82:
		tmp = -a * (y * (y3 * y5))
	elif y5 <= -2.1e-253:
		tmp = x * (c * (y0 * y2))
	elif y5 <= -3.6e-306:
		tmp = a * (y3 * (z * y1))
	elif y5 <= 5.5e+50:
		tmp = c * (y0 * (x * y2))
	else:
		tmp = -a * (y3 * (y * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y5 <= -5.3e+82)
		tmp = Float64(Float64(-a) * Float64(y * Float64(y3 * y5)));
	elseif (y5 <= -2.1e-253)
		tmp = Float64(x * Float64(c * Float64(y0 * y2)));
	elseif (y5 <= -3.6e-306)
		tmp = Float64(a * Float64(y3 * Float64(z * y1)));
	elseif (y5 <= 5.5e+50)
		tmp = Float64(c * Float64(y0 * Float64(x * y2)));
	else
		tmp = Float64(Float64(-a) * Float64(y3 * Float64(y * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y5 <= -5.3e+82)
		tmp = -a * (y * (y3 * y5));
	elseif (y5 <= -2.1e-253)
		tmp = x * (c * (y0 * y2));
	elseif (y5 <= -3.6e-306)
		tmp = a * (y3 * (z * y1));
	elseif (y5 <= 5.5e+50)
		tmp = c * (y0 * (x * y2));
	else
		tmp = -a * (y3 * (y * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y5, -5.3e+82], N[((-a) * N[(y * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -2.1e-253], N[(x * N[(c * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -3.6e-306], N[(a * N[(y3 * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 5.5e+50], N[(c * N[(y0 * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-a) * N[(y3 * N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y5 < -5.29999999999999977e82

   1. Initial program 31.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around -inf 36.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 36.2%

         \[\leadsto \color{blue}{-a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. distribute-rgt-neg-in 36.2%

         \[\leadsto \color{blue}{a \cdot \left(-\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      3. +-commutative 36.2%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. mul-1-neg 36.2%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-b \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. unsub-neg 36.2%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 36.2%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. *-commutative 36.2%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative 36.2%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   4. Simplified 36.2%

      \[\leadsto \color{blue}{a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(y \cdot x - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   5. Taylor expanded in y around -inf 41.5%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 41.5%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)} \]

      2. neg-mul-1 41.5%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(y \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right) \]

      3. +-commutative 41.5%

         \[\leadsto \left(-a\right) \cdot \left(y \cdot \color{blue}{\left(y3 \cdot y5 + -1 \cdot \left(b \cdot x\right)\right)}\right) \]

      4. mul-1-neg 41.5%

         \[\leadsto \left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5 + \color{blue}{\left(-b \cdot x\right)}\right)\right) \]

      5. unsub-neg 41.5%

         \[\leadsto \left(-a\right) \cdot \left(y \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]

   7. Simplified 41.5%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)} \]

   8. Taylor expanded in y3 around inf 39.3%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 39.3%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)} \]

      2. neg-mul-1 39.3%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(y \cdot \left(y3 \cdot y5\right)\right) \]

   10. Simplified 39.3%

       \[\leadsto \color{blue}{\left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)} \]

   if -5.29999999999999977e82 < y5 < -2.0999999999999999e-253

   1. Initial program 26.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 45.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 45.6%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 45.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 45.6%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 45.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 45.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 45.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 45.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 45.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 38.4%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 30.5%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 30.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y0 \cdot y2\right)\right) \cdot c} \]

      2. associate-*l* 31.8%

         \[\leadsto \color{blue}{x \cdot \left(\left(y0 \cdot y2\right) \cdot c\right)} \]

   8. Simplified 31.8%

      \[\leadsto \color{blue}{x \cdot \left(\left(y0 \cdot y2\right) \cdot c\right)} \]

   if -2.0999999999999999e-253 < y5 < -3.59999999999999991e-306

   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. Taylor expanded in a around -inf 40.3%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 40.3%

         \[\leadsto \color{blue}{-a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. distribute-rgt-neg-in 40.3%

         \[\leadsto \color{blue}{a \cdot \left(-\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      3. +-commutative 40.3%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. mul-1-neg 40.3%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-b \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. unsub-neg 40.3%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 40.3%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. *-commutative 40.3%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative 40.3%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   4. Simplified 40.3%

      \[\leadsto \color{blue}{a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(y \cdot x - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   5. Taylor expanded in y3 around -inf 60.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 60.2%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]

      2. neg-mul-1 60.2%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right) \]

      3. *-commutative 60.2%

         \[\leadsto \left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - \color{blue}{z \cdot y1}\right)\right) \]

   7. Simplified 60.2%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - z \cdot y1\right)\right)} \]

   8. Taylor expanded in y around 0 51.5%

      \[\leadsto \left(-a\right) \cdot \left(y3 \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot z\right)\right)}\right) \]
   9. Step-by-step derivation

      1. mul-1-neg 51.5%

         \[\leadsto \left(-a\right) \cdot \left(y3 \cdot \color{blue}{\left(-y1 \cdot z\right)}\right) \]

      2. *-commutative 51.5%

         \[\leadsto \left(-a\right) \cdot \left(y3 \cdot \left(-\color{blue}{z \cdot y1}\right)\right) \]

      3. distribute-rgt-neg-in 51.5%

         \[\leadsto \left(-a\right) \cdot \left(y3 \cdot \color{blue}{\left(z \cdot \left(-y1\right)\right)}\right) \]

   10. Simplified 51.5%

       \[\leadsto \left(-a\right) \cdot \left(y3 \cdot \color{blue}{\left(z \cdot \left(-y1\right)\right)}\right) \]

   if -3.59999999999999991e-306 < y5 < 5.4999999999999998e50

   1. Initial program 47.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 44.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 44.2%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 44.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 44.2%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 44.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 44.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 44.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 44.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 44.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 44.4%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 31.9%

      \[\leadsto c \cdot \color{blue}{\left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 32.0%

         \[\leadsto c \cdot \color{blue}{\left(\left(x \cdot y0\right) \cdot y2\right)} \]

      2. *-commutative 32.0%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot x\right)} \cdot y2\right) \]

      3. associate-*r* 32.3%

         \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2\right)\right)} \]

   8. Simplified 32.3%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2\right)\right)} \]

   if 5.4999999999999998e50 < y5

   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. Taylor expanded in a around -inf 39.6%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 39.6%

         \[\leadsto \color{blue}{-a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. distribute-rgt-neg-in 39.6%

         \[\leadsto \color{blue}{a \cdot \left(-\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      3. +-commutative 39.6%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. mul-1-neg 39.6%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-b \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. unsub-neg 39.6%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 39.6%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. *-commutative 39.6%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative 39.6%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   4. Simplified 39.6%

      \[\leadsto \color{blue}{a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(y \cdot x - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   5. Taylor expanded in y around -inf 33.1%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 33.1%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)} \]

      2. neg-mul-1 33.1%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(y \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right) \]

      3. +-commutative 33.1%

         \[\leadsto \left(-a\right) \cdot \left(y \cdot \color{blue}{\left(y3 \cdot y5 + -1 \cdot \left(b \cdot x\right)\right)}\right) \]

      4. mul-1-neg 33.1%

         \[\leadsto \left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5 + \color{blue}{\left(-b \cdot x\right)}\right)\right) \]

      5. unsub-neg 33.1%

         \[\leadsto \left(-a\right) \cdot \left(y \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]

   7. Simplified 33.1%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)} \]

   8. Taylor expanded in y3 around inf 26.8%

      \[\leadsto \left(-a\right) \cdot \color{blue}{\left(y \cdot \left(y3 \cdot y5\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 25.3%

         \[\leadsto \left(-a\right) \cdot \color{blue}{\left(\left(y \cdot y3\right) \cdot y5\right)} \]

      2. *-commutative 25.3%

         \[\leadsto \left(-a\right) \cdot \left(\color{blue}{\left(y3 \cdot y\right)} \cdot y5\right) \]

      3. associate-*l* 29.9%

         \[\leadsto \left(-a\right) \cdot \color{blue}{\left(y3 \cdot \left(y \cdot y5\right)\right)} \]

   10. Simplified 29.9%

       \[\leadsto \left(-a\right) \cdot \color{blue}{\left(y3 \cdot \left(y \cdot y5\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 33.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -5.3 \cdot 10^{+82}:\\ \;\;\;\;\left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq -2.1 \cdot 10^{-253}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq -3.6 \cdot 10^{-306}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;y5 \leq 5.5 \cdot 10^{+50}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5\right)\right)\\ \end{array} \]

Alternative 37: 22.8% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{if}\;y2 \leq -0.059:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq -4.5 \cdot 10^{-152}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 1.7 \cdot 10^{-131}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq 2 \cdot 10^{+45}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* x (* y0 y2)))))
   (if (<= y2 -0.059)
     t_1
     (if (<= y2 -4.5e-152)
       (* a (* y (* x b)))
       (if (<= y2 1.7e-131)
         (* i (* j (* x y1)))
         (if (<= y2 2e+45) (* a (* y1 (* z y3))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (x * (y0 * y2));
	double tmp;
	if (y2 <= -0.059) {
		tmp = t_1;
	} else if (y2 <= -4.5e-152) {
		tmp = a * (y * (x * b));
	} else if (y2 <= 1.7e-131) {
		tmp = i * (j * (x * y1));
	} else if (y2 <= 2e+45) {
		tmp = a * (y1 * (z * y3));
	} 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 = c * (x * (y0 * y2))
    if (y2 <= (-0.059d0)) then
        tmp = t_1
    else if (y2 <= (-4.5d-152)) then
        tmp = a * (y * (x * b))
    else if (y2 <= 1.7d-131) then
        tmp = i * (j * (x * y1))
    else if (y2 <= 2d+45) then
        tmp = a * (y1 * (z * y3))
    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 = c * (x * (y0 * y2));
	double tmp;
	if (y2 <= -0.059) {
		tmp = t_1;
	} else if (y2 <= -4.5e-152) {
		tmp = a * (y * (x * b));
	} else if (y2 <= 1.7e-131) {
		tmp = i * (j * (x * y1));
	} else if (y2 <= 2e+45) {
		tmp = a * (y1 * (z * y3));
	} 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 = c * (x * (y0 * y2))
	tmp = 0
	if y2 <= -0.059:
		tmp = t_1
	elif y2 <= -4.5e-152:
		tmp = a * (y * (x * b))
	elif y2 <= 1.7e-131:
		tmp = i * (j * (x * y1))
	elif y2 <= 2e+45:
		tmp = a * (y1 * (z * y3))
	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(c * Float64(x * Float64(y0 * y2)))
	tmp = 0.0
	if (y2 <= -0.059)
		tmp = t_1;
	elseif (y2 <= -4.5e-152)
		tmp = Float64(a * Float64(y * Float64(x * b)));
	elseif (y2 <= 1.7e-131)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (y2 <= 2e+45)
		tmp = Float64(a * Float64(y1 * Float64(z * y3)));
	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 = c * (x * (y0 * y2));
	tmp = 0.0;
	if (y2 <= -0.059)
		tmp = t_1;
	elseif (y2 <= -4.5e-152)
		tmp = a * (y * (x * b));
	elseif (y2 <= 1.7e-131)
		tmp = i * (j * (x * y1));
	elseif (y2 <= 2e+45)
		tmp = a * (y1 * (z * y3));
	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[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -0.059], t$95$1, If[LessEqual[y2, -4.5e-152], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.7e-131], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2e+45], N[(a * N[(y1 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y2 < -0.058999999999999997 or 1.9999999999999999e45 < y2

   1. Initial program 26.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 46.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 46.2%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 46.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 46.2%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 46.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 46.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 46.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 46.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 46.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 47.4%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 43.8%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]

   if -0.058999999999999997 < y2 < -4.5000000000000004e-152

   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. Taylor expanded in b around inf 51.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in a around inf 29.6%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   4. Taylor expanded in x around inf 20.8%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 23.4%

         \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot x\right) \cdot y\right)} \]

      2. *-commutative 23.4%

         \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot b\right)} \cdot y\right) \]

      3. associate-*l* 20.7%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

   6. Simplified 20.7%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

   7. Taylor expanded in x around 0 20.8%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 20.8%

         \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot b\right)} \]

      2. *-commutative 20.8%

         \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot b\right) \]

      3. associate-*l* 23.4%

         \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(x \cdot b\right)\right)} \]

   9. Simplified 23.4%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(x \cdot b\right)\right)} \]

   if -4.5000000000000004e-152 < y2 < 1.69999999999999998e-131

   1. Initial program 42.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in x around inf 40.2%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in j around inf 36.8%

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 36.8%

         \[\leadsto x \cdot \left(j \cdot \left(\color{blue}{y1 \cdot i} - b \cdot y0\right)\right) \]

      2. *-commutative 36.8%

         \[\leadsto x \cdot \left(j \cdot \left(y1 \cdot i - \color{blue}{y0 \cdot b}\right)\right) \]

   5. Simplified 36.8%

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(y1 \cdot i - y0 \cdot b\right)\right)} \]

   6. Taylor expanded in y1 around inf 23.8%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]

   if 1.69999999999999998e-131 < y2 < 1.9999999999999999e45

   1. Initial program 39.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around -inf 46.4%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 46.4%

         \[\leadsto \color{blue}{-a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. distribute-rgt-neg-in 46.4%

         \[\leadsto \color{blue}{a \cdot \left(-\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      3. +-commutative 46.4%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. mul-1-neg 46.4%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-b \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. unsub-neg 46.4%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 46.4%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. *-commutative 46.4%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative 46.4%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   4. Simplified 46.4%

      \[\leadsto \color{blue}{a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(y \cdot x - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   5. Taylor expanded in y3 around -inf 31.6%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 31.6%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]

      2. neg-mul-1 31.6%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right) \]

      3. *-commutative 31.6%

         \[\leadsto \left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - \color{blue}{z \cdot y1}\right)\right) \]

   7. Simplified 31.6%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - z \cdot y1\right)\right)} \]

   8. Taylor expanded in y around 0 25.6%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 32.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -0.059:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -4.5 \cdot 10^{-152}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 1.7 \cdot 10^{-131}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq 2 \cdot 10^{+45}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \end{array} \]

Alternative 38: 22.7% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -0.012:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -1.86 \cdot 10^{-152}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 5.6 \cdot 10^{-131}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq 2.1 \cdot 10^{+36}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -0.012)
   (* x (* c (* y0 y2)))
   (if (<= y2 -1.86e-152)
     (* a (* y (* x b)))
     (if (<= y2 5.6e-131)
       (* i (* j (* x y1)))
       (if (<= y2 2.1e+36) (* a (* y1 (* z y3))) (* c (* x (* y0 y2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -0.012) {
		tmp = x * (c * (y0 * y2));
	} else if (y2 <= -1.86e-152) {
		tmp = a * (y * (x * b));
	} else if (y2 <= 5.6e-131) {
		tmp = i * (j * (x * y1));
	} else if (y2 <= 2.1e+36) {
		tmp = a * (y1 * (z * y3));
	} else {
		tmp = c * (x * (y0 * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y2 <= (-0.012d0)) then
        tmp = x * (c * (y0 * y2))
    else if (y2 <= (-1.86d-152)) then
        tmp = a * (y * (x * b))
    else if (y2 <= 5.6d-131) then
        tmp = i * (j * (x * y1))
    else if (y2 <= 2.1d+36) then
        tmp = a * (y1 * (z * y3))
    else
        tmp = c * (x * (y0 * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -0.012) {
		tmp = x * (c * (y0 * y2));
	} else if (y2 <= -1.86e-152) {
		tmp = a * (y * (x * b));
	} else if (y2 <= 5.6e-131) {
		tmp = i * (j * (x * y1));
	} else if (y2 <= 2.1e+36) {
		tmp = a * (y1 * (z * y3));
	} else {
		tmp = c * (x * (y0 * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y2 <= -0.012:
		tmp = x * (c * (y0 * y2))
	elif y2 <= -1.86e-152:
		tmp = a * (y * (x * b))
	elif y2 <= 5.6e-131:
		tmp = i * (j * (x * y1))
	elif y2 <= 2.1e+36:
		tmp = a * (y1 * (z * y3))
	else:
		tmp = c * (x * (y0 * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y2 <= -0.012)
		tmp = Float64(x * Float64(c * Float64(y0 * y2)));
	elseif (y2 <= -1.86e-152)
		tmp = Float64(a * Float64(y * Float64(x * b)));
	elseif (y2 <= 5.6e-131)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (y2 <= 2.1e+36)
		tmp = Float64(a * Float64(y1 * Float64(z * y3)));
	else
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y2 <= -0.012)
		tmp = x * (c * (y0 * y2));
	elseif (y2 <= -1.86e-152)
		tmp = a * (y * (x * b));
	elseif (y2 <= 5.6e-131)
		tmp = i * (j * (x * y1));
	elseif (y2 <= 2.1e+36)
		tmp = a * (y1 * (z * y3));
	else
		tmp = c * (x * (y0 * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y2, -0.012], N[(x * N[(c * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1.86e-152], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 5.6e-131], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.1e+36], N[(a * N[(y1 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y2 < -0.012

   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. Taylor expanded in c around inf 37.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 37.2%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 37.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 37.2%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 37.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 37.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 37.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 37.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 37.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 37.7%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 41.1%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 41.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y0 \cdot y2\right)\right) \cdot c} \]

      2. associate-*l* 41.1%

         \[\leadsto \color{blue}{x \cdot \left(\left(y0 \cdot y2\right) \cdot c\right)} \]

   8. Simplified 41.1%

      \[\leadsto \color{blue}{x \cdot \left(\left(y0 \cdot y2\right) \cdot c\right)} \]

   if -0.012 < y2 < -1.8600000000000001e-152

   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. Taylor expanded in b around inf 51.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in a around inf 29.6%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   4. Taylor expanded in x around inf 20.8%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 23.4%

         \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot x\right) \cdot y\right)} \]

      2. *-commutative 23.4%

         \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot b\right)} \cdot y\right) \]

      3. associate-*l* 20.7%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

   6. Simplified 20.7%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

   7. Taylor expanded in x around 0 20.8%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 20.8%

         \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot b\right)} \]

      2. *-commutative 20.8%

         \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot b\right) \]

      3. associate-*l* 23.4%

         \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(x \cdot b\right)\right)} \]

   9. Simplified 23.4%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(x \cdot b\right)\right)} \]

   if -1.8600000000000001e-152 < y2 < 5.5999999999999999e-131

   1. Initial program 42.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in x around inf 40.2%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in j around inf 36.8%

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 36.8%

         \[\leadsto x \cdot \left(j \cdot \left(\color{blue}{y1 \cdot i} - b \cdot y0\right)\right) \]

      2. *-commutative 36.8%

         \[\leadsto x \cdot \left(j \cdot \left(y1 \cdot i - \color{blue}{y0 \cdot b}\right)\right) \]

   5. Simplified 36.8%

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(y1 \cdot i - y0 \cdot b\right)\right)} \]

   6. Taylor expanded in y1 around inf 23.8%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]

   if 5.5999999999999999e-131 < y2 < 2.10000000000000004e36

   1. Initial program 39.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around -inf 46.4%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 46.4%

         \[\leadsto \color{blue}{-a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. distribute-rgt-neg-in 46.4%

         \[\leadsto \color{blue}{a \cdot \left(-\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      3. +-commutative 46.4%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. mul-1-neg 46.4%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-b \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. unsub-neg 46.4%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 46.4%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. *-commutative 46.4%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative 46.4%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   4. Simplified 46.4%

      \[\leadsto \color{blue}{a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(y \cdot x - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   5. Taylor expanded in y3 around -inf 31.6%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 31.6%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]

      2. neg-mul-1 31.6%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right) \]

      3. *-commutative 31.6%

         \[\leadsto \left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - \color{blue}{z \cdot y1}\right)\right) \]

   7. Simplified 31.6%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - z \cdot y1\right)\right)} \]

   8. Taylor expanded in y around 0 25.6%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]

   if 2.10000000000000004e36 < y2

   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. Taylor expanded in c around inf 54.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 54.0%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 54.0%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 54.0%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 54.0%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 54.0%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 54.0%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 54.0%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 54.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 55.9%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 46.3%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 32.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -0.012:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -1.86 \cdot 10^{-152}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 5.6 \cdot 10^{-131}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq 2.1 \cdot 10^{+36}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \end{array} \]

Alternative 39: 22.6% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -5.2 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -2.05 \cdot 10^{-113}:\\ \;\;\;\;\left(z \cdot y3\right) \cdot \left(a \cdot y1\right)\\ \mathbf{elif}\;y2 \leq 3.3 \cdot 10^{-134}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq 4.2 \cdot 10^{+41}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -5.2e-8)
   (* x (* c (* y0 y2)))
   (if (<= y2 -2.05e-113)
     (* (* z y3) (* a y1))
     (if (<= y2 3.3e-134)
       (* i (* j (* x y1)))
       (if (<= y2 4.2e+41) (* a (* y1 (* z y3))) (* c (* x (* y0 y2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -5.2e-8) {
		tmp = x * (c * (y0 * y2));
	} else if (y2 <= -2.05e-113) {
		tmp = (z * y3) * (a * y1);
	} else if (y2 <= 3.3e-134) {
		tmp = i * (j * (x * y1));
	} else if (y2 <= 4.2e+41) {
		tmp = a * (y1 * (z * y3));
	} else {
		tmp = c * (x * (y0 * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y2 <= (-5.2d-8)) then
        tmp = x * (c * (y0 * y2))
    else if (y2 <= (-2.05d-113)) then
        tmp = (z * y3) * (a * y1)
    else if (y2 <= 3.3d-134) then
        tmp = i * (j * (x * y1))
    else if (y2 <= 4.2d+41) then
        tmp = a * (y1 * (z * y3))
    else
        tmp = c * (x * (y0 * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -5.2e-8) {
		tmp = x * (c * (y0 * y2));
	} else if (y2 <= -2.05e-113) {
		tmp = (z * y3) * (a * y1);
	} else if (y2 <= 3.3e-134) {
		tmp = i * (j * (x * y1));
	} else if (y2 <= 4.2e+41) {
		tmp = a * (y1 * (z * y3));
	} else {
		tmp = c * (x * (y0 * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y2 <= -5.2e-8:
		tmp = x * (c * (y0 * y2))
	elif y2 <= -2.05e-113:
		tmp = (z * y3) * (a * y1)
	elif y2 <= 3.3e-134:
		tmp = i * (j * (x * y1))
	elif y2 <= 4.2e+41:
		tmp = a * (y1 * (z * y3))
	else:
		tmp = c * (x * (y0 * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y2 <= -5.2e-8)
		tmp = Float64(x * Float64(c * Float64(y0 * y2)));
	elseif (y2 <= -2.05e-113)
		tmp = Float64(Float64(z * y3) * Float64(a * y1));
	elseif (y2 <= 3.3e-134)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (y2 <= 4.2e+41)
		tmp = Float64(a * Float64(y1 * Float64(z * y3)));
	else
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y2 <= -5.2e-8)
		tmp = x * (c * (y0 * y2));
	elseif (y2 <= -2.05e-113)
		tmp = (z * y3) * (a * y1);
	elseif (y2 <= 3.3e-134)
		tmp = i * (j * (x * y1));
	elseif (y2 <= 4.2e+41)
		tmp = a * (y1 * (z * y3));
	else
		tmp = c * (x * (y0 * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y2, -5.2e-8], N[(x * N[(c * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -2.05e-113], N[(N[(z * y3), $MachinePrecision] * N[(a * y1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 3.3e-134], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 4.2e+41], N[(a * N[(y1 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y2 < -5.2000000000000002e-8

   1. Initial program 24.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 38.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 38.4%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 38.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 38.4%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 38.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 38.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 38.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 38.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 38.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 37.0%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 40.3%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 40.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y0 \cdot y2\right)\right) \cdot c} \]

      2. associate-*l* 40.4%

         \[\leadsto \color{blue}{x \cdot \left(\left(y0 \cdot y2\right) \cdot c\right)} \]

   8. Simplified 40.4%

      \[\leadsto \color{blue}{x \cdot \left(\left(y0 \cdot y2\right) \cdot c\right)} \]

   if -5.2000000000000002e-8 < y2 < -2.05e-113

   1. Initial program 27.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around -inf 47.7%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 47.7%

         \[\leadsto \color{blue}{-a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. distribute-rgt-neg-in 47.7%

         \[\leadsto \color{blue}{a \cdot \left(-\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      3. +-commutative 47.7%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. mul-1-neg 47.7%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-b \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. unsub-neg 47.7%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 47.7%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. *-commutative 47.7%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative 47.7%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   4. Simplified 47.7%

      \[\leadsto \color{blue}{a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(y \cdot x - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   5. Taylor expanded in y3 around -inf 42.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 42.9%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]

      2. neg-mul-1 42.9%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right) \]

      3. *-commutative 42.9%

         \[\leadsto \left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - \color{blue}{z \cdot y1}\right)\right) \]

   7. Simplified 42.9%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - z \cdot y1\right)\right)} \]

   8. Taylor expanded in y around 0 24.7%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 31.8%

         \[\leadsto \color{blue}{\left(a \cdot y1\right) \cdot \left(y3 \cdot z\right)} \]

   10. Simplified 31.8%

       \[\leadsto \color{blue}{\left(a \cdot y1\right) \cdot \left(y3 \cdot z\right)} \]

   if -2.05e-113 < y2 < 3.30000000000000019e-134

   1. Initial program 43.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in x around inf 42.0%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in j around inf 36.6%

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 36.6%

         \[\leadsto x \cdot \left(j \cdot \left(\color{blue}{y1 \cdot i} - b \cdot y0\right)\right) \]

      2. *-commutative 36.6%

         \[\leadsto x \cdot \left(j \cdot \left(y1 \cdot i - \color{blue}{y0 \cdot b}\right)\right) \]

   5. Simplified 36.6%

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(y1 \cdot i - y0 \cdot b\right)\right)} \]

   6. Taylor expanded in y1 around inf 22.6%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]

   if 3.30000000000000019e-134 < y2 < 4.1999999999999999e41

   1. Initial program 39.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around -inf 46.4%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 46.4%

         \[\leadsto \color{blue}{-a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. distribute-rgt-neg-in 46.4%

         \[\leadsto \color{blue}{a \cdot \left(-\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      3. +-commutative 46.4%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. mul-1-neg 46.4%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-b \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. unsub-neg 46.4%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 46.4%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. *-commutative 46.4%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative 46.4%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   4. Simplified 46.4%

      \[\leadsto \color{blue}{a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(y \cdot x - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   5. Taylor expanded in y3 around -inf 31.6%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 31.6%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]

      2. neg-mul-1 31.6%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right) \]

      3. *-commutative 31.6%

         \[\leadsto \left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - \color{blue}{z \cdot y1}\right)\right) \]

   7. Simplified 31.6%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - z \cdot y1\right)\right)} \]

   8. Taylor expanded in y around 0 25.6%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]

   if 4.1999999999999999e41 < y2

   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. Taylor expanded in c around inf 54.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 54.0%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 54.0%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 54.0%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 54.0%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 54.0%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 54.0%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 54.0%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 54.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 55.9%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 46.3%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 33.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -5.2 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -2.05 \cdot 10^{-113}:\\ \;\;\;\;\left(z \cdot y3\right) \cdot \left(a \cdot y1\right)\\ \mathbf{elif}\;y2 \leq 3.3 \cdot 10^{-134}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq 4.2 \cdot 10^{+41}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \end{array} \]

Alternative 40: 22.5% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -3.5 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -2.5 \cdot 10^{-114}:\\ \;\;\;\;z \cdot \left(a \cdot \left(y1 \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 4.9 \cdot 10^{-135}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq 2.4 \cdot 10^{+44}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -3.5e-8)
   (* x (* c (* y0 y2)))
   (if (<= y2 -2.5e-114)
     (* z (* a (* y1 y3)))
     (if (<= y2 4.9e-135)
       (* i (* j (* x y1)))
       (if (<= y2 2.4e+44) (* a (* y1 (* z y3))) (* c (* x (* y0 y2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -3.5e-8) {
		tmp = x * (c * (y0 * y2));
	} else if (y2 <= -2.5e-114) {
		tmp = z * (a * (y1 * y3));
	} else if (y2 <= 4.9e-135) {
		tmp = i * (j * (x * y1));
	} else if (y2 <= 2.4e+44) {
		tmp = a * (y1 * (z * y3));
	} else {
		tmp = c * (x * (y0 * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y2 <= (-3.5d-8)) then
        tmp = x * (c * (y0 * y2))
    else if (y2 <= (-2.5d-114)) then
        tmp = z * (a * (y1 * y3))
    else if (y2 <= 4.9d-135) then
        tmp = i * (j * (x * y1))
    else if (y2 <= 2.4d+44) then
        tmp = a * (y1 * (z * y3))
    else
        tmp = c * (x * (y0 * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -3.5e-8) {
		tmp = x * (c * (y0 * y2));
	} else if (y2 <= -2.5e-114) {
		tmp = z * (a * (y1 * y3));
	} else if (y2 <= 4.9e-135) {
		tmp = i * (j * (x * y1));
	} else if (y2 <= 2.4e+44) {
		tmp = a * (y1 * (z * y3));
	} else {
		tmp = c * (x * (y0 * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y2 <= -3.5e-8:
		tmp = x * (c * (y0 * y2))
	elif y2 <= -2.5e-114:
		tmp = z * (a * (y1 * y3))
	elif y2 <= 4.9e-135:
		tmp = i * (j * (x * y1))
	elif y2 <= 2.4e+44:
		tmp = a * (y1 * (z * y3))
	else:
		tmp = c * (x * (y0 * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y2 <= -3.5e-8)
		tmp = Float64(x * Float64(c * Float64(y0 * y2)));
	elseif (y2 <= -2.5e-114)
		tmp = Float64(z * Float64(a * Float64(y1 * y3)));
	elseif (y2 <= 4.9e-135)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (y2 <= 2.4e+44)
		tmp = Float64(a * Float64(y1 * Float64(z * y3)));
	else
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y2 <= -3.5e-8)
		tmp = x * (c * (y0 * y2));
	elseif (y2 <= -2.5e-114)
		tmp = z * (a * (y1 * y3));
	elseif (y2 <= 4.9e-135)
		tmp = i * (j * (x * y1));
	elseif (y2 <= 2.4e+44)
		tmp = a * (y1 * (z * y3));
	else
		tmp = c * (x * (y0 * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y2, -3.5e-8], N[(x * N[(c * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -2.5e-114], N[(z * N[(a * N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 4.9e-135], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.4e+44], N[(a * N[(y1 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y2 < -3.50000000000000024e-8

   1. Initial program 24.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 38.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 38.4%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 38.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 38.4%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 38.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 38.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 38.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 38.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 38.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 37.0%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 40.3%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 40.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y0 \cdot y2\right)\right) \cdot c} \]

      2. associate-*l* 40.4%

         \[\leadsto \color{blue}{x \cdot \left(\left(y0 \cdot y2\right) \cdot c\right)} \]

   8. Simplified 40.4%

      \[\leadsto \color{blue}{x \cdot \left(\left(y0 \cdot y2\right) \cdot c\right)} \]

   if -3.50000000000000024e-8 < y2 < -2.49999999999999995e-114

   1. Initial program 27.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around -inf 47.7%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 47.7%

         \[\leadsto \color{blue}{-a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. distribute-rgt-neg-in 47.7%

         \[\leadsto \color{blue}{a \cdot \left(-\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      3. +-commutative 47.7%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. mul-1-neg 47.7%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-b \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. unsub-neg 47.7%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 47.7%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. *-commutative 47.7%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative 47.7%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   4. Simplified 47.7%

      \[\leadsto \color{blue}{a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(y \cdot x - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   5. Taylor expanded in y3 around -inf 42.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 42.9%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]

      2. neg-mul-1 42.9%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right) \]

      3. *-commutative 42.9%

         \[\leadsto \left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - \color{blue}{z \cdot y1}\right)\right) \]

   7. Simplified 42.9%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - z \cdot y1\right)\right)} \]

   8. Taylor expanded in y around 0 24.7%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 28.5%

         \[\leadsto a \cdot \color{blue}{\left(\left(y1 \cdot y3\right) \cdot z\right)} \]

      2. associate-*r* 32.1%

         \[\leadsto \color{blue}{\left(a \cdot \left(y1 \cdot y3\right)\right) \cdot z} \]

      3. *-commutative 32.1%

         \[\leadsto \left(a \cdot \color{blue}{\left(y3 \cdot y1\right)}\right) \cdot z \]

   10. Simplified 32.1%

       \[\leadsto \color{blue}{\left(a \cdot \left(y3 \cdot y1\right)\right) \cdot z} \]

   if -2.49999999999999995e-114 < y2 < 4.9000000000000003e-135

   1. Initial program 43.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in x around inf 42.0%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in j around inf 36.6%

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 36.6%

         \[\leadsto x \cdot \left(j \cdot \left(\color{blue}{y1 \cdot i} - b \cdot y0\right)\right) \]

      2. *-commutative 36.6%

         \[\leadsto x \cdot \left(j \cdot \left(y1 \cdot i - \color{blue}{y0 \cdot b}\right)\right) \]

   5. Simplified 36.6%

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(y1 \cdot i - y0 \cdot b\right)\right)} \]

   6. Taylor expanded in y1 around inf 22.6%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]

   if 4.9000000000000003e-135 < y2 < 2.40000000000000013e44

   1. Initial program 39.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around -inf 46.4%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 46.4%

         \[\leadsto \color{blue}{-a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. distribute-rgt-neg-in 46.4%

         \[\leadsto \color{blue}{a \cdot \left(-\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      3. +-commutative 46.4%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. mul-1-neg 46.4%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-b \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. unsub-neg 46.4%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 46.4%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. *-commutative 46.4%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative 46.4%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   4. Simplified 46.4%

      \[\leadsto \color{blue}{a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(y \cdot x - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   5. Taylor expanded in y3 around -inf 31.6%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 31.6%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]

      2. neg-mul-1 31.6%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right) \]

      3. *-commutative 31.6%

         \[\leadsto \left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - \color{blue}{z \cdot y1}\right)\right) \]

   7. Simplified 31.6%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - z \cdot y1\right)\right)} \]

   8. Taylor expanded in y around 0 25.6%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]

   if 2.40000000000000013e44 < y2

   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. Taylor expanded in c around inf 54.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 54.0%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 54.0%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 54.0%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 54.0%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 54.0%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 54.0%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 54.0%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 54.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 55.9%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 46.3%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 33.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -3.5 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -2.5 \cdot 10^{-114}:\\ \;\;\;\;z \cdot \left(a \cdot \left(y1 \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 4.9 \cdot 10^{-135}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq 2.4 \cdot 10^{+44}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \end{array} \]

Alternative 41: 22.7% accurate, 6.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+110}:\\ \;\;\;\;a \cdot \left(b \cdot \left(z \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;t \leq -8 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \left(j \cdot \left(b \cdot \left(-y0\right)\right)\right)\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+51}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(-a\right) \cdot \left(t \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= t -2.7e+110)
   (* a (* b (* z (- t))))
   (if (<= t -8e+32)
     (* x (* j (* b (- y0))))
     (if (<= t 7.5e+51) (* c (* x (* y0 y2))) (* z (* (- a) (* t b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (t <= -2.7e+110) {
		tmp = a * (b * (z * -t));
	} else if (t <= -8e+32) {
		tmp = x * (j * (b * -y0));
	} else if (t <= 7.5e+51) {
		tmp = c * (x * (y0 * y2));
	} else {
		tmp = z * (-a * (t * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (t <= (-2.7d+110)) then
        tmp = a * (b * (z * -t))
    else if (t <= (-8d+32)) then
        tmp = x * (j * (b * -y0))
    else if (t <= 7.5d+51) then
        tmp = c * (x * (y0 * y2))
    else
        tmp = z * (-a * (t * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (t <= -2.7e+110) {
		tmp = a * (b * (z * -t));
	} else if (t <= -8e+32) {
		tmp = x * (j * (b * -y0));
	} else if (t <= 7.5e+51) {
		tmp = c * (x * (y0 * y2));
	} else {
		tmp = z * (-a * (t * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if t <= -2.7e+110:
		tmp = a * (b * (z * -t))
	elif t <= -8e+32:
		tmp = x * (j * (b * -y0))
	elif t <= 7.5e+51:
		tmp = c * (x * (y0 * y2))
	else:
		tmp = z * (-a * (t * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (t <= -2.7e+110)
		tmp = Float64(a * Float64(b * Float64(z * Float64(-t))));
	elseif (t <= -8e+32)
		tmp = Float64(x * Float64(j * Float64(b * Float64(-y0))));
	elseif (t <= 7.5e+51)
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	else
		tmp = Float64(z * Float64(Float64(-a) * Float64(t * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (t <= -2.7e+110)
		tmp = a * (b * (z * -t));
	elseif (t <= -8e+32)
		tmp = x * (j * (b * -y0));
	elseif (t <= 7.5e+51)
		tmp = c * (x * (y0 * y2));
	else
		tmp = z * (-a * (t * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[t, -2.7e+110], N[(a * N[(b * N[(z * (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -8e+32], N[(x * N[(j * N[(b * (-y0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.5e+51], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[((-a) * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.7000000000000001e110

   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. Taylor expanded in b around inf 33.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in a around inf 45.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   4. Taylor expanded in x around 0 36.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 36.2%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(b \cdot \left(t \cdot z\right)\right)} \]

      2. neg-mul-1 36.2%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(b \cdot \left(t \cdot z\right)\right) \]

      3. *-commutative 36.2%

         \[\leadsto \left(-a\right) \cdot \left(b \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

   6. Simplified 36.2%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(b \cdot \left(z \cdot t\right)\right)} \]

   if -2.7000000000000001e110 < t < -8.00000000000000043e32

   1. Initial program 26.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in x around inf 39.2%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in j around inf 61.4%

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 61.4%

         \[\leadsto x \cdot \left(j \cdot \left(\color{blue}{y1 \cdot i} - b \cdot y0\right)\right) \]

      2. *-commutative 61.4%

         \[\leadsto x \cdot \left(j \cdot \left(y1 \cdot i - \color{blue}{y0 \cdot b}\right)\right) \]

   5. Simplified 61.4%

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(y1 \cdot i - y0 \cdot b\right)\right)} \]

   6. Taylor expanded in y1 around 0 40.9%

      \[\leadsto x \cdot \left(j \cdot \color{blue}{\left(-1 \cdot \left(b \cdot y0\right)\right)}\right) \]
   7. Step-by-step derivation

      1. mul-1-neg 40.9%

         \[\leadsto x \cdot \left(j \cdot \color{blue}{\left(-b \cdot y0\right)}\right) \]

      2. *-commutative 40.9%

         \[\leadsto x \cdot \left(j \cdot \left(-\color{blue}{y0 \cdot b}\right)\right) \]

      3. distribute-rgt-neg-in 40.9%

         \[\leadsto x \cdot \left(j \cdot \color{blue}{\left(y0 \cdot \left(-b\right)\right)}\right) \]

   8. Simplified 40.9%

      \[\leadsto x \cdot \left(j \cdot \color{blue}{\left(y0 \cdot \left(-b\right)\right)}\right) \]

   if -8.00000000000000043e32 < t < 7.4999999999999999e51

   1. Initial program 38.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 36.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 36.6%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 36.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 36.6%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 36.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 36.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 36.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 36.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 36.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 35.7%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 27.9%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]

   if 7.4999999999999999e51 < t

   1. Initial program 39.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf 41.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in a around inf 37.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   4. Taylor expanded in x around 0 29.0%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 29.0%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(b \cdot \left(t \cdot z\right)\right)} \]

      2. neg-mul-1 29.0%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(b \cdot \left(t \cdot z\right)\right) \]

      3. *-commutative 29.0%

         \[\leadsto \left(-a\right) \cdot \left(b \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

   6. Simplified 29.0%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(b \cdot \left(z \cdot t\right)\right)} \]

   7. Taylor expanded in a around 0 29.0%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 29.0%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(b \cdot \left(t \cdot z\right)\right)} \]

      2. *-commutative 29.0%

         \[\leadsto \left(-1 \cdot a\right) \cdot \left(b \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

      3. *-commutative 29.0%

         \[\leadsto \left(-1 \cdot a\right) \cdot \color{blue}{\left(\left(z \cdot t\right) \cdot b\right)} \]

      4. neg-mul-1 29.0%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(\left(z \cdot t\right) \cdot b\right) \]

      5. *-commutative 29.0%

         \[\leadsto \color{blue}{\left(\left(z \cdot t\right) \cdot b\right) \cdot \left(-a\right)} \]

      6. associate-*l* 30.6%

         \[\leadsto \color{blue}{\left(z \cdot \left(t \cdot b\right)\right)} \cdot \left(-a\right) \]

      7. associate-*l* 30.4%

         \[\leadsto \color{blue}{z \cdot \left(\left(t \cdot b\right) \cdot \left(-a\right)\right)} \]

   9. Simplified 30.4%

      \[\leadsto \color{blue}{z \cdot \left(\left(t \cdot b\right) \cdot \left(-a\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 31.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+110}:\\ \;\;\;\;a \cdot \left(b \cdot \left(z \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;t \leq -8 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \left(j \cdot \left(b \cdot \left(-y0\right)\right)\right)\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+51}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(-a\right) \cdot \left(t \cdot b\right)\right)\\ \end{array} \]

Alternative 42: 22.4% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -2.9 \cdot 10^{-8} \lor \neg \left(y2 \leq 4.2 \cdot 10^{+43}\right):\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= y2 -2.9e-8) (not (<= y2 4.2e+43)))
   (* c (* x (* y0 y2)))
   (* a (* y1 (* z y3)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y2 <= -2.9e-8) || !(y2 <= 4.2e+43)) {
		tmp = c * (x * (y0 * y2));
	} else {
		tmp = a * (y1 * (z * y3));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((y2 <= (-2.9d-8)) .or. (.not. (y2 <= 4.2d+43))) then
        tmp = c * (x * (y0 * y2))
    else
        tmp = a * (y1 * (z * y3))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y2 <= -2.9e-8) || !(y2 <= 4.2e+43)) {
		tmp = c * (x * (y0 * y2));
	} else {
		tmp = a * (y1 * (z * y3));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (y2 <= -2.9e-8) or not (y2 <= 4.2e+43):
		tmp = c * (x * (y0 * y2))
	else:
		tmp = a * (y1 * (z * y3))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((y2 <= -2.9e-8) || !(y2 <= 4.2e+43))
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	else
		tmp = Float64(a * Float64(y1 * Float64(z * y3)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((y2 <= -2.9e-8) || ~((y2 <= 4.2e+43)))
		tmp = c * (x * (y0 * y2));
	else
		tmp = a * (y1 * (z * y3));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[y2, -2.9e-8], N[Not[LessEqual[y2, 4.2e+43]], $MachinePrecision]], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y1 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y2 < -2.9000000000000002e-8 or 4.20000000000000003e43 < y2

   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. Taylor expanded in c around inf 46.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 46.7%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 46.7%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 46.7%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 46.7%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 46.7%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 46.7%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 46.7%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   4. Simplified 46.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   5. Taylor expanded in y0 around inf 46.9%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 43.5%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]

   if -2.9000000000000002e-8 < y2 < 4.20000000000000003e43

   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. Taylor expanded in a around -inf 35.7%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 35.7%

         \[\leadsto \color{blue}{-a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. distribute-rgt-neg-in 35.7%

         \[\leadsto \color{blue}{a \cdot \left(-\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      3. +-commutative 35.7%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. mul-1-neg 35.7%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-b \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. unsub-neg 35.7%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 35.7%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. *-commutative 35.7%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative 35.7%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   4. Simplified 35.7%

      \[\leadsto \color{blue}{a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(y \cdot x - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   5. Taylor expanded in y3 around -inf 32.4%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 32.4%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]

      2. neg-mul-1 32.4%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right) \]

      3. *-commutative 32.4%

         \[\leadsto \left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - \color{blue}{z \cdot y1}\right)\right) \]

   7. Simplified 32.4%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - z \cdot y1\right)\right)} \]

   8. Taylor expanded in y around 0 19.6%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 30.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -2.9 \cdot 10^{-8} \lor \neg \left(y2 \leq 4.2 \cdot 10^{+43}\right):\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \end{array} \]

Alternative 43: 19.5% accurate, 10.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 5 \cdot 10^{+104}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x 5e+104) (* a (* y1 (* z y3))) (* a (* y (* x b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= 5e+104) {
		tmp = a * (y1 * (z * y3));
	} else {
		tmp = a * (y * (x * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (x <= 5d+104) then
        tmp = a * (y1 * (z * y3))
    else
        tmp = a * (y * (x * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= 5e+104) {
		tmp = a * (y1 * (z * y3));
	} else {
		tmp = a * (y * (x * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if x <= 5e+104:
		tmp = a * (y1 * (z * y3))
	else:
		tmp = a * (y * (x * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (x <= 5e+104)
		tmp = Float64(a * Float64(y1 * Float64(z * y3)));
	else
		tmp = Float64(a * Float64(y * Float64(x * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (x <= 5e+104)
		tmp = a * (y1 * (z * y3));
	else
		tmp = a * (y * (x * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[x, 5e+104], N[(a * N[(y1 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.9999999999999997e104

   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. Taylor expanded in a around -inf 34.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 34.2%

         \[\leadsto \color{blue}{-a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. distribute-rgt-neg-in 34.2%

         \[\leadsto \color{blue}{a \cdot \left(-\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      3. +-commutative 34.2%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. mul-1-neg 34.2%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-b \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. unsub-neg 34.2%

         \[\leadsto a \cdot \left(-\left(\color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 34.2%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. *-commutative 34.2%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - b \cdot \left(x \cdot y - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative 34.2%

         \[\leadsto a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   4. Simplified 34.2%

      \[\leadsto \color{blue}{a \cdot \left(-\left(\left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(y \cdot x - t \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   5. Taylor expanded in y3 around -inf 29.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 29.2%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]

      2. neg-mul-1 29.2%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right) \]

      3. *-commutative 29.2%

         \[\leadsto \left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - \color{blue}{z \cdot y1}\right)\right) \]

   7. Simplified 29.2%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - z \cdot y1\right)\right)} \]

   8. Taylor expanded in y around 0 18.8%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]

   if 4.9999999999999997e104 < x

   1. Initial program 34.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf 45.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in a around inf 35.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   4. Taylor expanded in x around inf 29.8%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 32.0%

         \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot x\right) \cdot y\right)} \]

      2. *-commutative 32.0%

         \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot b\right)} \cdot y\right) \]

      3. associate-*l* 26.1%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

   6. Simplified 26.1%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

   7. Taylor expanded in x around 0 29.8%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 29.8%

         \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot b\right)} \]

      2. *-commutative 29.8%

         \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot b\right) \]

      3. associate-*l* 32.0%

         \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(x \cdot b\right)\right)} \]

   9. Simplified 32.0%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(x \cdot b\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 21.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 5 \cdot 10^{+104}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \end{array} \]

Alternative 44: 16.9% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(x \cdot \left(y \cdot b\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* x (* y b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (x * (y * b));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = a * (x * (y * b))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (x * (y * b));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * (x * (y * b))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(x * Float64(y * b)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * (x * (y * b));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(x * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 34.0%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

2. Taylor expanded in b around inf 36.2%

   \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

3. Taylor expanded in a around inf 25.9%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

4. Taylor expanded in x around inf 13.2%

   \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
5. Step-by-step derivation

   1. associate-*r* 14.0%

      \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot x\right) \cdot y\right)} \]

   2. *-commutative 14.0%

      \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot b\right)} \cdot y\right) \]

   3. associate-*l* 13.7%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

6. Simplified 13.7%

   \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

7. Final simplification 13.7%

   \[\leadsto a \cdot \left(x \cdot \left(y \cdot b\right)\right) \]

Alternative 45: 17.3% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(y \cdot \left(x \cdot b\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* y (* x b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (y * (x * b));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = a * (y * (x * b))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (y * (x * b));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * (y * (x * b))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(y * Float64(x * b)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * (y * (x * b));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 34.0%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

2. Taylor expanded in b around inf 36.2%

   \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

3. Taylor expanded in a around inf 25.9%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

4. Taylor expanded in x around inf 13.2%

   \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
5. Step-by-step derivation

   1. associate-*r* 14.0%

      \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot x\right) \cdot y\right)} \]

   2. *-commutative 14.0%

      \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot b\right)} \cdot y\right) \]

   3. associate-*l* 13.7%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

6. Simplified 13.7%

   \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

7. Taylor expanded in x around 0 13.2%

   \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
8. Step-by-step derivation

   1. *-commutative 13.2%

      \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot b\right)} \]

   2. *-commutative 13.2%

      \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot b\right) \]

   3. associate-*l* 14.0%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(x \cdot b\right)\right)} \]

9. Simplified 14.0%

   \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(x \cdot b\right)\right)} \]

10. Final simplification 14.0%

    \[\leadsto a \cdot \left(y \cdot \left(x \cdot b\right)\right) \]

Developer target: 27.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot c - y5 \cdot a\\ t_2 := x \cdot y2 - z \cdot y3\\ t_3 := y2 \cdot t - y3 \cdot y\\ t_4 := k \cdot y2 - j \cdot y3\\ t_5 := y4 \cdot b - y5 \cdot i\\ t_6 := \left(j \cdot t - k \cdot y\right) \cdot t_5\\ t_7 := b \cdot a - i \cdot c\\ t_8 := t_7 \cdot \left(y \cdot x - t \cdot z\right)\\ t_9 := j \cdot x - k \cdot z\\ t_10 := \left(b \cdot y0 - i \cdot y1\right) \cdot t_9\\ t_11 := t_9 \cdot \left(y0 \cdot b - i \cdot y1\right)\\ t_12 := y4 \cdot y1 - y5 \cdot y0\\ t_13 := t_4 \cdot t_12\\ t_14 := \left(y2 \cdot k - y3 \cdot j\right) \cdot t_12\\ t_15 := \left(\left(\left(\left(k \cdot y\right) \cdot \left(y5 \cdot i\right) - \left(y \cdot b\right) \cdot \left(y4 \cdot k\right)\right) - \left(y5 \cdot t\right) \cdot \left(i \cdot j\right)\right) - \left(t_3 \cdot t_1 - t_14\right)\right) + \left(t_8 - \left(t_11 - \left(y2 \cdot x - y3 \cdot z\right) \cdot \left(c \cdot y0 - y1 \cdot a\right)\right)\right)\\ t_16 := \left(\left(t_6 - \left(y3 \cdot y\right) \cdot \left(y5 \cdot a - y4 \cdot c\right)\right) + \left(\left(y5 \cdot a\right) \cdot \left(t \cdot y2\right) + t_13\right)\right) + \left(t_2 \cdot \left(c \cdot y0 - a \cdot y1\right) - \left(t_10 - \left(y \cdot x - z \cdot t\right) \cdot t_7\right)\right)\\ t_17 := t \cdot y2 - y \cdot y3\\ \mathbf{if}\;y4 < -7.206256231996481 \cdot 10^{+60}:\\ \;\;\;\;\left(t_8 - \left(t_11 - t_6\right)\right) - \left(\frac{t_3}{\frac{1}{t_1}} - t_14\right)\\ \mathbf{elif}\;y4 < -3.364603505246317 \cdot 10^{-66}:\\ \;\;\;\;\left(\left(\left(\left(t \cdot c\right) \cdot \left(i \cdot z\right) - \left(a \cdot t\right) \cdot \left(b \cdot z\right)\right) - \left(y \cdot c\right) \cdot \left(i \cdot x\right)\right) - t_10\right) + \left(\left(y0 \cdot c - a \cdot y1\right) \cdot t_2 - \left(t_17 \cdot \left(y4 \cdot c - a \cdot y5\right) - \left(y1 \cdot y4 - y5 \cdot y0\right) \cdot t_4\right)\right)\\ \mathbf{elif}\;y4 < -1.2000065055686116 \cdot 10^{-105}:\\ \;\;\;\;t_16\\ \mathbf{elif}\;y4 < 6.718963124057495 \cdot 10^{-279}:\\ \;\;\;\;t_15\\ \mathbf{elif}\;y4 < 4.77962681403792 \cdot 10^{-222}:\\ \;\;\;\;t_16\\ \mathbf{elif}\;y4 < 2.2852241541266835 \cdot 10^{-175}:\\ \;\;\;\;t_15\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(k \cdot \left(i \cdot \left(z \cdot y1\right)\right) - \left(j \cdot \left(i \cdot \left(x \cdot y1\right)\right) + y0 \cdot \left(k \cdot \left(z \cdot b\right)\right)\right)\right)\right) + \left(z \cdot \left(y3 \cdot \left(a \cdot y1\right)\right) - \left(y2 \cdot \left(x \cdot \left(a \cdot y1\right)\right) + y0 \cdot \left(z \cdot \left(c \cdot y3\right)\right)\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot t_5\right) - t_17 \cdot t_1\right) + t_13\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y4 c) (* y5 a)))
        (t_2 (- (* x y2) (* z y3)))
        (t_3 (- (* y2 t) (* y3 y)))
        (t_4 (- (* k y2) (* j y3)))
        (t_5 (- (* y4 b) (* y5 i)))
        (t_6 (* (- (* j t) (* k y)) t_5))
        (t_7 (- (* b a) (* i c)))
        (t_8 (* t_7 (- (* y x) (* t z))))
        (t_9 (- (* j x) (* k z)))
        (t_10 (* (- (* b y0) (* i y1)) t_9))
        (t_11 (* t_9 (- (* y0 b) (* i y1))))
        (t_12 (- (* y4 y1) (* y5 y0)))
        (t_13 (* t_4 t_12))
        (t_14 (* (- (* y2 k) (* y3 j)) t_12))
        (t_15
         (+
          (-
           (-
            (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k)))
            (* (* y5 t) (* i j)))
           (- (* t_3 t_1) t_14))
          (- t_8 (- t_11 (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))))
        (t_16
         (+
          (+
           (- t_6 (* (* y3 y) (- (* y5 a) (* y4 c))))
           (+ (* (* y5 a) (* t y2)) t_13))
          (-
           (* t_2 (- (* c y0) (* a y1)))
           (- t_10 (* (- (* y x) (* z t)) t_7)))))
        (t_17 (- (* t y2) (* y y3))))
   (if (< y4 -7.206256231996481e+60)
     (- (- t_8 (- t_11 t_6)) (- (/ t_3 (/ 1.0 t_1)) t_14))
     (if (< y4 -3.364603505246317e-66)
       (+
        (-
         (- (- (* (* t c) (* i z)) (* (* a t) (* b z))) (* (* y c) (* i x)))
         t_10)
        (-
         (* (- (* y0 c) (* a y1)) t_2)
         (- (* t_17 (- (* y4 c) (* a y5))) (* (- (* y1 y4) (* y5 y0)) t_4))))
       (if (< y4 -1.2000065055686116e-105)
         t_16
         (if (< y4 6.718963124057495e-279)
           t_15
           (if (< y4 4.77962681403792e-222)
             t_16
             (if (< y4 2.2852241541266835e-175)
               t_15
               (+
                (-
                 (+
                  (+
                   (-
                    (* (- (* x y) (* z t)) (- (* a b) (* c i)))
                    (-
                     (* k (* i (* z y1)))
                     (+ (* j (* i (* x y1))) (* y0 (* k (* z b))))))
                   (-
                    (* z (* y3 (* a y1)))
                    (+ (* y2 (* x (* a y1))) (* y0 (* z (* c y3))))))
                  (* (- (* t j) (* y k)) t_5))
                 (* t_17 t_1))
                t_13)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y4 * c) - (y5 * a);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (y2 * t) - (y3 * y);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = (y4 * b) - (y5 * i);
	double t_6 = ((j * t) - (k * y)) * t_5;
	double t_7 = (b * a) - (i * c);
	double t_8 = t_7 * ((y * x) - (t * z));
	double t_9 = (j * x) - (k * z);
	double t_10 = ((b * y0) - (i * y1)) * t_9;
	double t_11 = t_9 * ((y0 * b) - (i * y1));
	double t_12 = (y4 * y1) - (y5 * y0);
	double t_13 = t_4 * t_12;
	double t_14 = ((y2 * k) - (y3 * j)) * t_12;
	double t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	double t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	double t_17 = (t * y2) - (y * y3);
	double tmp;
	if (y4 < -7.206256231996481e+60) {
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	} else if (y4 < -3.364603505246317e-66) {
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	} else if (y4 < -1.2000065055686116e-105) {
		tmp = t_16;
	} else if (y4 < 6.718963124057495e-279) {
		tmp = t_15;
	} else if (y4 < 4.77962681403792e-222) {
		tmp = t_16;
	} else if (y4 < 2.2852241541266835e-175) {
		tmp = t_15;
	} else {
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_10
    real(8) :: t_11
    real(8) :: t_12
    real(8) :: t_13
    real(8) :: t_14
    real(8) :: t_15
    real(8) :: t_16
    real(8) :: t_17
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = (y4 * c) - (y5 * a)
    t_2 = (x * y2) - (z * y3)
    t_3 = (y2 * t) - (y3 * y)
    t_4 = (k * y2) - (j * y3)
    t_5 = (y4 * b) - (y5 * i)
    t_6 = ((j * t) - (k * y)) * t_5
    t_7 = (b * a) - (i * c)
    t_8 = t_7 * ((y * x) - (t * z))
    t_9 = (j * x) - (k * z)
    t_10 = ((b * y0) - (i * y1)) * t_9
    t_11 = t_9 * ((y0 * b) - (i * y1))
    t_12 = (y4 * y1) - (y5 * y0)
    t_13 = t_4 * t_12
    t_14 = ((y2 * k) - (y3 * j)) * t_12
    t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))))
    t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)))
    t_17 = (t * y2) - (y * y3)
    if (y4 < (-7.206256231996481d+60)) then
        tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0d0 / t_1)) - t_14)
    else if (y4 < (-3.364603505246317d-66)) then
        tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)))
    else if (y4 < (-1.2000065055686116d-105)) then
        tmp = t_16
    else if (y4 < 6.718963124057495d-279) then
        tmp = t_15
    else if (y4 < 4.77962681403792d-222) then
        tmp = t_16
    else if (y4 < 2.2852241541266835d-175) then
        tmp = t_15
    else
        tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y4 * c) - (y5 * a);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (y2 * t) - (y3 * y);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = (y4 * b) - (y5 * i);
	double t_6 = ((j * t) - (k * y)) * t_5;
	double t_7 = (b * a) - (i * c);
	double t_8 = t_7 * ((y * x) - (t * z));
	double t_9 = (j * x) - (k * z);
	double t_10 = ((b * y0) - (i * y1)) * t_9;
	double t_11 = t_9 * ((y0 * b) - (i * y1));
	double t_12 = (y4 * y1) - (y5 * y0);
	double t_13 = t_4 * t_12;
	double t_14 = ((y2 * k) - (y3 * j)) * t_12;
	double t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	double t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	double t_17 = (t * y2) - (y * y3);
	double tmp;
	if (y4 < -7.206256231996481e+60) {
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	} else if (y4 < -3.364603505246317e-66) {
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	} else if (y4 < -1.2000065055686116e-105) {
		tmp = t_16;
	} else if (y4 < 6.718963124057495e-279) {
		tmp = t_15;
	} else if (y4 < 4.77962681403792e-222) {
		tmp = t_16;
	} else if (y4 < 2.2852241541266835e-175) {
		tmp = t_15;
	} else {
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y4 * c) - (y5 * a)
	t_2 = (x * y2) - (z * y3)
	t_3 = (y2 * t) - (y3 * y)
	t_4 = (k * y2) - (j * y3)
	t_5 = (y4 * b) - (y5 * i)
	t_6 = ((j * t) - (k * y)) * t_5
	t_7 = (b * a) - (i * c)
	t_8 = t_7 * ((y * x) - (t * z))
	t_9 = (j * x) - (k * z)
	t_10 = ((b * y0) - (i * y1)) * t_9
	t_11 = t_9 * ((y0 * b) - (i * y1))
	t_12 = (y4 * y1) - (y5 * y0)
	t_13 = t_4 * t_12
	t_14 = ((y2 * k) - (y3 * j)) * t_12
	t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))))
	t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)))
	t_17 = (t * y2) - (y * y3)
	tmp = 0
	if y4 < -7.206256231996481e+60:
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14)
	elif y4 < -3.364603505246317e-66:
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)))
	elif y4 < -1.2000065055686116e-105:
		tmp = t_16
	elif y4 < 6.718963124057495e-279:
		tmp = t_15
	elif y4 < 4.77962681403792e-222:
		tmp = t_16
	elif y4 < 2.2852241541266835e-175:
		tmp = t_15
	else:
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y4 * c) - Float64(y5 * a))
	t_2 = Float64(Float64(x * y2) - Float64(z * y3))
	t_3 = Float64(Float64(y2 * t) - Float64(y3 * y))
	t_4 = Float64(Float64(k * y2) - Float64(j * y3))
	t_5 = Float64(Float64(y4 * b) - Float64(y5 * i))
	t_6 = Float64(Float64(Float64(j * t) - Float64(k * y)) * t_5)
	t_7 = Float64(Float64(b * a) - Float64(i * c))
	t_8 = Float64(t_7 * Float64(Float64(y * x) - Float64(t * z)))
	t_9 = Float64(Float64(j * x) - Float64(k * z))
	t_10 = Float64(Float64(Float64(b * y0) - Float64(i * y1)) * t_9)
	t_11 = Float64(t_9 * Float64(Float64(y0 * b) - Float64(i * y1)))
	t_12 = Float64(Float64(y4 * y1) - Float64(y5 * y0))
	t_13 = Float64(t_4 * t_12)
	t_14 = Float64(Float64(Float64(y2 * k) - Float64(y3 * j)) * t_12)
	t_15 = Float64(Float64(Float64(Float64(Float64(Float64(k * y) * Float64(y5 * i)) - Float64(Float64(y * b) * Float64(y4 * k))) - Float64(Float64(y5 * t) * Float64(i * j))) - Float64(Float64(t_3 * t_1) - t_14)) + Float64(t_8 - Float64(t_11 - Float64(Float64(Float64(y2 * x) - Float64(y3 * z)) * Float64(Float64(c * y0) - Float64(y1 * a))))))
	t_16 = Float64(Float64(Float64(t_6 - Float64(Float64(y3 * y) * Float64(Float64(y5 * a) - Float64(y4 * c)))) + Float64(Float64(Float64(y5 * a) * Float64(t * y2)) + t_13)) + Float64(Float64(t_2 * Float64(Float64(c * y0) - Float64(a * y1))) - Float64(t_10 - Float64(Float64(Float64(y * x) - Float64(z * t)) * t_7))))
	t_17 = Float64(Float64(t * y2) - Float64(y * y3))
	tmp = 0.0
	if (y4 < -7.206256231996481e+60)
		tmp = Float64(Float64(t_8 - Float64(t_11 - t_6)) - Float64(Float64(t_3 / Float64(1.0 / t_1)) - t_14));
	elseif (y4 < -3.364603505246317e-66)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(t * c) * Float64(i * z)) - Float64(Float64(a * t) * Float64(b * z))) - Float64(Float64(y * c) * Float64(i * x))) - t_10) + Float64(Float64(Float64(Float64(y0 * c) - Float64(a * y1)) * t_2) - Float64(Float64(t_17 * Float64(Float64(y4 * c) - Float64(a * y5))) - Float64(Float64(Float64(y1 * y4) - Float64(y5 * y0)) * t_4))));
	elseif (y4 < -1.2000065055686116e-105)
		tmp = t_16;
	elseif (y4 < 6.718963124057495e-279)
		tmp = t_15;
	elseif (y4 < 4.77962681403792e-222)
		tmp = t_16;
	elseif (y4 < 2.2852241541266835e-175)
		tmp = t_15;
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) - Float64(z * t)) * Float64(Float64(a * b) - Float64(c * i))) - Float64(Float64(k * Float64(i * Float64(z * y1))) - Float64(Float64(j * Float64(i * Float64(x * y1))) + Float64(y0 * Float64(k * Float64(z * b)))))) + Float64(Float64(z * Float64(y3 * Float64(a * y1))) - Float64(Float64(y2 * Float64(x * Float64(a * y1))) + Float64(y0 * Float64(z * Float64(c * y3)))))) + Float64(Float64(Float64(t * j) - Float64(y * k)) * t_5)) - Float64(t_17 * t_1)) + t_13);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y4 * c) - (y5 * a);
	t_2 = (x * y2) - (z * y3);
	t_3 = (y2 * t) - (y3 * y);
	t_4 = (k * y2) - (j * y3);
	t_5 = (y4 * b) - (y5 * i);
	t_6 = ((j * t) - (k * y)) * t_5;
	t_7 = (b * a) - (i * c);
	t_8 = t_7 * ((y * x) - (t * z));
	t_9 = (j * x) - (k * z);
	t_10 = ((b * y0) - (i * y1)) * t_9;
	t_11 = t_9 * ((y0 * b) - (i * y1));
	t_12 = (y4 * y1) - (y5 * y0);
	t_13 = t_4 * t_12;
	t_14 = ((y2 * k) - (y3 * j)) * t_12;
	t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	t_17 = (t * y2) - (y * y3);
	tmp = 0.0;
	if (y4 < -7.206256231996481e+60)
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	elseif (y4 < -3.364603505246317e-66)
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	elseif (y4 < -1.2000065055686116e-105)
		tmp = t_16;
	elseif (y4 < 6.718963124057495e-279)
		tmp = t_15;
	elseif (y4 < 4.77962681403792e-222)
		tmp = t_16;
	elseif (y4 < 2.2852241541266835e-175)
		tmp = t_15;
	else
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y4 * c), $MachinePrecision] - N[(y5 * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y2 * t), $MachinePrecision] - N[(y3 * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(y4 * b), $MachinePrecision] - N[(y5 * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision] * t$95$5), $MachinePrecision]}, Block[{t$95$7 = N[(N[(b * a), $MachinePrecision] - N[(i * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(t$95$7 * N[(N[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$10 = N[(N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision] * t$95$9), $MachinePrecision]}, Block[{t$95$11 = N[(t$95$9 * N[(N[(y0 * b), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$12 = N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$13 = N[(t$95$4 * t$95$12), $MachinePrecision]}, Block[{t$95$14 = N[(N[(N[(y2 * k), $MachinePrecision] - N[(y3 * j), $MachinePrecision]), $MachinePrecision] * t$95$12), $MachinePrecision]}, Block[{t$95$15 = N[(N[(N[(N[(N[(N[(k * y), $MachinePrecision] * N[(y5 * i), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] * N[(y4 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y5 * t), $MachinePrecision] * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$3 * t$95$1), $MachinePrecision] - t$95$14), $MachinePrecision]), $MachinePrecision] + N[(t$95$8 - N[(t$95$11 - N[(N[(N[(y2 * x), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision] * N[(N[(c * y0), $MachinePrecision] - N[(y1 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$16 = N[(N[(N[(t$95$6 - N[(N[(y3 * y), $MachinePrecision] * N[(N[(y5 * a), $MachinePrecision] - N[(y4 * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y5 * a), $MachinePrecision] * N[(t * y2), $MachinePrecision]), $MachinePrecision] + t$95$13), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$10 - N[(N[(N[(y * x), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$17 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, If[Less[y4, -7.206256231996481e+60], N[(N[(t$95$8 - N[(t$95$11 - t$95$6), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$3 / N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision] - t$95$14), $MachinePrecision]), $MachinePrecision], If[Less[y4, -3.364603505246317e-66], N[(N[(N[(N[(N[(N[(t * c), $MachinePrecision] * N[(i * z), $MachinePrecision]), $MachinePrecision] - N[(N[(a * t), $MachinePrecision] * N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * c), $MachinePrecision] * N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$10), $MachinePrecision] + N[(N[(N[(N[(y0 * c), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision] - N[(N[(t$95$17 * N[(N[(y4 * c), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(y1 * y4), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision] * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[y4, -1.2000065055686116e-105], t$95$16, If[Less[y4, 6.718963124057495e-279], t$95$15, If[Less[y4, 4.77962681403792e-222], t$95$16, If[Less[y4, 2.2852241541266835e-175], t$95$15, N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(k * N[(i * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * N[(i * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(k * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(y3 * N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y2 * N[(x * N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(z * N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * t$95$5), $MachinePrecision]), $MachinePrecision] - N[(t$95$17 * t$95$1), $MachinePrecision]), $MachinePrecision] + t$95$13), $MachinePrecision]]]]]]]]]]]]]]]]]]]]]]]]

Reproduce

herbie shell --seed 2023297 
(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :name "Linear.Matrix:det44 from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< y4 -7.206256231996481e+60) (- (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))))) (- (/ (- (* y2 t) (* y3 y)) (/ 1.0 (- (* y4 c) (* y5 a)))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (if (< y4 -3.364603505246317e-66) (+ (- (- (- (* (* t c) (* i z)) (* (* a t) (* b z))) (* (* y c) (* i x))) (* (- (* b y0) (* i y1)) (- (* j x) (* k z)))) (- (* (- (* y0 c) (* a y1)) (- (* x y2) (* z y3))) (- (* (- (* t y2) (* y y3)) (- (* y4 c) (* a y5))) (* (- (* y1 y4) (* y5 y0)) (- (* k y2) (* j y3)))))) (if (< y4 -1.2000065055686116e-105) (+ (+ (- (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))) (* (* y3 y) (- (* y5 a) (* y4 c)))) (+ (* (* y5 a) (* t y2)) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* x y2) (* z y3)) (- (* c y0) (* a y1))) (- (* (- (* b y0) (* i y1)) (- (* j x) (* k z))) (* (- (* y x) (* z t)) (- (* b a) (* i c)))))) (if (< y4 6.718963124057495e-279) (+ (- (- (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k))) (* (* y5 t) (* i j))) (- (* (- (* y2 t) (* y3 y)) (- (* y4 c) (* y5 a))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))) (if (< y4 4.77962681403792e-222) (+ (+ (- (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))) (* (* y3 y) (- (* y5 a) (* y4 c)))) (+ (* (* y5 a) (* t y2)) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* x y2) (* z y3)) (- (* c y0) (* a y1))) (- (* (- (* b y0) (* i y1)) (- (* j x) (* k z))) (* (- (* y x) (* z t)) (- (* b a) (* i c)))))) (if (< y4 2.2852241541266835e-175) (+ (- (- (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k))) (* (* y5 t) (* i j))) (- (* (- (* y2 t) (* y3 y)) (- (* y4 c) (* y5 a))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))) (+ (- (+ (+ (- (* (- (* x y) (* z t)) (- (* a b) (* c i))) (- (* k (* i (* z y1))) (+ (* j (* i (* x y1))) (* y0 (* k (* z b)))))) (- (* z (* y3 (* a y1))) (+ (* y2 (* x (* a y1))) (* y0 (* z (* c y3)))))) (* (- (* t j) (* y k)) (- (* y4 b) (* y5 i)))) (* (- (* t y2) (* y y3)) (- (* y4 c) (* y5 a)))) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))))))))

  (+ (- (+ (+ (- (* (- (* x y) (* z t)) (- (* a b) (* c i))) (* (- (* x j) (* z k)) (- (* y0 b) (* y1 i)))) (* (- (* x y2) (* z y3)) (- (* y0 c) (* y1 a)))) (* (- (* t j) (* y k)) (- (* y4 b) (* y5 i)))) (* (- (* t y2) (* y y3)) (- (* y4 c) (* y5 a)))) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0)))))