Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 29.7% → 39.1%

Time: 1.5min

Alternatives: 39

Speedup: 4.5×

• 89.5% 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: 29.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 39.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot y0 - a \cdot y1\\ t_2 := y \cdot k - t \cdot j\\ t_3 := a \cdot b - c \cdot i\\ t_4 := x \cdot \left(\left(y \cdot t_3 + y2 \cdot t_1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{if}\;y5 \leq -4 \cdot 10^{+199}:\\ \;\;\;\;y5 \cdot \left(i \cdot t_2 + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y5 \leq -2.55 \cdot 10^{-8}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot t_1 + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -8.2 \cdot 10^{-106}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq -8.5 \cdot 10^{-245}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y5 \leq 7.5 \cdot 10^{-112}:\\ \;\;\;\;y \cdot \left(k \cdot \left(i \cdot y5 - b \cdot y4\right) + \left(x \cdot t_3 + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 4.5 \cdot 10^{-62}:\\ \;\;\;\;\left(c \cdot y3 - b \cdot k\right) \cdot \left(y \cdot y4\right)\\ \mathbf{elif}\;y5 \leq 6.8:\\ \;\;\;\;\left(a \cdot y3 - i \cdot k\right) \cdot \left(z \cdot y1\right)\\ \mathbf{elif}\;y5 \leq 4 \cdot 10^{+55}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 1.9 \cdot 10^{+109}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y5 \cdot t_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* c y0) (* a y1)))
        (t_2 (- (* y k) (* t j)))
        (t_3 (- (* a b) (* c i)))
        (t_4 (* x (+ (+ (* y t_3) (* y2 t_1)) (* j (- (* i y1) (* b y0)))))))
   (if (<= y5 -4e+199)
     (*
      y5
      (+
       (* i t_2)
       (+ (* a (- (* t y2) (* y y3))) (* y0 (- (* j y3) (* k y2))))))
     (if (<= y5 -2.55e-8)
       (*
        y2
        (+
         (+ (* x t_1) (* k (- (* y1 y4) (* y0 y5))))
         (* t (- (* a y5) (* c y4)))))
       (if (<= y5 -8.2e-106)
         (*
          b
          (+
           (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
           (* y0 (- (* z k) (* x j)))))
         (if (<= y5 -8.5e-245)
           t_4
           (if (<= y5 7.5e-112)
             (*
              y
              (+
               (* k (- (* i y5) (* b y4)))
               (+ (* x t_3) (* y3 (- (* c y4) (* a y5))))))
             (if (<= y5 4.5e-62)
               (* (- (* c y3) (* b k)) (* y y4))
               (if (<= y5 6.8)
                 (* (- (* a y3) (* i k)) (* z y1))
                 (if (<= y5 4e+55)
                   (* c (* y2 (- (* x y0) (* t y4))))
                   (if (<= y5 1.9e+109) t_4 (* i (* y5 t_2)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y0) - (a * y1);
	double t_2 = (y * k) - (t * j);
	double t_3 = (a * b) - (c * i);
	double t_4 = x * (((y * t_3) + (y2 * t_1)) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (y5 <= -4e+199) {
		tmp = y5 * ((i * t_2) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))));
	} else if (y5 <= -2.55e-8) {
		tmp = y2 * (((x * t_1) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y5 <= -8.2e-106) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (y5 <= -8.5e-245) {
		tmp = t_4;
	} else if (y5 <= 7.5e-112) {
		tmp = y * ((k * ((i * y5) - (b * y4))) + ((x * t_3) + (y3 * ((c * y4) - (a * y5)))));
	} else if (y5 <= 4.5e-62) {
		tmp = ((c * y3) - (b * k)) * (y * y4);
	} else if (y5 <= 6.8) {
		tmp = ((a * y3) - (i * k)) * (z * y1);
	} else if (y5 <= 4e+55) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (y5 <= 1.9e+109) {
		tmp = t_4;
	} else {
		tmp = i * (y5 * t_2);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (c * y0) - (a * y1)
    t_2 = (y * k) - (t * j)
    t_3 = (a * b) - (c * i)
    t_4 = x * (((y * t_3) + (y2 * t_1)) + (j * ((i * y1) - (b * y0))))
    if (y5 <= (-4d+199)) then
        tmp = y5 * ((i * t_2) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))))
    else if (y5 <= (-2.55d-8)) then
        tmp = y2 * (((x * t_1) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
    else if (y5 <= (-8.2d-106)) then
        tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    else if (y5 <= (-8.5d-245)) then
        tmp = t_4
    else if (y5 <= 7.5d-112) then
        tmp = y * ((k * ((i * y5) - (b * y4))) + ((x * t_3) + (y3 * ((c * y4) - (a * y5)))))
    else if (y5 <= 4.5d-62) then
        tmp = ((c * y3) - (b * k)) * (y * y4)
    else if (y5 <= 6.8d0) then
        tmp = ((a * y3) - (i * k)) * (z * y1)
    else if (y5 <= 4d+55) then
        tmp = c * (y2 * ((x * y0) - (t * y4)))
    else if (y5 <= 1.9d+109) then
        tmp = t_4
    else
        tmp = i * (y5 * t_2)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y0) - (a * y1);
	double t_2 = (y * k) - (t * j);
	double t_3 = (a * b) - (c * i);
	double t_4 = x * (((y * t_3) + (y2 * t_1)) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (y5 <= -4e+199) {
		tmp = y5 * ((i * t_2) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))));
	} else if (y5 <= -2.55e-8) {
		tmp = y2 * (((x * t_1) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y5 <= -8.2e-106) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (y5 <= -8.5e-245) {
		tmp = t_4;
	} else if (y5 <= 7.5e-112) {
		tmp = y * ((k * ((i * y5) - (b * y4))) + ((x * t_3) + (y3 * ((c * y4) - (a * y5)))));
	} else if (y5 <= 4.5e-62) {
		tmp = ((c * y3) - (b * k)) * (y * y4);
	} else if (y5 <= 6.8) {
		tmp = ((a * y3) - (i * k)) * (z * y1);
	} else if (y5 <= 4e+55) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (y5 <= 1.9e+109) {
		tmp = t_4;
	} else {
		tmp = i * (y5 * t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (c * y0) - (a * y1)
	t_2 = (y * k) - (t * j)
	t_3 = (a * b) - (c * i)
	t_4 = x * (((y * t_3) + (y2 * t_1)) + (j * ((i * y1) - (b * y0))))
	tmp = 0
	if y5 <= -4e+199:
		tmp = y5 * ((i * t_2) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))))
	elif y5 <= -2.55e-8:
		tmp = y2 * (((x * t_1) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
	elif y5 <= -8.2e-106:
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	elif y5 <= -8.5e-245:
		tmp = t_4
	elif y5 <= 7.5e-112:
		tmp = y * ((k * ((i * y5) - (b * y4))) + ((x * t_3) + (y3 * ((c * y4) - (a * y5)))))
	elif y5 <= 4.5e-62:
		tmp = ((c * y3) - (b * k)) * (y * y4)
	elif y5 <= 6.8:
		tmp = ((a * y3) - (i * k)) * (z * y1)
	elif y5 <= 4e+55:
		tmp = c * (y2 * ((x * y0) - (t * y4)))
	elif y5 <= 1.9e+109:
		tmp = t_4
	else:
		tmp = i * (y5 * t_2)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(c * y0) - Float64(a * y1))
	t_2 = Float64(Float64(y * k) - Float64(t * j))
	t_3 = Float64(Float64(a * b) - Float64(c * i))
	t_4 = Float64(x * Float64(Float64(Float64(y * t_3) + Float64(y2 * t_1)) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))))
	tmp = 0.0
	if (y5 <= -4e+199)
		tmp = Float64(y5 * Float64(Float64(i * t_2) + Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))))));
	elseif (y5 <= -2.55e-8)
		tmp = Float64(y2 * Float64(Float64(Float64(x * t_1) + Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y5 <= -8.2e-106)
		tmp = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (y5 <= -8.5e-245)
		tmp = t_4;
	elseif (y5 <= 7.5e-112)
		tmp = Float64(y * Float64(Float64(k * Float64(Float64(i * y5) - Float64(b * y4))) + Float64(Float64(x * t_3) + Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))))));
	elseif (y5 <= 4.5e-62)
		tmp = Float64(Float64(Float64(c * y3) - Float64(b * k)) * Float64(y * y4));
	elseif (y5 <= 6.8)
		tmp = Float64(Float64(Float64(a * y3) - Float64(i * k)) * Float64(z * y1));
	elseif (y5 <= 4e+55)
		tmp = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))));
	elseif (y5 <= 1.9e+109)
		tmp = t_4;
	else
		tmp = Float64(i * Float64(y5 * t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (c * y0) - (a * y1);
	t_2 = (y * k) - (t * j);
	t_3 = (a * b) - (c * i);
	t_4 = x * (((y * t_3) + (y2 * t_1)) + (j * ((i * y1) - (b * y0))));
	tmp = 0.0;
	if (y5 <= -4e+199)
		tmp = y5 * ((i * t_2) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))));
	elseif (y5 <= -2.55e-8)
		tmp = y2 * (((x * t_1) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	elseif (y5 <= -8.2e-106)
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	elseif (y5 <= -8.5e-245)
		tmp = t_4;
	elseif (y5 <= 7.5e-112)
		tmp = y * ((k * ((i * y5) - (b * y4))) + ((x * t_3) + (y3 * ((c * y4) - (a * y5)))));
	elseif (y5 <= 4.5e-62)
		tmp = ((c * y3) - (b * k)) * (y * y4);
	elseif (y5 <= 6.8)
		tmp = ((a * y3) - (i * k)) * (z * y1);
	elseif (y5 <= 4e+55)
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	elseif (y5 <= 1.9e+109)
		tmp = t_4;
	else
		tmp = i * (y5 * t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x * N[(N[(N[(y * t$95$3), $MachinePrecision] + N[(y2 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -4e+199], N[(y5 * N[(N[(i * t$95$2), $MachinePrecision] + N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -2.55e-8], N[(y2 * N[(N[(N[(x * t$95$1), $MachinePrecision] + N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -8.2e-106], N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -8.5e-245], t$95$4, If[LessEqual[y5, 7.5e-112], N[(y * N[(N[(k * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * t$95$3), $MachinePrecision] + N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 4.5e-62], N[(N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision] * N[(y * y4), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 6.8], N[(N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision] * N[(z * y1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 4e+55], N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.9e+109], t$95$4, N[(i * N[(y5 * t$95$2), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y5 < -4.00000000000000039e199

   1. Initial program 20.8%

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

   3. Simplified 29.2%

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

   4. Taylor expanded in y5 around inf 70.8%

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

      1. mul-1-neg 70.8%

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

      2. mul-1-neg 70.8%

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

      3. mul-1-neg 70.8%

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

      4. sub-neg 70.8%

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

      5. sub-neg 70.8%

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

   6. Simplified 70.8%

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

   if -4.00000000000000039e199 < y5 < -2.55e-8

   1. Initial program 18.6%

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

   3. Simplified 18.6%

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

   4. Taylor expanded in y2 around inf 52.7%

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

   if -2.55e-8 < y5 < -8.1999999999999998e-106

   1. Initial program 39.3%

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

   3. Simplified 39.3%

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

   4. Taylor expanded in b around inf 71.5%

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

   if -8.1999999999999998e-106 < y5 < -8.50000000000000022e-245 or 4.00000000000000004e55 < y5 < 1.90000000000000019e109

   1. Initial program 16.6%

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

   3. Simplified 16.6%

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

   4. Taylor expanded in x around inf 56.2%

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

   if -8.50000000000000022e-245 < y5 < 7.5000000000000002e-112

   1. Initial program 32.9%

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

   3. Simplified 40.1%

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

   4. Taylor expanded in y around inf 55.3%

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

      1. mul-1-neg 55.3%

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

   6. Simplified 55.3%

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

   if 7.5000000000000002e-112 < y5 < 4.50000000000000018e-62

   1. Initial program 21.7%

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

   3. Simplified 21.7%

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

   4. Taylor expanded in y around inf 36.4%

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

      1. mul-1-neg 36.4%

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

   6. Simplified 36.4%

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

   7. Taylor expanded in y4 around inf 76.2%

      \[\leadsto \color{blue}{y4 \cdot \left(y \cdot \left(c \cdot y3 - k \cdot b\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 76.2%

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

      2. *-commutative 76.2%

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

   9. Simplified 76.2%

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

   if 4.50000000000000018e-62 < y5 < 6.79999999999999982

   1. Initial program 27.1%

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

   3. Simplified 27.1%

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

   4. Taylor expanded in z around -inf 33.8%

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

      1. mul-1-neg 33.8%

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

      2. associate--l+ 33.8%

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

   6. Simplified 33.8%

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

   7. Taylor expanded in y1 around inf 61.1%

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

      1. distribute-lft-out-- 61.1%

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

      2. *-commutative 61.1%

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

      3. *-commutative 61.1%

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

   9. Simplified 61.1%

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

   if 6.79999999999999982 < y5 < 4.00000000000000004e55

   1. Initial program 30.8%

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

   3. Simplified 30.8%

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

   4. Taylor expanded in y2 around inf 31.0%

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

   5. Taylor expanded in c around inf 70.7%

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

   if 1.90000000000000019e109 < y5

   1. Initial program 10.7%

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

   3. Simplified 21.4%

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

   4. Taylor expanded in y5 around inf 64.3%

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

      1. mul-1-neg 64.3%

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

      2. mul-1-neg 64.3%

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

      3. mul-1-neg 64.3%

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

      4. sub-neg 64.3%

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

      5. sub-neg 64.3%

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

   6. Simplified 64.3%

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

   7. Taylor expanded in i around inf 64.8%

      \[\leadsto \color{blue}{i \cdot \left(\left(k \cdot y - t \cdot j\right) \cdot y5\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -4 \cdot 10^{+199}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y5 \leq -2.55 \cdot 10^{-8}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -8.2 \cdot 10^{-106}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq -8.5 \cdot 10^{-245}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 7.5 \cdot 10^{-112}:\\ \;\;\;\;y \cdot \left(k \cdot \left(i \cdot y5 - b \cdot y4\right) + \left(x \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 4.5 \cdot 10^{-62}:\\ \;\;\;\;\left(c \cdot y3 - b \cdot k\right) \cdot \left(y \cdot y4\right)\\ \mathbf{elif}\;y5 \leq 6.8:\\ \;\;\;\;\left(a \cdot y3 - i \cdot k\right) \cdot \left(z \cdot y1\right)\\ \mathbf{elif}\;y5 \leq 4 \cdot 10^{+55}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 1.9 \cdot 10^{+109}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \end{array} \]

Alternative 2: 52.6% accurate, 0.5× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * y3) - (t * y2);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (((((((a * b) - (c * i)) * ((x * y) - (z * t))) + (((b * y0) - (i * y1)) * ((z * k) - (x * j)))) + (t_2 * ((c * y0) - (a * y1)))) + (((t * j) - (y * k)) * ((b * y4) - (i * y5)))) + (((c * y4) - (a * y5)) * t_1)) + (((y1 * y4) - (y0 * y5)) * ((k * y2) - (j * y3)));
	double tmp;
	if (t_3 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * t_2) + (y4 * t_1)));
	}
	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 = (y * y3) - (t * y2);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (((((((a * b) - (c * i)) * ((x * y) - (z * t))) + (((b * y0) - (i * y1)) * ((z * k) - (x * j)))) + (t_2 * ((c * y0) - (a * y1)))) + (((t * j) - (y * k)) * ((b * y4) - (i * y5)))) + (((c * y4) - (a * y5)) * t_1)) + (((y1 * y4) - (y0 * y5)) * ((k * y2) - (j * y3)));
	double tmp;
	if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * t_2) + (y4 * 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 = (y * y3) - (t * y2)
	t_2 = (x * y2) - (z * y3)
	t_3 = (((((((a * b) - (c * i)) * ((x * y) - (z * t))) + (((b * y0) - (i * y1)) * ((z * k) - (x * j)))) + (t_2 * ((c * y0) - (a * y1)))) + (((t * j) - (y * k)) * ((b * y4) - (i * y5)))) + (((c * y4) - (a * y5)) * t_1)) + (((y1 * y4) - (y0 * y5)) * ((k * y2) - (j * y3)))
	tmp = 0
	if t_3 <= math.inf:
		tmp = t_3
	else:
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * t_2) + (y4 * 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(y * y3) - Float64(t * y2))
	t_2 = Float64(Float64(x * y2) - Float64(z * y3))
	t_3 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(a * b) - Float64(c * i)) * Float64(Float64(x * y) - Float64(z * t))) + Float64(Float64(Float64(b * y0) - Float64(i * y1)) * Float64(Float64(z * k) - Float64(x * j)))) + Float64(t_2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(Float64(Float64(t * j) - Float64(y * k)) * Float64(Float64(b * y4) - Float64(i * y5)))) + Float64(Float64(Float64(c * y4) - Float64(a * y5)) * t_1)) + Float64(Float64(Float64(y1 * y4) - Float64(y0 * y5)) * Float64(Float64(k * y2) - Float64(j * y3))))
	tmp = 0.0
	if (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(c * Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(Float64(y0 * t_2) + Float64(y4 * 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 = (y * y3) - (t * y2);
	t_2 = (x * y2) - (z * y3);
	t_3 = (((((((a * b) - (c * i)) * ((x * y) - (z * t))) + (((b * y0) - (i * y1)) * ((z * k) - (x * j)))) + (t_2 * ((c * y0) - (a * y1)))) + (((t * j) - (y * k)) * ((b * y4) - (i * y5)))) + (((c * y4) - (a * y5)) * t_1)) + (((y1 * y4) - (y0 * y5)) * ((k * y2) - (j * y3)));
	tmp = 0.0;
	if (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * t_2) + (y4 * 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[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(N[(N[(N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision] * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision] * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, Infinity], t$95$3, N[(c * N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y0 * t$95$2), $MachinePrecision] + N[(y4 * t$95$1), $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 87.8%

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

   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%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in c around inf 40.5%

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

      1. associate--l+ 40.5%

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

      2. mul-1-neg 40.5%

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

   6. Simplified 40.5%

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

4. Final simplification 53.2%

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

Alternative 3: 37.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x \cdot y\\ t_2 := b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ t_3 := c \cdot y0 - a \cdot y1\\ \mathbf{if}\;y3 \leq -5 \cdot 10^{+59}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4 - z \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq -1.7 \cdot 10^{-217}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot t_3\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq 1.75 \cdot 10^{-233}:\\ \;\;\;\;y2 \cdot \left(y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;y3 \leq 1.05 \cdot 10^{-130}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y3 \leq 2.35 \cdot 10^{-54}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot t_3 + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 5.2 \cdot 10^{-12}:\\ \;\;\;\;\left(z \cdot y0\right) \cdot \left(b \cdot k - c \cdot y3\right)\\ \mathbf{elif}\;y3 \leq 2 \cdot 10^{+78}:\\ \;\;\;\;i \cdot \left(c \cdot t_1 + \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\right)\\ \mathbf{elif}\;y3 \leq 1.5 \cdot 10^{+170}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y3 \leq 2.65 \cdot 10^{+222}:\\ \;\;\;\;c \cdot \left(i \cdot t_1 + \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y3 \leq 6.8 \cdot 10^{+275}:\\ \;\;\;\;\left(z \cdot y3\right) \cdot \left(a \cdot y1 - c \cdot y0\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* z t) (* x y)))
        (t_2
         (*
          b
          (+
           (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
           (* y0 (- (* z k) (* x j))))))
        (t_3 (- (* c y0) (* a y1))))
   (if (<= y3 -5e+59)
     (* c (* y3 (- (* y y4) (* z y0))))
     (if (<= y3 -1.7e-217)
       (*
        x
        (+
         (+ (* y (- (* a b) (* c i))) (* y2 t_3))
         (* j (- (* i y1) (* b y0)))))
       (if (<= y3 1.75e-233)
         (* y2 (* y1 (- (* k y4) (* x a))))
         (if (<= y3 1.05e-130)
           t_2
           (if (<= y3 2.35e-54)
             (*
              y2
              (+
               (+ (* x t_3) (* k (- (* y1 y4) (* y0 y5))))
               (* t (- (* a y5) (* c y4)))))
             (if (<= y3 5.2e-12)
               (* (* z y0) (- (* b k) (* c y3)))
               (if (<= y3 2e+78)
                 (*
                  i
                  (+
                   (* c t_1)
                   (+ (* y1 (- (* x j) (* z k))) (* y5 (- (* y k) (* t j))))))
                 (if (<= y3 1.5e+170)
                   t_2
                   (if (<= y3 2.65e+222)
                     (*
                      c
                      (+
                       (* i t_1)
                       (+
                        (* y0 (- (* x y2) (* z y3)))
                        (* y4 (- (* y y3) (* t y2))))))
                     (if (<= y3 6.8e+275)
                       (* (* z y3) (- (* a y1) (* c y0)))
                       (* c (* y (- (* y3 y4) (* x i))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (z * t) - (x * y);
	double t_2 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double t_3 = (c * y0) - (a * y1);
	double tmp;
	if (y3 <= -5e+59) {
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	} else if (y3 <= -1.7e-217) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_3)) + (j * ((i * y1) - (b * y0))));
	} else if (y3 <= 1.75e-233) {
		tmp = y2 * (y1 * ((k * y4) - (x * a)));
	} else if (y3 <= 1.05e-130) {
		tmp = t_2;
	} else if (y3 <= 2.35e-54) {
		tmp = y2 * (((x * t_3) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y3 <= 5.2e-12) {
		tmp = (z * y0) * ((b * k) - (c * y3));
	} else if (y3 <= 2e+78) {
		tmp = i * ((c * t_1) + ((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j)))));
	} else if (y3 <= 1.5e+170) {
		tmp = t_2;
	} else if (y3 <= 2.65e+222) {
		tmp = c * ((i * t_1) + ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2)))));
	} else if (y3 <= 6.8e+275) {
		tmp = (z * y3) * ((a * y1) - (c * y0));
	} else {
		tmp = c * (y * ((y3 * y4) - (x * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (z * t) - (x * y)
    t_2 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    t_3 = (c * y0) - (a * y1)
    if (y3 <= (-5d+59)) then
        tmp = c * (y3 * ((y * y4) - (z * y0)))
    else if (y3 <= (-1.7d-217)) then
        tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_3)) + (j * ((i * y1) - (b * y0))))
    else if (y3 <= 1.75d-233) then
        tmp = y2 * (y1 * ((k * y4) - (x * a)))
    else if (y3 <= 1.05d-130) then
        tmp = t_2
    else if (y3 <= 2.35d-54) then
        tmp = y2 * (((x * t_3) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
    else if (y3 <= 5.2d-12) then
        tmp = (z * y0) * ((b * k) - (c * y3))
    else if (y3 <= 2d+78) then
        tmp = i * ((c * t_1) + ((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j)))))
    else if (y3 <= 1.5d+170) then
        tmp = t_2
    else if (y3 <= 2.65d+222) then
        tmp = c * ((i * t_1) + ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2)))))
    else if (y3 <= 6.8d+275) then
        tmp = (z * y3) * ((a * y1) - (c * y0))
    else
        tmp = c * (y * ((y3 * y4) - (x * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (z * t) - (x * y);
	double t_2 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double t_3 = (c * y0) - (a * y1);
	double tmp;
	if (y3 <= -5e+59) {
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	} else if (y3 <= -1.7e-217) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_3)) + (j * ((i * y1) - (b * y0))));
	} else if (y3 <= 1.75e-233) {
		tmp = y2 * (y1 * ((k * y4) - (x * a)));
	} else if (y3 <= 1.05e-130) {
		tmp = t_2;
	} else if (y3 <= 2.35e-54) {
		tmp = y2 * (((x * t_3) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y3 <= 5.2e-12) {
		tmp = (z * y0) * ((b * k) - (c * y3));
	} else if (y3 <= 2e+78) {
		tmp = i * ((c * t_1) + ((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j)))));
	} else if (y3 <= 1.5e+170) {
		tmp = t_2;
	} else if (y3 <= 2.65e+222) {
		tmp = c * ((i * t_1) + ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2)))));
	} else if (y3 <= 6.8e+275) {
		tmp = (z * y3) * ((a * y1) - (c * y0));
	} else {
		tmp = c * (y * ((y3 * y4) - (x * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (z * t) - (x * y)
	t_2 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	t_3 = (c * y0) - (a * y1)
	tmp = 0
	if y3 <= -5e+59:
		tmp = c * (y3 * ((y * y4) - (z * y0)))
	elif y3 <= -1.7e-217:
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_3)) + (j * ((i * y1) - (b * y0))))
	elif y3 <= 1.75e-233:
		tmp = y2 * (y1 * ((k * y4) - (x * a)))
	elif y3 <= 1.05e-130:
		tmp = t_2
	elif y3 <= 2.35e-54:
		tmp = y2 * (((x * t_3) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
	elif y3 <= 5.2e-12:
		tmp = (z * y0) * ((b * k) - (c * y3))
	elif y3 <= 2e+78:
		tmp = i * ((c * t_1) + ((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j)))))
	elif y3 <= 1.5e+170:
		tmp = t_2
	elif y3 <= 2.65e+222:
		tmp = c * ((i * t_1) + ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2)))))
	elif y3 <= 6.8e+275:
		tmp = (z * y3) * ((a * y1) - (c * y0))
	else:
		tmp = c * (y * ((y3 * y4) - (x * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(z * t) - Float64(x * y))
	t_2 = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))))
	t_3 = Float64(Float64(c * y0) - Float64(a * y1))
	tmp = 0.0
	if (y3 <= -5e+59)
		tmp = Float64(c * Float64(y3 * Float64(Float64(y * y4) - Float64(z * y0))));
	elseif (y3 <= -1.7e-217)
		tmp = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * t_3)) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (y3 <= 1.75e-233)
		tmp = Float64(y2 * Float64(y1 * Float64(Float64(k * y4) - Float64(x * a))));
	elseif (y3 <= 1.05e-130)
		tmp = t_2;
	elseif (y3 <= 2.35e-54)
		tmp = Float64(y2 * Float64(Float64(Float64(x * t_3) + Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y3 <= 5.2e-12)
		tmp = Float64(Float64(z * y0) * Float64(Float64(b * k) - Float64(c * y3)));
	elseif (y3 <= 2e+78)
		tmp = Float64(i * Float64(Float64(c * t_1) + Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) + Float64(y5 * Float64(Float64(y * k) - Float64(t * j))))));
	elseif (y3 <= 1.5e+170)
		tmp = t_2;
	elseif (y3 <= 2.65e+222)
		tmp = Float64(c * Float64(Float64(i * t_1) + Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))))));
	elseif (y3 <= 6.8e+275)
		tmp = Float64(Float64(z * y3) * Float64(Float64(a * y1) - Float64(c * y0)));
	else
		tmp = Float64(c * Float64(y * Float64(Float64(y3 * y4) - Float64(x * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (z * t) - (x * y);
	t_2 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	t_3 = (c * y0) - (a * y1);
	tmp = 0.0;
	if (y3 <= -5e+59)
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	elseif (y3 <= -1.7e-217)
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_3)) + (j * ((i * y1) - (b * y0))));
	elseif (y3 <= 1.75e-233)
		tmp = y2 * (y1 * ((k * y4) - (x * a)));
	elseif (y3 <= 1.05e-130)
		tmp = t_2;
	elseif (y3 <= 2.35e-54)
		tmp = y2 * (((x * t_3) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	elseif (y3 <= 5.2e-12)
		tmp = (z * y0) * ((b * k) - (c * y3));
	elseif (y3 <= 2e+78)
		tmp = i * ((c * t_1) + ((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j)))));
	elseif (y3 <= 1.5e+170)
		tmp = t_2;
	elseif (y3 <= 2.65e+222)
		tmp = c * ((i * t_1) + ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2)))));
	elseif (y3 <= 6.8e+275)
		tmp = (z * y3) * ((a * y1) - (c * y0));
	else
		tmp = c * (y * ((y3 * y4) - (x * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -5e+59], N[(c * N[(y3 * N[(N[(y * y4), $MachinePrecision] - N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -1.7e-217], N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.75e-233], N[(y2 * N[(y1 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.05e-130], t$95$2, If[LessEqual[y3, 2.35e-54], N[(y2 * N[(N[(N[(x * t$95$3), $MachinePrecision] + N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 5.2e-12], N[(N[(z * y0), $MachinePrecision] * N[(N[(b * k), $MachinePrecision] - N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 2e+78], N[(i * N[(N[(c * t$95$1), $MachinePrecision] + N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.5e+170], t$95$2, If[LessEqual[y3, 2.65e+222], N[(c * N[(N[(i * t$95$1), $MachinePrecision] + 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]), $MachinePrecision], If[LessEqual[y3, 6.8e+275], N[(N[(z * y3), $MachinePrecision] * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if y3 < -4.9999999999999997e59

   1. Initial program 12.9%

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

   3. Simplified 12.9%

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

   4. Taylor expanded in c around inf 51.4%

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

      1. associate--l+ 51.4%

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

      2. mul-1-neg 51.4%

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

   6. Simplified 51.4%

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

   7. Taylor expanded in y3 around -inf 58.4%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(\left(y0 \cdot z - y4 \cdot y\right) \cdot y3\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 58.4%

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

      2. neg-mul-1 58.4%

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

      3. *-commutative 58.4%

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

   9. Simplified 58.4%

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

   if -4.9999999999999997e59 < y3 < -1.70000000000000008e-217

   1. Initial program 28.4%

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

   3. Simplified 28.4%

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

   4. Taylor expanded in x around inf 52.1%

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

   if -1.70000000000000008e-217 < y3 < 1.74999999999999995e-233

   1. Initial program 23.2%

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

   3. Simplified 23.2%

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

   4. Taylor expanded in y2 around inf 40.6%

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

   5. Taylor expanded in y1 around inf 63.3%

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

      1. +-commutative 63.3%

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

      2. mul-1-neg 63.3%

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

      3. unsub-neg 63.3%

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

      4. *-commutative 63.3%

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

   7. Simplified 63.3%

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

   if 1.74999999999999995e-233 < y3 < 1.05000000000000001e-130 or 2.00000000000000002e78 < y3 < 1.49999999999999998e170

   1. Initial program 31.0%

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

   3. Simplified 31.0%

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

   4. Taylor expanded in b around inf 59.3%

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

   if 1.05000000000000001e-130 < y3 < 2.35e-54

   1. Initial program 28.2%

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

   3. Simplified 28.2%

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

   4. Taylor expanded in y2 around inf 56.2%

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

   if 2.35e-54 < y3 < 5.19999999999999965e-12

   1. Initial program 20.7%

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

   3. Simplified 20.7%

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

   4. Taylor expanded in z around -inf 51.1%

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

      1. mul-1-neg 51.1%

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

      2. associate--l+ 51.1%

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

   6. Simplified 51.1%

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

   7. Taylor expanded in y0 around inf 58.0%

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

      1. *-commutative 58.0%

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

      2. *-commutative 58.0%

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

      3. associate-*l* 58.0%

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

      4. *-commutative 58.0%

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

      5. *-commutative 58.0%

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

   9. Simplified 58.0%

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

   if 5.19999999999999965e-12 < y3 < 2.00000000000000002e78

   1. Initial program 21.7%

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

   3. Simplified 21.7%

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

   4. Taylor expanded in i around -inf 52.4%

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

      1. mul-1-neg 52.4%

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

      2. associate--l+ 52.4%

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

   6. Simplified 52.4%

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

   if 1.49999999999999998e170 < y3 < 2.64999999999999996e222

   1. Initial program 18.2%

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

   3. Simplified 18.2%

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

   4. Taylor expanded in c around inf 81.8%

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

      1. associate--l+ 81.8%

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

      2. mul-1-neg 81.8%

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

   6. Simplified 81.8%

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

   if 2.64999999999999996e222 < y3 < 6.8000000000000002e275

   1. Initial program 12.4%

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

   3. Simplified 12.4%

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

   4. Taylor expanded in z around -inf 55.6%

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

      1. mul-1-neg 55.6%

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

      2. associate--l+ 55.6%

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

   6. Simplified 55.6%

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

   7. Taylor expanded in y3 around inf 78.1%

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

   if 6.8000000000000002e275 < y3

   1. Initial program 50.0%

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

   3. Simplified 50.0%

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

   4. Taylor expanded in c around inf 74.6%

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

      1. associate--l+ 74.6%

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

      2. mul-1-neg 74.6%

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

   6. Simplified 74.6%

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

   7. Taylor expanded in y around -inf 99.6%

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

      1. mul-1-neg 99.6%

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

      2. unsub-neg 99.6%

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

      3. *-commutative 99.6%

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

   9. Simplified 99.6%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -5 \cdot 10^{+59}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4 - z \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq -1.7 \cdot 10^{-217}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq 1.75 \cdot 10^{-233}:\\ \;\;\;\;y2 \cdot \left(y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;y3 \leq 1.05 \cdot 10^{-130}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y3 \leq 2.35 \cdot 10^{-54}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 5.2 \cdot 10^{-12}:\\ \;\;\;\;\left(z \cdot y0\right) \cdot \left(b \cdot k - c \cdot y3\right)\\ \mathbf{elif}\;y3 \leq 2 \cdot 10^{+78}:\\ \;\;\;\;i \cdot \left(c \cdot \left(z \cdot t - x \cdot y\right) + \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\right)\\ \mathbf{elif}\;y3 \leq 1.5 \cdot 10^{+170}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y3 \leq 2.65 \cdot 10^{+222}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y3 \leq 6.8 \cdot 10^{+275}:\\ \;\;\;\;\left(z \cdot y3\right) \cdot \left(a \cdot y1 - c \cdot y0\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \end{array} \]

Alternative 4: 36.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b - c \cdot i\\ t_2 := c \cdot y0 - a \cdot y1\\ t_3 := x \cdot \left(\left(y \cdot t_1 + y2 \cdot t_2\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{if}\;y5 \leq -3.65 \cdot 10^{+204}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq -1.06 \cdot 10^{-10}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot t_2 + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -6.2 \cdot 10^{-109}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq -1 \cdot 10^{-244}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y5 \leq 5.2 \cdot 10^{-112}:\\ \;\;\;\;y \cdot \left(k \cdot \left(i \cdot y5 - b \cdot y4\right) + \left(x \cdot t_1 + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 1.9 \cdot 10^{-63}:\\ \;\;\;\;\left(c \cdot y3 - b \cdot k\right) \cdot \left(y \cdot y4\right)\\ \mathbf{elif}\;y5 \leq 1.45:\\ \;\;\;\;\left(a \cdot y3 - i \cdot k\right) \cdot \left(z \cdot y1\right)\\ \mathbf{elif}\;y5 \leq 7 \cdot 10^{+55}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 3.4 \cdot 10^{+109}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* a b) (* c i)))
        (t_2 (- (* c y0) (* a y1)))
        (t_3 (* x (+ (+ (* y t_1) (* y2 t_2)) (* j (- (* i y1) (* b y0)))))))
   (if (<= y5 -3.65e+204)
     (* k (* y (* i y5)))
     (if (<= y5 -1.06e-10)
       (*
        y2
        (+
         (+ (* x t_2) (* k (- (* y1 y4) (* y0 y5))))
         (* t (- (* a y5) (* c y4)))))
       (if (<= y5 -6.2e-109)
         (*
          b
          (+
           (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
           (* y0 (- (* z k) (* x j)))))
         (if (<= y5 -1e-244)
           t_3
           (if (<= y5 5.2e-112)
             (*
              y
              (+
               (* k (- (* i y5) (* b y4)))
               (+ (* x t_1) (* y3 (- (* c y4) (* a y5))))))
             (if (<= y5 1.9e-63)
               (* (- (* c y3) (* b k)) (* y y4))
               (if (<= y5 1.45)
                 (* (- (* a y3) (* i k)) (* z y1))
                 (if (<= y5 7e+55)
                   (* c (* y2 (- (* x y0) (* t y4))))
                   (if (<= y5 3.4e+109)
                     t_3
                     (* i (* y5 (- (* y k) (* t j)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (a * b) - (c * i);
	double t_2 = (c * y0) - (a * y1);
	double t_3 = x * (((y * t_1) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (y5 <= -3.65e+204) {
		tmp = k * (y * (i * y5));
	} else if (y5 <= -1.06e-10) {
		tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y5 <= -6.2e-109) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (y5 <= -1e-244) {
		tmp = t_3;
	} else if (y5 <= 5.2e-112) {
		tmp = y * ((k * ((i * y5) - (b * y4))) + ((x * t_1) + (y3 * ((c * y4) - (a * y5)))));
	} else if (y5 <= 1.9e-63) {
		tmp = ((c * y3) - (b * k)) * (y * y4);
	} else if (y5 <= 1.45) {
		tmp = ((a * y3) - (i * k)) * (z * y1);
	} else if (y5 <= 7e+55) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (y5 <= 3.4e+109) {
		tmp = t_3;
	} else {
		tmp = i * (y5 * ((y * k) - (t * j)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (a * b) - (c * i)
    t_2 = (c * y0) - (a * y1)
    t_3 = x * (((y * t_1) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))))
    if (y5 <= (-3.65d+204)) then
        tmp = k * (y * (i * y5))
    else if (y5 <= (-1.06d-10)) then
        tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
    else if (y5 <= (-6.2d-109)) then
        tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    else if (y5 <= (-1d-244)) then
        tmp = t_3
    else if (y5 <= 5.2d-112) then
        tmp = y * ((k * ((i * y5) - (b * y4))) + ((x * t_1) + (y3 * ((c * y4) - (a * y5)))))
    else if (y5 <= 1.9d-63) then
        tmp = ((c * y3) - (b * k)) * (y * y4)
    else if (y5 <= 1.45d0) then
        tmp = ((a * y3) - (i * k)) * (z * y1)
    else if (y5 <= 7d+55) then
        tmp = c * (y2 * ((x * y0) - (t * y4)))
    else if (y5 <= 3.4d+109) then
        tmp = t_3
    else
        tmp = i * (y5 * ((y * k) - (t * j)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (a * b) - (c * i);
	double t_2 = (c * y0) - (a * y1);
	double t_3 = x * (((y * t_1) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (y5 <= -3.65e+204) {
		tmp = k * (y * (i * y5));
	} else if (y5 <= -1.06e-10) {
		tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y5 <= -6.2e-109) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (y5 <= -1e-244) {
		tmp = t_3;
	} else if (y5 <= 5.2e-112) {
		tmp = y * ((k * ((i * y5) - (b * y4))) + ((x * t_1) + (y3 * ((c * y4) - (a * y5)))));
	} else if (y5 <= 1.9e-63) {
		tmp = ((c * y3) - (b * k)) * (y * y4);
	} else if (y5 <= 1.45) {
		tmp = ((a * y3) - (i * k)) * (z * y1);
	} else if (y5 <= 7e+55) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (y5 <= 3.4e+109) {
		tmp = t_3;
	} else {
		tmp = i * (y5 * ((y * k) - (t * j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (a * b) - (c * i)
	t_2 = (c * y0) - (a * y1)
	t_3 = x * (((y * t_1) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))))
	tmp = 0
	if y5 <= -3.65e+204:
		tmp = k * (y * (i * y5))
	elif y5 <= -1.06e-10:
		tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
	elif y5 <= -6.2e-109:
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	elif y5 <= -1e-244:
		tmp = t_3
	elif y5 <= 5.2e-112:
		tmp = y * ((k * ((i * y5) - (b * y4))) + ((x * t_1) + (y3 * ((c * y4) - (a * y5)))))
	elif y5 <= 1.9e-63:
		tmp = ((c * y3) - (b * k)) * (y * y4)
	elif y5 <= 1.45:
		tmp = ((a * y3) - (i * k)) * (z * y1)
	elif y5 <= 7e+55:
		tmp = c * (y2 * ((x * y0) - (t * y4)))
	elif y5 <= 3.4e+109:
		tmp = t_3
	else:
		tmp = i * (y5 * ((y * k) - (t * j)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(a * b) - Float64(c * i))
	t_2 = Float64(Float64(c * y0) - Float64(a * y1))
	t_3 = Float64(x * Float64(Float64(Float64(y * t_1) + Float64(y2 * t_2)) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))))
	tmp = 0.0
	if (y5 <= -3.65e+204)
		tmp = Float64(k * Float64(y * Float64(i * y5)));
	elseif (y5 <= -1.06e-10)
		tmp = Float64(y2 * Float64(Float64(Float64(x * t_2) + Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y5 <= -6.2e-109)
		tmp = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (y5 <= -1e-244)
		tmp = t_3;
	elseif (y5 <= 5.2e-112)
		tmp = Float64(y * Float64(Float64(k * Float64(Float64(i * y5) - Float64(b * y4))) + Float64(Float64(x * t_1) + Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))))));
	elseif (y5 <= 1.9e-63)
		tmp = Float64(Float64(Float64(c * y3) - Float64(b * k)) * Float64(y * y4));
	elseif (y5 <= 1.45)
		tmp = Float64(Float64(Float64(a * y3) - Float64(i * k)) * Float64(z * y1));
	elseif (y5 <= 7e+55)
		tmp = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))));
	elseif (y5 <= 3.4e+109)
		tmp = t_3;
	else
		tmp = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (a * b) - (c * i);
	t_2 = (c * y0) - (a * y1);
	t_3 = x * (((y * t_1) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))));
	tmp = 0.0;
	if (y5 <= -3.65e+204)
		tmp = k * (y * (i * y5));
	elseif (y5 <= -1.06e-10)
		tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	elseif (y5 <= -6.2e-109)
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	elseif (y5 <= -1e-244)
		tmp = t_3;
	elseif (y5 <= 5.2e-112)
		tmp = y * ((k * ((i * y5) - (b * y4))) + ((x * t_1) + (y3 * ((c * y4) - (a * y5)))));
	elseif (y5 <= 1.9e-63)
		tmp = ((c * y3) - (b * k)) * (y * y4);
	elseif (y5 <= 1.45)
		tmp = ((a * y3) - (i * k)) * (z * y1);
	elseif (y5 <= 7e+55)
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	elseif (y5 <= 3.4e+109)
		tmp = t_3;
	else
		tmp = i * (y5 * ((y * k) - (t * j)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(N[(y * t$95$1), $MachinePrecision] + N[(y2 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -3.65e+204], N[(k * N[(y * N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.06e-10], N[(y2 * N[(N[(N[(x * t$95$2), $MachinePrecision] + N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -6.2e-109], N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1e-244], t$95$3, If[LessEqual[y5, 5.2e-112], N[(y * N[(N[(k * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * t$95$1), $MachinePrecision] + N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.9e-63], N[(N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision] * N[(y * y4), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.45], N[(N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision] * N[(z * y1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 7e+55], N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 3.4e+109], t$95$3, N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y5 < -3.6500000000000001e204

   1. Initial program 20.8%

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

   3. Simplified 29.2%

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

   4. Taylor expanded in y5 around inf 70.8%

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

      1. mul-1-neg 70.8%

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

      2. mul-1-neg 70.8%

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

      3. mul-1-neg 70.8%

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

      4. sub-neg 70.8%

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

      5. sub-neg 70.8%

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

   6. Simplified 70.8%

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

   7. Taylor expanded in i around inf 46.4%

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

   8. Taylor expanded in k around inf 54.7%

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

   if -3.6500000000000001e204 < y5 < -1.06e-10

   1. Initial program 18.6%

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

   3. Simplified 18.6%

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

   4. Taylor expanded in y2 around inf 52.7%

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

   if -1.06e-10 < y5 < -6.1999999999999999e-109

   1. Initial program 39.3%

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

   3. Simplified 39.3%

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

   4. Taylor expanded in b around inf 71.5%

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

   if -6.1999999999999999e-109 < y5 < -9.9999999999999993e-245 or 7.00000000000000021e55 < y5 < 3.40000000000000006e109

   1. Initial program 16.6%

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

   3. Simplified 16.6%

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

   4. Taylor expanded in x around inf 56.2%

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

   if -9.9999999999999993e-245 < y5 < 5.19999999999999983e-112

   1. Initial program 32.9%

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

   3. Simplified 40.1%

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

   4. Taylor expanded in y around inf 55.3%

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

      1. mul-1-neg 55.3%

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

   6. Simplified 55.3%

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

   if 5.19999999999999983e-112 < y5 < 1.90000000000000009e-63

   1. Initial program 21.7%

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

   3. Simplified 21.7%

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

   4. Taylor expanded in y around inf 36.4%

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

      1. mul-1-neg 36.4%

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

   6. Simplified 36.4%

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

   7. Taylor expanded in y4 around inf 76.2%

      \[\leadsto \color{blue}{y4 \cdot \left(y \cdot \left(c \cdot y3 - k \cdot b\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 76.2%

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

      2. *-commutative 76.2%

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

   9. Simplified 76.2%

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

   if 1.90000000000000009e-63 < y5 < 1.44999999999999996

   1. Initial program 27.1%

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

   3. Simplified 27.1%

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

   4. Taylor expanded in z around -inf 33.8%

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

      1. mul-1-neg 33.8%

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

      2. associate--l+ 33.8%

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

   6. Simplified 33.8%

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

   7. Taylor expanded in y1 around inf 61.1%

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

      1. distribute-lft-out-- 61.1%

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

      2. *-commutative 61.1%

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

      3. *-commutative 61.1%

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

   9. Simplified 61.1%

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

   if 1.44999999999999996 < y5 < 7.00000000000000021e55

   1. Initial program 30.8%

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

   3. Simplified 30.8%

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

   4. Taylor expanded in y2 around inf 31.0%

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

   5. Taylor expanded in c around inf 70.7%

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

   if 3.40000000000000006e109 < y5

   1. Initial program 10.7%

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

   3. Simplified 21.4%

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

   4. Taylor expanded in y5 around inf 64.3%

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

      1. mul-1-neg 64.3%

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

      2. mul-1-neg 64.3%

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

      3. mul-1-neg 64.3%

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

      4. sub-neg 64.3%

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

      5. sub-neg 64.3%

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

   6. Simplified 64.3%

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

   7. Taylor expanded in i around inf 64.8%

      \[\leadsto \color{blue}{i \cdot \left(\left(k \cdot y - t \cdot j\right) \cdot y5\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -3.65 \cdot 10^{+204}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq -1.06 \cdot 10^{-10}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -6.2 \cdot 10^{-109}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq -1 \cdot 10^{-244}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 5.2 \cdot 10^{-112}:\\ \;\;\;\;y \cdot \left(k \cdot \left(i \cdot y5 - b \cdot y4\right) + \left(x \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 1.9 \cdot 10^{-63}:\\ \;\;\;\;\left(c \cdot y3 - b \cdot k\right) \cdot \left(y \cdot y4\right)\\ \mathbf{elif}\;y5 \leq 1.45:\\ \;\;\;\;\left(a \cdot y3 - i \cdot k\right) \cdot \left(z \cdot y1\right)\\ \mathbf{elif}\;y5 \leq 7 \cdot 10^{+55}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 3.4 \cdot 10^{+109}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \end{array} \]

Alternative 5: 36.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y2 \cdot \left(\left(c \cdot \left(x \cdot y0\right) + y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right) - c \cdot \left(t \cdot y4\right)\right)\\ t_2 := t \cdot j - y \cdot k\\ \mathbf{if}\;k \leq -3.1 \cdot 10^{+109}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;k \leq -9.6 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq -9.5 \cdot 10^{-122}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq -3 \cdot 10^{-153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq -9.2 \cdot 10^{-181}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot t_2\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;k \leq -2.02 \cdot 10^{-215}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 3.5 \cdot 10^{+52}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot t_2 + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 1.25 \cdot 10^{+199}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 2.55 \cdot 10^{+284}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b \cdot \left(k \cdot \left(-y4\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          y2
          (- (+ (* c (* x y0)) (* y1 (- (* k y4) (* x a)))) (* c (* t y4)))))
        (t_2 (- (* t j) (* y k))))
   (if (<= k -3.1e+109)
     (* y4 (* y (- (* c y3) (* b k))))
     (if (<= k -9.6e-33)
       t_1
       (if (<= k -9.5e-122)
         (* c (* z (- (* t i) (* y0 y3))))
         (if (<= k -3e-153)
           t_1
           (if (<= k -9.2e-181)
             (*
              b
              (+
               (+ (* a (- (* x y) (* z t))) (* y4 t_2))
               (* y0 (- (* z k) (* x j)))))
             (if (<= k -2.02e-215)
               t_1
               (if (<= k 3.5e+52)
                 (*
                  y4
                  (+
                   (+ (* b t_2) (* y1 (- (* k y2) (* j y3))))
                   (* c (- (* y y3) (* t y2)))))
                 (if (<= k 1.25e+199)
                   t_1
                   (if (<= k 2.55e+284)
                     (* z (* k (- (* b y0) (* i y1))))
                     (* y (* b (* k (- y4)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y2 * (((c * (x * y0)) + (y1 * ((k * y4) - (x * a)))) - (c * (t * y4)));
	double t_2 = (t * j) - (y * k);
	double tmp;
	if (k <= -3.1e+109) {
		tmp = y4 * (y * ((c * y3) - (b * k)));
	} else if (k <= -9.6e-33) {
		tmp = t_1;
	} else if (k <= -9.5e-122) {
		tmp = c * (z * ((t * i) - (y0 * y3)));
	} else if (k <= -3e-153) {
		tmp = t_1;
	} else if (k <= -9.2e-181) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))));
	} else if (k <= -2.02e-215) {
		tmp = t_1;
	} else if (k <= 3.5e+52) {
		tmp = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (k <= 1.25e+199) {
		tmp = t_1;
	} else if (k <= 2.55e+284) {
		tmp = z * (k * ((b * y0) - (i * y1)));
	} else {
		tmp = y * (b * (k * -y4));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y2 * (((c * (x * y0)) + (y1 * ((k * y4) - (x * a)))) - (c * (t * y4)))
    t_2 = (t * j) - (y * k)
    if (k <= (-3.1d+109)) then
        tmp = y4 * (y * ((c * y3) - (b * k)))
    else if (k <= (-9.6d-33)) then
        tmp = t_1
    else if (k <= (-9.5d-122)) then
        tmp = c * (z * ((t * i) - (y0 * y3)))
    else if (k <= (-3d-153)) then
        tmp = t_1
    else if (k <= (-9.2d-181)) then
        tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))))
    else if (k <= (-2.02d-215)) then
        tmp = t_1
    else if (k <= 3.5d+52) then
        tmp = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    else if (k <= 1.25d+199) then
        tmp = t_1
    else if (k <= 2.55d+284) then
        tmp = z * (k * ((b * y0) - (i * y1)))
    else
        tmp = y * (b * (k * -y4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y2 * (((c * (x * y0)) + (y1 * ((k * y4) - (x * a)))) - (c * (t * y4)));
	double t_2 = (t * j) - (y * k);
	double tmp;
	if (k <= -3.1e+109) {
		tmp = y4 * (y * ((c * y3) - (b * k)));
	} else if (k <= -9.6e-33) {
		tmp = t_1;
	} else if (k <= -9.5e-122) {
		tmp = c * (z * ((t * i) - (y0 * y3)));
	} else if (k <= -3e-153) {
		tmp = t_1;
	} else if (k <= -9.2e-181) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))));
	} else if (k <= -2.02e-215) {
		tmp = t_1;
	} else if (k <= 3.5e+52) {
		tmp = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (k <= 1.25e+199) {
		tmp = t_1;
	} else if (k <= 2.55e+284) {
		tmp = z * (k * ((b * y0) - (i * y1)));
	} else {
		tmp = y * (b * (k * -y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y2 * (((c * (x * y0)) + (y1 * ((k * y4) - (x * a)))) - (c * (t * y4)))
	t_2 = (t * j) - (y * k)
	tmp = 0
	if k <= -3.1e+109:
		tmp = y4 * (y * ((c * y3) - (b * k)))
	elif k <= -9.6e-33:
		tmp = t_1
	elif k <= -9.5e-122:
		tmp = c * (z * ((t * i) - (y0 * y3)))
	elif k <= -3e-153:
		tmp = t_1
	elif k <= -9.2e-181:
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))))
	elif k <= -2.02e-215:
		tmp = t_1
	elif k <= 3.5e+52:
		tmp = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	elif k <= 1.25e+199:
		tmp = t_1
	elif k <= 2.55e+284:
		tmp = z * (k * ((b * y0) - (i * y1)))
	else:
		tmp = y * (b * (k * -y4))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y2 * Float64(Float64(Float64(c * Float64(x * y0)) + Float64(y1 * Float64(Float64(k * y4) - Float64(x * a)))) - Float64(c * Float64(t * y4))))
	t_2 = Float64(Float64(t * j) - Float64(y * k))
	tmp = 0.0
	if (k <= -3.1e+109)
		tmp = Float64(y4 * Float64(y * Float64(Float64(c * y3) - Float64(b * k))));
	elseif (k <= -9.6e-33)
		tmp = t_1;
	elseif (k <= -9.5e-122)
		tmp = Float64(c * Float64(z * Float64(Float64(t * i) - Float64(y0 * y3))));
	elseif (k <= -3e-153)
		tmp = t_1;
	elseif (k <= -9.2e-181)
		tmp = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * t_2)) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (k <= -2.02e-215)
		tmp = t_1;
	elseif (k <= 3.5e+52)
		tmp = Float64(y4 * Float64(Float64(Float64(b * t_2) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (k <= 1.25e+199)
		tmp = t_1;
	elseif (k <= 2.55e+284)
		tmp = Float64(z * Float64(k * Float64(Float64(b * y0) - Float64(i * y1))));
	else
		tmp = Float64(y * Float64(b * Float64(k * Float64(-y4))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y2 * (((c * (x * y0)) + (y1 * ((k * y4) - (x * a)))) - (c * (t * y4)));
	t_2 = (t * j) - (y * k);
	tmp = 0.0;
	if (k <= -3.1e+109)
		tmp = y4 * (y * ((c * y3) - (b * k)));
	elseif (k <= -9.6e-33)
		tmp = t_1;
	elseif (k <= -9.5e-122)
		tmp = c * (z * ((t * i) - (y0 * y3)));
	elseif (k <= -3e-153)
		tmp = t_1;
	elseif (k <= -9.2e-181)
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))));
	elseif (k <= -2.02e-215)
		tmp = t_1;
	elseif (k <= 3.5e+52)
		tmp = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	elseif (k <= 1.25e+199)
		tmp = t_1;
	elseif (k <= 2.55e+284)
		tmp = z * (k * ((b * y0) - (i * y1)));
	else
		tmp = y * (b * (k * -y4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y2 * N[(N[(N[(c * N[(x * y0), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -3.1e+109], N[(y4 * N[(y * N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -9.6e-33], t$95$1, If[LessEqual[k, -9.5e-122], N[(c * N[(z * N[(N[(t * i), $MachinePrecision] - N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -3e-153], t$95$1, If[LessEqual[k, -9.2e-181], N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -2.02e-215], t$95$1, If[LessEqual[k, 3.5e+52], N[(y4 * N[(N[(N[(b * t$95$2), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.25e+199], t$95$1, If[LessEqual[k, 2.55e+284], N[(z * N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(b * N[(k * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if k < -3.09999999999999992e109

   1. Initial program 15.7%

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

   3. Simplified 18.2%

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

   4. Taylor expanded in y around inf 55.4%

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

      1. mul-1-neg 55.4%

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

   6. Simplified 55.4%

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

   7. Taylor expanded in y4 around inf 53.2%

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

   if -3.09999999999999992e109 < k < -9.6e-33 or -9.5000000000000002e-122 < k < -3e-153 or -9.19999999999999963e-181 < k < -2.02e-215 or 3.5e52 < k < 1.25e199

   1. Initial program 24.7%

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

   3. Simplified 24.7%

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

   4. Taylor expanded in y2 around inf 52.9%

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

   5. Taylor expanded in y1 around 0 56.1%

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

   6. Taylor expanded in y5 around 0 61.2%

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

   if -9.6e-33 < k < -9.5000000000000002e-122

   1. Initial program 24.2%

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

   3. Simplified 24.2%

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

   4. Taylor expanded in c around inf 44.5%

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

      1. associate--l+ 44.5%

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

      2. mul-1-neg 44.5%

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

   6. Simplified 44.5%

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

   7. Taylor expanded in z around inf 45.1%

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

      1. *-commutative 45.1%

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

      2. cancel-sign-sub-inv 45.1%

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

      3. metadata-eval 45.1%

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

      4. *-lft-identity 45.1%

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

      5. +-commutative 45.1%

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

      6. mul-1-neg 45.1%

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

      7. unsub-neg 45.1%

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

      8. *-commutative 45.1%

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

   9. Simplified 45.1%

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

   if -3e-153 < k < -9.19999999999999963e-181

   1. Initial program 85.7%

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

   3. Simplified 85.7%

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

   4. Taylor expanded in b around inf 100.0%

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

   if -2.02e-215 < k < 3.5e52

   1. Initial program 27.0%

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

   3. Simplified 27.0%

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

   4. Taylor expanded in y4 around inf 51.6%

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

   if 1.25e199 < k < 2.5499999999999999e284

   1. Initial program 6.9%

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

   3. Simplified 6.9%

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

   4. Taylor expanded in z around -inf 41.4%

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

      1. mul-1-neg 41.4%

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

      2. associate--l+ 41.4%

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

   6. Simplified 41.4%

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

   7. Taylor expanded in k around inf 62.3%

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

   if 2.5499999999999999e284 < k

   1. Initial program 25.0%

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

   3. Simplified 50.0%

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

   4. Taylor expanded in y around inf 87.5%

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

      1. mul-1-neg 87.5%

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

   6. Simplified 87.5%

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

   7. Taylor expanded in b around inf 87.9%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 87.9%

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

   9. Simplified 87.9%

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

   10. Taylor expanded in a around 0 87.9%

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

       1. mul-1-neg 87.9%

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

       2. distribute-rgt-neg-in 87.9%

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

   12. Simplified 87.9%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -3.1 \cdot 10^{+109}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;k \leq -9.6 \cdot 10^{-33}:\\ \;\;\;\;y2 \cdot \left(\left(c \cdot \left(x \cdot y0\right) + y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right) - c \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq -9.5 \cdot 10^{-122}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq -3 \cdot 10^{-153}:\\ \;\;\;\;y2 \cdot \left(\left(c \cdot \left(x \cdot y0\right) + y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right) - c \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq -9.2 \cdot 10^{-181}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;k \leq -2.02 \cdot 10^{-215}:\\ \;\;\;\;y2 \cdot \left(\left(c \cdot \left(x \cdot y0\right) + y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right) - c \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 3.5 \cdot 10^{+52}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 1.25 \cdot 10^{+199}:\\ \;\;\;\;y2 \cdot \left(\left(c \cdot \left(x \cdot y0\right) + y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right) - c \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 2.55 \cdot 10^{+284}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b \cdot \left(k \cdot \left(-y4\right)\right)\right)\\ \end{array} \]

Alternative 6: 36.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{if}\;y3 \leq -9.5 \cdot 10^{+58}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4 - z \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq -1.65 \cdot 10^{-217}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y3 \leq -2.75 \cdot 10^{-251}:\\ \;\;\;\;y2 \cdot \left(y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;y3 \leq 2 \cdot 10^{-107}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 6.6 \cdot 10^{-38}:\\ \;\;\;\;\left(i \cdot k\right) \cdot \left(y \cdot y5\right)\\ \mathbf{elif}\;y3 \leq 9.5 \cdot 10^{+22}:\\ \;\;\;\;y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 2.05 \cdot 10^{+126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y3 \leq 1.1 \cdot 10^{+170} \lor \neg \left(y3 \leq 1.3 \cdot 10^{+222}\right):\\ \;\;\;\;\left(z \cdot y3\right) \cdot \left(a \cdot y1 - c \cdot y0\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot y3 - b \cdot k\right) \cdot \left(y \cdot y4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          x
          (+
           (+ (* y (- (* a b) (* c i))) (* y2 (- (* c y0) (* a y1))))
           (* j (- (* i y1) (* b y0)))))))
   (if (<= y3 -9.5e+58)
     (* c (* y3 (- (* y y4) (* z y0))))
     (if (<= y3 -1.65e-217)
       t_1
       (if (<= y3 -2.75e-251)
         (* y2 (* y1 (- (* k y4) (* x a))))
         (if (<= y3 2e-107)
           (*
            y4
            (+
             (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
             (* c (- (* y y3) (* t y2)))))
           (if (<= y3 6.6e-38)
             (* (* i k) (* y y5))
             (if (<= y3 9.5e+22)
               (* y2 (* t (- (* a y5) (* c y4))))
               (if (<= y3 2.05e+126)
                 t_1
                 (if (or (<= y3 1.1e+170) (not (<= y3 1.3e+222)))
                   (* (* z y3) (- (* a y1) (* c y0)))
                   (* (- (* c y3) (* b k)) (* y y4))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (y3 <= -9.5e+58) {
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	} else if (y3 <= -1.65e-217) {
		tmp = t_1;
	} else if (y3 <= -2.75e-251) {
		tmp = y2 * (y1 * ((k * y4) - (x * a)));
	} else if (y3 <= 2e-107) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (y3 <= 6.6e-38) {
		tmp = (i * k) * (y * y5);
	} else if (y3 <= 9.5e+22) {
		tmp = y2 * (t * ((a * y5) - (c * y4)));
	} else if (y3 <= 2.05e+126) {
		tmp = t_1;
	} else if ((y3 <= 1.1e+170) || !(y3 <= 1.3e+222)) {
		tmp = (z * y3) * ((a * y1) - (c * y0));
	} else {
		tmp = ((c * y3) - (b * k)) * (y * y4);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
    if (y3 <= (-9.5d+58)) then
        tmp = c * (y3 * ((y * y4) - (z * y0)))
    else if (y3 <= (-1.65d-217)) then
        tmp = t_1
    else if (y3 <= (-2.75d-251)) then
        tmp = y2 * (y1 * ((k * y4) - (x * a)))
    else if (y3 <= 2d-107) then
        tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    else if (y3 <= 6.6d-38) then
        tmp = (i * k) * (y * y5)
    else if (y3 <= 9.5d+22) then
        tmp = y2 * (t * ((a * y5) - (c * y4)))
    else if (y3 <= 2.05d+126) then
        tmp = t_1
    else if ((y3 <= 1.1d+170) .or. (.not. (y3 <= 1.3d+222))) then
        tmp = (z * y3) * ((a * y1) - (c * y0))
    else
        tmp = ((c * y3) - (b * k)) * (y * y4)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (y3 <= -9.5e+58) {
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	} else if (y3 <= -1.65e-217) {
		tmp = t_1;
	} else if (y3 <= -2.75e-251) {
		tmp = y2 * (y1 * ((k * y4) - (x * a)));
	} else if (y3 <= 2e-107) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (y3 <= 6.6e-38) {
		tmp = (i * k) * (y * y5);
	} else if (y3 <= 9.5e+22) {
		tmp = y2 * (t * ((a * y5) - (c * y4)));
	} else if (y3 <= 2.05e+126) {
		tmp = t_1;
	} else if ((y3 <= 1.1e+170) || !(y3 <= 1.3e+222)) {
		tmp = (z * y3) * ((a * y1) - (c * y0));
	} else {
		tmp = ((c * y3) - (b * k)) * (y * y4);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
	tmp = 0
	if y3 <= -9.5e+58:
		tmp = c * (y3 * ((y * y4) - (z * y0)))
	elif y3 <= -1.65e-217:
		tmp = t_1
	elif y3 <= -2.75e-251:
		tmp = y2 * (y1 * ((k * y4) - (x * a)))
	elif y3 <= 2e-107:
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	elif y3 <= 6.6e-38:
		tmp = (i * k) * (y * y5)
	elif y3 <= 9.5e+22:
		tmp = y2 * (t * ((a * y5) - (c * y4)))
	elif y3 <= 2.05e+126:
		tmp = t_1
	elif (y3 <= 1.1e+170) or not (y3 <= 1.3e+222):
		tmp = (z * y3) * ((a * y1) - (c * y0))
	else:
		tmp = ((c * y3) - (b * k)) * (y * y4)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))))
	tmp = 0.0
	if (y3 <= -9.5e+58)
		tmp = Float64(c * Float64(y3 * Float64(Float64(y * y4) - Float64(z * y0))));
	elseif (y3 <= -1.65e-217)
		tmp = t_1;
	elseif (y3 <= -2.75e-251)
		tmp = Float64(y2 * Float64(y1 * Float64(Float64(k * y4) - Float64(x * a))));
	elseif (y3 <= 2e-107)
		tmp = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (y3 <= 6.6e-38)
		tmp = Float64(Float64(i * k) * Float64(y * y5));
	elseif (y3 <= 9.5e+22)
		tmp = Float64(y2 * Float64(t * Float64(Float64(a * y5) - Float64(c * y4))));
	elseif (y3 <= 2.05e+126)
		tmp = t_1;
	elseif ((y3 <= 1.1e+170) || !(y3 <= 1.3e+222))
		tmp = Float64(Float64(z * y3) * Float64(Float64(a * y1) - Float64(c * y0)));
	else
		tmp = Float64(Float64(Float64(c * y3) - Float64(b * k)) * Float64(y * y4));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	tmp = 0.0;
	if (y3 <= -9.5e+58)
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	elseif (y3 <= -1.65e-217)
		tmp = t_1;
	elseif (y3 <= -2.75e-251)
		tmp = y2 * (y1 * ((k * y4) - (x * a)));
	elseif (y3 <= 2e-107)
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	elseif (y3 <= 6.6e-38)
		tmp = (i * k) * (y * y5);
	elseif (y3 <= 9.5e+22)
		tmp = y2 * (t * ((a * y5) - (c * y4)));
	elseif (y3 <= 2.05e+126)
		tmp = t_1;
	elseif ((y3 <= 1.1e+170) || ~((y3 <= 1.3e+222)))
		tmp = (z * y3) * ((a * y1) - (c * y0));
	else
		tmp = ((c * y3) - (b * k)) * (y * y4);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -9.5e+58], N[(c * N[(y3 * N[(N[(y * y4), $MachinePrecision] - N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -1.65e-217], t$95$1, If[LessEqual[y3, -2.75e-251], N[(y2 * N[(y1 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 2e-107], N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 6.6e-38], N[(N[(i * k), $MachinePrecision] * N[(y * y5), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 9.5e+22], N[(y2 * N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 2.05e+126], t$95$1, If[Or[LessEqual[y3, 1.1e+170], N[Not[LessEqual[y3, 1.3e+222]], $MachinePrecision]], N[(N[(z * y3), $MachinePrecision] * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision] * N[(y * y4), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y3 < -9.5000000000000002e58

   1. Initial program 12.9%

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

   3. Simplified 12.9%

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

   4. Taylor expanded in c around inf 51.4%

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

      1. associate--l+ 51.4%

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

      2. mul-1-neg 51.4%

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

   6. Simplified 51.4%

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

   7. Taylor expanded in y3 around -inf 58.4%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(\left(y0 \cdot z - y4 \cdot y\right) \cdot y3\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 58.4%

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

      2. neg-mul-1 58.4%

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

      3. *-commutative 58.4%

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

   9. Simplified 58.4%

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

   if -9.5000000000000002e58 < y3 < -1.64999999999999996e-217 or 9.49999999999999937e22 < y3 < 2.05e126

   1. Initial program 26.8%

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

   3. Simplified 26.8%

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

   4. Taylor expanded in x around inf 51.1%

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

   if -1.64999999999999996e-217 < y3 < -2.75e-251

   1. Initial program 8.2%

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

   3. Simplified 8.2%

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

   4. Taylor expanded in y2 around inf 39.7%

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

   5. Taylor expanded in y1 around inf 62.7%

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

      1. +-commutative 62.7%

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

      2. mul-1-neg 62.7%

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

      3. unsub-neg 62.7%

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

      4. *-commutative 62.7%

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

   7. Simplified 62.7%

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

   if -2.75e-251 < y3 < 2e-107

   1. Initial program 28.3%

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

   3. Simplified 28.3%

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

   4. Taylor expanded in y4 around inf 58.0%

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

   if 2e-107 < y3 < 6.6000000000000005e-38

   1. Initial program 40.6%

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

   3. Simplified 40.6%

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

   4. Taylor expanded in y5 around inf 60.6%

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

      1. mul-1-neg 60.6%

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

      2. mul-1-neg 60.6%

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

      3. mul-1-neg 60.6%

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

      4. sub-neg 60.6%

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

      5. sub-neg 60.6%

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

   6. Simplified 60.6%

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

   7. Taylor expanded in i around inf 61.0%

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

   8. Taylor expanded in k around inf 54.4%

      \[\leadsto \color{blue}{k \cdot \left(y \cdot \left(i \cdot y5\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 54.4%

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

      2. associate-*r* 60.6%

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

      3. *-commutative 60.6%

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

      4. associate-*r* 67.0%

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

      5. *-commutative 67.0%

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

      6. *-commutative 67.0%

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

   10. Simplified 67.0%

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

   if 6.6000000000000005e-38 < y3 < 9.49999999999999937e22

   1. Initial program 16.0%

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

   3. Simplified 16.0%

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

   4. Taylor expanded in y2 around inf 31.3%

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

   5. Taylor expanded in t around inf 53.9%

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

   if 2.05e126 < y3 < 1.09999999999999994e170 or 1.3000000000000001e222 < y3

   1. Initial program 29.1%

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

   3. Simplified 29.1%

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

   4. Taylor expanded in z around -inf 43.4%

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

      1. mul-1-neg 43.4%

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

      2. associate--l+ 43.4%

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

   6. Simplified 43.4%

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

   7. Taylor expanded in y3 around inf 72.1%

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

   if 1.09999999999999994e170 < y3 < 1.3000000000000001e222

   1. Initial program 18.2%

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

   3. Simplified 27.3%

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

   4. Taylor expanded in y around inf 82.1%

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

      1. mul-1-neg 82.1%

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

   6. Simplified 82.1%

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

   7. Taylor expanded in y4 around inf 47.0%

      \[\leadsto \color{blue}{y4 \cdot \left(y \cdot \left(c \cdot y3 - k \cdot b\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 55.4%

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

      2. *-commutative 55.4%

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

   9. Simplified 55.4%

      \[\leadsto \color{blue}{\left(y4 \cdot y\right) \cdot \left(c \cdot y3 - b \cdot k\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -9.5 \cdot 10^{+58}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4 - z \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq -1.65 \cdot 10^{-217}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq -2.75 \cdot 10^{-251}:\\ \;\;\;\;y2 \cdot \left(y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;y3 \leq 2 \cdot 10^{-107}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 6.6 \cdot 10^{-38}:\\ \;\;\;\;\left(i \cdot k\right) \cdot \left(y \cdot y5\right)\\ \mathbf{elif}\;y3 \leq 9.5 \cdot 10^{+22}:\\ \;\;\;\;y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 2.05 \cdot 10^{+126}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq 1.1 \cdot 10^{+170} \lor \neg \left(y3 \leq 1.3 \cdot 10^{+222}\right):\\ \;\;\;\;\left(z \cdot y3\right) \cdot \left(a \cdot y1 - c \cdot y0\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot y3 - b \cdot k\right) \cdot \left(y \cdot y4\right)\\ \end{array} \]

Alternative 7: 36.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y2 \cdot \left(y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ t_2 := c \cdot y0 - a \cdot y1\\ \mathbf{if}\;y3 \leq -8 \cdot 10^{+59}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4 - z \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq -1.9 \cdot 10^{-222}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot t_2\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq 2.1 \cdot 10^{-233}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y3 \leq 1.02 \cdot 10^{-130}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y3 \leq 2.2 \cdot 10^{-54}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot t_2 + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 1.02 \cdot 10^{-11}:\\ \;\;\;\;\left(z \cdot y0\right) \cdot \left(b \cdot k - c \cdot y3\right)\\ \mathbf{elif}\;y3 \leq 3.7 \cdot 10^{+78}:\\ \;\;\;\;i \cdot \left(c \cdot \left(z \cdot t - x \cdot y\right) + \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\right)\\ \mathbf{elif}\;y3 \leq 10^{+118}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y3 \leq 1.4 \cdot 10^{+191} \lor \neg \left(y3 \leq 3.6 \cdot 10^{+227}\right):\\ \;\;\;\;\left(z \cdot y3\right) \cdot \left(a \cdot y1 - c \cdot y0\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y2 (* y1 (- (* k y4) (* x a))))) (t_2 (- (* c y0) (* a y1))))
   (if (<= y3 -8e+59)
     (* c (* y3 (- (* y y4) (* z y0))))
     (if (<= y3 -1.9e-222)
       (*
        x
        (+
         (+ (* y (- (* a b) (* c i))) (* y2 t_2))
         (* j (- (* i y1) (* b y0)))))
       (if (<= y3 2.1e-233)
         t_1
         (if (<= y3 1.02e-130)
           (*
            b
            (+
             (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
             (* y0 (- (* z k) (* x j)))))
           (if (<= y3 2.2e-54)
             (*
              y2
              (+
               (+ (* x t_2) (* k (- (* y1 y4) (* y0 y5))))
               (* t (- (* a y5) (* c y4)))))
             (if (<= y3 1.02e-11)
               (* (* z y0) (- (* b k) (* c y3)))
               (if (<= y3 3.7e+78)
                 (*
                  i
                  (+
                   (* c (- (* z t) (* x y)))
                   (+ (* y1 (- (* x j) (* z k))) (* y5 (- (* y k) (* t j))))))
                 (if (<= y3 1e+118)
                   t_1
                   (if (or (<= y3 1.4e+191) (not (<= y3 3.6e+227)))
                     (* (* z y3) (- (* a y1) (* c y0)))
                     (* y (* a (- (* x b) (* y3 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 = y2 * (y1 * ((k * y4) - (x * a)));
	double t_2 = (c * y0) - (a * y1);
	double tmp;
	if (y3 <= -8e+59) {
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	} else if (y3 <= -1.9e-222) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))));
	} else if (y3 <= 2.1e-233) {
		tmp = t_1;
	} else if (y3 <= 1.02e-130) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (y3 <= 2.2e-54) {
		tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y3 <= 1.02e-11) {
		tmp = (z * y0) * ((b * k) - (c * y3));
	} else if (y3 <= 3.7e+78) {
		tmp = i * ((c * ((z * t) - (x * y))) + ((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j)))));
	} else if (y3 <= 1e+118) {
		tmp = t_1;
	} else if ((y3 <= 1.4e+191) || !(y3 <= 3.6e+227)) {
		tmp = (z * y3) * ((a * y1) - (c * y0));
	} else {
		tmp = y * (a * ((x * b) - (y3 * 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) :: t_2
    real(8) :: tmp
    t_1 = y2 * (y1 * ((k * y4) - (x * a)))
    t_2 = (c * y0) - (a * y1)
    if (y3 <= (-8d+59)) then
        tmp = c * (y3 * ((y * y4) - (z * y0)))
    else if (y3 <= (-1.9d-222)) then
        tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))))
    else if (y3 <= 2.1d-233) then
        tmp = t_1
    else if (y3 <= 1.02d-130) then
        tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    else if (y3 <= 2.2d-54) then
        tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
    else if (y3 <= 1.02d-11) then
        tmp = (z * y0) * ((b * k) - (c * y3))
    else if (y3 <= 3.7d+78) then
        tmp = i * ((c * ((z * t) - (x * y))) + ((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j)))))
    else if (y3 <= 1d+118) then
        tmp = t_1
    else if ((y3 <= 1.4d+191) .or. (.not. (y3 <= 3.6d+227))) then
        tmp = (z * y3) * ((a * y1) - (c * y0))
    else
        tmp = y * (a * ((x * b) - (y3 * 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 = y2 * (y1 * ((k * y4) - (x * a)));
	double t_2 = (c * y0) - (a * y1);
	double tmp;
	if (y3 <= -8e+59) {
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	} else if (y3 <= -1.9e-222) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))));
	} else if (y3 <= 2.1e-233) {
		tmp = t_1;
	} else if (y3 <= 1.02e-130) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (y3 <= 2.2e-54) {
		tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y3 <= 1.02e-11) {
		tmp = (z * y0) * ((b * k) - (c * y3));
	} else if (y3 <= 3.7e+78) {
		tmp = i * ((c * ((z * t) - (x * y))) + ((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j)))));
	} else if (y3 <= 1e+118) {
		tmp = t_1;
	} else if ((y3 <= 1.4e+191) || !(y3 <= 3.6e+227)) {
		tmp = (z * y3) * ((a * y1) - (c * y0));
	} else {
		tmp = y * (a * ((x * b) - (y3 * y5)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y2 * (y1 * ((k * y4) - (x * a)))
	t_2 = (c * y0) - (a * y1)
	tmp = 0
	if y3 <= -8e+59:
		tmp = c * (y3 * ((y * y4) - (z * y0)))
	elif y3 <= -1.9e-222:
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))))
	elif y3 <= 2.1e-233:
		tmp = t_1
	elif y3 <= 1.02e-130:
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	elif y3 <= 2.2e-54:
		tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
	elif y3 <= 1.02e-11:
		tmp = (z * y0) * ((b * k) - (c * y3))
	elif y3 <= 3.7e+78:
		tmp = i * ((c * ((z * t) - (x * y))) + ((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j)))))
	elif y3 <= 1e+118:
		tmp = t_1
	elif (y3 <= 1.4e+191) or not (y3 <= 3.6e+227):
		tmp = (z * y3) * ((a * y1) - (c * y0))
	else:
		tmp = y * (a * ((x * b) - (y3 * 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(y2 * Float64(y1 * Float64(Float64(k * y4) - Float64(x * a))))
	t_2 = Float64(Float64(c * y0) - Float64(a * y1))
	tmp = 0.0
	if (y3 <= -8e+59)
		tmp = Float64(c * Float64(y3 * Float64(Float64(y * y4) - Float64(z * y0))));
	elseif (y3 <= -1.9e-222)
		tmp = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * t_2)) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (y3 <= 2.1e-233)
		tmp = t_1;
	elseif (y3 <= 1.02e-130)
		tmp = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (y3 <= 2.2e-54)
		tmp = Float64(y2 * Float64(Float64(Float64(x * t_2) + Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y3 <= 1.02e-11)
		tmp = Float64(Float64(z * y0) * Float64(Float64(b * k) - Float64(c * y3)));
	elseif (y3 <= 3.7e+78)
		tmp = Float64(i * Float64(Float64(c * Float64(Float64(z * t) - Float64(x * y))) + Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) + Float64(y5 * Float64(Float64(y * k) - Float64(t * j))))));
	elseif (y3 <= 1e+118)
		tmp = t_1;
	elseif ((y3 <= 1.4e+191) || !(y3 <= 3.6e+227))
		tmp = Float64(Float64(z * y3) * Float64(Float64(a * y1) - Float64(c * y0)));
	else
		tmp = Float64(y * Float64(a * Float64(Float64(x * b) - Float64(y3 * 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 = y2 * (y1 * ((k * y4) - (x * a)));
	t_2 = (c * y0) - (a * y1);
	tmp = 0.0;
	if (y3 <= -8e+59)
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	elseif (y3 <= -1.9e-222)
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))));
	elseif (y3 <= 2.1e-233)
		tmp = t_1;
	elseif (y3 <= 1.02e-130)
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	elseif (y3 <= 2.2e-54)
		tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	elseif (y3 <= 1.02e-11)
		tmp = (z * y0) * ((b * k) - (c * y3));
	elseif (y3 <= 3.7e+78)
		tmp = i * ((c * ((z * t) - (x * y))) + ((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j)))));
	elseif (y3 <= 1e+118)
		tmp = t_1;
	elseif ((y3 <= 1.4e+191) || ~((y3 <= 3.6e+227)))
		tmp = (z * y3) * ((a * y1) - (c * y0));
	else
		tmp = y * (a * ((x * b) - (y3 * 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[(y2 * N[(y1 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -8e+59], N[(c * N[(y3 * N[(N[(y * y4), $MachinePrecision] - N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -1.9e-222], N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 2.1e-233], t$95$1, If[LessEqual[y3, 1.02e-130], N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 2.2e-54], N[(y2 * N[(N[(N[(x * t$95$2), $MachinePrecision] + N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.02e-11], N[(N[(z * y0), $MachinePrecision] * N[(N[(b * k), $MachinePrecision] - N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 3.7e+78], N[(i * N[(N[(c * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1e+118], t$95$1, If[Or[LessEqual[y3, 1.4e+191], N[Not[LessEqual[y3, 3.6e+227]], $MachinePrecision]], N[(N[(z * y3), $MachinePrecision] * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(a * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y3 < -7.99999999999999977e59

   1. Initial program 12.9%

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

   3. Simplified 12.9%

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

   4. Taylor expanded in c around inf 51.4%

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

      1. associate--l+ 51.4%

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

      2. mul-1-neg 51.4%

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

   6. Simplified 51.4%

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

   7. Taylor expanded in y3 around -inf 58.4%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(\left(y0 \cdot z - y4 \cdot y\right) \cdot y3\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 58.4%

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

      2. neg-mul-1 58.4%

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

      3. *-commutative 58.4%

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

   9. Simplified 58.4%

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

   if -7.99999999999999977e59 < y3 < -1.89999999999999998e-222

   1. Initial program 28.4%

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

   3. Simplified 28.4%

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

   4. Taylor expanded in x around inf 52.1%

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

   if -1.89999999999999998e-222 < y3 < 2.0999999999999999e-233 or 3.69999999999999985e78 < y3 < 9.99999999999999967e117

   1. Initial program 26.5%

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

   3. Simplified 26.5%

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

   4. Taylor expanded in y2 around inf 43.4%

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

   5. Taylor expanded in y1 around inf 67.0%

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

      1. +-commutative 67.0%

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

      2. mul-1-neg 67.0%

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

      3. unsub-neg 67.0%

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

      4. *-commutative 67.0%

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

   7. Simplified 67.0%

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

   if 2.0999999999999999e-233 < y3 < 1.01999999999999994e-130

   1. Initial program 27.7%

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

   3. Simplified 27.7%

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

   4. Taylor expanded in b around inf 59.4%

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

   if 1.01999999999999994e-130 < y3 < 2.2e-54

   1. Initial program 28.2%

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

   3. Simplified 28.2%

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

   4. Taylor expanded in y2 around inf 56.2%

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

   if 2.2e-54 < y3 < 1.01999999999999994e-11

   1. Initial program 20.7%

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

   3. Simplified 20.7%

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

   4. Taylor expanded in z around -inf 51.1%

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

      1. mul-1-neg 51.1%

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

      2. associate--l+ 51.1%

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

   6. Simplified 51.1%

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

   7. Taylor expanded in y0 around inf 58.0%

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

      1. *-commutative 58.0%

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

      2. *-commutative 58.0%

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

      3. associate-*l* 58.0%

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

      4. *-commutative 58.0%

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

      5. *-commutative 58.0%

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

   9. Simplified 58.0%

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

   if 1.01999999999999994e-11 < y3 < 3.69999999999999985e78

   1. Initial program 21.7%

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

   3. Simplified 21.7%

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

   4. Taylor expanded in i around -inf 52.4%

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

      1. mul-1-neg 52.4%

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

      2. associate--l+ 52.4%

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

   6. Simplified 52.4%

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

   if 9.99999999999999967e117 < y3 < 1.3999999999999999e191 or 3.59999999999999991e227 < y3

   1. Initial program 24.6%

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

   3. Simplified 24.6%

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

   4. Taylor expanded in z around -inf 41.8%

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

      1. mul-1-neg 41.8%

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

      2. associate--l+ 41.8%

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

   6. Simplified 41.8%

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

   7. Taylor expanded in y3 around inf 59.2%

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

   if 1.3999999999999999e191 < y3 < 3.59999999999999991e227

   1. Initial program 20.0%

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

   3. Simplified 40.0%

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

   4. Taylor expanded in y around inf 100.0%

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

      1. mul-1-neg 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in a around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

   9. Simplified 100.0%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -8 \cdot 10^{+59}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4 - z \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq -1.9 \cdot 10^{-222}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq 2.1 \cdot 10^{-233}:\\ \;\;\;\;y2 \cdot \left(y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;y3 \leq 1.02 \cdot 10^{-130}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y3 \leq 2.2 \cdot 10^{-54}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 1.02 \cdot 10^{-11}:\\ \;\;\;\;\left(z \cdot y0\right) \cdot \left(b \cdot k - c \cdot y3\right)\\ \mathbf{elif}\;y3 \leq 3.7 \cdot 10^{+78}:\\ \;\;\;\;i \cdot \left(c \cdot \left(z \cdot t - x \cdot y\right) + \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\right)\\ \mathbf{elif}\;y3 \leq 10^{+118}:\\ \;\;\;\;y2 \cdot \left(y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;y3 \leq 1.4 \cdot 10^{+191} \lor \neg \left(y3 \leq 3.6 \cdot 10^{+227}\right):\\ \;\;\;\;\left(z \cdot y3\right) \cdot \left(a \cdot y1 - c \cdot y0\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \end{array} \]

Alternative 8: 40.8% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot y0 - a \cdot y1\\ t_2 := y \cdot k - t \cdot j\\ t_3 := a \cdot b - c \cdot i\\ t_4 := x \cdot \left(\left(y \cdot t_3 + y2 \cdot t_1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{if}\;y5 \leq -2.3 \cdot 10^{+199}:\\ \;\;\;\;y5 \cdot \left(i \cdot t_2 + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y5 \leq -6.8 \cdot 10^{-9}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot t_1 + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -4.6 \cdot 10^{-108}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq -9.5 \cdot 10^{-239}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y5 \leq 5.9 \cdot 10^{+16}:\\ \;\;\;\;y \cdot \left(\left(y4 \cdot \left(c \cdot y3 - b \cdot k\right) + \left(x \cdot t_3 - a \cdot \left(y3 \cdot y5\right)\right)\right) + k \cdot \left(i \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq 3.2 \cdot 10^{+109}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y5 \cdot t_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* c y0) (* a y1)))
        (t_2 (- (* y k) (* t j)))
        (t_3 (- (* a b) (* c i)))
        (t_4 (* x (+ (+ (* y t_3) (* y2 t_1)) (* j (- (* i y1) (* b y0)))))))
   (if (<= y5 -2.3e+199)
     (*
      y5
      (+
       (* i t_2)
       (+ (* a (- (* t y2) (* y y3))) (* y0 (- (* j y3) (* k y2))))))
     (if (<= y5 -6.8e-9)
       (*
        y2
        (+
         (+ (* x t_1) (* k (- (* y1 y4) (* y0 y5))))
         (* t (- (* a y5) (* c y4)))))
       (if (<= y5 -4.6e-108)
         (*
          b
          (+
           (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
           (* y0 (- (* z k) (* x j)))))
         (if (<= y5 -9.5e-239)
           t_4
           (if (<= y5 5.9e+16)
             (*
              y
              (+
               (+ (* y4 (- (* c y3) (* b k))) (- (* x t_3) (* a (* y3 y5))))
               (* k (* i y5))))
             (if (<= y5 3.2e+109) t_4 (* i (* y5 t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y0) - (a * y1);
	double t_2 = (y * k) - (t * j);
	double t_3 = (a * b) - (c * i);
	double t_4 = x * (((y * t_3) + (y2 * t_1)) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (y5 <= -2.3e+199) {
		tmp = y5 * ((i * t_2) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))));
	} else if (y5 <= -6.8e-9) {
		tmp = y2 * (((x * t_1) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y5 <= -4.6e-108) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (y5 <= -9.5e-239) {
		tmp = t_4;
	} else if (y5 <= 5.9e+16) {
		tmp = y * (((y4 * ((c * y3) - (b * k))) + ((x * t_3) - (a * (y3 * y5)))) + (k * (i * y5)));
	} else if (y5 <= 3.2e+109) {
		tmp = t_4;
	} else {
		tmp = i * (y5 * t_2);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (c * y0) - (a * y1)
    t_2 = (y * k) - (t * j)
    t_3 = (a * b) - (c * i)
    t_4 = x * (((y * t_3) + (y2 * t_1)) + (j * ((i * y1) - (b * y0))))
    if (y5 <= (-2.3d+199)) then
        tmp = y5 * ((i * t_2) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))))
    else if (y5 <= (-6.8d-9)) then
        tmp = y2 * (((x * t_1) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
    else if (y5 <= (-4.6d-108)) then
        tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    else if (y5 <= (-9.5d-239)) then
        tmp = t_4
    else if (y5 <= 5.9d+16) then
        tmp = y * (((y4 * ((c * y3) - (b * k))) + ((x * t_3) - (a * (y3 * y5)))) + (k * (i * y5)))
    else if (y5 <= 3.2d+109) then
        tmp = t_4
    else
        tmp = i * (y5 * t_2)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y0) - (a * y1);
	double t_2 = (y * k) - (t * j);
	double t_3 = (a * b) - (c * i);
	double t_4 = x * (((y * t_3) + (y2 * t_1)) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (y5 <= -2.3e+199) {
		tmp = y5 * ((i * t_2) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))));
	} else if (y5 <= -6.8e-9) {
		tmp = y2 * (((x * t_1) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y5 <= -4.6e-108) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (y5 <= -9.5e-239) {
		tmp = t_4;
	} else if (y5 <= 5.9e+16) {
		tmp = y * (((y4 * ((c * y3) - (b * k))) + ((x * t_3) - (a * (y3 * y5)))) + (k * (i * y5)));
	} else if (y5 <= 3.2e+109) {
		tmp = t_4;
	} else {
		tmp = i * (y5 * t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (c * y0) - (a * y1)
	t_2 = (y * k) - (t * j)
	t_3 = (a * b) - (c * i)
	t_4 = x * (((y * t_3) + (y2 * t_1)) + (j * ((i * y1) - (b * y0))))
	tmp = 0
	if y5 <= -2.3e+199:
		tmp = y5 * ((i * t_2) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))))
	elif y5 <= -6.8e-9:
		tmp = y2 * (((x * t_1) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
	elif y5 <= -4.6e-108:
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	elif y5 <= -9.5e-239:
		tmp = t_4
	elif y5 <= 5.9e+16:
		tmp = y * (((y4 * ((c * y3) - (b * k))) + ((x * t_3) - (a * (y3 * y5)))) + (k * (i * y5)))
	elif y5 <= 3.2e+109:
		tmp = t_4
	else:
		tmp = i * (y5 * t_2)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(c * y0) - Float64(a * y1))
	t_2 = Float64(Float64(y * k) - Float64(t * j))
	t_3 = Float64(Float64(a * b) - Float64(c * i))
	t_4 = Float64(x * Float64(Float64(Float64(y * t_3) + Float64(y2 * t_1)) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))))
	tmp = 0.0
	if (y5 <= -2.3e+199)
		tmp = Float64(y5 * Float64(Float64(i * t_2) + Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))))));
	elseif (y5 <= -6.8e-9)
		tmp = Float64(y2 * Float64(Float64(Float64(x * t_1) + Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y5 <= -4.6e-108)
		tmp = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (y5 <= -9.5e-239)
		tmp = t_4;
	elseif (y5 <= 5.9e+16)
		tmp = Float64(y * Float64(Float64(Float64(y4 * Float64(Float64(c * y3) - Float64(b * k))) + Float64(Float64(x * t_3) - Float64(a * Float64(y3 * y5)))) + Float64(k * Float64(i * y5))));
	elseif (y5 <= 3.2e+109)
		tmp = t_4;
	else
		tmp = Float64(i * Float64(y5 * t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (c * y0) - (a * y1);
	t_2 = (y * k) - (t * j);
	t_3 = (a * b) - (c * i);
	t_4 = x * (((y * t_3) + (y2 * t_1)) + (j * ((i * y1) - (b * y0))));
	tmp = 0.0;
	if (y5 <= -2.3e+199)
		tmp = y5 * ((i * t_2) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))));
	elseif (y5 <= -6.8e-9)
		tmp = y2 * (((x * t_1) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	elseif (y5 <= -4.6e-108)
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	elseif (y5 <= -9.5e-239)
		tmp = t_4;
	elseif (y5 <= 5.9e+16)
		tmp = y * (((y4 * ((c * y3) - (b * k))) + ((x * t_3) - (a * (y3 * y5)))) + (k * (i * y5)));
	elseif (y5 <= 3.2e+109)
		tmp = t_4;
	else
		tmp = i * (y5 * t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x * N[(N[(N[(y * t$95$3), $MachinePrecision] + N[(y2 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -2.3e+199], N[(y5 * N[(N[(i * t$95$2), $MachinePrecision] + N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -6.8e-9], N[(y2 * N[(N[(N[(x * t$95$1), $MachinePrecision] + N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -4.6e-108], N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -9.5e-239], t$95$4, If[LessEqual[y5, 5.9e+16], N[(y * N[(N[(N[(y4 * N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * t$95$3), $MachinePrecision] - N[(a * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 3.2e+109], t$95$4, N[(i * N[(y5 * t$95$2), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y5 < -2.29999999999999995e199

   1. Initial program 20.8%

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

   3. Simplified 29.2%

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

   4. Taylor expanded in y5 around inf 70.8%

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

      1. mul-1-neg 70.8%

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

      2. mul-1-neg 70.8%

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

      3. mul-1-neg 70.8%

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

      4. sub-neg 70.8%

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

      5. sub-neg 70.8%

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

   6. Simplified 70.8%

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

   if -2.29999999999999995e199 < y5 < -6.7999999999999997e-9

   1. Initial program 18.6%

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

   3. Simplified 18.6%

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

   4. Taylor expanded in y2 around inf 52.7%

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

   if -6.7999999999999997e-9 < y5 < -4.59999999999999992e-108

   1. Initial program 39.3%

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

   3. Simplified 39.3%

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

   4. Taylor expanded in b around inf 71.5%

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

   if -4.59999999999999992e-108 < y5 < -9.4999999999999992e-239 or 5.9e16 < y5 < 3.2000000000000001e109

   1. Initial program 19.2%

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

   3. Simplified 19.2%

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

   4. Taylor expanded in x around inf 55.0%

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

   if -9.4999999999999992e-239 < y5 < 5.9e16

   1. Initial program 30.1%

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

   3. Simplified 37.0%

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

   4. Taylor expanded in y around inf 50.2%

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

      1. mul-1-neg 50.2%

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

   6. Simplified 50.2%

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

   7. Taylor expanded in y4 around 0 53.6%

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

   if 3.2000000000000001e109 < y5

   1. Initial program 10.7%

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

   3. Simplified 21.4%

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

   4. Taylor expanded in y5 around inf 64.3%

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

      1. mul-1-neg 64.3%

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

      2. mul-1-neg 64.3%

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

      3. mul-1-neg 64.3%

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

      4. sub-neg 64.3%

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

      5. sub-neg 64.3%

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

   6. Simplified 64.3%

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

   7. Taylor expanded in i around inf 64.8%

      \[\leadsto \color{blue}{i \cdot \left(\left(k \cdot y - t \cdot j\right) \cdot y5\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -2.3 \cdot 10^{+199}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y5 \leq -6.8 \cdot 10^{-9}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -4.6 \cdot 10^{-108}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq -9.5 \cdot 10^{-239}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 5.9 \cdot 10^{+16}:\\ \;\;\;\;y \cdot \left(\left(y4 \cdot \left(c \cdot y3 - b \cdot k\right) + \left(x \cdot \left(a \cdot b - c \cdot i\right) - a \cdot \left(y3 \cdot y5\right)\right)\right) + k \cdot \left(i \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq 3.2 \cdot 10^{+109}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \end{array} \]

Alternative 9: 36.2% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y2 \cdot \left(\left(c \cdot \left(x \cdot y0\right) + y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right) - c \cdot \left(t \cdot y4\right)\right)\\ \mathbf{if}\;k \leq -1.4 \cdot 10^{+110}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;k \leq -4.2 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq -2.85 \cdot 10^{-120}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq -1.14 \cdot 10^{-215}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 2.25 \cdot 10^{+52}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 1.65 \cdot 10^{+199}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 1.85 \cdot 10^{+282}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b \cdot \left(k \cdot \left(-y4\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          y2
          (- (+ (* c (* x y0)) (* y1 (- (* k y4) (* x a)))) (* c (* t y4))))))
   (if (<= k -1.4e+110)
     (* y4 (* y (- (* c y3) (* b k))))
     (if (<= k -4.2e-33)
       t_1
       (if (<= k -2.85e-120)
         (* c (* z (- (* t i) (* y0 y3))))
         (if (<= k -1.14e-215)
           t_1
           (if (<= k 2.25e+52)
             (*
              y4
              (+
               (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
               (* c (- (* y y3) (* t y2)))))
             (if (<= k 1.65e+199)
               t_1
               (if (<= k 1.85e+282)
                 (* z (* k (- (* b y0) (* i y1))))
                 (* y (* b (* k (- y4)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y2 * (((c * (x * y0)) + (y1 * ((k * y4) - (x * a)))) - (c * (t * y4)));
	double tmp;
	if (k <= -1.4e+110) {
		tmp = y4 * (y * ((c * y3) - (b * k)));
	} else if (k <= -4.2e-33) {
		tmp = t_1;
	} else if (k <= -2.85e-120) {
		tmp = c * (z * ((t * i) - (y0 * y3)));
	} else if (k <= -1.14e-215) {
		tmp = t_1;
	} else if (k <= 2.25e+52) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (k <= 1.65e+199) {
		tmp = t_1;
	} else if (k <= 1.85e+282) {
		tmp = z * (k * ((b * y0) - (i * y1)));
	} else {
		tmp = y * (b * (k * -y4));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y2 * (((c * (x * y0)) + (y1 * ((k * y4) - (x * a)))) - (c * (t * y4)))
    if (k <= (-1.4d+110)) then
        tmp = y4 * (y * ((c * y3) - (b * k)))
    else if (k <= (-4.2d-33)) then
        tmp = t_1
    else if (k <= (-2.85d-120)) then
        tmp = c * (z * ((t * i) - (y0 * y3)))
    else if (k <= (-1.14d-215)) then
        tmp = t_1
    else if (k <= 2.25d+52) then
        tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    else if (k <= 1.65d+199) then
        tmp = t_1
    else if (k <= 1.85d+282) then
        tmp = z * (k * ((b * y0) - (i * y1)))
    else
        tmp = y * (b * (k * -y4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y2 * (((c * (x * y0)) + (y1 * ((k * y4) - (x * a)))) - (c * (t * y4)));
	double tmp;
	if (k <= -1.4e+110) {
		tmp = y4 * (y * ((c * y3) - (b * k)));
	} else if (k <= -4.2e-33) {
		tmp = t_1;
	} else if (k <= -2.85e-120) {
		tmp = c * (z * ((t * i) - (y0 * y3)));
	} else if (k <= -1.14e-215) {
		tmp = t_1;
	} else if (k <= 2.25e+52) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (k <= 1.65e+199) {
		tmp = t_1;
	} else if (k <= 1.85e+282) {
		tmp = z * (k * ((b * y0) - (i * y1)));
	} else {
		tmp = y * (b * (k * -y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y2 * (((c * (x * y0)) + (y1 * ((k * y4) - (x * a)))) - (c * (t * y4)))
	tmp = 0
	if k <= -1.4e+110:
		tmp = y4 * (y * ((c * y3) - (b * k)))
	elif k <= -4.2e-33:
		tmp = t_1
	elif k <= -2.85e-120:
		tmp = c * (z * ((t * i) - (y0 * y3)))
	elif k <= -1.14e-215:
		tmp = t_1
	elif k <= 2.25e+52:
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	elif k <= 1.65e+199:
		tmp = t_1
	elif k <= 1.85e+282:
		tmp = z * (k * ((b * y0) - (i * y1)))
	else:
		tmp = y * (b * (k * -y4))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y2 * Float64(Float64(Float64(c * Float64(x * y0)) + Float64(y1 * Float64(Float64(k * y4) - Float64(x * a)))) - Float64(c * Float64(t * y4))))
	tmp = 0.0
	if (k <= -1.4e+110)
		tmp = Float64(y4 * Float64(y * Float64(Float64(c * y3) - Float64(b * k))));
	elseif (k <= -4.2e-33)
		tmp = t_1;
	elseif (k <= -2.85e-120)
		tmp = Float64(c * Float64(z * Float64(Float64(t * i) - Float64(y0 * y3))));
	elseif (k <= -1.14e-215)
		tmp = t_1;
	elseif (k <= 2.25e+52)
		tmp = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (k <= 1.65e+199)
		tmp = t_1;
	elseif (k <= 1.85e+282)
		tmp = Float64(z * Float64(k * Float64(Float64(b * y0) - Float64(i * y1))));
	else
		tmp = Float64(y * Float64(b * Float64(k * Float64(-y4))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y2 * (((c * (x * y0)) + (y1 * ((k * y4) - (x * a)))) - (c * (t * y4)));
	tmp = 0.0;
	if (k <= -1.4e+110)
		tmp = y4 * (y * ((c * y3) - (b * k)));
	elseif (k <= -4.2e-33)
		tmp = t_1;
	elseif (k <= -2.85e-120)
		tmp = c * (z * ((t * i) - (y0 * y3)));
	elseif (k <= -1.14e-215)
		tmp = t_1;
	elseif (k <= 2.25e+52)
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	elseif (k <= 1.65e+199)
		tmp = t_1;
	elseif (k <= 1.85e+282)
		tmp = z * (k * ((b * y0) - (i * y1)));
	else
		tmp = y * (b * (k * -y4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y2 * N[(N[(N[(c * N[(x * y0), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -1.4e+110], N[(y4 * N[(y * N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -4.2e-33], t$95$1, If[LessEqual[k, -2.85e-120], N[(c * N[(z * N[(N[(t * i), $MachinePrecision] - N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -1.14e-215], t$95$1, If[LessEqual[k, 2.25e+52], N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.65e+199], t$95$1, If[LessEqual[k, 1.85e+282], N[(z * N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(b * N[(k * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if k < -1.39999999999999993e110

   1. Initial program 15.7%

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

   3. Simplified 18.2%

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

   4. Taylor expanded in y around inf 55.4%

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

      1. mul-1-neg 55.4%

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

   6. Simplified 55.4%

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

   7. Taylor expanded in y4 around inf 53.2%

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

   if -1.39999999999999993e110 < k < -4.2e-33 or -2.85000000000000015e-120 < k < -1.14000000000000001e-215 or 2.25e52 < k < 1.6499999999999999e199

   1. Initial program 31.0%

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

   3. Simplified 31.0%

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

   4. Taylor expanded in y2 around inf 50.5%

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

   5. Taylor expanded in y1 around 0 54.9%

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

   6. Taylor expanded in y5 around 0 58.1%

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

   if -4.2e-33 < k < -2.85000000000000015e-120

   1. Initial program 24.2%

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

   3. Simplified 24.2%

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

   4. Taylor expanded in c around inf 44.5%

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

      1. associate--l+ 44.5%

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

      2. mul-1-neg 44.5%

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

   6. Simplified 44.5%

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

   7. Taylor expanded in z around inf 45.1%

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

      1. *-commutative 45.1%

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

      2. cancel-sign-sub-inv 45.1%

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

      3. metadata-eval 45.1%

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

      4. *-lft-identity 45.1%

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

      5. +-commutative 45.1%

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

      6. mul-1-neg 45.1%

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

      7. unsub-neg 45.1%

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

      8. *-commutative 45.1%

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

   9. Simplified 45.1%

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

   if -1.14000000000000001e-215 < k < 2.25e52

   1. Initial program 27.0%

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

   3. Simplified 27.0%

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

   4. Taylor expanded in y4 around inf 51.6%

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

   if 1.6499999999999999e199 < k < 1.8500000000000001e282

   1. Initial program 6.9%

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

   3. Simplified 6.9%

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

   4. Taylor expanded in z around -inf 41.4%

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

      1. mul-1-neg 41.4%

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

      2. associate--l+ 41.4%

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

   6. Simplified 41.4%

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

   7. Taylor expanded in k around inf 62.3%

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

   if 1.8500000000000001e282 < k

   1. Initial program 25.0%

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

   3. Simplified 50.0%

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

   4. Taylor expanded in y around inf 87.5%

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

      1. mul-1-neg 87.5%

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

   6. Simplified 87.5%

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

   7. Taylor expanded in b around inf 87.9%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 87.9%

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

   9. Simplified 87.9%

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

   10. Taylor expanded in a around 0 87.9%

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

       1. mul-1-neg 87.9%

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

       2. distribute-rgt-neg-in 87.9%

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

   12. Simplified 87.9%

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

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.4 \cdot 10^{+110}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;k \leq -4.2 \cdot 10^{-33}:\\ \;\;\;\;y2 \cdot \left(\left(c \cdot \left(x \cdot y0\right) + y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right) - c \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq -2.85 \cdot 10^{-120}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq -1.14 \cdot 10^{-215}:\\ \;\;\;\;y2 \cdot \left(\left(c \cdot \left(x \cdot y0\right) + y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right) - c \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 2.25 \cdot 10^{+52}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 1.65 \cdot 10^{+199}:\\ \;\;\;\;y2 \cdot \left(\left(c \cdot \left(x \cdot y0\right) + y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right) - c \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 1.85 \cdot 10^{+282}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b \cdot \left(k \cdot \left(-y4\right)\right)\right)\\ \end{array} \]

Alternative 10: 33.1% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y2 \cdot \left(\left(c \cdot \left(x \cdot y0\right) + y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right) - c \cdot \left(t \cdot y4\right)\right)\\ \mathbf{if}\;i \leq -8.5 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -2.7 \cdot 10^{-127}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;i \leq 3.5 \cdot 10^{-217}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 2.15 \cdot 10^{-187}:\\ \;\;\;\;\left(z \cdot y3\right) \cdot \left(a \cdot y1 - c \cdot y0\right)\\ \mathbf{elif}\;i \leq 8 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          y2
          (- (+ (* c (* x y0)) (* y1 (- (* k y4) (* x a)))) (* c (* t y4))))))
   (if (<= i -8.5e+20)
     t_1
     (if (<= i -2.7e-127)
       (* y (* a (- (* x b) (* y3 y5))))
       (if (<= i 3.5e-217)
         t_1
         (if (<= i 2.15e-187)
           (* (* z y3) (- (* a y1) (* c y0)))
           (if (<= i 8e+58) t_1 (* k (* z (- (* b y0) (* i y1)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y2 * (((c * (x * y0)) + (y1 * ((k * y4) - (x * a)))) - (c * (t * y4)));
	double tmp;
	if (i <= -8.5e+20) {
		tmp = t_1;
	} else if (i <= -2.7e-127) {
		tmp = y * (a * ((x * b) - (y3 * y5)));
	} else if (i <= 3.5e-217) {
		tmp = t_1;
	} else if (i <= 2.15e-187) {
		tmp = (z * y3) * ((a * y1) - (c * y0));
	} else if (i <= 8e+58) {
		tmp = t_1;
	} else {
		tmp = k * (z * ((b * y0) - (i * y1)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y2 * (((c * (x * y0)) + (y1 * ((k * y4) - (x * a)))) - (c * (t * y4)))
    if (i <= (-8.5d+20)) then
        tmp = t_1
    else if (i <= (-2.7d-127)) then
        tmp = y * (a * ((x * b) - (y3 * y5)))
    else if (i <= 3.5d-217) then
        tmp = t_1
    else if (i <= 2.15d-187) then
        tmp = (z * y3) * ((a * y1) - (c * y0))
    else if (i <= 8d+58) then
        tmp = t_1
    else
        tmp = k * (z * ((b * y0) - (i * y1)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y2 * (((c * (x * y0)) + (y1 * ((k * y4) - (x * a)))) - (c * (t * y4)));
	double tmp;
	if (i <= -8.5e+20) {
		tmp = t_1;
	} else if (i <= -2.7e-127) {
		tmp = y * (a * ((x * b) - (y3 * y5)));
	} else if (i <= 3.5e-217) {
		tmp = t_1;
	} else if (i <= 2.15e-187) {
		tmp = (z * y3) * ((a * y1) - (c * y0));
	} else if (i <= 8e+58) {
		tmp = t_1;
	} else {
		tmp = k * (z * ((b * y0) - (i * y1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y2 * (((c * (x * y0)) + (y1 * ((k * y4) - (x * a)))) - (c * (t * y4)))
	tmp = 0
	if i <= -8.5e+20:
		tmp = t_1
	elif i <= -2.7e-127:
		tmp = y * (a * ((x * b) - (y3 * y5)))
	elif i <= 3.5e-217:
		tmp = t_1
	elif i <= 2.15e-187:
		tmp = (z * y3) * ((a * y1) - (c * y0))
	elif i <= 8e+58:
		tmp = t_1
	else:
		tmp = k * (z * ((b * y0) - (i * y1)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y2 * Float64(Float64(Float64(c * Float64(x * y0)) + Float64(y1 * Float64(Float64(k * y4) - Float64(x * a)))) - Float64(c * Float64(t * y4))))
	tmp = 0.0
	if (i <= -8.5e+20)
		tmp = t_1;
	elseif (i <= -2.7e-127)
		tmp = Float64(y * Float64(a * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (i <= 3.5e-217)
		tmp = t_1;
	elseif (i <= 2.15e-187)
		tmp = Float64(Float64(z * y3) * Float64(Float64(a * y1) - Float64(c * y0)));
	elseif (i <= 8e+58)
		tmp = t_1;
	else
		tmp = Float64(k * Float64(z * Float64(Float64(b * y0) - Float64(i * y1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y2 * (((c * (x * y0)) + (y1 * ((k * y4) - (x * a)))) - (c * (t * y4)));
	tmp = 0.0;
	if (i <= -8.5e+20)
		tmp = t_1;
	elseif (i <= -2.7e-127)
		tmp = y * (a * ((x * b) - (y3 * y5)));
	elseif (i <= 3.5e-217)
		tmp = t_1;
	elseif (i <= 2.15e-187)
		tmp = (z * y3) * ((a * y1) - (c * y0));
	elseif (i <= 8e+58)
		tmp = t_1;
	else
		tmp = k * (z * ((b * y0) - (i * y1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y2 * N[(N[(N[(c * N[(x * y0), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -8.5e+20], t$95$1, If[LessEqual[i, -2.7e-127], N[(y * N[(a * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.5e-217], t$95$1, If[LessEqual[i, 2.15e-187], N[(N[(z * y3), $MachinePrecision] * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 8e+58], t$95$1, N[(k * N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -8.5e20 or -2.7e-127 < i < 3.5e-217 or 2.15e-187 < i < 7.99999999999999955e58

   1. Initial program 23.1%

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

   3. Simplified 23.1%

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

   4. Taylor expanded in y2 around inf 45.9%

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

   5. Taylor expanded in y1 around 0 47.0%

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

   6. Taylor expanded in y5 around 0 47.8%

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

   if -8.5e20 < i < -2.7e-127

   1. Initial program 18.8%

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

   3. Simplified 31.3%

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

   4. Taylor expanded in y around inf 56.7%

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

      1. mul-1-neg 56.7%

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

   6. Simplified 56.7%

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

   7. Taylor expanded in a around inf 57.2%

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

      1. +-commutative 57.2%

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

      2. mul-1-neg 57.2%

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

      3. unsub-neg 57.2%

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

   9. Simplified 57.2%

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

   if 3.5e-217 < i < 2.15e-187

   1. Initial program 42.9%

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

   3. Simplified 42.9%

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

   4. Taylor expanded in z around -inf 71.4%

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

      1. mul-1-neg 71.4%

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

      2. associate--l+ 71.4%

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

   6. Simplified 71.4%

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

   7. Taylor expanded in y3 around inf 85.7%

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

   if 7.99999999999999955e58 < i

   1. Initial program 28.9%

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

   3. Simplified 28.9%

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

   4. Taylor expanded in z around -inf 42.7%

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

      1. mul-1-neg 42.7%

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

      2. associate--l+ 42.7%

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

   6. Simplified 42.7%

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

   7. Taylor expanded in k around inf 48.0%

      \[\leadsto -\color{blue}{k \cdot \left(\left(i \cdot y1 - y0 \cdot b\right) \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -8.5 \cdot 10^{+20}:\\ \;\;\;\;y2 \cdot \left(\left(c \cdot \left(x \cdot y0\right) + y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right) - c \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq -2.7 \cdot 10^{-127}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;i \leq 3.5 \cdot 10^{-217}:\\ \;\;\;\;y2 \cdot \left(\left(c \cdot \left(x \cdot y0\right) + y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right) - c \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq 2.15 \cdot 10^{-187}:\\ \;\;\;\;\left(z \cdot y3\right) \cdot \left(a \cdot y1 - c \cdot y0\right)\\ \mathbf{elif}\;i \leq 8 \cdot 10^{+58}:\\ \;\;\;\;y2 \cdot \left(\left(c \cdot \left(x \cdot y0\right) + y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right) - c \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \end{array} \]

Alternative 11: 33.8% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y2 \cdot \left(\left(c \cdot \left(x \cdot y0\right) + y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right) - c \cdot \left(t \cdot y4\right)\right)\\ \mathbf{if}\;i \leq -2.05 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -3.15 \cdot 10^{-127}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;i \leq 6.2 \cdot 10^{-217}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.25 \cdot 10^{-187}:\\ \;\;\;\;\left(z \cdot y3\right) \cdot \left(a \cdot y1 - c \cdot y0\right)\\ \mathbf{elif}\;i \leq 3.4 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(a \cdot \left(y1 \cdot y3\right) + t \cdot \left(c \cdot i - a \cdot b\right)\right) - k \cdot \left(i \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          y2
          (- (+ (* c (* x y0)) (* y1 (- (* k y4) (* x a)))) (* c (* t y4))))))
   (if (<= i -2.05e+21)
     t_1
     (if (<= i -3.15e-127)
       (* y (* a (- (* x b) (* y3 y5))))
       (if (<= i 6.2e-217)
         t_1
         (if (<= i 1.25e-187)
           (* (* z y3) (- (* a y1) (* c y0)))
           (if (<= i 3.4e+59)
             t_1
             (*
              z
              (-
               (+ (* a (* y1 y3)) (* t (- (* c i) (* a b))))
               (* k (* i y1)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y2 * (((c * (x * y0)) + (y1 * ((k * y4) - (x * a)))) - (c * (t * y4)));
	double tmp;
	if (i <= -2.05e+21) {
		tmp = t_1;
	} else if (i <= -3.15e-127) {
		tmp = y * (a * ((x * b) - (y3 * y5)));
	} else if (i <= 6.2e-217) {
		tmp = t_1;
	} else if (i <= 1.25e-187) {
		tmp = (z * y3) * ((a * y1) - (c * y0));
	} else if (i <= 3.4e+59) {
		tmp = t_1;
	} else {
		tmp = z * (((a * (y1 * y3)) + (t * ((c * i) - (a * b)))) - (k * (i * y1)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y2 * (((c * (x * y0)) + (y1 * ((k * y4) - (x * a)))) - (c * (t * y4)))
    if (i <= (-2.05d+21)) then
        tmp = t_1
    else if (i <= (-3.15d-127)) then
        tmp = y * (a * ((x * b) - (y3 * y5)))
    else if (i <= 6.2d-217) then
        tmp = t_1
    else if (i <= 1.25d-187) then
        tmp = (z * y3) * ((a * y1) - (c * y0))
    else if (i <= 3.4d+59) then
        tmp = t_1
    else
        tmp = z * (((a * (y1 * y3)) + (t * ((c * i) - (a * b)))) - (k * (i * y1)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y2 * (((c * (x * y0)) + (y1 * ((k * y4) - (x * a)))) - (c * (t * y4)));
	double tmp;
	if (i <= -2.05e+21) {
		tmp = t_1;
	} else if (i <= -3.15e-127) {
		tmp = y * (a * ((x * b) - (y3 * y5)));
	} else if (i <= 6.2e-217) {
		tmp = t_1;
	} else if (i <= 1.25e-187) {
		tmp = (z * y3) * ((a * y1) - (c * y0));
	} else if (i <= 3.4e+59) {
		tmp = t_1;
	} else {
		tmp = z * (((a * (y1 * y3)) + (t * ((c * i) - (a * b)))) - (k * (i * y1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y2 * (((c * (x * y0)) + (y1 * ((k * y4) - (x * a)))) - (c * (t * y4)))
	tmp = 0
	if i <= -2.05e+21:
		tmp = t_1
	elif i <= -3.15e-127:
		tmp = y * (a * ((x * b) - (y3 * y5)))
	elif i <= 6.2e-217:
		tmp = t_1
	elif i <= 1.25e-187:
		tmp = (z * y3) * ((a * y1) - (c * y0))
	elif i <= 3.4e+59:
		tmp = t_1
	else:
		tmp = z * (((a * (y1 * y3)) + (t * ((c * i) - (a * b)))) - (k * (i * y1)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y2 * Float64(Float64(Float64(c * Float64(x * y0)) + Float64(y1 * Float64(Float64(k * y4) - Float64(x * a)))) - Float64(c * Float64(t * y4))))
	tmp = 0.0
	if (i <= -2.05e+21)
		tmp = t_1;
	elseif (i <= -3.15e-127)
		tmp = Float64(y * Float64(a * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (i <= 6.2e-217)
		tmp = t_1;
	elseif (i <= 1.25e-187)
		tmp = Float64(Float64(z * y3) * Float64(Float64(a * y1) - Float64(c * y0)));
	elseif (i <= 3.4e+59)
		tmp = t_1;
	else
		tmp = Float64(z * Float64(Float64(Float64(a * Float64(y1 * y3)) + Float64(t * Float64(Float64(c * i) - Float64(a * b)))) - Float64(k * Float64(i * y1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y2 * (((c * (x * y0)) + (y1 * ((k * y4) - (x * a)))) - (c * (t * y4)));
	tmp = 0.0;
	if (i <= -2.05e+21)
		tmp = t_1;
	elseif (i <= -3.15e-127)
		tmp = y * (a * ((x * b) - (y3 * y5)));
	elseif (i <= 6.2e-217)
		tmp = t_1;
	elseif (i <= 1.25e-187)
		tmp = (z * y3) * ((a * y1) - (c * y0));
	elseif (i <= 3.4e+59)
		tmp = t_1;
	else
		tmp = z * (((a * (y1 * y3)) + (t * ((c * i) - (a * b)))) - (k * (i * y1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y2 * N[(N[(N[(c * N[(x * y0), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.05e+21], t$95$1, If[LessEqual[i, -3.15e-127], N[(y * N[(a * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 6.2e-217], t$95$1, If[LessEqual[i, 1.25e-187], N[(N[(z * y3), $MachinePrecision] * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.4e+59], t$95$1, N[(z * N[(N[(N[(a * N[(y1 * y3), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -2.05e21 or -3.1499999999999999e-127 < i < 6.1999999999999997e-217 or 1.2499999999999999e-187 < i < 3.40000000000000006e59

   1. Initial program 23.1%

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

   3. Simplified 23.1%

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

   4. Taylor expanded in y2 around inf 45.9%

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

   5. Taylor expanded in y1 around 0 47.0%

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

   6. Taylor expanded in y5 around 0 47.8%

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

   if -2.05e21 < i < -3.1499999999999999e-127

   1. Initial program 18.8%

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

   3. Simplified 31.3%

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

   4. Taylor expanded in y around inf 56.7%

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

      1. mul-1-neg 56.7%

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

   6. Simplified 56.7%

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

   7. Taylor expanded in a around inf 57.2%

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

      1. +-commutative 57.2%

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

      2. mul-1-neg 57.2%

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

      3. unsub-neg 57.2%

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

   9. Simplified 57.2%

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

   if 6.1999999999999997e-217 < i < 1.2499999999999999e-187

   1. Initial program 42.9%

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

   3. Simplified 42.9%

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

   4. Taylor expanded in z around -inf 71.4%

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

      1. mul-1-neg 71.4%

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

      2. associate--l+ 71.4%

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

   6. Simplified 71.4%

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

   7. Taylor expanded in y3 around inf 85.7%

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

   if 3.40000000000000006e59 < i

   1. Initial program 28.9%

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

   3. Simplified 28.9%

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

   4. Taylor expanded in z around -inf 42.7%

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

      1. mul-1-neg 42.7%

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

      2. associate--l+ 42.7%

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

   6. Simplified 42.7%

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

   7. Taylor expanded in y0 around 0 50.6%

      \[\leadsto -\color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(a \cdot \left(y1 \cdot y3\right)\right)\right) - -1 \cdot \left(k \cdot \left(y1 \cdot i\right)\right)\right) \cdot z} \]
3. Recombined 4 regimes into one program.

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.05 \cdot 10^{+21}:\\ \;\;\;\;y2 \cdot \left(\left(c \cdot \left(x \cdot y0\right) + y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right) - c \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq -3.15 \cdot 10^{-127}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;i \leq 6.2 \cdot 10^{-217}:\\ \;\;\;\;y2 \cdot \left(\left(c \cdot \left(x \cdot y0\right) + y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right) - c \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq 1.25 \cdot 10^{-187}:\\ \;\;\;\;\left(z \cdot y3\right) \cdot \left(a \cdot y1 - c \cdot y0\right)\\ \mathbf{elif}\;i \leq 3.4 \cdot 10^{+59}:\\ \;\;\;\;y2 \cdot \left(\left(c \cdot \left(x \cdot y0\right) + y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right) - c \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(a \cdot \left(y1 \cdot y3\right) + t \cdot \left(c \cdot i - a \cdot b\right)\right) - k \cdot \left(i \cdot y1\right)\right)\\ \end{array} \]

Alternative 12: 31.0% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ t_2 := y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{if}\;y2 \leq -9.6 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq -5.4 \cdot 10^{-67}:\\ \;\;\;\;y2 \cdot \left(y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;y2 \leq -1.7 \cdot 10^{-133}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq -4.8 \cdot 10^{-157}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y2 \leq -4.8 \cdot 10^{-179}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y2 \leq -1.76 \cdot 10^{-276}:\\ \;\;\;\;\left(z \cdot a\right) \cdot \left(y1 \cdot y3 - t \cdot b\right)\\ \mathbf{elif}\;y2 \leq 1.15 \cdot 10^{+100}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;y2 \leq 3.65 \cdot 10^{+164}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq 5.8 \cdot 10^{+205}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4 - z \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 1.15 \cdot 10^{+249}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y2 (- (* x y0) (* t y4)))))
        (t_2 (* y4 (* y1 (- (* k y2) (* j y3))))))
   (if (<= y2 -9.6e+52)
     t_1
     (if (<= y2 -5.4e-67)
       (* y2 (* y1 (- (* k y4) (* x a))))
       (if (<= y2 -1.7e-133)
         (* y (* a (- (* x b) (* y3 y5))))
         (if (<= y2 -4.8e-157)
           t_2
           (if (<= y2 -4.8e-179)
             (* y4 (* b (- (* t j) (* y k))))
             (if (<= y2 -1.76e-276)
               (* (* z a) (- (* y1 y3) (* t b)))
               (if (<= y2 1.15e+100)
                 (* y4 (* y (- (* c y3) (* b k))))
                 (if (<= y2 3.65e+164)
                   t_1
                   (if (<= y2 5.8e+205)
                     (* c (* y3 (- (* y y4) (* z y0))))
                     (if (<= y2 1.15e+249) t_2 t_1))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y2 * ((x * y0) - (t * y4)));
	double t_2 = y4 * (y1 * ((k * y2) - (j * y3)));
	double tmp;
	if (y2 <= -9.6e+52) {
		tmp = t_1;
	} else if (y2 <= -5.4e-67) {
		tmp = y2 * (y1 * ((k * y4) - (x * a)));
	} else if (y2 <= -1.7e-133) {
		tmp = y * (a * ((x * b) - (y3 * y5)));
	} else if (y2 <= -4.8e-157) {
		tmp = t_2;
	} else if (y2 <= -4.8e-179) {
		tmp = y4 * (b * ((t * j) - (y * k)));
	} else if (y2 <= -1.76e-276) {
		tmp = (z * a) * ((y1 * y3) - (t * b));
	} else if (y2 <= 1.15e+100) {
		tmp = y4 * (y * ((c * y3) - (b * k)));
	} else if (y2 <= 3.65e+164) {
		tmp = t_1;
	} else if (y2 <= 5.8e+205) {
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	} else if (y2 <= 1.15e+249) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * (y2 * ((x * y0) - (t * y4)))
    t_2 = y4 * (y1 * ((k * y2) - (j * y3)))
    if (y2 <= (-9.6d+52)) then
        tmp = t_1
    else if (y2 <= (-5.4d-67)) then
        tmp = y2 * (y1 * ((k * y4) - (x * a)))
    else if (y2 <= (-1.7d-133)) then
        tmp = y * (a * ((x * b) - (y3 * y5)))
    else if (y2 <= (-4.8d-157)) then
        tmp = t_2
    else if (y2 <= (-4.8d-179)) then
        tmp = y4 * (b * ((t * j) - (y * k)))
    else if (y2 <= (-1.76d-276)) then
        tmp = (z * a) * ((y1 * y3) - (t * b))
    else if (y2 <= 1.15d+100) then
        tmp = y4 * (y * ((c * y3) - (b * k)))
    else if (y2 <= 3.65d+164) then
        tmp = t_1
    else if (y2 <= 5.8d+205) then
        tmp = c * (y3 * ((y * y4) - (z * y0)))
    else if (y2 <= 1.15d+249) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y2 * ((x * y0) - (t * y4)));
	double t_2 = y4 * (y1 * ((k * y2) - (j * y3)));
	double tmp;
	if (y2 <= -9.6e+52) {
		tmp = t_1;
	} else if (y2 <= -5.4e-67) {
		tmp = y2 * (y1 * ((k * y4) - (x * a)));
	} else if (y2 <= -1.7e-133) {
		tmp = y * (a * ((x * b) - (y3 * y5)));
	} else if (y2 <= -4.8e-157) {
		tmp = t_2;
	} else if (y2 <= -4.8e-179) {
		tmp = y4 * (b * ((t * j) - (y * k)));
	} else if (y2 <= -1.76e-276) {
		tmp = (z * a) * ((y1 * y3) - (t * b));
	} else if (y2 <= 1.15e+100) {
		tmp = y4 * (y * ((c * y3) - (b * k)));
	} else if (y2 <= 3.65e+164) {
		tmp = t_1;
	} else if (y2 <= 5.8e+205) {
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	} else if (y2 <= 1.15e+249) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (y2 * ((x * y0) - (t * y4)))
	t_2 = y4 * (y1 * ((k * y2) - (j * y3)))
	tmp = 0
	if y2 <= -9.6e+52:
		tmp = t_1
	elif y2 <= -5.4e-67:
		tmp = y2 * (y1 * ((k * y4) - (x * a)))
	elif y2 <= -1.7e-133:
		tmp = y * (a * ((x * b) - (y3 * y5)))
	elif y2 <= -4.8e-157:
		tmp = t_2
	elif y2 <= -4.8e-179:
		tmp = y4 * (b * ((t * j) - (y * k)))
	elif y2 <= -1.76e-276:
		tmp = (z * a) * ((y1 * y3) - (t * b))
	elif y2 <= 1.15e+100:
		tmp = y4 * (y * ((c * y3) - (b * k)))
	elif y2 <= 3.65e+164:
		tmp = t_1
	elif y2 <= 5.8e+205:
		tmp = c * (y3 * ((y * y4) - (z * y0)))
	elif y2 <= 1.15e+249:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))))
	t_2 = Float64(y4 * Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))))
	tmp = 0.0
	if (y2 <= -9.6e+52)
		tmp = t_1;
	elseif (y2 <= -5.4e-67)
		tmp = Float64(y2 * Float64(y1 * Float64(Float64(k * y4) - Float64(x * a))));
	elseif (y2 <= -1.7e-133)
		tmp = Float64(y * Float64(a * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (y2 <= -4.8e-157)
		tmp = t_2;
	elseif (y2 <= -4.8e-179)
		tmp = Float64(y4 * Float64(b * Float64(Float64(t * j) - Float64(y * k))));
	elseif (y2 <= -1.76e-276)
		tmp = Float64(Float64(z * a) * Float64(Float64(y1 * y3) - Float64(t * b)));
	elseif (y2 <= 1.15e+100)
		tmp = Float64(y4 * Float64(y * Float64(Float64(c * y3) - Float64(b * k))));
	elseif (y2 <= 3.65e+164)
		tmp = t_1;
	elseif (y2 <= 5.8e+205)
		tmp = Float64(c * Float64(y3 * Float64(Float64(y * y4) - Float64(z * y0))));
	elseif (y2 <= 1.15e+249)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (y2 * ((x * y0) - (t * y4)));
	t_2 = y4 * (y1 * ((k * y2) - (j * y3)));
	tmp = 0.0;
	if (y2 <= -9.6e+52)
		tmp = t_1;
	elseif (y2 <= -5.4e-67)
		tmp = y2 * (y1 * ((k * y4) - (x * a)));
	elseif (y2 <= -1.7e-133)
		tmp = y * (a * ((x * b) - (y3 * y5)));
	elseif (y2 <= -4.8e-157)
		tmp = t_2;
	elseif (y2 <= -4.8e-179)
		tmp = y4 * (b * ((t * j) - (y * k)));
	elseif (y2 <= -1.76e-276)
		tmp = (z * a) * ((y1 * y3) - (t * b));
	elseif (y2 <= 1.15e+100)
		tmp = y4 * (y * ((c * y3) - (b * k)));
	elseif (y2 <= 3.65e+164)
		tmp = t_1;
	elseif (y2 <= 5.8e+205)
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	elseif (y2 <= 1.15e+249)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y4 * N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -9.6e+52], t$95$1, If[LessEqual[y2, -5.4e-67], N[(y2 * N[(y1 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1.7e-133], N[(y * N[(a * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -4.8e-157], t$95$2, If[LessEqual[y2, -4.8e-179], N[(y4 * N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1.76e-276], N[(N[(z * a), $MachinePrecision] * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.15e+100], N[(y4 * N[(y * N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 3.65e+164], t$95$1, If[LessEqual[y2, 5.8e+205], N[(c * N[(y3 * N[(N[(y * y4), $MachinePrecision] - N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.15e+249], t$95$2, t$95$1]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y2 < -9.5999999999999999e52 or 1.14999999999999995e100 < y2 < 3.65000000000000024e164 or 1.1499999999999999e249 < y2

   1. Initial program 21.2%

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

   3. Simplified 21.2%

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

   4. Taylor expanded in y2 around inf 57.2%

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

   5. Taylor expanded in c around inf 63.8%

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

   if -9.5999999999999999e52 < y2 < -5.40000000000000032e-67

   1. Initial program 24.9%

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

   3. Simplified 24.9%

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

   4. Taylor expanded in y2 around inf 41.7%

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

   5. Taylor expanded in y1 around inf 45.4%

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

      1. +-commutative 45.4%

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

      2. mul-1-neg 45.4%

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

      3. unsub-neg 45.4%

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

      4. *-commutative 45.4%

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

   7. Simplified 45.4%

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

   if -5.40000000000000032e-67 < y2 < -1.70000000000000003e-133

   1. Initial program 22.2%

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

   3. Simplified 33.3%

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

   4. Taylor expanded in y around inf 50.4%

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

      1. mul-1-neg 50.4%

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

   6. Simplified 50.4%

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

   7. Taylor expanded in a around inf 56.6%

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

      1. +-commutative 56.6%

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

      2. mul-1-neg 56.6%

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

      3. unsub-neg 56.6%

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

   9. Simplified 56.6%

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

   if -1.70000000000000003e-133 < y2 < -4.8e-157 or 5.8000000000000003e205 < y2 < 1.1499999999999999e249

   1. Initial program 20.9%

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

   3. Simplified 20.9%

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

   4. Taylor expanded in y4 around inf 47.7%

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

   5. Taylor expanded in y1 around inf 68.9%

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

   if -4.8e-157 < y2 < -4.8000000000000001e-179

   1. Initial program 16.7%

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

   3. Simplified 16.7%

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

   4. Taylor expanded in y4 around inf 33.4%

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

   5. Taylor expanded in b around inf 83.8%

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

   if -4.8000000000000001e-179 < y2 < -1.75999999999999997e-276

   1. Initial program 35.7%

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

   3. Simplified 35.7%

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

   4. Taylor expanded in z around -inf 53.7%

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

      1. mul-1-neg 53.7%

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

      2. associate--l+ 53.7%

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

   6. Simplified 53.7%

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

   7. Taylor expanded in a around inf 57.7%

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

      1. *-commutative 57.7%

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

      2. associate-*r* 57.7%

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

      3. *-commutative 57.7%

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

      4. associate-*l* 54.4%

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

      5. mul-1-neg 54.4%

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

      6. unsub-neg 54.4%

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

      7. *-commutative 54.4%

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

      8. *-commutative 54.4%

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

   9. Simplified 54.4%

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

   if -1.75999999999999997e-276 < y2 < 1.14999999999999995e100

   1. Initial program 22.8%

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

   3. Simplified 25.9%

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

   4. Taylor expanded in y around inf 43.5%

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

      1. mul-1-neg 43.5%

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

   6. Simplified 43.5%

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

   7. Taylor expanded in y4 around inf 49.6%

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

   if 3.65000000000000024e164 < y2 < 5.8000000000000003e205

   1. Initial program 28.6%

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

   3. Simplified 28.6%

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

   4. Taylor expanded in c around inf 43.7%

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

      1. associate--l+ 43.7%

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

      2. mul-1-neg 43.7%

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

   6. Simplified 43.7%

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

   7. Taylor expanded in y3 around -inf 57.9%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(\left(y0 \cdot z - y4 \cdot y\right) \cdot y3\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 57.9%

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

      2. neg-mul-1 57.9%

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

      3. *-commutative 57.9%

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

   9. Simplified 57.9%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -9.6 \cdot 10^{+52}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -5.4 \cdot 10^{-67}:\\ \;\;\;\;y2 \cdot \left(y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;y2 \leq -1.7 \cdot 10^{-133}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq -4.8 \cdot 10^{-157}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq -4.8 \cdot 10^{-179}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y2 \leq -1.76 \cdot 10^{-276}:\\ \;\;\;\;\left(z \cdot a\right) \cdot \left(y1 \cdot y3 - t \cdot b\right)\\ \mathbf{elif}\;y2 \leq 1.15 \cdot 10^{+100}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;y2 \leq 3.65 \cdot 10^{+164}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 5.8 \cdot 10^{+205}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4 - z \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 1.15 \cdot 10^{+249}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \end{array} \]

Alternative 13: 29.5% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ t_2 := c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{if}\;y2 \leq -7.1 \cdot 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq -2 \cdot 10^{-94}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(j \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -2.6 \cdot 10^{-146}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq -1.2 \cdot 10^{-183}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y2 \leq 1.12 \cdot 10^{-170}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;y2 \leq 1.8 \cdot 10^{-28}:\\ \;\;\;\;y \cdot \left(b \cdot \left(k \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 2.65 \cdot 10^{+29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y2 \leq 1.1 \cdot 10^{+67}:\\ \;\;\;\;\left(x \cdot b\right) \cdot \left(y \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y2 (- (* x y0) (* t y4)))))
        (t_2 (* c (* z (- (* t i) (* y0 y3))))))
   (if (<= y2 -7.1e+53)
     t_1
     (if (<= y2 -2e-94)
       (* i (* y5 (* j (- t))))
       (if (<= y2 -2.6e-146)
         (* a (* x (* y b)))
         (if (<= y2 -1.2e-183)
           t_2
           (if (<= y2 1.12e-170)
             (* c (* y (- (* y3 y4) (* x i))))
             (if (<= y2 1.8e-28)
               (* y (* b (* k (- y4))))
               (if (<= y2 2.65e+29)
                 t_2
                 (if (<= y2 1.1e+67) (* (* x b) (* y a)) t_1))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y2 * ((x * y0) - (t * y4)));
	double t_2 = c * (z * ((t * i) - (y0 * y3)));
	double tmp;
	if (y2 <= -7.1e+53) {
		tmp = t_1;
	} else if (y2 <= -2e-94) {
		tmp = i * (y5 * (j * -t));
	} else if (y2 <= -2.6e-146) {
		tmp = a * (x * (y * b));
	} else if (y2 <= -1.2e-183) {
		tmp = t_2;
	} else if (y2 <= 1.12e-170) {
		tmp = c * (y * ((y3 * y4) - (x * i)));
	} else if (y2 <= 1.8e-28) {
		tmp = y * (b * (k * -y4));
	} else if (y2 <= 2.65e+29) {
		tmp = t_2;
	} else if (y2 <= 1.1e+67) {
		tmp = (x * b) * (y * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * (y2 * ((x * y0) - (t * y4)))
    t_2 = c * (z * ((t * i) - (y0 * y3)))
    if (y2 <= (-7.1d+53)) then
        tmp = t_1
    else if (y2 <= (-2d-94)) then
        tmp = i * (y5 * (j * -t))
    else if (y2 <= (-2.6d-146)) then
        tmp = a * (x * (y * b))
    else if (y2 <= (-1.2d-183)) then
        tmp = t_2
    else if (y2 <= 1.12d-170) then
        tmp = c * (y * ((y3 * y4) - (x * i)))
    else if (y2 <= 1.8d-28) then
        tmp = y * (b * (k * -y4))
    else if (y2 <= 2.65d+29) then
        tmp = t_2
    else if (y2 <= 1.1d+67) then
        tmp = (x * b) * (y * a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y2 * ((x * y0) - (t * y4)));
	double t_2 = c * (z * ((t * i) - (y0 * y3)));
	double tmp;
	if (y2 <= -7.1e+53) {
		tmp = t_1;
	} else if (y2 <= -2e-94) {
		tmp = i * (y5 * (j * -t));
	} else if (y2 <= -2.6e-146) {
		tmp = a * (x * (y * b));
	} else if (y2 <= -1.2e-183) {
		tmp = t_2;
	} else if (y2 <= 1.12e-170) {
		tmp = c * (y * ((y3 * y4) - (x * i)));
	} else if (y2 <= 1.8e-28) {
		tmp = y * (b * (k * -y4));
	} else if (y2 <= 2.65e+29) {
		tmp = t_2;
	} else if (y2 <= 1.1e+67) {
		tmp = (x * b) * (y * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (y2 * ((x * y0) - (t * y4)))
	t_2 = c * (z * ((t * i) - (y0 * y3)))
	tmp = 0
	if y2 <= -7.1e+53:
		tmp = t_1
	elif y2 <= -2e-94:
		tmp = i * (y5 * (j * -t))
	elif y2 <= -2.6e-146:
		tmp = a * (x * (y * b))
	elif y2 <= -1.2e-183:
		tmp = t_2
	elif y2 <= 1.12e-170:
		tmp = c * (y * ((y3 * y4) - (x * i)))
	elif y2 <= 1.8e-28:
		tmp = y * (b * (k * -y4))
	elif y2 <= 2.65e+29:
		tmp = t_2
	elif y2 <= 1.1e+67:
		tmp = (x * b) * (y * a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))))
	t_2 = Float64(c * Float64(z * Float64(Float64(t * i) - Float64(y0 * y3))))
	tmp = 0.0
	if (y2 <= -7.1e+53)
		tmp = t_1;
	elseif (y2 <= -2e-94)
		tmp = Float64(i * Float64(y5 * Float64(j * Float64(-t))));
	elseif (y2 <= -2.6e-146)
		tmp = Float64(a * Float64(x * Float64(y * b)));
	elseif (y2 <= -1.2e-183)
		tmp = t_2;
	elseif (y2 <= 1.12e-170)
		tmp = Float64(c * Float64(y * Float64(Float64(y3 * y4) - Float64(x * i))));
	elseif (y2 <= 1.8e-28)
		tmp = Float64(y * Float64(b * Float64(k * Float64(-y4))));
	elseif (y2 <= 2.65e+29)
		tmp = t_2;
	elseif (y2 <= 1.1e+67)
		tmp = Float64(Float64(x * b) * Float64(y * a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (y2 * ((x * y0) - (t * y4)));
	t_2 = c * (z * ((t * i) - (y0 * y3)));
	tmp = 0.0;
	if (y2 <= -7.1e+53)
		tmp = t_1;
	elseif (y2 <= -2e-94)
		tmp = i * (y5 * (j * -t));
	elseif (y2 <= -2.6e-146)
		tmp = a * (x * (y * b));
	elseif (y2 <= -1.2e-183)
		tmp = t_2;
	elseif (y2 <= 1.12e-170)
		tmp = c * (y * ((y3 * y4) - (x * i)));
	elseif (y2 <= 1.8e-28)
		tmp = y * (b * (k * -y4));
	elseif (y2 <= 2.65e+29)
		tmp = t_2;
	elseif (y2 <= 1.1e+67)
		tmp = (x * b) * (y * a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(z * N[(N[(t * i), $MachinePrecision] - N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -7.1e+53], t$95$1, If[LessEqual[y2, -2e-94], N[(i * N[(y5 * N[(j * (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -2.6e-146], N[(a * N[(x * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1.2e-183], t$95$2, If[LessEqual[y2, 1.12e-170], N[(c * N[(y * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.8e-28], N[(y * N[(b * N[(k * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.65e+29], t$95$2, If[LessEqual[y2, 1.1e+67], N[(N[(x * b), $MachinePrecision] * N[(y * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y2 < -7.09999999999999974e53 or 1.1e67 < y2

   1. Initial program 20.8%

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

   3. Simplified 20.8%

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

   4. Taylor expanded in y2 around inf 51.8%

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

   5. Taylor expanded in c around inf 59.1%

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

   if -7.09999999999999974e53 < y2 < -1.9999999999999999e-94

   1. Initial program 24.2%

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

   3. Simplified 33.0%

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

   4. Taylor expanded in y5 around inf 45.0%

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

      1. mul-1-neg 45.0%

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

      2. mul-1-neg 45.0%

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

      3. mul-1-neg 45.0%

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

      4. sub-neg 45.0%

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

      5. sub-neg 45.0%

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

   6. Simplified 45.0%

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

   7. Taylor expanded in i around inf 30.8%

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

   8. Taylor expanded in k around 0 27.7%

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

      1. mul-1-neg 27.7%

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

      2. *-commutative 27.7%

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

      3. distribute-rgt-neg-in 27.7%

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

      4. associate-*r* 27.8%

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

      5. *-commutative 27.8%

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

   10. Simplified 27.8%

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

   if -1.9999999999999999e-94 < y2 < -2.59999999999999987e-146

   1. Initial program 31.1%

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

   3. Simplified 37.3%

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

   4. Taylor expanded in y around inf 56.9%

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

      1. mul-1-neg 56.9%

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

   6. Simplified 56.9%

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

   7. Taylor expanded in b around inf 32.2%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 32.2%

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

   9. Simplified 32.2%

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

   10. Taylor expanded in x around -inf 39.4%

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

       1. pow1 39.4%

          \[\leadsto a \cdot \color{blue}{{\left(y \cdot \left(b \cdot x\right)\right)}^{1}} \]

       2. *-commutative 39.4%

          \[\leadsto a \cdot {\left(y \cdot \color{blue}{\left(x \cdot b\right)}\right)}^{1} \]

   12. Applied egg-rr 39.4%

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

       1. unpow1 39.4%

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

       2. *-commutative 39.4%

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

       3. associate-*l* 45.6%

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

   14. Simplified 45.6%

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

   if -2.59999999999999987e-146 < y2 < -1.19999999999999996e-183 or 1.7999999999999999e-28 < y2 < 2.65e29

   1. Initial program 5.6%

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

   3. Simplified 5.6%

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

   4. Taylor expanded in c around inf 40.6%

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

      1. associate--l+ 40.6%

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

      2. mul-1-neg 40.6%

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

   6. Simplified 40.6%

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

   7. Taylor expanded in z around inf 46.2%

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

      1. *-commutative 46.2%

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

      2. cancel-sign-sub-inv 46.2%

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

      3. metadata-eval 46.2%

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

      4. *-lft-identity 46.2%

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

      5. +-commutative 46.2%

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

      6. mul-1-neg 46.2%

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

      7. unsub-neg 46.2%

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

      8. *-commutative 46.2%

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

   9. Simplified 46.2%

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

   if -1.19999999999999996e-183 < y2 < 1.12000000000000009e-170

   1. Initial program 34.2%

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

   3. Simplified 34.2%

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

   4. Taylor expanded in c around inf 47.6%

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

      1. associate--l+ 47.6%

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

      2. mul-1-neg 47.6%

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

   6. Simplified 47.6%

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

   7. Taylor expanded in y around -inf 43.3%

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

      1. mul-1-neg 43.3%

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

      2. unsub-neg 43.3%

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

      3. *-commutative 43.3%

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

   9. Simplified 43.3%

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

   if 1.12000000000000009e-170 < y2 < 1.7999999999999999e-28

   1. Initial program 30.3%

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

   3. Simplified 30.3%

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

   4. Taylor expanded in y around inf 45.2%

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

      1. mul-1-neg 45.2%

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

   6. Simplified 45.2%

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

   7. Taylor expanded in b around inf 50.4%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 50.4%

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

   9. Simplified 50.4%

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

   10. Taylor expanded in a around 0 50.6%

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

       1. mul-1-neg 50.6%

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

       2. distribute-rgt-neg-in 50.6%

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

   12. Simplified 50.6%

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

   if 2.65e29 < y2 < 1.1e67

   1. Initial program 13.2%

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

   3. Simplified 25.7%

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

   4. Taylor expanded in y around inf 63.8%

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

      1. mul-1-neg 63.8%

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

   6. Simplified 63.8%

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

   7. Taylor expanded in b around inf 40.3%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 40.3%

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

   9. Simplified 40.3%

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

   10. Taylor expanded in a around inf 40.3%

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

       1. associate-*r* 51.5%

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

   12. Simplified 51.5%

       \[\leadsto \color{blue}{\left(y \cdot a\right) \cdot \left(b \cdot x\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -7.1 \cdot 10^{+53}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -2 \cdot 10^{-94}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(j \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -2.6 \cdot 10^{-146}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq -1.2 \cdot 10^{-183}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 1.12 \cdot 10^{-170}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;y2 \leq 1.8 \cdot 10^{-28}:\\ \;\;\;\;y \cdot \left(b \cdot \left(k \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 2.65 \cdot 10^{+29}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 1.1 \cdot 10^{+67}:\\ \;\;\;\;\left(x \cdot b\right) \cdot \left(y \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \end{array} \]

Alternative 14: 30.8% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ t_2 := c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{if}\;y2 \leq -1.75 \cdot 10^{+44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y2 \leq -3.4 \cdot 10^{-94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq -6.4 \cdot 10^{-145}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq -6.4 \cdot 10^{-257}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq 2.05 \cdot 10^{-171}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;y2 \leq 8.5 \cdot 10^{-29}:\\ \;\;\;\;y \cdot \left(b \cdot \left(k \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 1.7 \cdot 10^{+27}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 1.16 \cdot 10^{+67}:\\ \;\;\;\;\left(x \cdot b\right) \cdot \left(y \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* y5 (- (* y k) (* t j)))))
        (t_2 (* c (* y2 (- (* x y0) (* t y4))))))
   (if (<= y2 -1.75e+44)
     t_2
     (if (<= y2 -3.4e-94)
       t_1
       (if (<= y2 -6.4e-145)
         (* a (* x (* y b)))
         (if (<= y2 -6.4e-257)
           t_1
           (if (<= y2 2.05e-171)
             (* c (* y (- (* y3 y4) (* x i))))
             (if (<= y2 8.5e-29)
               (* y (* b (* k (- y4))))
               (if (<= y2 1.7e+27)
                 (* c (* z (- (* t i) (* y0 y3))))
                 (if (<= y2 1.16e+67) (* (* x b) (* y a)) t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (y5 * ((y * k) - (t * j)));
	double t_2 = c * (y2 * ((x * y0) - (t * y4)));
	double tmp;
	if (y2 <= -1.75e+44) {
		tmp = t_2;
	} else if (y2 <= -3.4e-94) {
		tmp = t_1;
	} else if (y2 <= -6.4e-145) {
		tmp = a * (x * (y * b));
	} else if (y2 <= -6.4e-257) {
		tmp = t_1;
	} else if (y2 <= 2.05e-171) {
		tmp = c * (y * ((y3 * y4) - (x * i)));
	} else if (y2 <= 8.5e-29) {
		tmp = y * (b * (k * -y4));
	} else if (y2 <= 1.7e+27) {
		tmp = c * (z * ((t * i) - (y0 * y3)));
	} else if (y2 <= 1.16e+67) {
		tmp = (x * b) * (y * a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * (y5 * ((y * k) - (t * j)))
    t_2 = c * (y2 * ((x * y0) - (t * y4)))
    if (y2 <= (-1.75d+44)) then
        tmp = t_2
    else if (y2 <= (-3.4d-94)) then
        tmp = t_1
    else if (y2 <= (-6.4d-145)) then
        tmp = a * (x * (y * b))
    else if (y2 <= (-6.4d-257)) then
        tmp = t_1
    else if (y2 <= 2.05d-171) then
        tmp = c * (y * ((y3 * y4) - (x * i)))
    else if (y2 <= 8.5d-29) then
        tmp = y * (b * (k * -y4))
    else if (y2 <= 1.7d+27) then
        tmp = c * (z * ((t * i) - (y0 * y3)))
    else if (y2 <= 1.16d+67) then
        tmp = (x * b) * (y * a)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (y5 * ((y * k) - (t * j)));
	double t_2 = c * (y2 * ((x * y0) - (t * y4)));
	double tmp;
	if (y2 <= -1.75e+44) {
		tmp = t_2;
	} else if (y2 <= -3.4e-94) {
		tmp = t_1;
	} else if (y2 <= -6.4e-145) {
		tmp = a * (x * (y * b));
	} else if (y2 <= -6.4e-257) {
		tmp = t_1;
	} else if (y2 <= 2.05e-171) {
		tmp = c * (y * ((y3 * y4) - (x * i)));
	} else if (y2 <= 8.5e-29) {
		tmp = y * (b * (k * -y4));
	} else if (y2 <= 1.7e+27) {
		tmp = c * (z * ((t * i) - (y0 * y3)));
	} else if (y2 <= 1.16e+67) {
		tmp = (x * b) * (y * a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = i * (y5 * ((y * k) - (t * j)))
	t_2 = c * (y2 * ((x * y0) - (t * y4)))
	tmp = 0
	if y2 <= -1.75e+44:
		tmp = t_2
	elif y2 <= -3.4e-94:
		tmp = t_1
	elif y2 <= -6.4e-145:
		tmp = a * (x * (y * b))
	elif y2 <= -6.4e-257:
		tmp = t_1
	elif y2 <= 2.05e-171:
		tmp = c * (y * ((y3 * y4) - (x * i)))
	elif y2 <= 8.5e-29:
		tmp = y * (b * (k * -y4))
	elif y2 <= 1.7e+27:
		tmp = c * (z * ((t * i) - (y0 * y3)))
	elif y2 <= 1.16e+67:
		tmp = (x * b) * (y * a)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))))
	t_2 = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))))
	tmp = 0.0
	if (y2 <= -1.75e+44)
		tmp = t_2;
	elseif (y2 <= -3.4e-94)
		tmp = t_1;
	elseif (y2 <= -6.4e-145)
		tmp = Float64(a * Float64(x * Float64(y * b)));
	elseif (y2 <= -6.4e-257)
		tmp = t_1;
	elseif (y2 <= 2.05e-171)
		tmp = Float64(c * Float64(y * Float64(Float64(y3 * y4) - Float64(x * i))));
	elseif (y2 <= 8.5e-29)
		tmp = Float64(y * Float64(b * Float64(k * Float64(-y4))));
	elseif (y2 <= 1.7e+27)
		tmp = Float64(c * Float64(z * Float64(Float64(t * i) - Float64(y0 * y3))));
	elseif (y2 <= 1.16e+67)
		tmp = Float64(Float64(x * b) * Float64(y * a));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = i * (y5 * ((y * k) - (t * j)));
	t_2 = c * (y2 * ((x * y0) - (t * y4)));
	tmp = 0.0;
	if (y2 <= -1.75e+44)
		tmp = t_2;
	elseif (y2 <= -3.4e-94)
		tmp = t_1;
	elseif (y2 <= -6.4e-145)
		tmp = a * (x * (y * b));
	elseif (y2 <= -6.4e-257)
		tmp = t_1;
	elseif (y2 <= 2.05e-171)
		tmp = c * (y * ((y3 * y4) - (x * i)));
	elseif (y2 <= 8.5e-29)
		tmp = y * (b * (k * -y4));
	elseif (y2 <= 1.7e+27)
		tmp = c * (z * ((t * i) - (y0 * y3)));
	elseif (y2 <= 1.16e+67)
		tmp = (x * b) * (y * a);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -1.75e+44], t$95$2, If[LessEqual[y2, -3.4e-94], t$95$1, If[LessEqual[y2, -6.4e-145], N[(a * N[(x * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -6.4e-257], t$95$1, If[LessEqual[y2, 2.05e-171], N[(c * N[(y * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 8.5e-29], N[(y * N[(b * N[(k * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.7e+27], N[(c * N[(z * N[(N[(t * i), $MachinePrecision] - N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.16e+67], N[(N[(x * b), $MachinePrecision] * N[(y * a), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y2 < -1.75e44 or 1.15999999999999994e67 < y2

   1. Initial program 20.4%

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

   3. Simplified 20.4%

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

   4. Taylor expanded in y2 around inf 52.6%

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

   5. Taylor expanded in c around inf 58.1%

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

   if -1.75e44 < y2 < -3.3999999999999998e-94 or -6.40000000000000017e-145 < y2 < -6.39999999999999971e-257

   1. Initial program 28.0%

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

   3. Simplified 37.2%

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

   4. Taylor expanded in y5 around inf 43.7%

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

      1. mul-1-neg 43.7%

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

      2. mul-1-neg 43.7%

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

      3. mul-1-neg 43.7%

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

      4. sub-neg 43.7%

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

      5. sub-neg 43.7%

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

   6. Simplified 43.7%

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

   7. Taylor expanded in i around inf 36.4%

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

   if -3.3999999999999998e-94 < y2 < -6.40000000000000017e-145

   1. Initial program 26.6%

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

   3. Simplified 33.2%

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

   4. Taylor expanded in y around inf 60.6%

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

      1. mul-1-neg 60.6%

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

   6. Simplified 60.6%

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

   7. Taylor expanded in b around inf 34.3%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 34.3%

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

   9. Simplified 34.3%

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

   10. Taylor expanded in x around -inf 42.0%

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

       1. pow1 42.0%

          \[\leadsto a \cdot \color{blue}{{\left(y \cdot \left(b \cdot x\right)\right)}^{1}} \]

       2. *-commutative 42.0%

          \[\leadsto a \cdot {\left(y \cdot \color{blue}{\left(x \cdot b\right)}\right)}^{1} \]

   12. Applied egg-rr 42.0%

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

       1. unpow1 42.0%

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

       2. *-commutative 42.0%

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

       3. associate-*l* 48.6%

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

   14. Simplified 48.6%

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

   if -6.39999999999999971e-257 < y2 < 2.05e-171

   1. Initial program 32.4%

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

   3. Simplified 32.4%

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

   4. Taylor expanded in c around inf 52.9%

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

      1. associate--l+ 52.9%

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

      2. mul-1-neg 52.9%

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

   6. Simplified 52.9%

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

   7. Taylor expanded in y around -inf 48.9%

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

      1. mul-1-neg 48.9%

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

      2. unsub-neg 48.9%

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

      3. *-commutative 48.9%

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

   9. Simplified 48.9%

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

   if 2.05e-171 < y2 < 8.5000000000000001e-29

   1. Initial program 30.3%

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

   3. Simplified 30.3%

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

   4. Taylor expanded in y around inf 45.2%

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

      1. mul-1-neg 45.2%

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

   6. Simplified 45.2%

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

   7. Taylor expanded in b around inf 50.4%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 50.4%

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

   9. Simplified 50.4%

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

   10. Taylor expanded in a around 0 50.6%

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

       1. mul-1-neg 50.6%

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

       2. distribute-rgt-neg-in 50.6%

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

   12. Simplified 50.6%

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

   if 8.5000000000000001e-29 < y2 < 1.7e27

   1. Initial program 1.2%

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

   3. Simplified 1.2%

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

   4. Taylor expanded in c around inf 51.0%

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

      1. associate--l+ 51.0%

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

      2. mul-1-neg 51.0%

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

   6. Simplified 51.0%

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

   7. Taylor expanded in z around inf 41.9%

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

      1. *-commutative 41.9%

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

      2. cancel-sign-sub-inv 41.9%

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

      3. metadata-eval 41.9%

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

      4. *-lft-identity 41.9%

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

      5. +-commutative 41.9%

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

      6. mul-1-neg 41.9%

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

      7. unsub-neg 41.9%

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

      8. *-commutative 41.9%

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

   9. Simplified 41.9%

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

   if 1.7e27 < y2 < 1.15999999999999994e67

   1. Initial program 13.2%

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

   3. Simplified 25.7%

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

   4. Taylor expanded in y around inf 63.8%

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

      1. mul-1-neg 63.8%

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

   6. Simplified 63.8%

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

   7. Taylor expanded in b around inf 40.3%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 40.3%

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

   9. Simplified 40.3%

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

   10. Taylor expanded in a around inf 40.3%

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

       1. associate-*r* 51.5%

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

   12. Simplified 51.5%

       \[\leadsto \color{blue}{\left(y \cdot a\right) \cdot \left(b \cdot x\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 49.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.75 \cdot 10^{+44}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -3.4 \cdot 10^{-94}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq -6.4 \cdot 10^{-145}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq -6.4 \cdot 10^{-257}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq 2.05 \cdot 10^{-171}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;y2 \leq 8.5 \cdot 10^{-29}:\\ \;\;\;\;y \cdot \left(b \cdot \left(k \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 1.7 \cdot 10^{+27}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 1.16 \cdot 10^{+67}:\\ \;\;\;\;\left(x \cdot b\right) \cdot \left(y \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \end{array} \]

Alternative 15: 32.3% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ t_2 := c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ t_3 := i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{if}\;y2 \leq -1.05 \cdot 10^{+54}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y2 \leq -4.6 \cdot 10^{-52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq -2 \cdot 10^{-94}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y2 \leq -2.2 \cdot 10^{-157}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq -4 \cdot 10^{-204}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -1.05 \cdot 10^{-254}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y2 \leq 4.1 \cdot 10^{+95}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y4 (* y1 (- (* k y2) (* j y3)))))
        (t_2 (* c (* y2 (- (* x y0) (* t y4)))))
        (t_3 (* i (* y5 (- (* y k) (* t j))))))
   (if (<= y2 -1.05e+54)
     t_2
     (if (<= y2 -4.6e-52)
       t_1
       (if (<= y2 -2e-94)
         t_3
         (if (<= y2 -2.2e-157)
           t_1
           (if (<= y2 -4e-204)
             (* y (* b (- (* x a) (* k y4))))
             (if (<= y2 -1.05e-254)
               t_3
               (if (<= y2 4.1e+95)
                 (* y4 (* y (- (* c y3) (* b k))))
                 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 = y4 * (y1 * ((k * y2) - (j * y3)));
	double t_2 = c * (y2 * ((x * y0) - (t * y4)));
	double t_3 = i * (y5 * ((y * k) - (t * j)));
	double tmp;
	if (y2 <= -1.05e+54) {
		tmp = t_2;
	} else if (y2 <= -4.6e-52) {
		tmp = t_1;
	} else if (y2 <= -2e-94) {
		tmp = t_3;
	} else if (y2 <= -2.2e-157) {
		tmp = t_1;
	} else if (y2 <= -4e-204) {
		tmp = y * (b * ((x * a) - (k * y4)));
	} else if (y2 <= -1.05e-254) {
		tmp = t_3;
	} else if (y2 <= 4.1e+95) {
		tmp = y4 * (y * ((c * y3) - (b * k)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y4 * (y1 * ((k * y2) - (j * y3)))
    t_2 = c * (y2 * ((x * y0) - (t * y4)))
    t_3 = i * (y5 * ((y * k) - (t * j)))
    if (y2 <= (-1.05d+54)) then
        tmp = t_2
    else if (y2 <= (-4.6d-52)) then
        tmp = t_1
    else if (y2 <= (-2d-94)) then
        tmp = t_3
    else if (y2 <= (-2.2d-157)) then
        tmp = t_1
    else if (y2 <= (-4d-204)) then
        tmp = y * (b * ((x * a) - (k * y4)))
    else if (y2 <= (-1.05d-254)) then
        tmp = t_3
    else if (y2 <= 4.1d+95) then
        tmp = y4 * (y * ((c * y3) - (b * k)))
    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 = y4 * (y1 * ((k * y2) - (j * y3)));
	double t_2 = c * (y2 * ((x * y0) - (t * y4)));
	double t_3 = i * (y5 * ((y * k) - (t * j)));
	double tmp;
	if (y2 <= -1.05e+54) {
		tmp = t_2;
	} else if (y2 <= -4.6e-52) {
		tmp = t_1;
	} else if (y2 <= -2e-94) {
		tmp = t_3;
	} else if (y2 <= -2.2e-157) {
		tmp = t_1;
	} else if (y2 <= -4e-204) {
		tmp = y * (b * ((x * a) - (k * y4)));
	} else if (y2 <= -1.05e-254) {
		tmp = t_3;
	} else if (y2 <= 4.1e+95) {
		tmp = y4 * (y * ((c * y3) - (b * k)));
	} 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 = y4 * (y1 * ((k * y2) - (j * y3)))
	t_2 = c * (y2 * ((x * y0) - (t * y4)))
	t_3 = i * (y5 * ((y * k) - (t * j)))
	tmp = 0
	if y2 <= -1.05e+54:
		tmp = t_2
	elif y2 <= -4.6e-52:
		tmp = t_1
	elif y2 <= -2e-94:
		tmp = t_3
	elif y2 <= -2.2e-157:
		tmp = t_1
	elif y2 <= -4e-204:
		tmp = y * (b * ((x * a) - (k * y4)))
	elif y2 <= -1.05e-254:
		tmp = t_3
	elif y2 <= 4.1e+95:
		tmp = y4 * (y * ((c * y3) - (b * k)))
	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(y4 * Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))))
	t_2 = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))))
	t_3 = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))))
	tmp = 0.0
	if (y2 <= -1.05e+54)
		tmp = t_2;
	elseif (y2 <= -4.6e-52)
		tmp = t_1;
	elseif (y2 <= -2e-94)
		tmp = t_3;
	elseif (y2 <= -2.2e-157)
		tmp = t_1;
	elseif (y2 <= -4e-204)
		tmp = Float64(y * Float64(b * Float64(Float64(x * a) - Float64(k * y4))));
	elseif (y2 <= -1.05e-254)
		tmp = t_3;
	elseif (y2 <= 4.1e+95)
		tmp = Float64(y4 * Float64(y * Float64(Float64(c * y3) - Float64(b * k))));
	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 = y4 * (y1 * ((k * y2) - (j * y3)));
	t_2 = c * (y2 * ((x * y0) - (t * y4)));
	t_3 = i * (y5 * ((y * k) - (t * j)));
	tmp = 0.0;
	if (y2 <= -1.05e+54)
		tmp = t_2;
	elseif (y2 <= -4.6e-52)
		tmp = t_1;
	elseif (y2 <= -2e-94)
		tmp = t_3;
	elseif (y2 <= -2.2e-157)
		tmp = t_1;
	elseif (y2 <= -4e-204)
		tmp = y * (b * ((x * a) - (k * y4)));
	elseif (y2 <= -1.05e-254)
		tmp = t_3;
	elseif (y2 <= 4.1e+95)
		tmp = y4 * (y * ((c * y3) - (b * k)));
	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[(y4 * N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -1.05e+54], t$95$2, If[LessEqual[y2, -4.6e-52], t$95$1, If[LessEqual[y2, -2e-94], t$95$3, If[LessEqual[y2, -2.2e-157], t$95$1, If[LessEqual[y2, -4e-204], N[(y * N[(b * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1.05e-254], t$95$3, If[LessEqual[y2, 4.1e+95], N[(y4 * N[(y * N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y2 < -1.04999999999999993e54 or 4.09999999999999986e95 < y2

   1. Initial program 20.8%

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

   3. Simplified 20.8%

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

   4. Taylor expanded in y2 around inf 54.2%

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

   5. Taylor expanded in c around inf 60.9%

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

   if -1.04999999999999993e54 < y2 < -4.59999999999999989e-52 or -1.9999999999999999e-94 < y2 < -2.2000000000000001e-157

   1. Initial program 24.1%

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

   3. Simplified 24.1%

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

   4. Taylor expanded in y4 around inf 43.7%

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

   5. Taylor expanded in y1 around inf 50.9%

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

   if -4.59999999999999989e-52 < y2 < -1.9999999999999999e-94 or -4e-204 < y2 < -1.04999999999999998e-254

   1. Initial program 22.5%

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

   3. Simplified 29.9%

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

   4. Taylor expanded in y5 around inf 67.4%

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

      1. mul-1-neg 67.4%

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

      2. mul-1-neg 67.4%

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

      3. mul-1-neg 67.4%

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

      4. sub-neg 67.4%

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

      5. sub-neg 67.4%

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

   6. Simplified 67.4%

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

   7. Taylor expanded in i around inf 52.9%

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

   if -2.2000000000000001e-157 < y2 < -4e-204

   1. Initial program 49.9%

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

   3. Simplified 58.2%

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

   4. Taylor expanded in y around inf 58.4%

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

      1. mul-1-neg 58.4%

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

   6. Simplified 58.4%

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

   7. Taylor expanded in b around inf 59.3%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 59.3%

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

   9. Simplified 59.3%

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

   if -1.04999999999999998e-254 < y2 < 4.09999999999999986e95

   1. Initial program 23.7%

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

   3. Simplified 30.9%

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

   4. Taylor expanded in y around inf 44.1%

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

      1. mul-1-neg 44.1%

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

   6. Simplified 44.1%

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

   7. Taylor expanded in y4 around inf 49.7%

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

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.05 \cdot 10^{+54}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -4.6 \cdot 10^{-52}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq -2 \cdot 10^{-94}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq -2.2 \cdot 10^{-157}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq -4 \cdot 10^{-204}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -1.05 \cdot 10^{-254}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq 4.1 \cdot 10^{+95}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \end{array} \]

Alternative 16: 32.4% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ t_2 := c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ t_3 := i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{if}\;y2 \leq -3.75 \cdot 10^{+53}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y2 \leq -4.3 \cdot 10^{-52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq -2.2 \cdot 10^{-94}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y2 \leq -3.4 \cdot 10^{-156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq -3.8 \cdot 10^{-201}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y2 \leq -5 \cdot 10^{-253}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y2 \leq 1.75 \cdot 10^{+105}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y4 (* y1 (- (* k y2) (* j y3)))))
        (t_2 (* c (* y2 (- (* x y0) (* t y4)))))
        (t_3 (* i (* y5 (- (* y k) (* t j))))))
   (if (<= y2 -3.75e+53)
     t_2
     (if (<= y2 -4.3e-52)
       t_1
       (if (<= y2 -2.2e-94)
         t_3
         (if (<= y2 -3.4e-156)
           t_1
           (if (<= y2 -3.8e-201)
             (* y4 (* b (- (* t j) (* y k))))
             (if (<= y2 -5e-253)
               t_3
               (if (<= y2 1.75e+105)
                 (* y4 (* y (- (* c y3) (* b k))))
                 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 = y4 * (y1 * ((k * y2) - (j * y3)));
	double t_2 = c * (y2 * ((x * y0) - (t * y4)));
	double t_3 = i * (y5 * ((y * k) - (t * j)));
	double tmp;
	if (y2 <= -3.75e+53) {
		tmp = t_2;
	} else if (y2 <= -4.3e-52) {
		tmp = t_1;
	} else if (y2 <= -2.2e-94) {
		tmp = t_3;
	} else if (y2 <= -3.4e-156) {
		tmp = t_1;
	} else if (y2 <= -3.8e-201) {
		tmp = y4 * (b * ((t * j) - (y * k)));
	} else if (y2 <= -5e-253) {
		tmp = t_3;
	} else if (y2 <= 1.75e+105) {
		tmp = y4 * (y * ((c * y3) - (b * k)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y4 * (y1 * ((k * y2) - (j * y3)))
    t_2 = c * (y2 * ((x * y0) - (t * y4)))
    t_3 = i * (y5 * ((y * k) - (t * j)))
    if (y2 <= (-3.75d+53)) then
        tmp = t_2
    else if (y2 <= (-4.3d-52)) then
        tmp = t_1
    else if (y2 <= (-2.2d-94)) then
        tmp = t_3
    else if (y2 <= (-3.4d-156)) then
        tmp = t_1
    else if (y2 <= (-3.8d-201)) then
        tmp = y4 * (b * ((t * j) - (y * k)))
    else if (y2 <= (-5d-253)) then
        tmp = t_3
    else if (y2 <= 1.75d+105) then
        tmp = y4 * (y * ((c * y3) - (b * k)))
    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 = y4 * (y1 * ((k * y2) - (j * y3)));
	double t_2 = c * (y2 * ((x * y0) - (t * y4)));
	double t_3 = i * (y5 * ((y * k) - (t * j)));
	double tmp;
	if (y2 <= -3.75e+53) {
		tmp = t_2;
	} else if (y2 <= -4.3e-52) {
		tmp = t_1;
	} else if (y2 <= -2.2e-94) {
		tmp = t_3;
	} else if (y2 <= -3.4e-156) {
		tmp = t_1;
	} else if (y2 <= -3.8e-201) {
		tmp = y4 * (b * ((t * j) - (y * k)));
	} else if (y2 <= -5e-253) {
		tmp = t_3;
	} else if (y2 <= 1.75e+105) {
		tmp = y4 * (y * ((c * y3) - (b * k)));
	} 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 = y4 * (y1 * ((k * y2) - (j * y3)))
	t_2 = c * (y2 * ((x * y0) - (t * y4)))
	t_3 = i * (y5 * ((y * k) - (t * j)))
	tmp = 0
	if y2 <= -3.75e+53:
		tmp = t_2
	elif y2 <= -4.3e-52:
		tmp = t_1
	elif y2 <= -2.2e-94:
		tmp = t_3
	elif y2 <= -3.4e-156:
		tmp = t_1
	elif y2 <= -3.8e-201:
		tmp = y4 * (b * ((t * j) - (y * k)))
	elif y2 <= -5e-253:
		tmp = t_3
	elif y2 <= 1.75e+105:
		tmp = y4 * (y * ((c * y3) - (b * k)))
	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(y4 * Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))))
	t_2 = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))))
	t_3 = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))))
	tmp = 0.0
	if (y2 <= -3.75e+53)
		tmp = t_2;
	elseif (y2 <= -4.3e-52)
		tmp = t_1;
	elseif (y2 <= -2.2e-94)
		tmp = t_3;
	elseif (y2 <= -3.4e-156)
		tmp = t_1;
	elseif (y2 <= -3.8e-201)
		tmp = Float64(y4 * Float64(b * Float64(Float64(t * j) - Float64(y * k))));
	elseif (y2 <= -5e-253)
		tmp = t_3;
	elseif (y2 <= 1.75e+105)
		tmp = Float64(y4 * Float64(y * Float64(Float64(c * y3) - Float64(b * k))));
	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 = y4 * (y1 * ((k * y2) - (j * y3)));
	t_2 = c * (y2 * ((x * y0) - (t * y4)));
	t_3 = i * (y5 * ((y * k) - (t * j)));
	tmp = 0.0;
	if (y2 <= -3.75e+53)
		tmp = t_2;
	elseif (y2 <= -4.3e-52)
		tmp = t_1;
	elseif (y2 <= -2.2e-94)
		tmp = t_3;
	elseif (y2 <= -3.4e-156)
		tmp = t_1;
	elseif (y2 <= -3.8e-201)
		tmp = y4 * (b * ((t * j) - (y * k)));
	elseif (y2 <= -5e-253)
		tmp = t_3;
	elseif (y2 <= 1.75e+105)
		tmp = y4 * (y * ((c * y3) - (b * k)));
	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[(y4 * N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -3.75e+53], t$95$2, If[LessEqual[y2, -4.3e-52], t$95$1, If[LessEqual[y2, -2.2e-94], t$95$3, If[LessEqual[y2, -3.4e-156], t$95$1, If[LessEqual[y2, -3.8e-201], N[(y4 * N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -5e-253], t$95$3, If[LessEqual[y2, 1.75e+105], N[(y4 * N[(y * N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y2 < -3.7499999999999999e53 or 1.74999999999999996e105 < y2

   1. Initial program 20.8%

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

   3. Simplified 20.8%

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

   4. Taylor expanded in y2 around inf 54.2%

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

   5. Taylor expanded in c around inf 60.9%

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

   if -3.7499999999999999e53 < y2 < -4.3000000000000003e-52 or -2.20000000000000001e-94 < y2 < -3.3999999999999999e-156

   1. Initial program 25.3%

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

   3. Simplified 25.3%

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

   4. Taylor expanded in y4 around inf 40.8%

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

   5. Taylor expanded in y1 around inf 48.5%

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

   if -4.3000000000000003e-52 < y2 < -2.20000000000000001e-94 or -3.8e-201 < y2 < -4.99999999999999971e-253

   1. Initial program 22.5%

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

   3. Simplified 29.9%

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

   4. Taylor expanded in y5 around inf 67.4%

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

      1. mul-1-neg 67.4%

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

      2. mul-1-neg 67.4%

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

      3. mul-1-neg 67.4%

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

      4. sub-neg 67.4%

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

      5. sub-neg 67.4%

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

   6. Simplified 67.4%

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

   7. Taylor expanded in i around inf 52.9%

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

   if -3.3999999999999999e-156 < y2 < -3.8e-201

   1. Initial program 42.7%

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

   3. Simplified 42.7%

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

   4. Taylor expanded in y4 around inf 50.1%

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

   5. Taylor expanded in b around inf 71.8%

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

   if -4.99999999999999971e-253 < y2 < 1.74999999999999996e105

   1. Initial program 23.7%

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

   3. Simplified 30.9%

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

   4. Taylor expanded in y around inf 44.1%

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

      1. mul-1-neg 44.1%

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

   6. Simplified 44.1%

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

   7. Taylor expanded in y4 around inf 49.7%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -3.75 \cdot 10^{+53}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -4.3 \cdot 10^{-52}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq -2.2 \cdot 10^{-94}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq -3.4 \cdot 10^{-156}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq -3.8 \cdot 10^{-201}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y2 \leq -5 \cdot 10^{-253}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq 1.75 \cdot 10^{+105}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \end{array} \]

Alternative 17: 32.3% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{if}\;y2 \leq -6.5 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq -9 \cdot 10^{-67}:\\ \;\;\;\;y2 \cdot \left(y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;y2 \leq -3.2 \cdot 10^{-129}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq -1.5 \cdot 10^{-156}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq -1.06 \cdot 10^{-206}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y2 \leq -8.5 \cdot 10^{-254}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq 8 \cdot 10^{+104}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y2 (- (* x y0) (* t y4))))))
   (if (<= y2 -6.5e+54)
     t_1
     (if (<= y2 -9e-67)
       (* y2 (* y1 (- (* k y4) (* x a))))
       (if (<= y2 -3.2e-129)
         (* y (* a (- (* x b) (* y3 y5))))
         (if (<= y2 -1.5e-156)
           (* y4 (* y1 (- (* k y2) (* j y3))))
           (if (<= y2 -1.06e-206)
             (* y4 (* b (- (* t j) (* y k))))
             (if (<= y2 -8.5e-254)
               (* i (* y5 (- (* y k) (* t j))))
               (if (<= y2 8e+104)
                 (* y4 (* y (- (* c y3) (* b k))))
                 t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y2 * ((x * y0) - (t * y4)));
	double tmp;
	if (y2 <= -6.5e+54) {
		tmp = t_1;
	} else if (y2 <= -9e-67) {
		tmp = y2 * (y1 * ((k * y4) - (x * a)));
	} else if (y2 <= -3.2e-129) {
		tmp = y * (a * ((x * b) - (y3 * y5)));
	} else if (y2 <= -1.5e-156) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (y2 <= -1.06e-206) {
		tmp = y4 * (b * ((t * j) - (y * k)));
	} else if (y2 <= -8.5e-254) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (y2 <= 8e+104) {
		tmp = y4 * (y * ((c * y3) - (b * k)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (y2 * ((x * y0) - (t * y4)))
    if (y2 <= (-6.5d+54)) then
        tmp = t_1
    else if (y2 <= (-9d-67)) then
        tmp = y2 * (y1 * ((k * y4) - (x * a)))
    else if (y2 <= (-3.2d-129)) then
        tmp = y * (a * ((x * b) - (y3 * y5)))
    else if (y2 <= (-1.5d-156)) then
        tmp = y4 * (y1 * ((k * y2) - (j * y3)))
    else if (y2 <= (-1.06d-206)) then
        tmp = y4 * (b * ((t * j) - (y * k)))
    else if (y2 <= (-8.5d-254)) then
        tmp = i * (y5 * ((y * k) - (t * j)))
    else if (y2 <= 8d+104) then
        tmp = y4 * (y * ((c * y3) - (b * k)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y2 * ((x * y0) - (t * y4)));
	double tmp;
	if (y2 <= -6.5e+54) {
		tmp = t_1;
	} else if (y2 <= -9e-67) {
		tmp = y2 * (y1 * ((k * y4) - (x * a)));
	} else if (y2 <= -3.2e-129) {
		tmp = y * (a * ((x * b) - (y3 * y5)));
	} else if (y2 <= -1.5e-156) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (y2 <= -1.06e-206) {
		tmp = y4 * (b * ((t * j) - (y * k)));
	} else if (y2 <= -8.5e-254) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (y2 <= 8e+104) {
		tmp = y4 * (y * ((c * y3) - (b * k)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (y2 * ((x * y0) - (t * y4)))
	tmp = 0
	if y2 <= -6.5e+54:
		tmp = t_1
	elif y2 <= -9e-67:
		tmp = y2 * (y1 * ((k * y4) - (x * a)))
	elif y2 <= -3.2e-129:
		tmp = y * (a * ((x * b) - (y3 * y5)))
	elif y2 <= -1.5e-156:
		tmp = y4 * (y1 * ((k * y2) - (j * y3)))
	elif y2 <= -1.06e-206:
		tmp = y4 * (b * ((t * j) - (y * k)))
	elif y2 <= -8.5e-254:
		tmp = i * (y5 * ((y * k) - (t * j)))
	elif y2 <= 8e+104:
		tmp = y4 * (y * ((c * y3) - (b * k)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))))
	tmp = 0.0
	if (y2 <= -6.5e+54)
		tmp = t_1;
	elseif (y2 <= -9e-67)
		tmp = Float64(y2 * Float64(y1 * Float64(Float64(k * y4) - Float64(x * a))));
	elseif (y2 <= -3.2e-129)
		tmp = Float64(y * Float64(a * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (y2 <= -1.5e-156)
		tmp = Float64(y4 * Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif (y2 <= -1.06e-206)
		tmp = Float64(y4 * Float64(b * Float64(Float64(t * j) - Float64(y * k))));
	elseif (y2 <= -8.5e-254)
		tmp = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))));
	elseif (y2 <= 8e+104)
		tmp = Float64(y4 * Float64(y * Float64(Float64(c * y3) - Float64(b * k))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (y2 * ((x * y0) - (t * y4)));
	tmp = 0.0;
	if (y2 <= -6.5e+54)
		tmp = t_1;
	elseif (y2 <= -9e-67)
		tmp = y2 * (y1 * ((k * y4) - (x * a)));
	elseif (y2 <= -3.2e-129)
		tmp = y * (a * ((x * b) - (y3 * y5)));
	elseif (y2 <= -1.5e-156)
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	elseif (y2 <= -1.06e-206)
		tmp = y4 * (b * ((t * j) - (y * k)));
	elseif (y2 <= -8.5e-254)
		tmp = i * (y5 * ((y * k) - (t * j)));
	elseif (y2 <= 8e+104)
		tmp = y4 * (y * ((c * y3) - (b * k)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -6.5e+54], t$95$1, If[LessEqual[y2, -9e-67], N[(y2 * N[(y1 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -3.2e-129], N[(y * N[(a * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1.5e-156], N[(y4 * N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1.06e-206], N[(y4 * N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -8.5e-254], N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 8e+104], N[(y4 * N[(y * N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y2 < -6.5e54 or 8e104 < y2

   1. Initial program 20.8%

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

   3. Simplified 20.8%

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

   4. Taylor expanded in y2 around inf 54.2%

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

   5. Taylor expanded in c around inf 60.9%

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

   if -6.5e54 < y2 < -9.00000000000000031e-67

   1. Initial program 24.9%

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

   3. Simplified 24.9%

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

   4. Taylor expanded in y2 around inf 41.7%

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

   5. Taylor expanded in y1 around inf 45.4%

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

      1. +-commutative 45.4%

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

      2. mul-1-neg 45.4%

         \[\leadsto \left(y1 \cdot \left(k \cdot y4 + \color{blue}{\left(-a \cdot x\right)}\right)\right) \cdot y2 \]

      3. unsub-neg 45.4%

         \[\leadsto \left(y1 \cdot \color{blue}{\left(k \cdot y4 - a \cdot x\right)}\right) \cdot y2 \]

      4. *-commutative 45.4%

         \[\leadsto \left(y1 \cdot \left(\color{blue}{y4 \cdot k} - a \cdot x\right)\right) \cdot y2 \]

   7. Simplified 45.4%

      \[\leadsto \color{blue}{\left(y1 \cdot \left(y4 \cdot k - a \cdot x\right)\right)} \cdot y2 \]

   if -9.00000000000000031e-67 < y2 < -3.2000000000000003e-129

   1. Initial program 22.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 33.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 50.4%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 50.4%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 50.4%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in a around inf 56.6%

      \[\leadsto y \cdot \color{blue}{\left(a \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. +-commutative 56.6%

         \[\leadsto y \cdot \left(a \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      2. mul-1-neg 56.6%

         \[\leadsto y \cdot \left(a \cdot \left(b \cdot x + \color{blue}{\left(-y3 \cdot y5\right)}\right)\right) \]

      3. unsub-neg 56.6%

         \[\leadsto y \cdot \left(a \cdot \color{blue}{\left(b \cdot x - y3 \cdot y5\right)}\right) \]

   9. Simplified 56.6%

      \[\leadsto y \cdot \color{blue}{\left(a \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]

   if -3.2000000000000003e-129 < y2 < -1.5e-156

   1. Initial program 29.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 29.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 50.5%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y1 around inf 60.8%

      \[\leadsto y4 \cdot \color{blue}{\left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} \]

   if -1.5e-156 < y2 < -1.06e-206

   1. Initial program 46.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 46.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 46.2%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in b around inf 69.6%

      \[\leadsto y4 \cdot \color{blue}{\left(\left(t \cdot j - k \cdot y\right) \cdot b\right)} \]

   if -1.06e-206 < y2 < -8.49999999999999963e-254

   1. Initial program 20.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 26.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 60.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 60.3%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 60.3%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 60.3%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 60.3%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 60.3%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 60.3%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in i around inf 53.8%

      \[\leadsto \color{blue}{i \cdot \left(\left(k \cdot y - t \cdot j\right) \cdot y5\right)} \]

   if -8.49999999999999963e-254 < y2 < 8e104

   1. Initial program 23.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 44.1%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 44.1%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 44.1%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in y4 around inf 49.7%

      \[\leadsto \color{blue}{y4 \cdot \left(y \cdot \left(c \cdot y3 - k \cdot b\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -6.5 \cdot 10^{+54}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -9 \cdot 10^{-67}:\\ \;\;\;\;y2 \cdot \left(y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;y2 \leq -3.2 \cdot 10^{-129}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq -1.5 \cdot 10^{-156}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq -1.06 \cdot 10^{-206}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y2 \leq -8.5 \cdot 10^{-254}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq 8 \cdot 10^{+104}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \end{array} \]

Alternative 18: 31.8% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{if}\;y2 \leq -3.35 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq -2.85 \cdot 10^{-65}:\\ \;\;\;\;y2 \cdot \left(y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;y2 \leq -4.6 \cdot 10^{-133}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq -1.5 \cdot 10^{-156}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq -1.8 \cdot 10^{-180}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y2 \leq -6.8 \cdot 10^{-281}:\\ \;\;\;\;\left(z \cdot a\right) \cdot \left(y1 \cdot y3 - t \cdot b\right)\\ \mathbf{elif}\;y2 \leq 1.6 \cdot 10^{+102}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y2 (- (* x y0) (* t y4))))))
   (if (<= y2 -3.35e+55)
     t_1
     (if (<= y2 -2.85e-65)
       (* y2 (* y1 (- (* k y4) (* x a))))
       (if (<= y2 -4.6e-133)
         (* y (* a (- (* x b) (* y3 y5))))
         (if (<= y2 -1.5e-156)
           (* y4 (* y1 (- (* k y2) (* j y3))))
           (if (<= y2 -1.8e-180)
             (* y4 (* b (- (* t j) (* y k))))
             (if (<= y2 -6.8e-281)
               (* (* z a) (- (* y1 y3) (* t b)))
               (if (<= y2 1.6e+102)
                 (* y4 (* y (- (* c y3) (* b k))))
                 t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y2 * ((x * y0) - (t * y4)));
	double tmp;
	if (y2 <= -3.35e+55) {
		tmp = t_1;
	} else if (y2 <= -2.85e-65) {
		tmp = y2 * (y1 * ((k * y4) - (x * a)));
	} else if (y2 <= -4.6e-133) {
		tmp = y * (a * ((x * b) - (y3 * y5)));
	} else if (y2 <= -1.5e-156) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (y2 <= -1.8e-180) {
		tmp = y4 * (b * ((t * j) - (y * k)));
	} else if (y2 <= -6.8e-281) {
		tmp = (z * a) * ((y1 * y3) - (t * b));
	} else if (y2 <= 1.6e+102) {
		tmp = y4 * (y * ((c * y3) - (b * k)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (y2 * ((x * y0) - (t * y4)))
    if (y2 <= (-3.35d+55)) then
        tmp = t_1
    else if (y2 <= (-2.85d-65)) then
        tmp = y2 * (y1 * ((k * y4) - (x * a)))
    else if (y2 <= (-4.6d-133)) then
        tmp = y * (a * ((x * b) - (y3 * y5)))
    else if (y2 <= (-1.5d-156)) then
        tmp = y4 * (y1 * ((k * y2) - (j * y3)))
    else if (y2 <= (-1.8d-180)) then
        tmp = y4 * (b * ((t * j) - (y * k)))
    else if (y2 <= (-6.8d-281)) then
        tmp = (z * a) * ((y1 * y3) - (t * b))
    else if (y2 <= 1.6d+102) then
        tmp = y4 * (y * ((c * y3) - (b * k)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y2 * ((x * y0) - (t * y4)));
	double tmp;
	if (y2 <= -3.35e+55) {
		tmp = t_1;
	} else if (y2 <= -2.85e-65) {
		tmp = y2 * (y1 * ((k * y4) - (x * a)));
	} else if (y2 <= -4.6e-133) {
		tmp = y * (a * ((x * b) - (y3 * y5)));
	} else if (y2 <= -1.5e-156) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (y2 <= -1.8e-180) {
		tmp = y4 * (b * ((t * j) - (y * k)));
	} else if (y2 <= -6.8e-281) {
		tmp = (z * a) * ((y1 * y3) - (t * b));
	} else if (y2 <= 1.6e+102) {
		tmp = y4 * (y * ((c * y3) - (b * k)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (y2 * ((x * y0) - (t * y4)))
	tmp = 0
	if y2 <= -3.35e+55:
		tmp = t_1
	elif y2 <= -2.85e-65:
		tmp = y2 * (y1 * ((k * y4) - (x * a)))
	elif y2 <= -4.6e-133:
		tmp = y * (a * ((x * b) - (y3 * y5)))
	elif y2 <= -1.5e-156:
		tmp = y4 * (y1 * ((k * y2) - (j * y3)))
	elif y2 <= -1.8e-180:
		tmp = y4 * (b * ((t * j) - (y * k)))
	elif y2 <= -6.8e-281:
		tmp = (z * a) * ((y1 * y3) - (t * b))
	elif y2 <= 1.6e+102:
		tmp = y4 * (y * ((c * y3) - (b * k)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))))
	tmp = 0.0
	if (y2 <= -3.35e+55)
		tmp = t_1;
	elseif (y2 <= -2.85e-65)
		tmp = Float64(y2 * Float64(y1 * Float64(Float64(k * y4) - Float64(x * a))));
	elseif (y2 <= -4.6e-133)
		tmp = Float64(y * Float64(a * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (y2 <= -1.5e-156)
		tmp = Float64(y4 * Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif (y2 <= -1.8e-180)
		tmp = Float64(y4 * Float64(b * Float64(Float64(t * j) - Float64(y * k))));
	elseif (y2 <= -6.8e-281)
		tmp = Float64(Float64(z * a) * Float64(Float64(y1 * y3) - Float64(t * b)));
	elseif (y2 <= 1.6e+102)
		tmp = Float64(y4 * Float64(y * Float64(Float64(c * y3) - Float64(b * k))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (y2 * ((x * y0) - (t * y4)));
	tmp = 0.0;
	if (y2 <= -3.35e+55)
		tmp = t_1;
	elseif (y2 <= -2.85e-65)
		tmp = y2 * (y1 * ((k * y4) - (x * a)));
	elseif (y2 <= -4.6e-133)
		tmp = y * (a * ((x * b) - (y3 * y5)));
	elseif (y2 <= -1.5e-156)
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	elseif (y2 <= -1.8e-180)
		tmp = y4 * (b * ((t * j) - (y * k)));
	elseif (y2 <= -6.8e-281)
		tmp = (z * a) * ((y1 * y3) - (t * b));
	elseif (y2 <= 1.6e+102)
		tmp = y4 * (y * ((c * y3) - (b * k)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -3.35e+55], t$95$1, If[LessEqual[y2, -2.85e-65], N[(y2 * N[(y1 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -4.6e-133], N[(y * N[(a * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1.5e-156], N[(y4 * N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1.8e-180], N[(y4 * N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -6.8e-281], N[(N[(z * a), $MachinePrecision] * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.6e+102], N[(y4 * N[(y * N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y2 < -3.3499999999999999e55 or 1.6e102 < y2

   1. Initial program 20.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 20.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 54.2%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in c around inf 60.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot x - y4 \cdot t\right) \cdot y2\right)} \]

   if -3.3499999999999999e55 < y2 < -2.8500000000000001e-65

   1. Initial program 24.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 24.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 41.7%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in y1 around inf 45.4%

      \[\leadsto \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)} \cdot y2 \]
   6. Step-by-step derivation

      1. +-commutative 45.4%

         \[\leadsto \left(y1 \cdot \color{blue}{\left(k \cdot y4 + -1 \cdot \left(a \cdot x\right)\right)}\right) \cdot y2 \]

      2. mul-1-neg 45.4%

         \[\leadsto \left(y1 \cdot \left(k \cdot y4 + \color{blue}{\left(-a \cdot x\right)}\right)\right) \cdot y2 \]

      3. unsub-neg 45.4%

         \[\leadsto \left(y1 \cdot \color{blue}{\left(k \cdot y4 - a \cdot x\right)}\right) \cdot y2 \]

      4. *-commutative 45.4%

         \[\leadsto \left(y1 \cdot \left(\color{blue}{y4 \cdot k} - a \cdot x\right)\right) \cdot y2 \]

   7. Simplified 45.4%

      \[\leadsto \color{blue}{\left(y1 \cdot \left(y4 \cdot k - a \cdot x\right)\right)} \cdot y2 \]

   if -2.8500000000000001e-65 < y2 < -4.6000000000000001e-133

   1. Initial program 22.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 33.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 50.4%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 50.4%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 50.4%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in a around inf 56.6%

      \[\leadsto y \cdot \color{blue}{\left(a \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. +-commutative 56.6%

         \[\leadsto y \cdot \left(a \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      2. mul-1-neg 56.6%

         \[\leadsto y \cdot \left(a \cdot \left(b \cdot x + \color{blue}{\left(-y3 \cdot y5\right)}\right)\right) \]

      3. unsub-neg 56.6%

         \[\leadsto y \cdot \left(a \cdot \color{blue}{\left(b \cdot x - y3 \cdot y5\right)}\right) \]

   9. Simplified 56.6%

      \[\leadsto y \cdot \color{blue}{\left(a \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]

   if -4.6000000000000001e-133 < y2 < -1.5e-156

   1. Initial program 29.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 29.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 50.5%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y1 around inf 60.8%

      \[\leadsto y4 \cdot \color{blue}{\left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} \]

   if -1.5e-156 < y2 < -1.8e-180

   1. Initial program 16.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 16.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 33.4%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in b around inf 83.8%

      \[\leadsto y4 \cdot \color{blue}{\left(\left(t \cdot j - k \cdot y\right) \cdot b\right)} \]

   if -1.8e-180 < y2 < -6.8e-281

   1. Initial program 35.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 35.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 53.7%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 53.7%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. associate--l+ 53.7%

         \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \cdot z \]

   6. Simplified 53.7%

      \[\leadsto \color{blue}{-\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   7. Taylor expanded in a around inf 57.7%

      \[\leadsto -\color{blue}{a \cdot \left(z \cdot \left(t \cdot b + -1 \cdot \left(y1 \cdot y3\right)\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 57.7%

         \[\leadsto -a \cdot \color{blue}{\left(\left(t \cdot b + -1 \cdot \left(y1 \cdot y3\right)\right) \cdot z\right)} \]

      2. associate-*r* 57.7%

         \[\leadsto -\color{blue}{\left(a \cdot \left(t \cdot b + -1 \cdot \left(y1 \cdot y3\right)\right)\right) \cdot z} \]

      3. *-commutative 57.7%

         \[\leadsto -\color{blue}{\left(\left(t \cdot b + -1 \cdot \left(y1 \cdot y3\right)\right) \cdot a\right)} \cdot z \]

      4. associate-*l* 54.4%

         \[\leadsto -\color{blue}{\left(t \cdot b + -1 \cdot \left(y1 \cdot y3\right)\right) \cdot \left(a \cdot z\right)} \]

      5. mul-1-neg 54.4%

         \[\leadsto -\left(t \cdot b + \color{blue}{\left(-y1 \cdot y3\right)}\right) \cdot \left(a \cdot z\right) \]

      6. unsub-neg 54.4%

         \[\leadsto -\color{blue}{\left(t \cdot b - y1 \cdot y3\right)} \cdot \left(a \cdot z\right) \]

      7. *-commutative 54.4%

         \[\leadsto -\left(\color{blue}{b \cdot t} - y1 \cdot y3\right) \cdot \left(a \cdot z\right) \]

      8. *-commutative 54.4%

         \[\leadsto -\left(b \cdot t - \color{blue}{y3 \cdot y1}\right) \cdot \left(a \cdot z\right) \]

   9. Simplified 54.4%

      \[\leadsto -\color{blue}{\left(b \cdot t - y3 \cdot y1\right) \cdot \left(a \cdot z\right)} \]

   if -6.8e-281 < y2 < 1.6e102

   1. Initial program 22.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 43.5%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 43.5%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 43.5%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in y4 around inf 49.6%

      \[\leadsto \color{blue}{y4 \cdot \left(y \cdot \left(c \cdot y3 - k \cdot b\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -3.35 \cdot 10^{+55}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -2.85 \cdot 10^{-65}:\\ \;\;\;\;y2 \cdot \left(y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;y2 \leq -4.6 \cdot 10^{-133}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq -1.5 \cdot 10^{-156}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq -1.8 \cdot 10^{-180}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y2 \leq -6.8 \cdot 10^{-281}:\\ \;\;\;\;\left(z \cdot a\right) \cdot \left(y1 \cdot y3 - t \cdot b\right)\\ \mathbf{elif}\;y2 \leq 1.6 \cdot 10^{+102}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \end{array} \]

Alternative 19: 23.0% accurate, 3.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ t_2 := a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{if}\;t \leq -3.05 \cdot 10^{+106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{-253}:\\ \;\;\;\;y \cdot \left(b \cdot \left(k \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{-130}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-66}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k\right)\right)\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+49}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{+120}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i\right)\right)\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+162} \lor \neg \left(t \leq 6.5 \cdot 10^{+265}\right):\\ \;\;\;\;c \cdot \left(y2 \cdot \left(-t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* (* z t) i))) (t_2 (* a (* x (* y b)))))
   (if (<= t -3.05e+106)
     t_1
     (if (<= t -1.12e-253)
       (* y (* b (* k (- y4))))
       (if (<= t 2.95e-130)
         t_2
         (if (<= t 7e-66)
           (* i (* y5 (* y k)))
           (if (<= t 2.9e+49)
             t_2
             (if (<= t 9.2e+120)
               (* c (* z (* t i)))
               (if (or (<= t 1.75e+162) (not (<= t 6.5e+265)))
                 (* c (* y2 (- (* t y4))))
                 t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * ((z * t) * i);
	double t_2 = a * (x * (y * b));
	double tmp;
	if (t <= -3.05e+106) {
		tmp = t_1;
	} else if (t <= -1.12e-253) {
		tmp = y * (b * (k * -y4));
	} else if (t <= 2.95e-130) {
		tmp = t_2;
	} else if (t <= 7e-66) {
		tmp = i * (y5 * (y * k));
	} else if (t <= 2.9e+49) {
		tmp = t_2;
	} else if (t <= 9.2e+120) {
		tmp = c * (z * (t * i));
	} else if ((t <= 1.75e+162) || !(t <= 6.5e+265)) {
		tmp = c * (y2 * -(t * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * ((z * t) * i)
    t_2 = a * (x * (y * b))
    if (t <= (-3.05d+106)) then
        tmp = t_1
    else if (t <= (-1.12d-253)) then
        tmp = y * (b * (k * -y4))
    else if (t <= 2.95d-130) then
        tmp = t_2
    else if (t <= 7d-66) then
        tmp = i * (y5 * (y * k))
    else if (t <= 2.9d+49) then
        tmp = t_2
    else if (t <= 9.2d+120) then
        tmp = c * (z * (t * i))
    else if ((t <= 1.75d+162) .or. (.not. (t <= 6.5d+265))) then
        tmp = c * (y2 * -(t * y4))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * ((z * t) * i);
	double t_2 = a * (x * (y * b));
	double tmp;
	if (t <= -3.05e+106) {
		tmp = t_1;
	} else if (t <= -1.12e-253) {
		tmp = y * (b * (k * -y4));
	} else if (t <= 2.95e-130) {
		tmp = t_2;
	} else if (t <= 7e-66) {
		tmp = i * (y5 * (y * k));
	} else if (t <= 2.9e+49) {
		tmp = t_2;
	} else if (t <= 9.2e+120) {
		tmp = c * (z * (t * i));
	} else if ((t <= 1.75e+162) || !(t <= 6.5e+265)) {
		tmp = c * (y2 * -(t * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * ((z * t) * i)
	t_2 = a * (x * (y * b))
	tmp = 0
	if t <= -3.05e+106:
		tmp = t_1
	elif t <= -1.12e-253:
		tmp = y * (b * (k * -y4))
	elif t <= 2.95e-130:
		tmp = t_2
	elif t <= 7e-66:
		tmp = i * (y5 * (y * k))
	elif t <= 2.9e+49:
		tmp = t_2
	elif t <= 9.2e+120:
		tmp = c * (z * (t * i))
	elif (t <= 1.75e+162) or not (t <= 6.5e+265):
		tmp = c * (y2 * -(t * y4))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(Float64(z * t) * i))
	t_2 = Float64(a * Float64(x * Float64(y * b)))
	tmp = 0.0
	if (t <= -3.05e+106)
		tmp = t_1;
	elseif (t <= -1.12e-253)
		tmp = Float64(y * Float64(b * Float64(k * Float64(-y4))));
	elseif (t <= 2.95e-130)
		tmp = t_2;
	elseif (t <= 7e-66)
		tmp = Float64(i * Float64(y5 * Float64(y * k)));
	elseif (t <= 2.9e+49)
		tmp = t_2;
	elseif (t <= 9.2e+120)
		tmp = Float64(c * Float64(z * Float64(t * i)));
	elseif ((t <= 1.75e+162) || !(t <= 6.5e+265))
		tmp = Float64(c * Float64(y2 * Float64(-Float64(t * y4))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * ((z * t) * i);
	t_2 = a * (x * (y * b));
	tmp = 0.0;
	if (t <= -3.05e+106)
		tmp = t_1;
	elseif (t <= -1.12e-253)
		tmp = y * (b * (k * -y4));
	elseif (t <= 2.95e-130)
		tmp = t_2;
	elseif (t <= 7e-66)
		tmp = i * (y5 * (y * k));
	elseif (t <= 2.9e+49)
		tmp = t_2;
	elseif (t <= 9.2e+120)
		tmp = c * (z * (t * i));
	elseif ((t <= 1.75e+162) || ~((t <= 6.5e+265)))
		tmp = c * (y2 * -(t * y4));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(N[(z * t), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(x * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.05e+106], t$95$1, If[LessEqual[t, -1.12e-253], N[(y * N[(b * N[(k * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.95e-130], t$95$2, If[LessEqual[t, 7e-66], N[(i * N[(y5 * N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.9e+49], t$95$2, If[LessEqual[t, 9.2e+120], N[(c * N[(z * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 1.75e+162], N[Not[LessEqual[t, 6.5e+265]], $MachinePrecision]], N[(c * N[(y2 * (-N[(t * y4), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -3.05e106 or 1.75000000000000009e162 < t < 6.50000000000000034e265

   1. Initial program 16.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 16.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 43.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 43.7%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 43.7%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 43.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in t around -inf 47.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right) \cdot t\right)} \]
   8. Step-by-step derivation

      1. *-commutative 47.4%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot \left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right)\right)} \]

      2. mul-1-neg 47.4%

         \[\leadsto c \cdot \left(t \cdot \left(i \cdot z + \color{blue}{\left(-y4 \cdot y2\right)}\right)\right) \]

      3. unsub-neg 47.4%

         \[\leadsto c \cdot \left(t \cdot \color{blue}{\left(i \cdot z - y4 \cdot y2\right)}\right) \]

   9. Simplified 47.4%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(i \cdot z - y4 \cdot y2\right)\right)} \]

   10. Taylor expanded in i around inf 42.8%

       \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(t \cdot z\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative 42.8%

          \[\leadsto c \cdot \left(i \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

   12. Simplified 42.8%

       \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(z \cdot t\right)\right)} \]

   if -3.05e106 < t < -1.11999999999999993e-253

   1. Initial program 34.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 40.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 49.9%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 49.9%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 49.9%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in b around inf 35.4%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 35.4%

         \[\leadsto y \cdot \left(b \cdot \left(a \cdot x - \color{blue}{y4 \cdot k}\right)\right) \]

   9. Simplified 35.4%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - y4 \cdot k\right)\right)} \]

   10. Taylor expanded in a around 0 33.3%

       \[\leadsto y \cdot \left(b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot y4\right)\right)}\right) \]
   11. Step-by-step derivation

       1. mul-1-neg 33.3%

          \[\leadsto y \cdot \left(b \cdot \color{blue}{\left(-k \cdot y4\right)}\right) \]

       2. distribute-rgt-neg-in 33.3%

          \[\leadsto y \cdot \left(b \cdot \color{blue}{\left(k \cdot \left(-y4\right)\right)}\right) \]

   12. Simplified 33.3%

       \[\leadsto y \cdot \left(b \cdot \color{blue}{\left(k \cdot \left(-y4\right)\right)}\right) \]

   if -1.11999999999999993e-253 < t < 2.9500000000000001e-130 or 7.0000000000000001e-66 < t < 2.9e49

   1. Initial program 15.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 24.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 39.5%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 39.5%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 39.5%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in b around inf 36.7%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 36.7%

         \[\leadsto y \cdot \left(b \cdot \left(a \cdot x - \color{blue}{y4 \cdot k}\right)\right) \]

   9. Simplified 36.7%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - y4 \cdot k\right)\right)} \]

   10. Taylor expanded in x around -inf 33.7%

       \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x\right)\right)} \]
   11. Step-by-step derivation

       1. pow1 33.7%

          \[\leadsto a \cdot \color{blue}{{\left(y \cdot \left(b \cdot x\right)\right)}^{1}} \]

       2. *-commutative 33.7%

          \[\leadsto a \cdot {\left(y \cdot \color{blue}{\left(x \cdot b\right)}\right)}^{1} \]

   12. Applied egg-rr 33.7%

       \[\leadsto a \cdot \color{blue}{{\left(y \cdot \left(x \cdot b\right)\right)}^{1}} \]
   13. Step-by-step derivation

       1. unpow1 33.7%

          \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(x \cdot b\right)\right)} \]

       2. *-commutative 33.7%

          \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot b\right) \cdot y\right)} \]

       3. associate-*l* 33.7%

          \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

   14. Simplified 33.7%

       \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

   if 2.9500000000000001e-130 < t < 7.0000000000000001e-66

   1. Initial program 32.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 42.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 32.4%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 32.4%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 32.4%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 32.4%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 32.4%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 32.4%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 32.4%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in i around inf 43.3%

      \[\leadsto \color{blue}{i \cdot \left(\left(k \cdot y - t \cdot j\right) \cdot y5\right)} \]

   8. Taylor expanded in k around inf 43.3%

      \[\leadsto i \cdot \left(\color{blue}{\left(k \cdot y\right)} \cdot y5\right) \]

   if 2.9e49 < t < 9.1999999999999997e120

   1. Initial program 12.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 12.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 50.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 50.7%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 50.7%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 50.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in t around -inf 38.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right) \cdot t\right)} \]
   8. Step-by-step derivation

      1. *-commutative 38.4%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot \left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right)\right)} \]

      2. mul-1-neg 38.4%

         \[\leadsto c \cdot \left(t \cdot \left(i \cdot z + \color{blue}{\left(-y4 \cdot y2\right)}\right)\right) \]

      3. unsub-neg 38.4%

         \[\leadsto c \cdot \left(t \cdot \color{blue}{\left(i \cdot z - y4 \cdot y2\right)}\right) \]

   9. Simplified 38.4%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(i \cdot z - y4 \cdot y2\right)\right)} \]

   10. Taylor expanded in i around inf 27.0%

       \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 38.9%

          \[\leadsto c \cdot \color{blue}{\left(\left(i \cdot t\right) \cdot z\right)} \]

   12. Simplified 38.9%

       \[\leadsto \color{blue}{c \cdot \left(\left(i \cdot t\right) \cdot z\right)} \]

   if 9.1999999999999997e120 < t < 1.75000000000000009e162 or 6.50000000000000034e265 < t

   1. Initial program 28.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 48.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 48.2%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 48.2%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 48.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in t around -inf 57.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right) \cdot t\right)} \]
   8. Step-by-step derivation

      1. *-commutative 57.3%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot \left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right)\right)} \]

      2. mul-1-neg 57.3%

         \[\leadsto c \cdot \left(t \cdot \left(i \cdot z + \color{blue}{\left(-y4 \cdot y2\right)}\right)\right) \]

      3. unsub-neg 57.3%

         \[\leadsto c \cdot \left(t \cdot \color{blue}{\left(i \cdot z - y4 \cdot y2\right)}\right) \]

   9. Simplified 57.3%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(i \cdot z - y4 \cdot y2\right)\right)} \]

   10. Taylor expanded in i around 0 57.4%

       \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 57.4%

          \[\leadsto \color{blue}{-c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)} \]

       2. distribute-rgt-neg-in 57.4%

          \[\leadsto \color{blue}{c \cdot \left(-y4 \cdot \left(t \cdot y2\right)\right)} \]

       3. associate-*r* 62.1%

          \[\leadsto c \cdot \left(-\color{blue}{\left(y4 \cdot t\right) \cdot y2}\right) \]

       4. distribute-lft-neg-in 62.1%

          \[\leadsto c \cdot \color{blue}{\left(\left(-y4 \cdot t\right) \cdot y2\right)} \]

   12. Simplified 62.1%

       \[\leadsto \color{blue}{c \cdot \left(\left(-y4 \cdot t\right) \cdot y2\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 39.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.05 \cdot 10^{+106}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{-253}:\\ \;\;\;\;y \cdot \left(b \cdot \left(k \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{-130}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-66}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k\right)\right)\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+49}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{+120}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i\right)\right)\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+162} \lor \neg \left(t \leq 6.5 \cdot 10^{+265}\right):\\ \;\;\;\;c \cdot \left(y2 \cdot \left(-t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \end{array} \]

Alternative 20: 22.9% accurate, 3.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ t_2 := a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{if}\;t \leq -2 \cdot 10^{+107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.7 \cdot 10^{-254}:\\ \;\;\;\;y \cdot \left(b \cdot \left(k \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;t \leq 10^{-131}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-58}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k\right)\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+49}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+119}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i\right)\right)\\ \mathbf{elif}\;t \leq 1.66 \cdot 10^{+162}:\\ \;\;\;\;c \cdot \left(\left(t \cdot y2\right) \cdot \left(-y4\right)\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+260}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(-t \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* (* z t) i))) (t_2 (* a (* x (* y b)))))
   (if (<= t -2e+107)
     t_1
     (if (<= t -4.7e-254)
       (* y (* b (* k (- y4))))
       (if (<= t 1e-131)
         t_2
         (if (<= t 7.2e-58)
           (* i (* y5 (* y k)))
           (if (<= t 1.8e+49)
             t_2
             (if (<= t 1.15e+119)
               (* c (* z (* t i)))
               (if (<= t 1.66e+162)
                 (* c (* (* t y2) (- y4)))
                 (if (<= t 2.8e+260) t_1 (* c (* y2 (- (* t y4))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * ((z * t) * i);
	double t_2 = a * (x * (y * b));
	double tmp;
	if (t <= -2e+107) {
		tmp = t_1;
	} else if (t <= -4.7e-254) {
		tmp = y * (b * (k * -y4));
	} else if (t <= 1e-131) {
		tmp = t_2;
	} else if (t <= 7.2e-58) {
		tmp = i * (y5 * (y * k));
	} else if (t <= 1.8e+49) {
		tmp = t_2;
	} else if (t <= 1.15e+119) {
		tmp = c * (z * (t * i));
	} else if (t <= 1.66e+162) {
		tmp = c * ((t * y2) * -y4);
	} else if (t <= 2.8e+260) {
		tmp = t_1;
	} else {
		tmp = c * (y2 * -(t * y4));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * ((z * t) * i)
    t_2 = a * (x * (y * b))
    if (t <= (-2d+107)) then
        tmp = t_1
    else if (t <= (-4.7d-254)) then
        tmp = y * (b * (k * -y4))
    else if (t <= 1d-131) then
        tmp = t_2
    else if (t <= 7.2d-58) then
        tmp = i * (y5 * (y * k))
    else if (t <= 1.8d+49) then
        tmp = t_2
    else if (t <= 1.15d+119) then
        tmp = c * (z * (t * i))
    else if (t <= 1.66d+162) then
        tmp = c * ((t * y2) * -y4)
    else if (t <= 2.8d+260) then
        tmp = t_1
    else
        tmp = c * (y2 * -(t * y4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * ((z * t) * i);
	double t_2 = a * (x * (y * b));
	double tmp;
	if (t <= -2e+107) {
		tmp = t_1;
	} else if (t <= -4.7e-254) {
		tmp = y * (b * (k * -y4));
	} else if (t <= 1e-131) {
		tmp = t_2;
	} else if (t <= 7.2e-58) {
		tmp = i * (y5 * (y * k));
	} else if (t <= 1.8e+49) {
		tmp = t_2;
	} else if (t <= 1.15e+119) {
		tmp = c * (z * (t * i));
	} else if (t <= 1.66e+162) {
		tmp = c * ((t * y2) * -y4);
	} else if (t <= 2.8e+260) {
		tmp = t_1;
	} else {
		tmp = c * (y2 * -(t * y4));
	}
	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 * t) * i)
	t_2 = a * (x * (y * b))
	tmp = 0
	if t <= -2e+107:
		tmp = t_1
	elif t <= -4.7e-254:
		tmp = y * (b * (k * -y4))
	elif t <= 1e-131:
		tmp = t_2
	elif t <= 7.2e-58:
		tmp = i * (y5 * (y * k))
	elif t <= 1.8e+49:
		tmp = t_2
	elif t <= 1.15e+119:
		tmp = c * (z * (t * i))
	elif t <= 1.66e+162:
		tmp = c * ((t * y2) * -y4)
	elif t <= 2.8e+260:
		tmp = t_1
	else:
		tmp = c * (y2 * -(t * y4))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(Float64(z * t) * i))
	t_2 = Float64(a * Float64(x * Float64(y * b)))
	tmp = 0.0
	if (t <= -2e+107)
		tmp = t_1;
	elseif (t <= -4.7e-254)
		tmp = Float64(y * Float64(b * Float64(k * Float64(-y4))));
	elseif (t <= 1e-131)
		tmp = t_2;
	elseif (t <= 7.2e-58)
		tmp = Float64(i * Float64(y5 * Float64(y * k)));
	elseif (t <= 1.8e+49)
		tmp = t_2;
	elseif (t <= 1.15e+119)
		tmp = Float64(c * Float64(z * Float64(t * i)));
	elseif (t <= 1.66e+162)
		tmp = Float64(c * Float64(Float64(t * y2) * Float64(-y4)));
	elseif (t <= 2.8e+260)
		tmp = t_1;
	else
		tmp = Float64(c * Float64(y2 * Float64(-Float64(t * y4))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * ((z * t) * i);
	t_2 = a * (x * (y * b));
	tmp = 0.0;
	if (t <= -2e+107)
		tmp = t_1;
	elseif (t <= -4.7e-254)
		tmp = y * (b * (k * -y4));
	elseif (t <= 1e-131)
		tmp = t_2;
	elseif (t <= 7.2e-58)
		tmp = i * (y5 * (y * k));
	elseif (t <= 1.8e+49)
		tmp = t_2;
	elseif (t <= 1.15e+119)
		tmp = c * (z * (t * i));
	elseif (t <= 1.66e+162)
		tmp = c * ((t * y2) * -y4);
	elseif (t <= 2.8e+260)
		tmp = t_1;
	else
		tmp = c * (y2 * -(t * y4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(N[(z * t), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(x * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2e+107], t$95$1, If[LessEqual[t, -4.7e-254], N[(y * N[(b * N[(k * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e-131], t$95$2, If[LessEqual[t, 7.2e-58], N[(i * N[(y5 * N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.8e+49], t$95$2, If[LessEqual[t, 1.15e+119], N[(c * N[(z * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.66e+162], N[(c * N[(N[(t * y2), $MachinePrecision] * (-y4)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e+260], t$95$1, N[(c * N[(y2 * (-N[(t * y4), $MachinePrecision])), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -1.9999999999999999e107 or 1.66000000000000003e162 < t < 2.7999999999999998e260

   1. Initial program 16.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 16.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 43.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 43.7%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 43.7%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 43.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in t around -inf 47.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right) \cdot t\right)} \]
   8. Step-by-step derivation

      1. *-commutative 47.4%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot \left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right)\right)} \]

      2. mul-1-neg 47.4%

         \[\leadsto c \cdot \left(t \cdot \left(i \cdot z + \color{blue}{\left(-y4 \cdot y2\right)}\right)\right) \]

      3. unsub-neg 47.4%

         \[\leadsto c \cdot \left(t \cdot \color{blue}{\left(i \cdot z - y4 \cdot y2\right)}\right) \]

   9. Simplified 47.4%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(i \cdot z - y4 \cdot y2\right)\right)} \]

   10. Taylor expanded in i around inf 42.8%

       \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(t \cdot z\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative 42.8%

          \[\leadsto c \cdot \left(i \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

   12. Simplified 42.8%

       \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(z \cdot t\right)\right)} \]

   if -1.9999999999999999e107 < t < -4.70000000000000027e-254

   1. Initial program 34.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 40.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 49.9%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 49.9%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 49.9%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in b around inf 35.4%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 35.4%

         \[\leadsto y \cdot \left(b \cdot \left(a \cdot x - \color{blue}{y4 \cdot k}\right)\right) \]

   9. Simplified 35.4%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - y4 \cdot k\right)\right)} \]

   10. Taylor expanded in a around 0 33.3%

       \[\leadsto y \cdot \left(b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot y4\right)\right)}\right) \]
   11. Step-by-step derivation

       1. mul-1-neg 33.3%

          \[\leadsto y \cdot \left(b \cdot \color{blue}{\left(-k \cdot y4\right)}\right) \]

       2. distribute-rgt-neg-in 33.3%

          \[\leadsto y \cdot \left(b \cdot \color{blue}{\left(k \cdot \left(-y4\right)\right)}\right) \]

   12. Simplified 33.3%

       \[\leadsto y \cdot \left(b \cdot \color{blue}{\left(k \cdot \left(-y4\right)\right)}\right) \]

   if -4.70000000000000027e-254 < t < 9.9999999999999999e-132 or 7.20000000000000019e-58 < t < 1.79999999999999998e49

   1. Initial program 15.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 24.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 39.5%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 39.5%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 39.5%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in b around inf 36.7%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 36.7%

         \[\leadsto y \cdot \left(b \cdot \left(a \cdot x - \color{blue}{y4 \cdot k}\right)\right) \]

   9. Simplified 36.7%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - y4 \cdot k\right)\right)} \]

   10. Taylor expanded in x around -inf 33.7%

       \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x\right)\right)} \]
   11. Step-by-step derivation

       1. pow1 33.7%

          \[\leadsto a \cdot \color{blue}{{\left(y \cdot \left(b \cdot x\right)\right)}^{1}} \]

       2. *-commutative 33.7%

          \[\leadsto a \cdot {\left(y \cdot \color{blue}{\left(x \cdot b\right)}\right)}^{1} \]

   12. Applied egg-rr 33.7%

       \[\leadsto a \cdot \color{blue}{{\left(y \cdot \left(x \cdot b\right)\right)}^{1}} \]
   13. Step-by-step derivation

       1. unpow1 33.7%

          \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(x \cdot b\right)\right)} \]

       2. *-commutative 33.7%

          \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot b\right) \cdot y\right)} \]

       3. associate-*l* 33.7%

          \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

   14. Simplified 33.7%

       \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

   if 9.9999999999999999e-132 < t < 7.20000000000000019e-58

   1. Initial program 32.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 42.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 32.4%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 32.4%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 32.4%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 32.4%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 32.4%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 32.4%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 32.4%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in i around inf 43.3%

      \[\leadsto \color{blue}{i \cdot \left(\left(k \cdot y - t \cdot j\right) \cdot y5\right)} \]

   8. Taylor expanded in k around inf 43.3%

      \[\leadsto i \cdot \left(\color{blue}{\left(k \cdot y\right)} \cdot y5\right) \]

   if 1.79999999999999998e49 < t < 1.15e119

   1. Initial program 12.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 12.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 50.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 50.7%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 50.7%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 50.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in t around -inf 38.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right) \cdot t\right)} \]
   8. Step-by-step derivation

      1. *-commutative 38.4%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot \left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right)\right)} \]

      2. mul-1-neg 38.4%

         \[\leadsto c \cdot \left(t \cdot \left(i \cdot z + \color{blue}{\left(-y4 \cdot y2\right)}\right)\right) \]

      3. unsub-neg 38.4%

         \[\leadsto c \cdot \left(t \cdot \color{blue}{\left(i \cdot z - y4 \cdot y2\right)}\right) \]

   9. Simplified 38.4%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(i \cdot z - y4 \cdot y2\right)\right)} \]

   10. Taylor expanded in i around inf 27.0%

       \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 38.9%

          \[\leadsto c \cdot \color{blue}{\left(\left(i \cdot t\right) \cdot z\right)} \]

   12. Simplified 38.9%

       \[\leadsto \color{blue}{c \cdot \left(\left(i \cdot t\right) \cdot z\right)} \]

   if 1.15e119 < t < 1.66000000000000003e162

   1. Initial program 45.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 45.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 37.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 37.2%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 37.2%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 37.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in t around -inf 45.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right) \cdot t\right)} \]
   8. Step-by-step derivation

      1. *-commutative 45.6%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot \left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right)\right)} \]

      2. mul-1-neg 45.6%

         \[\leadsto c \cdot \left(t \cdot \left(i \cdot z + \color{blue}{\left(-y4 \cdot y2\right)}\right)\right) \]

      3. unsub-neg 45.6%

         \[\leadsto c \cdot \left(t \cdot \color{blue}{\left(i \cdot z - y4 \cdot y2\right)}\right) \]

   9. Simplified 45.6%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(i \cdot z - y4 \cdot y2\right)\right)} \]

   10. Taylor expanded in i around 0 45.8%

       \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)\right)} \]

   if 2.7999999999999998e260 < t

   1. Initial program 10.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 10.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 60.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 60.3%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 60.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 60.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in t around -inf 70.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right) \cdot t\right)} \]
   8. Step-by-step derivation

      1. *-commutative 70.3%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot \left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right)\right)} \]

      2. mul-1-neg 70.3%

         \[\leadsto c \cdot \left(t \cdot \left(i \cdot z + \color{blue}{\left(-y4 \cdot y2\right)}\right)\right) \]

      3. unsub-neg 70.3%

         \[\leadsto c \cdot \left(t \cdot \color{blue}{\left(i \cdot z - y4 \cdot y2\right)}\right) \]

   9. Simplified 70.3%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(i \cdot z - y4 \cdot y2\right)\right)} \]

   10. Taylor expanded in i around 0 70.3%

       \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 70.3%

          \[\leadsto \color{blue}{-c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)} \]

       2. distribute-rgt-neg-in 70.3%

          \[\leadsto \color{blue}{c \cdot \left(-y4 \cdot \left(t \cdot y2\right)\right)} \]

       3. associate-*r* 80.0%

          \[\leadsto c \cdot \left(-\color{blue}{\left(y4 \cdot t\right) \cdot y2}\right) \]

       4. distribute-lft-neg-in 80.0%

          \[\leadsto c \cdot \color{blue}{\left(\left(-y4 \cdot t\right) \cdot y2\right)} \]

   12. Simplified 80.0%

       \[\leadsto \color{blue}{c \cdot \left(\left(-y4 \cdot t\right) \cdot y2\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 39.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+107}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{elif}\;t \leq -4.7 \cdot 10^{-254}:\\ \;\;\;\;y \cdot \left(b \cdot \left(k \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;t \leq 10^{-131}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-58}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k\right)\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+49}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+119}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i\right)\right)\\ \mathbf{elif}\;t \leq 1.66 \cdot 10^{+162}:\\ \;\;\;\;c \cdot \left(\left(t \cdot y2\right) \cdot \left(-y4\right)\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+260}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(-t \cdot y4\right)\right)\\ \end{array} \]

Alternative 21: 32.0% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(a \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ t_2 := c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{if}\;y2 \leq -3.1 \cdot 10^{+54}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y2 \leq -7.2 \cdot 10^{-212}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq 2.5 \cdot 10^{-170}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;y2 \leq 5.4 \cdot 10^{-36}:\\ \;\;\;\;y \cdot \left(b \cdot \left(k \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 5.5 \cdot 10^{+28}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 3.4 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y (* a (- (* x b) (* y3 y5)))))
        (t_2 (* c (* y2 (- (* x y0) (* t y4))))))
   (if (<= y2 -3.1e+54)
     t_2
     (if (<= y2 -7.2e-212)
       t_1
       (if (<= y2 2.5e-170)
         (* c (* y (- (* y3 y4) (* x i))))
         (if (<= y2 5.4e-36)
           (* y (* b (* k (- y4))))
           (if (<= y2 5.5e+28)
             (* c (* z (- (* t i) (* y0 y3))))
             (if (<= y2 3.4e+67) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y * (a * ((x * b) - (y3 * y5)));
	double t_2 = c * (y2 * ((x * y0) - (t * y4)));
	double tmp;
	if (y2 <= -3.1e+54) {
		tmp = t_2;
	} else if (y2 <= -7.2e-212) {
		tmp = t_1;
	} else if (y2 <= 2.5e-170) {
		tmp = c * (y * ((y3 * y4) - (x * i)));
	} else if (y2 <= 5.4e-36) {
		tmp = y * (b * (k * -y4));
	} else if (y2 <= 5.5e+28) {
		tmp = c * (z * ((t * i) - (y0 * y3)));
	} else if (y2 <= 3.4e+67) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (a * ((x * b) - (y3 * y5)))
    t_2 = c * (y2 * ((x * y0) - (t * y4)))
    if (y2 <= (-3.1d+54)) then
        tmp = t_2
    else if (y2 <= (-7.2d-212)) then
        tmp = t_1
    else if (y2 <= 2.5d-170) then
        tmp = c * (y * ((y3 * y4) - (x * i)))
    else if (y2 <= 5.4d-36) then
        tmp = y * (b * (k * -y4))
    else if (y2 <= 5.5d+28) then
        tmp = c * (z * ((t * i) - (y0 * y3)))
    else if (y2 <= 3.4d+67) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y * (a * ((x * b) - (y3 * y5)));
	double t_2 = c * (y2 * ((x * y0) - (t * y4)));
	double tmp;
	if (y2 <= -3.1e+54) {
		tmp = t_2;
	} else if (y2 <= -7.2e-212) {
		tmp = t_1;
	} else if (y2 <= 2.5e-170) {
		tmp = c * (y * ((y3 * y4) - (x * i)));
	} else if (y2 <= 5.4e-36) {
		tmp = y * (b * (k * -y4));
	} else if (y2 <= 5.5e+28) {
		tmp = c * (z * ((t * i) - (y0 * y3)));
	} else if (y2 <= 3.4e+67) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y * (a * ((x * b) - (y3 * y5)))
	t_2 = c * (y2 * ((x * y0) - (t * y4)))
	tmp = 0
	if y2 <= -3.1e+54:
		tmp = t_2
	elif y2 <= -7.2e-212:
		tmp = t_1
	elif y2 <= 2.5e-170:
		tmp = c * (y * ((y3 * y4) - (x * i)))
	elif y2 <= 5.4e-36:
		tmp = y * (b * (k * -y4))
	elif y2 <= 5.5e+28:
		tmp = c * (z * ((t * i) - (y0 * y3)))
	elif y2 <= 3.4e+67:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y * Float64(a * Float64(Float64(x * b) - Float64(y3 * y5))))
	t_2 = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))))
	tmp = 0.0
	if (y2 <= -3.1e+54)
		tmp = t_2;
	elseif (y2 <= -7.2e-212)
		tmp = t_1;
	elseif (y2 <= 2.5e-170)
		tmp = Float64(c * Float64(y * Float64(Float64(y3 * y4) - Float64(x * i))));
	elseif (y2 <= 5.4e-36)
		tmp = Float64(y * Float64(b * Float64(k * Float64(-y4))));
	elseif (y2 <= 5.5e+28)
		tmp = Float64(c * Float64(z * Float64(Float64(t * i) - Float64(y0 * y3))));
	elseif (y2 <= 3.4e+67)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y * (a * ((x * b) - (y3 * y5)));
	t_2 = c * (y2 * ((x * y0) - (t * y4)));
	tmp = 0.0;
	if (y2 <= -3.1e+54)
		tmp = t_2;
	elseif (y2 <= -7.2e-212)
		tmp = t_1;
	elseif (y2 <= 2.5e-170)
		tmp = c * (y * ((y3 * y4) - (x * i)));
	elseif (y2 <= 5.4e-36)
		tmp = y * (b * (k * -y4));
	elseif (y2 <= 5.5e+28)
		tmp = c * (z * ((t * i) - (y0 * y3)));
	elseif (y2 <= 3.4e+67)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y * N[(a * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -3.1e+54], t$95$2, If[LessEqual[y2, -7.2e-212], t$95$1, If[LessEqual[y2, 2.5e-170], N[(c * N[(y * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 5.4e-36], N[(y * N[(b * N[(k * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 5.5e+28], N[(c * N[(z * N[(N[(t * i), $MachinePrecision] - N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 3.4e+67], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y2 < -3.0999999999999999e54 or 3.4000000000000002e67 < y2

   1. Initial program 20.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 20.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 51.8%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in c around inf 59.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot x - y4 \cdot t\right) \cdot y2\right)} \]

   if -3.0999999999999999e54 < y2 < -7.2000000000000002e-212 or 5.5000000000000003e28 < y2 < 3.4000000000000002e67

   1. Initial program 26.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 37.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 46.6%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 46.6%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 46.6%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in a around inf 40.6%

      \[\leadsto y \cdot \color{blue}{\left(a \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. +-commutative 40.6%

         \[\leadsto y \cdot \left(a \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      2. mul-1-neg 40.6%

         \[\leadsto y \cdot \left(a \cdot \left(b \cdot x + \color{blue}{\left(-y3 \cdot y5\right)}\right)\right) \]

      3. unsub-neg 40.6%

         \[\leadsto y \cdot \left(a \cdot \color{blue}{\left(b \cdot x - y3 \cdot y5\right)}\right) \]

   9. Simplified 40.6%

      \[\leadsto y \cdot \color{blue}{\left(a \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]

   if -7.2000000000000002e-212 < y2 < 2.50000000000000005e-170

   1. Initial program 28.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 47.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 47.0%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 47.0%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 47.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y around -inf 44.4%

      \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y4 \cdot y3 + -1 \cdot \left(i \cdot x\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 44.4%

         \[\leadsto c \cdot \left(y \cdot \left(y4 \cdot y3 + \color{blue}{\left(-i \cdot x\right)}\right)\right) \]

      2. unsub-neg 44.4%

         \[\leadsto c \cdot \left(y \cdot \color{blue}{\left(y4 \cdot y3 - i \cdot x\right)}\right) \]

      3. *-commutative 44.4%

         \[\leadsto c \cdot \left(y \cdot \left(\color{blue}{y3 \cdot y4} - i \cdot x\right)\right) \]

   9. Simplified 44.4%

      \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y3 \cdot y4 - i \cdot x\right)\right)} \]

   if 2.50000000000000005e-170 < y2 < 5.40000000000000015e-36

   1. Initial program 30.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 45.2%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 45.2%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 45.2%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in b around inf 50.4%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 50.4%

         \[\leadsto y \cdot \left(b \cdot \left(a \cdot x - \color{blue}{y4 \cdot k}\right)\right) \]

   9. Simplified 50.4%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - y4 \cdot k\right)\right)} \]

   10. Taylor expanded in a around 0 50.6%

       \[\leadsto y \cdot \left(b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot y4\right)\right)}\right) \]
   11. Step-by-step derivation

       1. mul-1-neg 50.6%

          \[\leadsto y \cdot \left(b \cdot \color{blue}{\left(-k \cdot y4\right)}\right) \]

       2. distribute-rgt-neg-in 50.6%

          \[\leadsto y \cdot \left(b \cdot \color{blue}{\left(k \cdot \left(-y4\right)\right)}\right) \]

   12. Simplified 50.6%

       \[\leadsto y \cdot \left(b \cdot \color{blue}{\left(k \cdot \left(-y4\right)\right)}\right) \]

   if 5.40000000000000015e-36 < y2 < 5.5000000000000003e28

   1. Initial program 1.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 1.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 51.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 51.0%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 51.0%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 51.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in z around inf 41.9%

      \[\leadsto c \cdot \color{blue}{\left(\left(-1 \cdot \left(y0 \cdot y3\right) - -1 \cdot \left(i \cdot t\right)\right) \cdot z\right)} \]
   8. Step-by-step derivation

      1. *-commutative 41.9%

         \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(y0 \cdot y3\right) - -1 \cdot \left(i \cdot t\right)\right)\right)} \]

      2. cancel-sign-sub-inv 41.9%

         \[\leadsto c \cdot \left(z \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot y3\right) + \left(--1\right) \cdot \left(i \cdot t\right)\right)}\right) \]

      3. metadata-eval 41.9%

         \[\leadsto c \cdot \left(z \cdot \left(-1 \cdot \left(y0 \cdot y3\right) + \color{blue}{1} \cdot \left(i \cdot t\right)\right)\right) \]

      4. *-lft-identity 41.9%

         \[\leadsto c \cdot \left(z \cdot \left(-1 \cdot \left(y0 \cdot y3\right) + \color{blue}{i \cdot t}\right)\right) \]

      5. +-commutative 41.9%

         \[\leadsto c \cdot \left(z \cdot \color{blue}{\left(i \cdot t + -1 \cdot \left(y0 \cdot y3\right)\right)}\right) \]

      6. mul-1-neg 41.9%

         \[\leadsto c \cdot \left(z \cdot \left(i \cdot t + \color{blue}{\left(-y0 \cdot y3\right)}\right)\right) \]

      7. unsub-neg 41.9%

         \[\leadsto c \cdot \left(z \cdot \color{blue}{\left(i \cdot t - y0 \cdot y3\right)}\right) \]

      8. *-commutative 41.9%

         \[\leadsto c \cdot \left(z \cdot \left(i \cdot t - \color{blue}{y3 \cdot y0}\right)\right) \]

   9. Simplified 41.9%

      \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(i \cdot t - y3 \cdot y0\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -3.1 \cdot 10^{+54}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -7.2 \cdot 10^{-212}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 2.5 \cdot 10^{-170}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;y2 \leq 5.4 \cdot 10^{-36}:\\ \;\;\;\;y \cdot \left(b \cdot \left(k \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 5.5 \cdot 10^{+28}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 3.4 \cdot 10^{+67}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \end{array} \]

Alternative 22: 33.2% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(a \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ t_2 := c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{if}\;y2 \leq -2.55 \cdot 10^{+53}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y2 \leq -3.4 \cdot 10^{-212}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq -2.5 \cdot 10^{-240}:\\ \;\;\;\;-\left(t \cdot i\right) \cdot \left(j \cdot y5\right)\\ \mathbf{elif}\;y2 \leq 6 \cdot 10^{-44}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 5.4 \cdot 10^{+29}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 3 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y (* a (- (* x b) (* y3 y5)))))
        (t_2 (* c (* y2 (- (* x y0) (* t y4))))))
   (if (<= y2 -2.55e+53)
     t_2
     (if (<= y2 -3.4e-212)
       t_1
       (if (<= y2 -2.5e-240)
         (- (* (* t i) (* j y5)))
         (if (<= y2 6e-44)
           (* y (* b (- (* x a) (* k y4))))
           (if (<= y2 5.4e+29)
             (* c (* t (- (* z i) (* y2 y4))))
             (if (<= y2 3e+67) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y * (a * ((x * b) - (y3 * y5)));
	double t_2 = c * (y2 * ((x * y0) - (t * y4)));
	double tmp;
	if (y2 <= -2.55e+53) {
		tmp = t_2;
	} else if (y2 <= -3.4e-212) {
		tmp = t_1;
	} else if (y2 <= -2.5e-240) {
		tmp = -((t * i) * (j * y5));
	} else if (y2 <= 6e-44) {
		tmp = y * (b * ((x * a) - (k * y4)));
	} else if (y2 <= 5.4e+29) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (y2 <= 3e+67) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (a * ((x * b) - (y3 * y5)))
    t_2 = c * (y2 * ((x * y0) - (t * y4)))
    if (y2 <= (-2.55d+53)) then
        tmp = t_2
    else if (y2 <= (-3.4d-212)) then
        tmp = t_1
    else if (y2 <= (-2.5d-240)) then
        tmp = -((t * i) * (j * y5))
    else if (y2 <= 6d-44) then
        tmp = y * (b * ((x * a) - (k * y4)))
    else if (y2 <= 5.4d+29) then
        tmp = c * (t * ((z * i) - (y2 * y4)))
    else if (y2 <= 3d+67) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y * (a * ((x * b) - (y3 * y5)));
	double t_2 = c * (y2 * ((x * y0) - (t * y4)));
	double tmp;
	if (y2 <= -2.55e+53) {
		tmp = t_2;
	} else if (y2 <= -3.4e-212) {
		tmp = t_1;
	} else if (y2 <= -2.5e-240) {
		tmp = -((t * i) * (j * y5));
	} else if (y2 <= 6e-44) {
		tmp = y * (b * ((x * a) - (k * y4)));
	} else if (y2 <= 5.4e+29) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (y2 <= 3e+67) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y * (a * ((x * b) - (y3 * y5)))
	t_2 = c * (y2 * ((x * y0) - (t * y4)))
	tmp = 0
	if y2 <= -2.55e+53:
		tmp = t_2
	elif y2 <= -3.4e-212:
		tmp = t_1
	elif y2 <= -2.5e-240:
		tmp = -((t * i) * (j * y5))
	elif y2 <= 6e-44:
		tmp = y * (b * ((x * a) - (k * y4)))
	elif y2 <= 5.4e+29:
		tmp = c * (t * ((z * i) - (y2 * y4)))
	elif y2 <= 3e+67:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y * Float64(a * Float64(Float64(x * b) - Float64(y3 * y5))))
	t_2 = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))))
	tmp = 0.0
	if (y2 <= -2.55e+53)
		tmp = t_2;
	elseif (y2 <= -3.4e-212)
		tmp = t_1;
	elseif (y2 <= -2.5e-240)
		tmp = Float64(-Float64(Float64(t * i) * Float64(j * y5)));
	elseif (y2 <= 6e-44)
		tmp = Float64(y * Float64(b * Float64(Float64(x * a) - Float64(k * y4))));
	elseif (y2 <= 5.4e+29)
		tmp = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (y2 <= 3e+67)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y * (a * ((x * b) - (y3 * y5)));
	t_2 = c * (y2 * ((x * y0) - (t * y4)));
	tmp = 0.0;
	if (y2 <= -2.55e+53)
		tmp = t_2;
	elseif (y2 <= -3.4e-212)
		tmp = t_1;
	elseif (y2 <= -2.5e-240)
		tmp = -((t * i) * (j * y5));
	elseif (y2 <= 6e-44)
		tmp = y * (b * ((x * a) - (k * y4)));
	elseif (y2 <= 5.4e+29)
		tmp = c * (t * ((z * i) - (y2 * y4)));
	elseif (y2 <= 3e+67)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y * N[(a * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -2.55e+53], t$95$2, If[LessEqual[y2, -3.4e-212], t$95$1, If[LessEqual[y2, -2.5e-240], (-N[(N[(t * i), $MachinePrecision] * N[(j * y5), $MachinePrecision]), $MachinePrecision]), If[LessEqual[y2, 6e-44], N[(y * N[(b * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 5.4e+29], N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 3e+67], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y2 < -2.5499999999999999e53 or 3.0000000000000001e67 < y2

   1. Initial program 20.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 20.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 51.8%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in c around inf 59.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot x - y4 \cdot t\right) \cdot y2\right)} \]

   if -2.5499999999999999e53 < y2 < -3.39999999999999998e-212 or 5.4e29 < y2 < 3.0000000000000001e67

   1. Initial program 26.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 37.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 46.6%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 46.6%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 46.6%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in a around inf 40.6%

      \[\leadsto y \cdot \color{blue}{\left(a \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. +-commutative 40.6%

         \[\leadsto y \cdot \left(a \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      2. mul-1-neg 40.6%

         \[\leadsto y \cdot \left(a \cdot \left(b \cdot x + \color{blue}{\left(-y3 \cdot y5\right)}\right)\right) \]

      3. unsub-neg 40.6%

         \[\leadsto y \cdot \left(a \cdot \color{blue}{\left(b \cdot x - y3 \cdot y5\right)}\right) \]

   9. Simplified 40.6%

      \[\leadsto y \cdot \color{blue}{\left(a \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]

   if -3.39999999999999998e-212 < y2 < -2.5000000000000002e-240

   1. Initial program 37.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 50.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 62.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 62.7%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 62.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 62.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 62.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 62.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 62.7%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in i around inf 62.7%

      \[\leadsto \color{blue}{i \cdot \left(\left(k \cdot y - t \cdot j\right) \cdot y5\right)} \]

   8. Taylor expanded in k around 0 62.9%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(t \cdot \left(j \cdot y5\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 62.9%

         \[\leadsto \color{blue}{-i \cdot \left(t \cdot \left(j \cdot y5\right)\right)} \]

      2. associate-*r* 63.0%

         \[\leadsto -\color{blue}{\left(i \cdot t\right) \cdot \left(j \cdot y5\right)} \]

      3. *-commutative 63.0%

         \[\leadsto -\left(i \cdot t\right) \cdot \color{blue}{\left(y5 \cdot j\right)} \]

   10. Simplified 63.0%

       \[\leadsto \color{blue}{-\left(i \cdot t\right) \cdot \left(y5 \cdot j\right)} \]

   if -2.5000000000000002e-240 < y2 < 6.0000000000000005e-44

   1. Initial program 29.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 35.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 46.3%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 46.3%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 46.3%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in b around inf 48.5%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 48.5%

         \[\leadsto y \cdot \left(b \cdot \left(a \cdot x - \color{blue}{y4 \cdot k}\right)\right) \]

   9. Simplified 48.5%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - y4 \cdot k\right)\right)} \]

   if 6.0000000000000005e-44 < y2 < 5.4e29

   1. Initial program 0.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 0.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 46.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 46.9%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 46.9%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 46.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in t around -inf 40.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right) \cdot t\right)} \]
   8. Step-by-step derivation

      1. *-commutative 40.2%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot \left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right)\right)} \]

      2. mul-1-neg 40.2%

         \[\leadsto c \cdot \left(t \cdot \left(i \cdot z + \color{blue}{\left(-y4 \cdot y2\right)}\right)\right) \]

      3. unsub-neg 40.2%

         \[\leadsto c \cdot \left(t \cdot \color{blue}{\left(i \cdot z - y4 \cdot y2\right)}\right) \]

   9. Simplified 40.2%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(i \cdot z - y4 \cdot y2\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -2.55 \cdot 10^{+53}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -3.4 \cdot 10^{-212}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq -2.5 \cdot 10^{-240}:\\ \;\;\;\;-\left(t \cdot i\right) \cdot \left(j \cdot y5\right)\\ \mathbf{elif}\;y2 \leq 6 \cdot 10^{-44}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 5.4 \cdot 10^{+29}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 3 \cdot 10^{+67}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \end{array} \]

Alternative 23: 30.7% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ t_2 := c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{if}\;t \leq -6 \cdot 10^{+29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-20}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+149}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+193}:\\ \;\;\;\;y \cdot \left(b \cdot \left(k \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+271}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(-t \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y (- (* y3 y4) (* x i)))))
        (t_2 (* c (* t (- (* z i) (* y2 y4))))))
   (if (<= t -6e+29)
     t_2
     (if (<= t 1.75e-54)
       t_1
       (if (<= t 4.8e-20)
         (* a (* x (* y b)))
         (if (<= t 7.2e+80)
           t_1
           (if (<= t 5.5e+149)
             t_2
             (if (<= t 1.2e+193)
               (* y (* b (* k (- y4))))
               (if (<= t 2.3e+271)
                 (* c (* (* z t) i))
                 (* c (* y2 (- (* t y4)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y * ((y3 * y4) - (x * i)));
	double t_2 = c * (t * ((z * i) - (y2 * y4)));
	double tmp;
	if (t <= -6e+29) {
		tmp = t_2;
	} else if (t <= 1.75e-54) {
		tmp = t_1;
	} else if (t <= 4.8e-20) {
		tmp = a * (x * (y * b));
	} else if (t <= 7.2e+80) {
		tmp = t_1;
	} else if (t <= 5.5e+149) {
		tmp = t_2;
	} else if (t <= 1.2e+193) {
		tmp = y * (b * (k * -y4));
	} else if (t <= 2.3e+271) {
		tmp = c * ((z * t) * i);
	} else {
		tmp = c * (y2 * -(t * y4));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * (y * ((y3 * y4) - (x * i)))
    t_2 = c * (t * ((z * i) - (y2 * y4)))
    if (t <= (-6d+29)) then
        tmp = t_2
    else if (t <= 1.75d-54) then
        tmp = t_1
    else if (t <= 4.8d-20) then
        tmp = a * (x * (y * b))
    else if (t <= 7.2d+80) then
        tmp = t_1
    else if (t <= 5.5d+149) then
        tmp = t_2
    else if (t <= 1.2d+193) then
        tmp = y * (b * (k * -y4))
    else if (t <= 2.3d+271) then
        tmp = c * ((z * t) * i)
    else
        tmp = c * (y2 * -(t * y4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y * ((y3 * y4) - (x * i)));
	double t_2 = c * (t * ((z * i) - (y2 * y4)));
	double tmp;
	if (t <= -6e+29) {
		tmp = t_2;
	} else if (t <= 1.75e-54) {
		tmp = t_1;
	} else if (t <= 4.8e-20) {
		tmp = a * (x * (y * b));
	} else if (t <= 7.2e+80) {
		tmp = t_1;
	} else if (t <= 5.5e+149) {
		tmp = t_2;
	} else if (t <= 1.2e+193) {
		tmp = y * (b * (k * -y4));
	} else if (t <= 2.3e+271) {
		tmp = c * ((z * t) * i);
	} else {
		tmp = c * (y2 * -(t * y4));
	}
	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) - (x * i)))
	t_2 = c * (t * ((z * i) - (y2 * y4)))
	tmp = 0
	if t <= -6e+29:
		tmp = t_2
	elif t <= 1.75e-54:
		tmp = t_1
	elif t <= 4.8e-20:
		tmp = a * (x * (y * b))
	elif t <= 7.2e+80:
		tmp = t_1
	elif t <= 5.5e+149:
		tmp = t_2
	elif t <= 1.2e+193:
		tmp = y * (b * (k * -y4))
	elif t <= 2.3e+271:
		tmp = c * ((z * t) * i)
	else:
		tmp = c * (y2 * -(t * y4))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(y * Float64(Float64(y3 * y4) - Float64(x * i))))
	t_2 = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))))
	tmp = 0.0
	if (t <= -6e+29)
		tmp = t_2;
	elseif (t <= 1.75e-54)
		tmp = t_1;
	elseif (t <= 4.8e-20)
		tmp = Float64(a * Float64(x * Float64(y * b)));
	elseif (t <= 7.2e+80)
		tmp = t_1;
	elseif (t <= 5.5e+149)
		tmp = t_2;
	elseif (t <= 1.2e+193)
		tmp = Float64(y * Float64(b * Float64(k * Float64(-y4))));
	elseif (t <= 2.3e+271)
		tmp = Float64(c * Float64(Float64(z * t) * i));
	else
		tmp = Float64(c * Float64(y2 * Float64(-Float64(t * y4))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (y * ((y3 * y4) - (x * i)));
	t_2 = c * (t * ((z * i) - (y2 * y4)));
	tmp = 0.0;
	if (t <= -6e+29)
		tmp = t_2;
	elseif (t <= 1.75e-54)
		tmp = t_1;
	elseif (t <= 4.8e-20)
		tmp = a * (x * (y * b));
	elseif (t <= 7.2e+80)
		tmp = t_1;
	elseif (t <= 5.5e+149)
		tmp = t_2;
	elseif (t <= 1.2e+193)
		tmp = y * (b * (k * -y4));
	elseif (t <= 2.3e+271)
		tmp = c * ((z * t) * i);
	else
		tmp = c * (y2 * -(t * y4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(y * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6e+29], t$95$2, If[LessEqual[t, 1.75e-54], t$95$1, If[LessEqual[t, 4.8e-20], N[(a * N[(x * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.2e+80], t$95$1, If[LessEqual[t, 5.5e+149], t$95$2, If[LessEqual[t, 1.2e+193], N[(y * N[(b * N[(k * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3e+271], N[(c * N[(N[(z * t), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(y2 * (-N[(t * y4), $MachinePrecision])), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -5.9999999999999998e29 or 7.1999999999999999e80 < t < 5.49999999999999999e149

   1. Initial program 20.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 20.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 43.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 43.4%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 43.4%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 43.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in t around -inf 49.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right) \cdot t\right)} \]
   8. Step-by-step derivation

      1. *-commutative 49.2%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot \left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right)\right)} \]

      2. mul-1-neg 49.2%

         \[\leadsto c \cdot \left(t \cdot \left(i \cdot z + \color{blue}{\left(-y4 \cdot y2\right)}\right)\right) \]

      3. unsub-neg 49.2%

         \[\leadsto c \cdot \left(t \cdot \color{blue}{\left(i \cdot z - y4 \cdot y2\right)}\right) \]

   9. Simplified 49.2%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(i \cdot z - y4 \cdot y2\right)\right)} \]

   if -5.9999999999999998e29 < t < 1.74999999999999991e-54 or 4.79999999999999986e-20 < t < 7.1999999999999999e80

   1. Initial program 26.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 26.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 37.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 37.7%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 37.7%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 37.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y around -inf 33.2%

      \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y4 \cdot y3 + -1 \cdot \left(i \cdot x\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 33.2%

         \[\leadsto c \cdot \left(y \cdot \left(y4 \cdot y3 + \color{blue}{\left(-i \cdot x\right)}\right)\right) \]

      2. unsub-neg 33.2%

         \[\leadsto c \cdot \left(y \cdot \color{blue}{\left(y4 \cdot y3 - i \cdot x\right)}\right) \]

      3. *-commutative 33.2%

         \[\leadsto c \cdot \left(y \cdot \left(\color{blue}{y3 \cdot y4} - i \cdot x\right)\right) \]

   9. Simplified 33.2%

      \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y3 \cdot y4 - i \cdot x\right)\right)} \]

   if 1.74999999999999991e-54 < t < 4.79999999999999986e-20

   1. Initial program 14.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 58.6%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 58.6%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 58.6%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in b around inf 58.8%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 58.8%

         \[\leadsto y \cdot \left(b \cdot \left(a \cdot x - \color{blue}{y4 \cdot k}\right)\right) \]

   9. Simplified 58.8%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - y4 \cdot k\right)\right)} \]

   10. Taylor expanded in x around -inf 72.1%

       \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x\right)\right)} \]
   11. Step-by-step derivation

       1. pow1 72.1%

          \[\leadsto a \cdot \color{blue}{{\left(y \cdot \left(b \cdot x\right)\right)}^{1}} \]

       2. *-commutative 72.1%

          \[\leadsto a \cdot {\left(y \cdot \color{blue}{\left(x \cdot b\right)}\right)}^{1} \]

   12. Applied egg-rr 72.1%

       \[\leadsto a \cdot \color{blue}{{\left(y \cdot \left(x \cdot b\right)\right)}^{1}} \]
   13. Step-by-step derivation

       1. unpow1 72.1%

          \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(x \cdot b\right)\right)} \]

       2. *-commutative 72.1%

          \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot b\right) \cdot y\right)} \]

       3. associate-*l* 72.1%

          \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

   14. Simplified 72.1%

       \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

   if 5.49999999999999999e149 < t < 1.2e193

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 42.4%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 42.4%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 42.4%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in b around inf 50.3%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 50.3%

         \[\leadsto y \cdot \left(b \cdot \left(a \cdot x - \color{blue}{y4 \cdot k}\right)\right) \]

   9. Simplified 50.3%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - y4 \cdot k\right)\right)} \]

   10. Taylor expanded in a around 0 42.6%

       \[\leadsto y \cdot \left(b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot y4\right)\right)}\right) \]
   11. Step-by-step derivation

       1. mul-1-neg 42.6%

          \[\leadsto y \cdot \left(b \cdot \color{blue}{\left(-k \cdot y4\right)}\right) \]

       2. distribute-rgt-neg-in 42.6%

          \[\leadsto y \cdot \left(b \cdot \color{blue}{\left(k \cdot \left(-y4\right)\right)}\right) \]

   12. Simplified 42.6%

       \[\leadsto y \cdot \left(b \cdot \color{blue}{\left(k \cdot \left(-y4\right)\right)}\right) \]

   if 1.2e193 < t < 2.3000000000000001e271

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 41.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 41.7%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 41.7%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 41.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in t around -inf 42.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right) \cdot t\right)} \]
   8. Step-by-step derivation

      1. *-commutative 42.4%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot \left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right)\right)} \]

      2. mul-1-neg 42.4%

         \[\leadsto c \cdot \left(t \cdot \left(i \cdot z + \color{blue}{\left(-y4 \cdot y2\right)}\right)\right) \]

      3. unsub-neg 42.4%

         \[\leadsto c \cdot \left(t \cdot \color{blue}{\left(i \cdot z - y4 \cdot y2\right)}\right) \]

   9. Simplified 42.4%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(i \cdot z - y4 \cdot y2\right)\right)} \]

   10. Taylor expanded in i around inf 59.6%

       \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(t \cdot z\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative 59.6%

          \[\leadsto c \cdot \left(i \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

   12. Simplified 59.6%

       \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(z \cdot t\right)\right)} \]

   if 2.3000000000000001e271 < t

   1. Initial program 10.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 10.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 60.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 60.3%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 60.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 60.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in t around -inf 70.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right) \cdot t\right)} \]
   8. Step-by-step derivation

      1. *-commutative 70.3%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot \left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right)\right)} \]

      2. mul-1-neg 70.3%

         \[\leadsto c \cdot \left(t \cdot \left(i \cdot z + \color{blue}{\left(-y4 \cdot y2\right)}\right)\right) \]

      3. unsub-neg 70.3%

         \[\leadsto c \cdot \left(t \cdot \color{blue}{\left(i \cdot z - y4 \cdot y2\right)}\right) \]

   9. Simplified 70.3%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(i \cdot z - y4 \cdot y2\right)\right)} \]

   10. Taylor expanded in i around 0 70.3%

       \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 70.3%

          \[\leadsto \color{blue}{-c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)} \]

       2. distribute-rgt-neg-in 70.3%

          \[\leadsto \color{blue}{c \cdot \left(-y4 \cdot \left(t \cdot y2\right)\right)} \]

       3. associate-*r* 80.0%

          \[\leadsto c \cdot \left(-\color{blue}{\left(y4 \cdot t\right) \cdot y2}\right) \]

       4. distribute-lft-neg-in 80.0%

          \[\leadsto c \cdot \color{blue}{\left(\left(-y4 \cdot t\right) \cdot y2\right)} \]

   12. Simplified 80.0%

       \[\leadsto \color{blue}{c \cdot \left(\left(-y4 \cdot t\right) \cdot y2\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+29}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-54}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-20}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+80}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+149}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+193}:\\ \;\;\;\;y \cdot \left(b \cdot \left(k \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+271}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(-t \cdot y4\right)\right)\\ \end{array} \]

Alternative 24: 21.7% accurate, 4.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ t_2 := k \cdot \left(i \cdot \left(-z \cdot y1\right)\right)\\ \mathbf{if}\;y \leq -3.9 \cdot 10^{+164}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-85}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-214}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-251}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+37}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a\right)\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+146}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* (* z t) i))) (t_2 (* k (* i (- (* z y1))))))
   (if (<= y -3.9e+164)
     (* a (* x (* y b)))
     (if (<= y -1.05e-85)
       t_2
       (if (<= y -5.2e-214)
         t_1
         (if (<= y 7e-251)
           t_2
           (if (<= y 4e-6)
             t_1
             (if (<= y 1.2e+37)
               (* y (* b (* x a)))
               (if (<= y 1.75e+146)
                 (* i (* y5 (* y k)))
                 (* c (* y3 (* y y4))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * ((z * t) * i);
	double t_2 = k * (i * -(z * y1));
	double tmp;
	if (y <= -3.9e+164) {
		tmp = a * (x * (y * b));
	} else if (y <= -1.05e-85) {
		tmp = t_2;
	} else if (y <= -5.2e-214) {
		tmp = t_1;
	} else if (y <= 7e-251) {
		tmp = t_2;
	} else if (y <= 4e-6) {
		tmp = t_1;
	} else if (y <= 1.2e+37) {
		tmp = y * (b * (x * a));
	} else if (y <= 1.75e+146) {
		tmp = i * (y5 * (y * k));
	} else {
		tmp = c * (y3 * (y * y4));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * ((z * t) * i)
    t_2 = k * (i * -(z * y1))
    if (y <= (-3.9d+164)) then
        tmp = a * (x * (y * b))
    else if (y <= (-1.05d-85)) then
        tmp = t_2
    else if (y <= (-5.2d-214)) then
        tmp = t_1
    else if (y <= 7d-251) then
        tmp = t_2
    else if (y <= 4d-6) then
        tmp = t_1
    else if (y <= 1.2d+37) then
        tmp = y * (b * (x * a))
    else if (y <= 1.75d+146) then
        tmp = i * (y5 * (y * k))
    else
        tmp = c * (y3 * (y * y4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * ((z * t) * i);
	double t_2 = k * (i * -(z * y1));
	double tmp;
	if (y <= -3.9e+164) {
		tmp = a * (x * (y * b));
	} else if (y <= -1.05e-85) {
		tmp = t_2;
	} else if (y <= -5.2e-214) {
		tmp = t_1;
	} else if (y <= 7e-251) {
		tmp = t_2;
	} else if (y <= 4e-6) {
		tmp = t_1;
	} else if (y <= 1.2e+37) {
		tmp = y * (b * (x * a));
	} else if (y <= 1.75e+146) {
		tmp = i * (y5 * (y * k));
	} else {
		tmp = c * (y3 * (y * y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * ((z * t) * i)
	t_2 = k * (i * -(z * y1))
	tmp = 0
	if y <= -3.9e+164:
		tmp = a * (x * (y * b))
	elif y <= -1.05e-85:
		tmp = t_2
	elif y <= -5.2e-214:
		tmp = t_1
	elif y <= 7e-251:
		tmp = t_2
	elif y <= 4e-6:
		tmp = t_1
	elif y <= 1.2e+37:
		tmp = y * (b * (x * a))
	elif y <= 1.75e+146:
		tmp = i * (y5 * (y * k))
	else:
		tmp = c * (y3 * (y * y4))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(Float64(z * t) * i))
	t_2 = Float64(k * Float64(i * Float64(-Float64(z * y1))))
	tmp = 0.0
	if (y <= -3.9e+164)
		tmp = Float64(a * Float64(x * Float64(y * b)));
	elseif (y <= -1.05e-85)
		tmp = t_2;
	elseif (y <= -5.2e-214)
		tmp = t_1;
	elseif (y <= 7e-251)
		tmp = t_2;
	elseif (y <= 4e-6)
		tmp = t_1;
	elseif (y <= 1.2e+37)
		tmp = Float64(y * Float64(b * Float64(x * a)));
	elseif (y <= 1.75e+146)
		tmp = Float64(i * Float64(y5 * Float64(y * k)));
	else
		tmp = Float64(c * Float64(y3 * Float64(y * y4)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * ((z * t) * i);
	t_2 = k * (i * -(z * y1));
	tmp = 0.0;
	if (y <= -3.9e+164)
		tmp = a * (x * (y * b));
	elseif (y <= -1.05e-85)
		tmp = t_2;
	elseif (y <= -5.2e-214)
		tmp = t_1;
	elseif (y <= 7e-251)
		tmp = t_2;
	elseif (y <= 4e-6)
		tmp = t_1;
	elseif (y <= 1.2e+37)
		tmp = y * (b * (x * a));
	elseif (y <= 1.75e+146)
		tmp = i * (y5 * (y * k));
	else
		tmp = c * (y3 * (y * y4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(N[(z * t), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(i * (-N[(z * y1), $MachinePrecision])), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.9e+164], N[(a * N[(x * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.05e-85], t$95$2, If[LessEqual[y, -5.2e-214], t$95$1, If[LessEqual[y, 7e-251], t$95$2, If[LessEqual[y, 4e-6], t$95$1, If[LessEqual[y, 1.2e+37], N[(y * N[(b * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.75e+146], N[(i * N[(y5 * N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y3 * N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -3.89999999999999985e164

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 27.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 63.1%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 63.1%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 63.1%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in b around inf 46.1%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 46.1%

         \[\leadsto y \cdot \left(b \cdot \left(a \cdot x - \color{blue}{y4 \cdot k}\right)\right) \]

   9. Simplified 46.1%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - y4 \cdot k\right)\right)} \]

   10. Taylor expanded in x around -inf 43.6%

       \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x\right)\right)} \]
   11. Step-by-step derivation

       1. pow1 43.6%

          \[\leadsto a \cdot \color{blue}{{\left(y \cdot \left(b \cdot x\right)\right)}^{1}} \]

       2. *-commutative 43.6%

          \[\leadsto a \cdot {\left(y \cdot \color{blue}{\left(x \cdot b\right)}\right)}^{1} \]

   12. Applied egg-rr 43.6%

       \[\leadsto a \cdot \color{blue}{{\left(y \cdot \left(x \cdot b\right)\right)}^{1}} \]
   13. Step-by-step derivation

       1. unpow1 43.6%

          \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(x \cdot b\right)\right)} \]

       2. *-commutative 43.6%

          \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot b\right) \cdot y\right)} \]

       3. associate-*l* 43.7%

          \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

   14. Simplified 43.7%

       \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

   if -3.89999999999999985e164 < y < -1.05e-85 or -5.2e-214 < y < 7.00000000000000069e-251

   1. Initial program 30.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 40.8%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 40.8%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. associate--l+ 40.8%

         \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \cdot z \]

   6. Simplified 40.8%

      \[\leadsto \color{blue}{-\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   7. Taylor expanded in k around inf 39.8%

      \[\leadsto -\color{blue}{k \cdot \left(\left(i \cdot y1 - y0 \cdot b\right) \cdot z\right)} \]

   8. Taylor expanded in y1 around inf 29.0%

      \[\leadsto -k \cdot \color{blue}{\left(i \cdot \left(y1 \cdot z\right)\right)} \]

   if -1.05e-85 < y < -5.2e-214 or 7.00000000000000069e-251 < y < 3.99999999999999982e-6

   1. Initial program 22.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 22.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 49.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 49.6%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 49.6%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 49.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in t around -inf 32.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right) \cdot t\right)} \]
   8. Step-by-step derivation

      1. *-commutative 32.0%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot \left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right)\right)} \]

      2. mul-1-neg 32.0%

         \[\leadsto c \cdot \left(t \cdot \left(i \cdot z + \color{blue}{\left(-y4 \cdot y2\right)}\right)\right) \]

      3. unsub-neg 32.0%

         \[\leadsto c \cdot \left(t \cdot \color{blue}{\left(i \cdot z - y4 \cdot y2\right)}\right) \]

   9. Simplified 32.0%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(i \cdot z - y4 \cdot y2\right)\right)} \]

   10. Taylor expanded in i around inf 24.6%

       \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(t \cdot z\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative 24.6%

          \[\leadsto c \cdot \left(i \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

   12. Simplified 24.6%

       \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(z \cdot t\right)\right)} \]

   if 3.99999999999999982e-6 < y < 1.2e37

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 38.3%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 38.3%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 38.3%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in b around inf 62.9%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 62.9%

         \[\leadsto y \cdot \left(b \cdot \left(a \cdot x - \color{blue}{y4 \cdot k}\right)\right) \]

   9. Simplified 62.9%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - y4 \cdot k\right)\right)} \]

   10. Taylor expanded in a around inf 51.2%

       \[\leadsto y \cdot \left(b \cdot \color{blue}{\left(a \cdot x\right)}\right) \]

   if 1.2e37 < y < 1.7500000000000001e146

   1. Initial program 13.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 13.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 33.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 33.8%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 33.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 33.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 33.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 33.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 33.8%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in i around inf 42.3%

      \[\leadsto \color{blue}{i \cdot \left(\left(k \cdot y - t \cdot j\right) \cdot y5\right)} \]

   8. Taylor expanded in k around inf 42.4%

      \[\leadsto i \cdot \left(\color{blue}{\left(k \cdot y\right)} \cdot y5\right) \]

   if 1.7500000000000001e146 < y

   1. Initial program 15.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 23.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 69.2%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 69.2%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 69.2%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in y4 around inf 73.4%

      \[\leadsto \color{blue}{y4 \cdot \left(y \cdot \left(c \cdot y3 - k \cdot b\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 76.9%

         \[\leadsto \color{blue}{\left(y4 \cdot y\right) \cdot \left(c \cdot y3 - k \cdot b\right)} \]

      2. *-commutative 76.9%

         \[\leadsto \left(y4 \cdot y\right) \cdot \left(c \cdot y3 - \color{blue}{b \cdot k}\right) \]

   9. Simplified 76.9%

      \[\leadsto \color{blue}{\left(y4 \cdot y\right) \cdot \left(c \cdot y3 - b \cdot k\right)} \]

   10. Taylor expanded in c around inf 58.1%

       \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 65.5%

          \[\leadsto c \cdot \color{blue}{\left(\left(y4 \cdot y\right) \cdot y3\right)} \]

   12. Simplified 65.5%

       \[\leadsto \color{blue}{c \cdot \left(\left(y4 \cdot y\right) \cdot y3\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 35.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+164}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-85}:\\ \;\;\;\;k \cdot \left(i \cdot \left(-z \cdot y1\right)\right)\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-214}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-251}:\\ \;\;\;\;k \cdot \left(i \cdot \left(-z \cdot y1\right)\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-6}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+37}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a\right)\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+146}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4\right)\right)\\ \end{array} \]

Alternative 25: 21.7% accurate, 4.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{if}\;y \leq -1.4 \cdot 10^{+166}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-87}:\\ \;\;\;\;k \cdot \left(\left(z \cdot i\right) \cdot \left(-y1\right)\right)\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-214}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-247}:\\ \;\;\;\;k \cdot \left(i \cdot \left(-z \cdot y1\right)\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+35}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a\right)\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+146}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* (* z t) i))))
   (if (<= y -1.4e+166)
     (* a (* x (* y b)))
     (if (<= y -3.2e-87)
       (* k (* (* z i) (- y1)))
       (if (<= y -1.75e-214)
         t_1
         (if (<= y 1.2e-247)
           (* k (* i (- (* z y1))))
           (if (<= y 3.6e-6)
             t_1
             (if (<= y 7.5e+35)
               (* y (* b (* x a)))
               (if (<= y 1.05e+146)
                 (* i (* y5 (* y k)))
                 (* c (* y3 (* y y4))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * ((z * t) * i);
	double tmp;
	if (y <= -1.4e+166) {
		tmp = a * (x * (y * b));
	} else if (y <= -3.2e-87) {
		tmp = k * ((z * i) * -y1);
	} else if (y <= -1.75e-214) {
		tmp = t_1;
	} else if (y <= 1.2e-247) {
		tmp = k * (i * -(z * y1));
	} else if (y <= 3.6e-6) {
		tmp = t_1;
	} else if (y <= 7.5e+35) {
		tmp = y * (b * (x * a));
	} else if (y <= 1.05e+146) {
		tmp = i * (y5 * (y * k));
	} else {
		tmp = c * (y3 * (y * y4));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((z * t) * i)
    if (y <= (-1.4d+166)) then
        tmp = a * (x * (y * b))
    else if (y <= (-3.2d-87)) then
        tmp = k * ((z * i) * -y1)
    else if (y <= (-1.75d-214)) then
        tmp = t_1
    else if (y <= 1.2d-247) then
        tmp = k * (i * -(z * y1))
    else if (y <= 3.6d-6) then
        tmp = t_1
    else if (y <= 7.5d+35) then
        tmp = y * (b * (x * a))
    else if (y <= 1.05d+146) then
        tmp = i * (y5 * (y * k))
    else
        tmp = c * (y3 * (y * y4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * ((z * t) * i);
	double tmp;
	if (y <= -1.4e+166) {
		tmp = a * (x * (y * b));
	} else if (y <= -3.2e-87) {
		tmp = k * ((z * i) * -y1);
	} else if (y <= -1.75e-214) {
		tmp = t_1;
	} else if (y <= 1.2e-247) {
		tmp = k * (i * -(z * y1));
	} else if (y <= 3.6e-6) {
		tmp = t_1;
	} else if (y <= 7.5e+35) {
		tmp = y * (b * (x * a));
	} else if (y <= 1.05e+146) {
		tmp = i * (y5 * (y * k));
	} else {
		tmp = c * (y3 * (y * y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * ((z * t) * i)
	tmp = 0
	if y <= -1.4e+166:
		tmp = a * (x * (y * b))
	elif y <= -3.2e-87:
		tmp = k * ((z * i) * -y1)
	elif y <= -1.75e-214:
		tmp = t_1
	elif y <= 1.2e-247:
		tmp = k * (i * -(z * y1))
	elif y <= 3.6e-6:
		tmp = t_1
	elif y <= 7.5e+35:
		tmp = y * (b * (x * a))
	elif y <= 1.05e+146:
		tmp = i * (y5 * (y * k))
	else:
		tmp = c * (y3 * (y * y4))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(Float64(z * t) * i))
	tmp = 0.0
	if (y <= -1.4e+166)
		tmp = Float64(a * Float64(x * Float64(y * b)));
	elseif (y <= -3.2e-87)
		tmp = Float64(k * Float64(Float64(z * i) * Float64(-y1)));
	elseif (y <= -1.75e-214)
		tmp = t_1;
	elseif (y <= 1.2e-247)
		tmp = Float64(k * Float64(i * Float64(-Float64(z * y1))));
	elseif (y <= 3.6e-6)
		tmp = t_1;
	elseif (y <= 7.5e+35)
		tmp = Float64(y * Float64(b * Float64(x * a)));
	elseif (y <= 1.05e+146)
		tmp = Float64(i * Float64(y5 * Float64(y * k)));
	else
		tmp = Float64(c * Float64(y3 * Float64(y * y4)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * ((z * t) * i);
	tmp = 0.0;
	if (y <= -1.4e+166)
		tmp = a * (x * (y * b));
	elseif (y <= -3.2e-87)
		tmp = k * ((z * i) * -y1);
	elseif (y <= -1.75e-214)
		tmp = t_1;
	elseif (y <= 1.2e-247)
		tmp = k * (i * -(z * y1));
	elseif (y <= 3.6e-6)
		tmp = t_1;
	elseif (y <= 7.5e+35)
		tmp = y * (b * (x * a));
	elseif (y <= 1.05e+146)
		tmp = i * (y5 * (y * k));
	else
		tmp = c * (y3 * (y * y4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(N[(z * t), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.4e+166], N[(a * N[(x * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.2e-87], N[(k * N[(N[(z * i), $MachinePrecision] * (-y1)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.75e-214], t$95$1, If[LessEqual[y, 1.2e-247], N[(k * N[(i * (-N[(z * y1), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e-6], t$95$1, If[LessEqual[y, 7.5e+35], N[(y * N[(b * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05e+146], N[(i * N[(y5 * N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y3 * N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -1.39999999999999998e166

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 27.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 63.1%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 63.1%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 63.1%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in b around inf 46.1%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 46.1%

         \[\leadsto y \cdot \left(b \cdot \left(a \cdot x - \color{blue}{y4 \cdot k}\right)\right) \]

   9. Simplified 46.1%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - y4 \cdot k\right)\right)} \]

   10. Taylor expanded in x around -inf 43.6%

       \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x\right)\right)} \]
   11. Step-by-step derivation

       1. pow1 43.6%

          \[\leadsto a \cdot \color{blue}{{\left(y \cdot \left(b \cdot x\right)\right)}^{1}} \]

       2. *-commutative 43.6%

          \[\leadsto a \cdot {\left(y \cdot \color{blue}{\left(x \cdot b\right)}\right)}^{1} \]

   12. Applied egg-rr 43.6%

       \[\leadsto a \cdot \color{blue}{{\left(y \cdot \left(x \cdot b\right)\right)}^{1}} \]
   13. Step-by-step derivation

       1. unpow1 43.6%

          \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(x \cdot b\right)\right)} \]

       2. *-commutative 43.6%

          \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot b\right) \cdot y\right)} \]

       3. associate-*l* 43.7%

          \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

   14. Simplified 43.7%

       \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

   if -1.39999999999999998e166 < y < -3.19999999999999979e-87

   1. Initial program 23.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 23.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 33.1%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 33.1%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. associate--l+ 33.1%

         \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \cdot z \]

   6. Simplified 33.1%

      \[\leadsto \color{blue}{-\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   7. Taylor expanded in k around inf 28.9%

      \[\leadsto -\color{blue}{k \cdot \left(\left(i \cdot y1 - y0 \cdot b\right) \cdot z\right)} \]

   8. Taylor expanded in i around inf 22.8%

      \[\leadsto -k \cdot \color{blue}{\left(y1 \cdot \left(i \cdot z\right)\right)} \]

   if -3.19999999999999979e-87 < y < -1.75e-214 or 1.20000000000000005e-247 < y < 3.59999999999999984e-6

   1. Initial program 22.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 22.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 49.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 49.6%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 49.6%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 49.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in t around -inf 32.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right) \cdot t\right)} \]
   8. Step-by-step derivation

      1. *-commutative 32.0%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot \left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right)\right)} \]

      2. mul-1-neg 32.0%

         \[\leadsto c \cdot \left(t \cdot \left(i \cdot z + \color{blue}{\left(-y4 \cdot y2\right)}\right)\right) \]

      3. unsub-neg 32.0%

         \[\leadsto c \cdot \left(t \cdot \color{blue}{\left(i \cdot z - y4 \cdot y2\right)}\right) \]

   9. Simplified 32.0%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(i \cdot z - y4 \cdot y2\right)\right)} \]

   10. Taylor expanded in i around inf 24.6%

       \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(t \cdot z\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative 24.6%

          \[\leadsto c \cdot \left(i \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

   12. Simplified 24.6%

       \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(z \cdot t\right)\right)} \]

   if -1.75e-214 < y < 1.20000000000000005e-247

   1. Initial program 39.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 39.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 51.8%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 51.8%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. associate--l+ 51.8%

         \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \cdot z \]

   6. Simplified 51.8%

      \[\leadsto \color{blue}{-\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   7. Taylor expanded in k around inf 55.2%

      \[\leadsto -\color{blue}{k \cdot \left(\left(i \cdot y1 - y0 \cdot b\right) \cdot z\right)} \]

   8. Taylor expanded in y1 around inf 40.6%

      \[\leadsto -k \cdot \color{blue}{\left(i \cdot \left(y1 \cdot z\right)\right)} \]

   if 3.59999999999999984e-6 < y < 7.4999999999999999e35

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 38.3%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 38.3%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 38.3%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in b around inf 62.9%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 62.9%

         \[\leadsto y \cdot \left(b \cdot \left(a \cdot x - \color{blue}{y4 \cdot k}\right)\right) \]

   9. Simplified 62.9%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - y4 \cdot k\right)\right)} \]

   10. Taylor expanded in a around inf 51.2%

       \[\leadsto y \cdot \left(b \cdot \color{blue}{\left(a \cdot x\right)}\right) \]

   if 7.4999999999999999e35 < y < 1.05e146

   1. Initial program 13.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 13.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 33.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 33.8%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 33.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 33.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 33.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 33.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 33.8%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in i around inf 42.3%

      \[\leadsto \color{blue}{i \cdot \left(\left(k \cdot y - t \cdot j\right) \cdot y5\right)} \]

   8. Taylor expanded in k around inf 42.4%

      \[\leadsto i \cdot \left(\color{blue}{\left(k \cdot y\right)} \cdot y5\right) \]

   if 1.05e146 < y

   1. Initial program 15.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 23.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 69.2%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 69.2%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 69.2%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in y4 around inf 73.4%

      \[\leadsto \color{blue}{y4 \cdot \left(y \cdot \left(c \cdot y3 - k \cdot b\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 76.9%

         \[\leadsto \color{blue}{\left(y4 \cdot y\right) \cdot \left(c \cdot y3 - k \cdot b\right)} \]

      2. *-commutative 76.9%

         \[\leadsto \left(y4 \cdot y\right) \cdot \left(c \cdot y3 - \color{blue}{b \cdot k}\right) \]

   9. Simplified 76.9%

      \[\leadsto \color{blue}{\left(y4 \cdot y\right) \cdot \left(c \cdot y3 - b \cdot k\right)} \]

   10. Taylor expanded in c around inf 58.1%

       \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 65.5%

          \[\leadsto c \cdot \color{blue}{\left(\left(y4 \cdot y\right) \cdot y3\right)} \]

   12. Simplified 65.5%

       \[\leadsto \color{blue}{c \cdot \left(\left(y4 \cdot y\right) \cdot y3\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 36.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+166}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-87}:\\ \;\;\;\;k \cdot \left(\left(z \cdot i\right) \cdot \left(-y1\right)\right)\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-214}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-247}:\\ \;\;\;\;k \cdot \left(i \cdot \left(-z \cdot y1\right)\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-6}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+35}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a\right)\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+146}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4\right)\right)\\ \end{array} \]

Alternative 26: 27.2% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ t_2 := a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{if}\;t \leq -9.5 \cdot 10^{+99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-254}:\\ \;\;\;\;y \cdot \left(b \cdot \left(k \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;t \leq 3.45 \cdot 10^{-125}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-61}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k\right)\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+46}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* t (- (* z i) (* y2 y4))))) (t_2 (* a (* x (* y b)))))
   (if (<= t -9.5e+99)
     t_1
     (if (<= t -5e-254)
       (* y (* b (* k (- y4))))
       (if (<= t 3.45e-125)
         t_2
         (if (<= t 9e-61)
           (* i (* y5 (* y k)))
           (if (<= t 4.6e+46) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (t * ((z * i) - (y2 * y4)));
	double t_2 = a * (x * (y * b));
	double tmp;
	if (t <= -9.5e+99) {
		tmp = t_1;
	} else if (t <= -5e-254) {
		tmp = y * (b * (k * -y4));
	} else if (t <= 3.45e-125) {
		tmp = t_2;
	} else if (t <= 9e-61) {
		tmp = i * (y5 * (y * k));
	} else if (t <= 4.6e+46) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * (t * ((z * i) - (y2 * y4)))
    t_2 = a * (x * (y * b))
    if (t <= (-9.5d+99)) then
        tmp = t_1
    else if (t <= (-5d-254)) then
        tmp = y * (b * (k * -y4))
    else if (t <= 3.45d-125) then
        tmp = t_2
    else if (t <= 9d-61) then
        tmp = i * (y5 * (y * k))
    else if (t <= 4.6d+46) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (t * ((z * i) - (y2 * y4)));
	double t_2 = a * (x * (y * b));
	double tmp;
	if (t <= -9.5e+99) {
		tmp = t_1;
	} else if (t <= -5e-254) {
		tmp = y * (b * (k * -y4));
	} else if (t <= 3.45e-125) {
		tmp = t_2;
	} else if (t <= 9e-61) {
		tmp = i * (y5 * (y * k));
	} else if (t <= 4.6e+46) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (t * ((z * i) - (y2 * y4)))
	t_2 = a * (x * (y * b))
	tmp = 0
	if t <= -9.5e+99:
		tmp = t_1
	elif t <= -5e-254:
		tmp = y * (b * (k * -y4))
	elif t <= 3.45e-125:
		tmp = t_2
	elif t <= 9e-61:
		tmp = i * (y5 * (y * k))
	elif t <= 4.6e+46:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))))
	t_2 = Float64(a * Float64(x * Float64(y * b)))
	tmp = 0.0
	if (t <= -9.5e+99)
		tmp = t_1;
	elseif (t <= -5e-254)
		tmp = Float64(y * Float64(b * Float64(k * Float64(-y4))));
	elseif (t <= 3.45e-125)
		tmp = t_2;
	elseif (t <= 9e-61)
		tmp = Float64(i * Float64(y5 * Float64(y * k)));
	elseif (t <= 4.6e+46)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (t * ((z * i) - (y2 * y4)));
	t_2 = a * (x * (y * b));
	tmp = 0.0;
	if (t <= -9.5e+99)
		tmp = t_1;
	elseif (t <= -5e-254)
		tmp = y * (b * (k * -y4));
	elseif (t <= 3.45e-125)
		tmp = t_2;
	elseif (t <= 9e-61)
		tmp = i * (y5 * (y * k));
	elseif (t <= 4.6e+46)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(x * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.5e+99], t$95$1, If[LessEqual[t, -5e-254], N[(y * N[(b * N[(k * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.45e-125], t$95$2, If[LessEqual[t, 9e-61], N[(i * N[(y5 * N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.6e+46], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -9.49999999999999908e99 or 4.6000000000000001e46 < t

   1. Initial program 18.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 18.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 45.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 45.9%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 45.9%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 45.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in t around -inf 48.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right) \cdot t\right)} \]
   8. Step-by-step derivation

      1. *-commutative 48.1%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot \left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right)\right)} \]

      2. mul-1-neg 48.1%

         \[\leadsto c \cdot \left(t \cdot \left(i \cdot z + \color{blue}{\left(-y4 \cdot y2\right)}\right)\right) \]

      3. unsub-neg 48.1%

         \[\leadsto c \cdot \left(t \cdot \color{blue}{\left(i \cdot z - y4 \cdot y2\right)}\right) \]

   9. Simplified 48.1%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(i \cdot z - y4 \cdot y2\right)\right)} \]

   if -9.49999999999999908e99 < t < -5.0000000000000003e-254

   1. Initial program 34.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 40.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 49.8%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 49.8%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 49.8%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in b around inf 35.0%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 35.0%

         \[\leadsto y \cdot \left(b \cdot \left(a \cdot x - \color{blue}{y4 \cdot k}\right)\right) \]

   9. Simplified 35.0%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - y4 \cdot k\right)\right)} \]

   10. Taylor expanded in a around 0 32.8%

       \[\leadsto y \cdot \left(b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot y4\right)\right)}\right) \]
   11. Step-by-step derivation

       1. mul-1-neg 32.8%

          \[\leadsto y \cdot \left(b \cdot \color{blue}{\left(-k \cdot y4\right)}\right) \]

       2. distribute-rgt-neg-in 32.8%

          \[\leadsto y \cdot \left(b \cdot \color{blue}{\left(k \cdot \left(-y4\right)\right)}\right) \]

   12. Simplified 32.8%

       \[\leadsto y \cdot \left(b \cdot \color{blue}{\left(k \cdot \left(-y4\right)\right)}\right) \]

   if -5.0000000000000003e-254 < t < 3.44999999999999986e-125 or 9e-61 < t < 4.6000000000000001e46

   1. Initial program 15.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 24.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 39.5%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 39.5%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 39.5%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in b around inf 36.7%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 36.7%

         \[\leadsto y \cdot \left(b \cdot \left(a \cdot x - \color{blue}{y4 \cdot k}\right)\right) \]

   9. Simplified 36.7%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - y4 \cdot k\right)\right)} \]

   10. Taylor expanded in x around -inf 33.7%

       \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x\right)\right)} \]
   11. Step-by-step derivation

       1. pow1 33.7%

          \[\leadsto a \cdot \color{blue}{{\left(y \cdot \left(b \cdot x\right)\right)}^{1}} \]

       2. *-commutative 33.7%

          \[\leadsto a \cdot {\left(y \cdot \color{blue}{\left(x \cdot b\right)}\right)}^{1} \]

   12. Applied egg-rr 33.7%

       \[\leadsto a \cdot \color{blue}{{\left(y \cdot \left(x \cdot b\right)\right)}^{1}} \]
   13. Step-by-step derivation

       1. unpow1 33.7%

          \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(x \cdot b\right)\right)} \]

       2. *-commutative 33.7%

          \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot b\right) \cdot y\right)} \]

       3. associate-*l* 33.7%

          \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

   14. Simplified 33.7%

       \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

   if 3.44999999999999986e-125 < t < 9e-61

   1. Initial program 32.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 42.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 32.4%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 32.4%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 32.4%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 32.4%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 32.4%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 32.4%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 32.4%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in i around inf 43.3%

      \[\leadsto \color{blue}{i \cdot \left(\left(k \cdot y - t \cdot j\right) \cdot y5\right)} \]

   8. Taylor expanded in k around inf 43.3%

      \[\leadsto i \cdot \left(\color{blue}{\left(k \cdot y\right)} \cdot y5\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+99}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-254}:\\ \;\;\;\;y \cdot \left(b \cdot \left(k \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;t \leq 3.45 \cdot 10^{-125}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-61}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k\right)\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+46}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \end{array} \]

Alternative 27: 27.5% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -32000000000:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-142}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-232}:\\ \;\;\;\;y \cdot \left(b \cdot \left(k \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-113}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 1.06 \cdot 10^{+206}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -32000000000.0)
   (* a (* y (* x b)))
   (if (<= x -4.5e-142)
     (* c (* z (- (* t i) (* y0 y3))))
     (if (<= x -4.2e-232)
       (* y (* b (* k (- y4))))
       (if (<= x 2.7e-113)
         (* c (* t (- (* z i) (* y2 y4))))
         (if (<= x 1.06e+206)
           (* c (* y (- (* y3 y4) (* x i))))
           (* y (* b (* x a)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -32000000000.0) {
		tmp = a * (y * (x * b));
	} else if (x <= -4.5e-142) {
		tmp = c * (z * ((t * i) - (y0 * y3)));
	} else if (x <= -4.2e-232) {
		tmp = y * (b * (k * -y4));
	} else if (x <= 2.7e-113) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (x <= 1.06e+206) {
		tmp = c * (y * ((y3 * y4) - (x * i)));
	} else {
		tmp = y * (b * (x * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (x <= (-32000000000.0d0)) then
        tmp = a * (y * (x * b))
    else if (x <= (-4.5d-142)) then
        tmp = c * (z * ((t * i) - (y0 * y3)))
    else if (x <= (-4.2d-232)) then
        tmp = y * (b * (k * -y4))
    else if (x <= 2.7d-113) then
        tmp = c * (t * ((z * i) - (y2 * y4)))
    else if (x <= 1.06d+206) then
        tmp = c * (y * ((y3 * y4) - (x * i)))
    else
        tmp = y * (b * (x * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -32000000000.0) {
		tmp = a * (y * (x * b));
	} else if (x <= -4.5e-142) {
		tmp = c * (z * ((t * i) - (y0 * y3)));
	} else if (x <= -4.2e-232) {
		tmp = y * (b * (k * -y4));
	} else if (x <= 2.7e-113) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (x <= 1.06e+206) {
		tmp = c * (y * ((y3 * y4) - (x * i)));
	} else {
		tmp = y * (b * (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if x <= -32000000000.0:
		tmp = a * (y * (x * b))
	elif x <= -4.5e-142:
		tmp = c * (z * ((t * i) - (y0 * y3)))
	elif x <= -4.2e-232:
		tmp = y * (b * (k * -y4))
	elif x <= 2.7e-113:
		tmp = c * (t * ((z * i) - (y2 * y4)))
	elif x <= 1.06e+206:
		tmp = c * (y * ((y3 * y4) - (x * i)))
	else:
		tmp = y * (b * (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (x <= -32000000000.0)
		tmp = Float64(a * Float64(y * Float64(x * b)));
	elseif (x <= -4.5e-142)
		tmp = Float64(c * Float64(z * Float64(Float64(t * i) - Float64(y0 * y3))));
	elseif (x <= -4.2e-232)
		tmp = Float64(y * Float64(b * Float64(k * Float64(-y4))));
	elseif (x <= 2.7e-113)
		tmp = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (x <= 1.06e+206)
		tmp = Float64(c * Float64(y * Float64(Float64(y3 * y4) - Float64(x * i))));
	else
		tmp = Float64(y * Float64(b * Float64(x * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (x <= -32000000000.0)
		tmp = a * (y * (x * b));
	elseif (x <= -4.5e-142)
		tmp = c * (z * ((t * i) - (y0 * y3)));
	elseif (x <= -4.2e-232)
		tmp = y * (b * (k * -y4));
	elseif (x <= 2.7e-113)
		tmp = c * (t * ((z * i) - (y2 * y4)));
	elseif (x <= 1.06e+206)
		tmp = c * (y * ((y3 * y4) - (x * i)));
	else
		tmp = y * (b * (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[x, -32000000000.0], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.5e-142], N[(c * N[(z * N[(N[(t * i), $MachinePrecision] - N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.2e-232], N[(y * N[(b * N[(k * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.7e-113], N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.06e+206], N[(c * N[(y * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(b * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -3.2e10

   1. Initial program 21.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 42.4%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 42.4%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 42.4%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in b around inf 32.1%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 32.1%

         \[\leadsto y \cdot \left(b \cdot \left(a \cdot x - \color{blue}{y4 \cdot k}\right)\right) \]

   9. Simplified 32.1%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - y4 \cdot k\right)\right)} \]

   10. Taylor expanded in x around -inf 32.4%

       \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x\right)\right)} \]

   if -3.2e10 < x < -4.50000000000000019e-142

   1. Initial program 30.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 41.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 41.0%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 41.0%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 41.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in z around inf 51.3%

      \[\leadsto c \cdot \color{blue}{\left(\left(-1 \cdot \left(y0 \cdot y3\right) - -1 \cdot \left(i \cdot t\right)\right) \cdot z\right)} \]
   8. Step-by-step derivation

      1. *-commutative 51.3%

         \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(y0 \cdot y3\right) - -1 \cdot \left(i \cdot t\right)\right)\right)} \]

      2. cancel-sign-sub-inv 51.3%

         \[\leadsto c \cdot \left(z \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot y3\right) + \left(--1\right) \cdot \left(i \cdot t\right)\right)}\right) \]

      3. metadata-eval 51.3%

         \[\leadsto c \cdot \left(z \cdot \left(-1 \cdot \left(y0 \cdot y3\right) + \color{blue}{1} \cdot \left(i \cdot t\right)\right)\right) \]

      4. *-lft-identity 51.3%

         \[\leadsto c \cdot \left(z \cdot \left(-1 \cdot \left(y0 \cdot y3\right) + \color{blue}{i \cdot t}\right)\right) \]

      5. +-commutative 51.3%

         \[\leadsto c \cdot \left(z \cdot \color{blue}{\left(i \cdot t + -1 \cdot \left(y0 \cdot y3\right)\right)}\right) \]

      6. mul-1-neg 51.3%

         \[\leadsto c \cdot \left(z \cdot \left(i \cdot t + \color{blue}{\left(-y0 \cdot y3\right)}\right)\right) \]

      7. unsub-neg 51.3%

         \[\leadsto c \cdot \left(z \cdot \color{blue}{\left(i \cdot t - y0 \cdot y3\right)}\right) \]

      8. *-commutative 51.3%

         \[\leadsto c \cdot \left(z \cdot \left(i \cdot t - \color{blue}{y3 \cdot y0}\right)\right) \]

   9. Simplified 51.3%

      \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(i \cdot t - y3 \cdot y0\right)\right)} \]

   if -4.50000000000000019e-142 < x < -4.2000000000000001e-232

   1. Initial program 25.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 35.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 40.5%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 40.5%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 40.5%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in b around inf 55.9%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 55.9%

         \[\leadsto y \cdot \left(b \cdot \left(a \cdot x - \color{blue}{y4 \cdot k}\right)\right) \]

   9. Simplified 55.9%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - y4 \cdot k\right)\right)} \]

   10. Taylor expanded in a around 0 55.3%

       \[\leadsto y \cdot \left(b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot y4\right)\right)}\right) \]
   11. Step-by-step derivation

       1. mul-1-neg 55.3%

          \[\leadsto y \cdot \left(b \cdot \color{blue}{\left(-k \cdot y4\right)}\right) \]

       2. distribute-rgt-neg-in 55.3%

          \[\leadsto y \cdot \left(b \cdot \color{blue}{\left(k \cdot \left(-y4\right)\right)}\right) \]

   12. Simplified 55.3%

       \[\leadsto y \cdot \left(b \cdot \color{blue}{\left(k \cdot \left(-y4\right)\right)}\right) \]

   if -4.2000000000000001e-232 < x < 2.69999999999999996e-113

   1. Initial program 28.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 47.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 47.2%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 47.2%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 47.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in t around -inf 39.5%

      \[\leadsto \color{blue}{c \cdot \left(\left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right) \cdot t\right)} \]
   8. Step-by-step derivation

      1. *-commutative 39.5%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot \left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right)\right)} \]

      2. mul-1-neg 39.5%

         \[\leadsto c \cdot \left(t \cdot \left(i \cdot z + \color{blue}{\left(-y4 \cdot y2\right)}\right)\right) \]

      3. unsub-neg 39.5%

         \[\leadsto c \cdot \left(t \cdot \color{blue}{\left(i \cdot z - y4 \cdot y2\right)}\right) \]

   9. Simplified 39.5%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(i \cdot z - y4 \cdot y2\right)\right)} \]

   if 2.69999999999999996e-113 < x < 1.0599999999999999e206

   1. Initial program 19.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 19.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 45.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 45.3%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 45.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 45.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y around -inf 34.0%

      \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y4 \cdot y3 + -1 \cdot \left(i \cdot x\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 34.0%

         \[\leadsto c \cdot \left(y \cdot \left(y4 \cdot y3 + \color{blue}{\left(-i \cdot x\right)}\right)\right) \]

      2. unsub-neg 34.0%

         \[\leadsto c \cdot \left(y \cdot \color{blue}{\left(y4 \cdot y3 - i \cdot x\right)}\right) \]

      3. *-commutative 34.0%

         \[\leadsto c \cdot \left(y \cdot \left(\color{blue}{y3 \cdot y4} - i \cdot x\right)\right) \]

   9. Simplified 34.0%

      \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y3 \cdot y4 - i \cdot x\right)\right)} \]

   if 1.0599999999999999e206 < x

   1. Initial program 24.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 36.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 44.2%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 44.2%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 44.2%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in b around inf 52.2%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 52.2%

         \[\leadsto y \cdot \left(b \cdot \left(a \cdot x - \color{blue}{y4 \cdot k}\right)\right) \]

   9. Simplified 52.2%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - y4 \cdot k\right)\right)} \]

   10. Taylor expanded in a around inf 56.3%

       \[\leadsto y \cdot \left(b \cdot \color{blue}{\left(a \cdot x\right)}\right) \]
3. Recombined 6 regimes into one program.

4. Final simplification 40.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -32000000000:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-142}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-232}:\\ \;\;\;\;y \cdot \left(b \cdot \left(k \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-113}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 1.06 \cdot 10^{+206}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a\right)\right)\\ \end{array} \]

Alternative 28: 33.1% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{if}\;y2 \leq -9.4 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq -3.3 \cdot 10^{-212}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq -2.8 \cdot 10^{-240}:\\ \;\;\;\;-\left(t \cdot i\right) \cdot \left(j \cdot y5\right)\\ \mathbf{elif}\;y2 \leq -1.25 \cdot 10^{-254}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 2.8 \cdot 10^{+97}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y2 (- (* x y0) (* t y4))))))
   (if (<= y2 -9.4e+52)
     t_1
     (if (<= y2 -3.3e-212)
       (* y (* a (- (* x b) (* y3 y5))))
       (if (<= y2 -2.8e-240)
         (- (* (* t i) (* j y5)))
         (if (<= y2 -1.25e-254)
           (* y (* b (- (* x a) (* k y4))))
           (if (<= y2 2.8e+97) (* y4 (* y (- (* c y3) (* b k)))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y2 * ((x * y0) - (t * y4)));
	double tmp;
	if (y2 <= -9.4e+52) {
		tmp = t_1;
	} else if (y2 <= -3.3e-212) {
		tmp = y * (a * ((x * b) - (y3 * y5)));
	} else if (y2 <= -2.8e-240) {
		tmp = -((t * i) * (j * y5));
	} else if (y2 <= -1.25e-254) {
		tmp = y * (b * ((x * a) - (k * y4)));
	} else if (y2 <= 2.8e+97) {
		tmp = y4 * (y * ((c * y3) - (b * k)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (y2 * ((x * y0) - (t * y4)))
    if (y2 <= (-9.4d+52)) then
        tmp = t_1
    else if (y2 <= (-3.3d-212)) then
        tmp = y * (a * ((x * b) - (y3 * y5)))
    else if (y2 <= (-2.8d-240)) then
        tmp = -((t * i) * (j * y5))
    else if (y2 <= (-1.25d-254)) then
        tmp = y * (b * ((x * a) - (k * y4)))
    else if (y2 <= 2.8d+97) then
        tmp = y4 * (y * ((c * y3) - (b * k)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y2 * ((x * y0) - (t * y4)));
	double tmp;
	if (y2 <= -9.4e+52) {
		tmp = t_1;
	} else if (y2 <= -3.3e-212) {
		tmp = y * (a * ((x * b) - (y3 * y5)));
	} else if (y2 <= -2.8e-240) {
		tmp = -((t * i) * (j * y5));
	} else if (y2 <= -1.25e-254) {
		tmp = y * (b * ((x * a) - (k * y4)));
	} else if (y2 <= 2.8e+97) {
		tmp = y4 * (y * ((c * y3) - (b * k)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (y2 * ((x * y0) - (t * y4)))
	tmp = 0
	if y2 <= -9.4e+52:
		tmp = t_1
	elif y2 <= -3.3e-212:
		tmp = y * (a * ((x * b) - (y3 * y5)))
	elif y2 <= -2.8e-240:
		tmp = -((t * i) * (j * y5))
	elif y2 <= -1.25e-254:
		tmp = y * (b * ((x * a) - (k * y4)))
	elif y2 <= 2.8e+97:
		tmp = y4 * (y * ((c * y3) - (b * k)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))))
	tmp = 0.0
	if (y2 <= -9.4e+52)
		tmp = t_1;
	elseif (y2 <= -3.3e-212)
		tmp = Float64(y * Float64(a * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (y2 <= -2.8e-240)
		tmp = Float64(-Float64(Float64(t * i) * Float64(j * y5)));
	elseif (y2 <= -1.25e-254)
		tmp = Float64(y * Float64(b * Float64(Float64(x * a) - Float64(k * y4))));
	elseif (y2 <= 2.8e+97)
		tmp = Float64(y4 * Float64(y * Float64(Float64(c * y3) - Float64(b * k))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (y2 * ((x * y0) - (t * y4)));
	tmp = 0.0;
	if (y2 <= -9.4e+52)
		tmp = t_1;
	elseif (y2 <= -3.3e-212)
		tmp = y * (a * ((x * b) - (y3 * y5)));
	elseif (y2 <= -2.8e-240)
		tmp = -((t * i) * (j * y5));
	elseif (y2 <= -1.25e-254)
		tmp = y * (b * ((x * a) - (k * y4)));
	elseif (y2 <= 2.8e+97)
		tmp = y4 * (y * ((c * y3) - (b * k)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -9.4e+52], t$95$1, If[LessEqual[y2, -3.3e-212], N[(y * N[(a * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -2.8e-240], (-N[(N[(t * i), $MachinePrecision] * N[(j * y5), $MachinePrecision]), $MachinePrecision]), If[LessEqual[y2, -1.25e-254], N[(y * N[(b * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.8e+97], N[(y4 * N[(y * N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y2 < -9.3999999999999999e52 or 2.7999999999999999e97 < y2

   1. Initial program 20.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 20.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 54.2%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in c around inf 60.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot x - y4 \cdot t\right) \cdot y2\right)} \]

   if -9.3999999999999999e52 < y2 < -3.3000000000000002e-212

   1. Initial program 28.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 38.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 44.5%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 44.5%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 44.5%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in a around inf 37.9%

      \[\leadsto y \cdot \color{blue}{\left(a \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. +-commutative 37.9%

         \[\leadsto y \cdot \left(a \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      2. mul-1-neg 37.9%

         \[\leadsto y \cdot \left(a \cdot \left(b \cdot x + \color{blue}{\left(-y3 \cdot y5\right)}\right)\right) \]

      3. unsub-neg 37.9%

         \[\leadsto y \cdot \left(a \cdot \color{blue}{\left(b \cdot x - y3 \cdot y5\right)}\right) \]

   9. Simplified 37.9%

      \[\leadsto y \cdot \color{blue}{\left(a \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]

   if -3.3000000000000002e-212 < y2 < -2.7999999999999999e-240

   1. Initial program 37.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 50.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 62.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 62.7%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 62.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 62.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 62.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 62.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 62.7%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in i around inf 62.7%

      \[\leadsto \color{blue}{i \cdot \left(\left(k \cdot y - t \cdot j\right) \cdot y5\right)} \]

   8. Taylor expanded in k around 0 62.9%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(t \cdot \left(j \cdot y5\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 62.9%

         \[\leadsto \color{blue}{-i \cdot \left(t \cdot \left(j \cdot y5\right)\right)} \]

      2. associate-*r* 63.0%

         \[\leadsto -\color{blue}{\left(i \cdot t\right) \cdot \left(j \cdot y5\right)} \]

      3. *-commutative 63.0%

         \[\leadsto -\left(i \cdot t\right) \cdot \color{blue}{\left(y5 \cdot j\right)} \]

   10. Simplified 63.0%

       \[\leadsto \color{blue}{-\left(i \cdot t\right) \cdot \left(y5 \cdot j\right)} \]

   if -2.7999999999999999e-240 < y2 < -1.2500000000000001e-254

   1. Initial program 0.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 0.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 40.9%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 40.9%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 40.9%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in b around inf 41.0%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 41.0%

         \[\leadsto y \cdot \left(b \cdot \left(a \cdot x - \color{blue}{y4 \cdot k}\right)\right) \]

   9. Simplified 41.0%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - y4 \cdot k\right)\right)} \]

   if -1.2500000000000001e-254 < y2 < 2.7999999999999999e97

   1. Initial program 23.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 44.1%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 44.1%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 44.1%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in y4 around inf 49.7%

      \[\leadsto \color{blue}{y4 \cdot \left(y \cdot \left(c \cdot y3 - k \cdot b\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -9.4 \cdot 10^{+52}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -3.3 \cdot 10^{-212}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq -2.8 \cdot 10^{-240}:\\ \;\;\;\;-\left(t \cdot i\right) \cdot \left(j \cdot y5\right)\\ \mathbf{elif}\;y2 \leq -1.25 \cdot 10^{-254}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 2.8 \cdot 10^{+97}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \end{array} \]

Alternative 29: 21.9% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot \left(y2 \cdot \left(-y4\right)\right)\right)\\ \mathbf{if}\;x \leq -5.2 \cdot 10^{+25}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-201}:\\ \;\;\;\;-\left(t \cdot i\right) \cdot \left(j \cdot y5\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-18}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+167}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* t (* y2 (- y4))))))
   (if (<= x -5.2e+25)
     (* a (* y (* x b)))
     (if (<= x -7.5e-201)
       (- (* (* t i) (* j y5)))
       (if (<= x 1.7e-184)
         t_1
         (if (<= x 9e-18)
           (* c (* (* z t) i))
           (if (<= x 5.8e-8)
             t_1
             (if (<= x 1.35e+167)
               (* k (* y (* i y5)))
               (* y (* b (* x a)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (t * (y2 * -y4));
	double tmp;
	if (x <= -5.2e+25) {
		tmp = a * (y * (x * b));
	} else if (x <= -7.5e-201) {
		tmp = -((t * i) * (j * y5));
	} else if (x <= 1.7e-184) {
		tmp = t_1;
	} else if (x <= 9e-18) {
		tmp = c * ((z * t) * i);
	} else if (x <= 5.8e-8) {
		tmp = t_1;
	} else if (x <= 1.35e+167) {
		tmp = k * (y * (i * y5));
	} else {
		tmp = y * (b * (x * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (t * (y2 * -y4))
    if (x <= (-5.2d+25)) then
        tmp = a * (y * (x * b))
    else if (x <= (-7.5d-201)) then
        tmp = -((t * i) * (j * y5))
    else if (x <= 1.7d-184) then
        tmp = t_1
    else if (x <= 9d-18) then
        tmp = c * ((z * t) * i)
    else if (x <= 5.8d-8) then
        tmp = t_1
    else if (x <= 1.35d+167) then
        tmp = k * (y * (i * y5))
    else
        tmp = y * (b * (x * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (t * (y2 * -y4));
	double tmp;
	if (x <= -5.2e+25) {
		tmp = a * (y * (x * b));
	} else if (x <= -7.5e-201) {
		tmp = -((t * i) * (j * y5));
	} else if (x <= 1.7e-184) {
		tmp = t_1;
	} else if (x <= 9e-18) {
		tmp = c * ((z * t) * i);
	} else if (x <= 5.8e-8) {
		tmp = t_1;
	} else if (x <= 1.35e+167) {
		tmp = k * (y * (i * y5));
	} else {
		tmp = y * (b * (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (t * (y2 * -y4))
	tmp = 0
	if x <= -5.2e+25:
		tmp = a * (y * (x * b))
	elif x <= -7.5e-201:
		tmp = -((t * i) * (j * y5))
	elif x <= 1.7e-184:
		tmp = t_1
	elif x <= 9e-18:
		tmp = c * ((z * t) * i)
	elif x <= 5.8e-8:
		tmp = t_1
	elif x <= 1.35e+167:
		tmp = k * (y * (i * y5))
	else:
		tmp = y * (b * (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(t * Float64(y2 * Float64(-y4))))
	tmp = 0.0
	if (x <= -5.2e+25)
		tmp = Float64(a * Float64(y * Float64(x * b)));
	elseif (x <= -7.5e-201)
		tmp = Float64(-Float64(Float64(t * i) * Float64(j * y5)));
	elseif (x <= 1.7e-184)
		tmp = t_1;
	elseif (x <= 9e-18)
		tmp = Float64(c * Float64(Float64(z * t) * i));
	elseif (x <= 5.8e-8)
		tmp = t_1;
	elseif (x <= 1.35e+167)
		tmp = Float64(k * Float64(y * Float64(i * y5)));
	else
		tmp = Float64(y * Float64(b * Float64(x * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (t * (y2 * -y4));
	tmp = 0.0;
	if (x <= -5.2e+25)
		tmp = a * (y * (x * b));
	elseif (x <= -7.5e-201)
		tmp = -((t * i) * (j * y5));
	elseif (x <= 1.7e-184)
		tmp = t_1;
	elseif (x <= 9e-18)
		tmp = c * ((z * t) * i);
	elseif (x <= 5.8e-8)
		tmp = t_1;
	elseif (x <= 1.35e+167)
		tmp = k * (y * (i * y5));
	else
		tmp = y * (b * (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(t * N[(y2 * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.2e+25], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7.5e-201], (-N[(N[(t * i), $MachinePrecision] * N[(j * y5), $MachinePrecision]), $MachinePrecision]), If[LessEqual[x, 1.7e-184], t$95$1, If[LessEqual[x, 9e-18], N[(c * N[(N[(z * t), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.8e-8], t$95$1, If[LessEqual[x, 1.35e+167], N[(k * N[(y * N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(b * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -5.1999999999999997e25

   1. Initial program 22.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 32.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 41.1%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 41.1%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 41.1%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in b around inf 32.9%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 32.9%

         \[\leadsto y \cdot \left(b \cdot \left(a \cdot x - \color{blue}{y4 \cdot k}\right)\right) \]

   9. Simplified 32.9%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - y4 \cdot k\right)\right)} \]

   10. Taylor expanded in x around -inf 33.4%

       \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x\right)\right)} \]

   if -5.1999999999999997e25 < x < -7.49999999999999987e-201

   1. Initial program 27.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 35.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 35.9%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 35.9%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 35.9%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 35.9%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 35.9%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 35.9%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in i around inf 40.7%

      \[\leadsto \color{blue}{i \cdot \left(\left(k \cdot y - t \cdot j\right) \cdot y5\right)} \]

   8. Taylor expanded in k around 0 32.6%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(t \cdot \left(j \cdot y5\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 32.6%

         \[\leadsto \color{blue}{-i \cdot \left(t \cdot \left(j \cdot y5\right)\right)} \]

      2. associate-*r* 28.6%

         \[\leadsto -\color{blue}{\left(i \cdot t\right) \cdot \left(j \cdot y5\right)} \]

      3. *-commutative 28.6%

         \[\leadsto -\left(i \cdot t\right) \cdot \color{blue}{\left(y5 \cdot j\right)} \]

   10. Simplified 28.6%

       \[\leadsto \color{blue}{-\left(i \cdot t\right) \cdot \left(y5 \cdot j\right)} \]

   if -7.49999999999999987e-201 < x < 1.70000000000000002e-184 or 8.99999999999999987e-18 < x < 5.8000000000000003e-8

   1. Initial program 24.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 24.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 43.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 43.9%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 43.9%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 43.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in t around -inf 35.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right) \cdot t\right)} \]
   8. Step-by-step derivation

      1. *-commutative 35.4%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot \left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right)\right)} \]

      2. mul-1-neg 35.4%

         \[\leadsto c \cdot \left(t \cdot \left(i \cdot z + \color{blue}{\left(-y4 \cdot y2\right)}\right)\right) \]

      3. unsub-neg 35.4%

         \[\leadsto c \cdot \left(t \cdot \color{blue}{\left(i \cdot z - y4 \cdot y2\right)}\right) \]

   9. Simplified 35.4%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(i \cdot z - y4 \cdot y2\right)\right)} \]

   10. Taylor expanded in i around 0 33.5%

       \[\leadsto c \cdot \left(t \cdot \color{blue}{\left(-1 \cdot \left(y4 \cdot y2\right)\right)}\right) \]
   11. Step-by-step derivation

       1. neg-mul-1 33.5%

          \[\leadsto c \cdot \left(t \cdot \color{blue}{\left(-y4 \cdot y2\right)}\right) \]

       2. distribute-rgt-neg-in 33.5%

          \[\leadsto c \cdot \left(t \cdot \color{blue}{\left(y4 \cdot \left(-y2\right)\right)}\right) \]

   12. Simplified 33.5%

       \[\leadsto c \cdot \left(t \cdot \color{blue}{\left(y4 \cdot \left(-y2\right)\right)}\right) \]

   if 1.70000000000000002e-184 < x < 8.99999999999999987e-18

   1. Initial program 32.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 32.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 47.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 47.3%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 47.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 47.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in t around -inf 37.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right) \cdot t\right)} \]
   8. Step-by-step derivation

      1. *-commutative 37.8%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot \left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right)\right)} \]

      2. mul-1-neg 37.8%

         \[\leadsto c \cdot \left(t \cdot \left(i \cdot z + \color{blue}{\left(-y4 \cdot y2\right)}\right)\right) \]

      3. unsub-neg 37.8%

         \[\leadsto c \cdot \left(t \cdot \color{blue}{\left(i \cdot z - y4 \cdot y2\right)}\right) \]

   9. Simplified 37.8%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(i \cdot z - y4 \cdot y2\right)\right)} \]

   10. Taylor expanded in i around inf 38.0%

       \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(t \cdot z\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative 38.0%

          \[\leadsto c \cdot \left(i \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

   12. Simplified 38.0%

       \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(z \cdot t\right)\right)} \]

   if 5.8000000000000003e-8 < x < 1.35000000000000003e167

   1. Initial program 13.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 18.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 45.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 45.3%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 45.3%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 45.3%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 45.3%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 45.3%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 45.3%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in i around inf 43.1%

      \[\leadsto \color{blue}{i \cdot \left(\left(k \cdot y - t \cdot j\right) \cdot y5\right)} \]

   8. Taylor expanded in k around inf 33.0%

      \[\leadsto \color{blue}{k \cdot \left(y \cdot \left(i \cdot y5\right)\right)} \]

   if 1.35000000000000003e167 < x

   1. Initial program 25.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 38.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 38.9%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 38.9%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 38.9%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in b around inf 44.1%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 44.1%

         \[\leadsto y \cdot \left(b \cdot \left(a \cdot x - \color{blue}{y4 \cdot k}\right)\right) \]

   9. Simplified 44.1%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - y4 \cdot k\right)\right)} \]

   10. Taylor expanded in a around inf 44.3%

       \[\leadsto y \cdot \left(b \cdot \color{blue}{\left(a \cdot x\right)}\right) \]
3. Recombined 6 regimes into one program.

4. Final simplification 34.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+25}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-201}:\\ \;\;\;\;-\left(t \cdot i\right) \cdot \left(j \cdot y5\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-184}:\\ \;\;\;\;c \cdot \left(t \cdot \left(y2 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-18}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-8}:\\ \;\;\;\;c \cdot \left(t \cdot \left(y2 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+167}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a\right)\right)\\ \end{array} \]

Alternative 30: 21.8% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{if}\;b \leq -4.3 \cdot 10^{-61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-256}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k\right)\right)\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-133}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{elif}\;b \leq 9.6 \cdot 10^{+60}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y (* x b)))))
   (if (<= b -4.3e-61)
     t_1
     (if (<= b 9.5e-256)
       (* i (* y5 (* y k)))
       (if (<= b 4.4e-133)
         (* c (* (* z t) i))
         (if (<= b 9.6e+60) (* c (* y3 (* y y4))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y * (x * b));
	double tmp;
	if (b <= -4.3e-61) {
		tmp = t_1;
	} else if (b <= 9.5e-256) {
		tmp = i * (y5 * (y * k));
	} else if (b <= 4.4e-133) {
		tmp = c * ((z * t) * i);
	} else if (b <= 9.6e+60) {
		tmp = c * (y3 * (y * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (y * (x * b))
    if (b <= (-4.3d-61)) then
        tmp = t_1
    else if (b <= 9.5d-256) then
        tmp = i * (y5 * (y * k))
    else if (b <= 4.4d-133) then
        tmp = c * ((z * t) * i)
    else if (b <= 9.6d+60) then
        tmp = c * (y3 * (y * y4))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y * (x * b));
	double tmp;
	if (b <= -4.3e-61) {
		tmp = t_1;
	} else if (b <= 9.5e-256) {
		tmp = i * (y5 * (y * k));
	} else if (b <= 4.4e-133) {
		tmp = c * ((z * t) * i);
	} else if (b <= 9.6e+60) {
		tmp = c * (y3 * (y * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y * (x * b))
	tmp = 0
	if b <= -4.3e-61:
		tmp = t_1
	elif b <= 9.5e-256:
		tmp = i * (y5 * (y * k))
	elif b <= 4.4e-133:
		tmp = c * ((z * t) * i)
	elif b <= 9.6e+60:
		tmp = c * (y3 * (y * y4))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y * Float64(x * b)))
	tmp = 0.0
	if (b <= -4.3e-61)
		tmp = t_1;
	elseif (b <= 9.5e-256)
		tmp = Float64(i * Float64(y5 * Float64(y * k)));
	elseif (b <= 4.4e-133)
		tmp = Float64(c * Float64(Float64(z * t) * i));
	elseif (b <= 9.6e+60)
		tmp = Float64(c * Float64(y3 * Float64(y * y4)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y * (x * b));
	tmp = 0.0;
	if (b <= -4.3e-61)
		tmp = t_1;
	elseif (b <= 9.5e-256)
		tmp = i * (y5 * (y * k));
	elseif (b <= 4.4e-133)
		tmp = c * ((z * t) * i);
	elseif (b <= 9.6e+60)
		tmp = c * (y3 * (y * y4));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.3e-61], t$95$1, If[LessEqual[b, 9.5e-256], N[(i * N[(y5 * N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.4e-133], N[(c * N[(N[(z * t), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.6e+60], N[(c * N[(y3 * N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -4.3000000000000003e-61 or 9.6000000000000001e60 < b

   1. Initial program 20.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 27.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 38.7%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 38.7%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 38.7%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in b around inf 40.7%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 40.7%

         \[\leadsto y \cdot \left(b \cdot \left(a \cdot x - \color{blue}{y4 \cdot k}\right)\right) \]

   9. Simplified 40.7%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - y4 \cdot k\right)\right)} \]

   10. Taylor expanded in x around -inf 31.7%

       \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x\right)\right)} \]

   if -4.3000000000000003e-61 < b < 9.5e-256

   1. Initial program 32.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 36.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 25.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 25.1%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 25.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 25.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 25.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 25.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 25.1%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in i around inf 31.9%

      \[\leadsto \color{blue}{i \cdot \left(\left(k \cdot y - t \cdot j\right) \cdot y5\right)} \]

   8. Taylor expanded in k around inf 23.7%

      \[\leadsto i \cdot \left(\color{blue}{\left(k \cdot y\right)} \cdot y5\right) \]

   if 9.5e-256 < b < 4.4000000000000001e-133

   1. Initial program 20.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 20.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 39.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 39.8%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 39.8%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 39.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in t around -inf 47.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right) \cdot t\right)} \]
   8. Step-by-step derivation

      1. *-commutative 47.7%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot \left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right)\right)} \]

      2. mul-1-neg 47.7%

         \[\leadsto c \cdot \left(t \cdot \left(i \cdot z + \color{blue}{\left(-y4 \cdot y2\right)}\right)\right) \]

      3. unsub-neg 47.7%

         \[\leadsto c \cdot \left(t \cdot \color{blue}{\left(i \cdot z - y4 \cdot y2\right)}\right) \]

   9. Simplified 47.7%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(i \cdot z - y4 \cdot y2\right)\right)} \]

   10. Taylor expanded in i around inf 40.9%

       \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(t \cdot z\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative 40.9%

          \[\leadsto c \cdot \left(i \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

   12. Simplified 40.9%

       \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(z \cdot t\right)\right)} \]

   if 4.4000000000000001e-133 < b < 9.6000000000000001e60

   1. Initial program 24.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 47.5%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 47.5%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 47.5%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in y4 around inf 36.2%

      \[\leadsto \color{blue}{y4 \cdot \left(y \cdot \left(c \cdot y3 - k \cdot b\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 37.9%

         \[\leadsto \color{blue}{\left(y4 \cdot y\right) \cdot \left(c \cdot y3 - k \cdot b\right)} \]

      2. *-commutative 37.9%

         \[\leadsto \left(y4 \cdot y\right) \cdot \left(c \cdot y3 - \color{blue}{b \cdot k}\right) \]

   9. Simplified 37.9%

      \[\leadsto \color{blue}{\left(y4 \cdot y\right) \cdot \left(c \cdot y3 - b \cdot k\right)} \]

   10. Taylor expanded in c around inf 30.0%

       \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 32.0%

          \[\leadsto c \cdot \color{blue}{\left(\left(y4 \cdot y\right) \cdot y3\right)} \]

   12. Simplified 32.0%

       \[\leadsto \color{blue}{c \cdot \left(\left(y4 \cdot y\right) \cdot y3\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 31.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.3 \cdot 10^{-61}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-256}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k\right)\right)\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-133}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{elif}\;b \leq 9.6 \cdot 10^{+60}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \end{array} \]

Alternative 31: 21.8% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{if}\;b \leq -3.6 \cdot 10^{-61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 8.6 \cdot 10^{-256}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k\right)\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-133}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+56}:\\ \;\;\;\;\left(y \cdot y3\right) \cdot \left(c \cdot y4\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y (* x b)))))
   (if (<= b -3.6e-61)
     t_1
     (if (<= b 8.6e-256)
       (* i (* y5 (* y k)))
       (if (<= b 5.5e-133)
         (* c (* (* z t) i))
         (if (<= b 7e+56) (* (* y y3) (* c y4)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y * (x * b));
	double tmp;
	if (b <= -3.6e-61) {
		tmp = t_1;
	} else if (b <= 8.6e-256) {
		tmp = i * (y5 * (y * k));
	} else if (b <= 5.5e-133) {
		tmp = c * ((z * t) * i);
	} else if (b <= 7e+56) {
		tmp = (y * y3) * (c * y4);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (y * (x * b))
    if (b <= (-3.6d-61)) then
        tmp = t_1
    else if (b <= 8.6d-256) then
        tmp = i * (y5 * (y * k))
    else if (b <= 5.5d-133) then
        tmp = c * ((z * t) * i)
    else if (b <= 7d+56) then
        tmp = (y * y3) * (c * y4)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y * (x * b));
	double tmp;
	if (b <= -3.6e-61) {
		tmp = t_1;
	} else if (b <= 8.6e-256) {
		tmp = i * (y5 * (y * k));
	} else if (b <= 5.5e-133) {
		tmp = c * ((z * t) * i);
	} else if (b <= 7e+56) {
		tmp = (y * y3) * (c * y4);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y * (x * b))
	tmp = 0
	if b <= -3.6e-61:
		tmp = t_1
	elif b <= 8.6e-256:
		tmp = i * (y5 * (y * k))
	elif b <= 5.5e-133:
		tmp = c * ((z * t) * i)
	elif b <= 7e+56:
		tmp = (y * y3) * (c * y4)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y * Float64(x * b)))
	tmp = 0.0
	if (b <= -3.6e-61)
		tmp = t_1;
	elseif (b <= 8.6e-256)
		tmp = Float64(i * Float64(y5 * Float64(y * k)));
	elseif (b <= 5.5e-133)
		tmp = Float64(c * Float64(Float64(z * t) * i));
	elseif (b <= 7e+56)
		tmp = Float64(Float64(y * y3) * Float64(c * y4));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y * (x * b));
	tmp = 0.0;
	if (b <= -3.6e-61)
		tmp = t_1;
	elseif (b <= 8.6e-256)
		tmp = i * (y5 * (y * k));
	elseif (b <= 5.5e-133)
		tmp = c * ((z * t) * i);
	elseif (b <= 7e+56)
		tmp = (y * y3) * (c * y4);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.6e-61], t$95$1, If[LessEqual[b, 8.6e-256], N[(i * N[(y5 * N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.5e-133], N[(c * N[(N[(z * t), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7e+56], N[(N[(y * y3), $MachinePrecision] * N[(c * y4), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.60000000000000014e-61 or 6.99999999999999999e56 < b

   1. Initial program 20.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 27.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 38.7%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 38.7%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 38.7%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in b around inf 40.7%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 40.7%

         \[\leadsto y \cdot \left(b \cdot \left(a \cdot x - \color{blue}{y4 \cdot k}\right)\right) \]

   9. Simplified 40.7%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - y4 \cdot k\right)\right)} \]

   10. Taylor expanded in x around -inf 31.7%

       \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x\right)\right)} \]

   if -3.60000000000000014e-61 < b < 8.6000000000000002e-256

   1. Initial program 32.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 36.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 25.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 25.1%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 25.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 25.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 25.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 25.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 25.1%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in i around inf 31.9%

      \[\leadsto \color{blue}{i \cdot \left(\left(k \cdot y - t \cdot j\right) \cdot y5\right)} \]

   8. Taylor expanded in k around inf 23.7%

      \[\leadsto i \cdot \left(\color{blue}{\left(k \cdot y\right)} \cdot y5\right) \]

   if 8.6000000000000002e-256 < b < 5.49999999999999977e-133

   1. Initial program 20.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 20.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 39.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 39.8%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 39.8%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 39.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in t around -inf 47.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right) \cdot t\right)} \]
   8. Step-by-step derivation

      1. *-commutative 47.7%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot \left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right)\right)} \]

      2. mul-1-neg 47.7%

         \[\leadsto c \cdot \left(t \cdot \left(i \cdot z + \color{blue}{\left(-y4 \cdot y2\right)}\right)\right) \]

      3. unsub-neg 47.7%

         \[\leadsto c \cdot \left(t \cdot \color{blue}{\left(i \cdot z - y4 \cdot y2\right)}\right) \]

   9. Simplified 47.7%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(i \cdot z - y4 \cdot y2\right)\right)} \]

   10. Taylor expanded in i around inf 40.9%

       \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(t \cdot z\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative 40.9%

          \[\leadsto c \cdot \left(i \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

   12. Simplified 40.9%

       \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(z \cdot t\right)\right)} \]

   if 5.49999999999999977e-133 < b < 6.99999999999999999e56

   1. Initial program 24.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 47.5%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 47.5%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 47.5%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in y4 around inf 36.2%

      \[\leadsto \color{blue}{y4 \cdot \left(y \cdot \left(c \cdot y3 - k \cdot b\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 37.9%

         \[\leadsto \color{blue}{\left(y4 \cdot y\right) \cdot \left(c \cdot y3 - k \cdot b\right)} \]

      2. *-commutative 37.9%

         \[\leadsto \left(y4 \cdot y\right) \cdot \left(c \cdot y3 - \color{blue}{b \cdot k}\right) \]

   9. Simplified 37.9%

      \[\leadsto \color{blue}{\left(y4 \cdot y\right) \cdot \left(c \cdot y3 - b \cdot k\right)} \]

   10. Taylor expanded in c around inf 30.0%

       \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative 30.0%

          \[\leadsto \color{blue}{\left(y4 \cdot \left(y \cdot y3\right)\right) \cdot c} \]

       2. associate-*r* 32.0%

          \[\leadsto \color{blue}{\left(\left(y4 \cdot y\right) \cdot y3\right)} \cdot c \]

       3. associate-*l* 30.1%

          \[\leadsto \color{blue}{\left(y4 \cdot y\right) \cdot \left(y3 \cdot c\right)} \]

   12. Simplified 30.1%

       \[\leadsto \color{blue}{\left(y4 \cdot y\right) \cdot \left(y3 \cdot c\right)} \]

   13. Taylor expanded in y4 around 0 30.0%

       \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]
   14. Step-by-step derivation

       1. associate-*r* 33.9%

          \[\leadsto \color{blue}{\left(c \cdot y4\right) \cdot \left(y \cdot y3\right)} \]

       2. *-commutative 33.9%

          \[\leadsto \color{blue}{\left(y4 \cdot c\right)} \cdot \left(y \cdot y3\right) \]

   15. Simplified 33.9%

       \[\leadsto \color{blue}{\left(y4 \cdot c\right) \cdot \left(y \cdot y3\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 31.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{-61}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;b \leq 8.6 \cdot 10^{-256}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k\right)\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-133}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+56}:\\ \;\;\;\;\left(y \cdot y3\right) \cdot \left(c \cdot y4\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \end{array} \]

Alternative 32: 21.2% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y3 \leq -6.4 \cdot 10^{+52}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq -4.3 \cdot 10^{-281}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;y3 \leq 5.4 \cdot 10^{-131}:\\ \;\;\;\;k \cdot \left(\left(i \cdot y1\right) \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y3 \leq 8 \cdot 10^{-37}:\\ \;\;\;\;\left(i \cdot k\right) \cdot \left(y \cdot y5\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot y3\right) \cdot \left(c \cdot y4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y3 -6.4e+52)
   (* c (* y3 (* y y4)))
   (if (<= y3 -4.3e-281)
     (* a (* y (* x b)))
     (if (<= y3 5.4e-131)
       (* k (* (* i y1) (- z)))
       (if (<= y3 8e-37) (* (* i k) (* y y5)) (* (* y y3) (* c y4)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y3 <= -6.4e+52) {
		tmp = c * (y3 * (y * y4));
	} else if (y3 <= -4.3e-281) {
		tmp = a * (y * (x * b));
	} else if (y3 <= 5.4e-131) {
		tmp = k * ((i * y1) * -z);
	} else if (y3 <= 8e-37) {
		tmp = (i * k) * (y * y5);
	} else {
		tmp = (y * y3) * (c * y4);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y3 <= (-6.4d+52)) then
        tmp = c * (y3 * (y * y4))
    else if (y3 <= (-4.3d-281)) then
        tmp = a * (y * (x * b))
    else if (y3 <= 5.4d-131) then
        tmp = k * ((i * y1) * -z)
    else if (y3 <= 8d-37) then
        tmp = (i * k) * (y * y5)
    else
        tmp = (y * y3) * (c * y4)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y3 <= -6.4e+52) {
		tmp = c * (y3 * (y * y4));
	} else if (y3 <= -4.3e-281) {
		tmp = a * (y * (x * b));
	} else if (y3 <= 5.4e-131) {
		tmp = k * ((i * y1) * -z);
	} else if (y3 <= 8e-37) {
		tmp = (i * k) * (y * y5);
	} else {
		tmp = (y * y3) * (c * y4);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y3 <= -6.4e+52:
		tmp = c * (y3 * (y * y4))
	elif y3 <= -4.3e-281:
		tmp = a * (y * (x * b))
	elif y3 <= 5.4e-131:
		tmp = k * ((i * y1) * -z)
	elif y3 <= 8e-37:
		tmp = (i * k) * (y * y5)
	else:
		tmp = (y * y3) * (c * y4)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y3 <= -6.4e+52)
		tmp = Float64(c * Float64(y3 * Float64(y * y4)));
	elseif (y3 <= -4.3e-281)
		tmp = Float64(a * Float64(y * Float64(x * b)));
	elseif (y3 <= 5.4e-131)
		tmp = Float64(k * Float64(Float64(i * y1) * Float64(-z)));
	elseif (y3 <= 8e-37)
		tmp = Float64(Float64(i * k) * Float64(y * y5));
	else
		tmp = Float64(Float64(y * y3) * Float64(c * y4));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y3 <= -6.4e+52)
		tmp = c * (y3 * (y * y4));
	elseif (y3 <= -4.3e-281)
		tmp = a * (y * (x * b));
	elseif (y3 <= 5.4e-131)
		tmp = k * ((i * y1) * -z);
	elseif (y3 <= 8e-37)
		tmp = (i * k) * (y * y5);
	else
		tmp = (y * y3) * (c * y4);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y3, -6.4e+52], N[(c * N[(y3 * N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -4.3e-281], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 5.4e-131], N[(k * N[(N[(i * y1), $MachinePrecision] * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 8e-37], N[(N[(i * k), $MachinePrecision] * N[(y * y5), $MachinePrecision]), $MachinePrecision], N[(N[(y * y3), $MachinePrecision] * N[(c * y4), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y3 < -6.4e52

   1. Initial program 14.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 24.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 35.2%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 35.2%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 35.2%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in y4 around inf 50.2%

      \[\leadsto \color{blue}{y4 \cdot \left(y \cdot \left(c \cdot y3 - k \cdot b\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 51.9%

         \[\leadsto \color{blue}{\left(y4 \cdot y\right) \cdot \left(c \cdot y3 - k \cdot b\right)} \]

      2. *-commutative 51.9%

         \[\leadsto \left(y4 \cdot y\right) \cdot \left(c \cdot y3 - \color{blue}{b \cdot k}\right) \]

   9. Simplified 51.9%

      \[\leadsto \color{blue}{\left(y4 \cdot y\right) \cdot \left(c \cdot y3 - b \cdot k\right)} \]

   10. Taylor expanded in c around inf 42.0%

       \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 42.0%

          \[\leadsto c \cdot \color{blue}{\left(\left(y4 \cdot y\right) \cdot y3\right)} \]

   12. Simplified 42.0%

       \[\leadsto \color{blue}{c \cdot \left(\left(y4 \cdot y\right) \cdot y3\right)} \]

   if -6.4e52 < y3 < -4.30000000000000023e-281

   1. Initial program 25.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 36.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 42.2%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 42.2%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 42.2%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in b around inf 39.6%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 39.6%

         \[\leadsto y \cdot \left(b \cdot \left(a \cdot x - \color{blue}{y4 \cdot k}\right)\right) \]

   9. Simplified 39.6%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - y4 \cdot k\right)\right)} \]

   10. Taylor expanded in x around -inf 30.5%

       \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x\right)\right)} \]

   if -4.30000000000000023e-281 < y3 < 5.40000000000000042e-131

   1. Initial program 26.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 26.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 46.6%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 46.6%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. associate--l+ 46.6%

         \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \cdot z \]

   6. Simplified 46.6%

      \[\leadsto \color{blue}{-\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   7. Taylor expanded in k around inf 36.8%

      \[\leadsto -\color{blue}{k \cdot \left(\left(i \cdot y1 - y0 \cdot b\right) \cdot z\right)} \]

   8. Taylor expanded in i around inf 24.7%

      \[\leadsto -k \cdot \left(\color{blue}{\left(y1 \cdot i\right)} \cdot z\right) \]

   if 5.40000000000000042e-131 < y3 < 8.00000000000000053e-37

   1. Initial program 36.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 45.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 46.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 46.2%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 46.2%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 46.2%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 46.2%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 46.2%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 46.2%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in i around inf 47.0%

      \[\leadsto \color{blue}{i \cdot \left(\left(k \cdot y - t \cdot j\right) \cdot y5\right)} \]

   8. Taylor expanded in k around inf 46.5%

      \[\leadsto \color{blue}{k \cdot \left(y \cdot \left(i \cdot y5\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 46.5%

         \[\leadsto k \cdot \color{blue}{\left(\left(i \cdot y5\right) \cdot y\right)} \]

      2. associate-*r* 46.4%

         \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(y5 \cdot y\right)\right)} \]

      3. *-commutative 46.4%

         \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y \cdot y5\right)}\right) \]

      4. associate-*r* 50.7%

         \[\leadsto \color{blue}{\left(k \cdot i\right) \cdot \left(y \cdot y5\right)} \]

      5. *-commutative 50.7%

         \[\leadsto \color{blue}{\left(y \cdot y5\right) \cdot \left(k \cdot i\right)} \]

      6. *-commutative 50.7%

         \[\leadsto \color{blue}{\left(y5 \cdot y\right)} \cdot \left(k \cdot i\right) \]

   10. Simplified 50.7%

       \[\leadsto \color{blue}{\left(y5 \cdot y\right) \cdot \left(k \cdot i\right)} \]

   if 8.00000000000000053e-37 < y3

   1. Initial program 22.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 29.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 45.4%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 45.4%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 45.4%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in y4 around inf 36.3%

      \[\leadsto \color{blue}{y4 \cdot \left(y \cdot \left(c \cdot y3 - k \cdot b\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 36.2%

         \[\leadsto \color{blue}{\left(y4 \cdot y\right) \cdot \left(c \cdot y3 - k \cdot b\right)} \]

      2. *-commutative 36.2%

         \[\leadsto \left(y4 \cdot y\right) \cdot \left(c \cdot y3 - \color{blue}{b \cdot k}\right) \]

   9. Simplified 36.2%

      \[\leadsto \color{blue}{\left(y4 \cdot y\right) \cdot \left(c \cdot y3 - b \cdot k\right)} \]

   10. Taylor expanded in c around inf 27.8%

       \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative 27.8%

          \[\leadsto \color{blue}{\left(y4 \cdot \left(y \cdot y3\right)\right) \cdot c} \]

       2. associate-*r* 26.5%

          \[\leadsto \color{blue}{\left(\left(y4 \cdot y\right) \cdot y3\right)} \cdot c \]

       3. associate-*l* 26.5%

          \[\leadsto \color{blue}{\left(y4 \cdot y\right) \cdot \left(y3 \cdot c\right)} \]

   12. Simplified 26.5%

       \[\leadsto \color{blue}{\left(y4 \cdot y\right) \cdot \left(y3 \cdot c\right)} \]

   13. Taylor expanded in y4 around 0 27.8%

       \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]
   14. Step-by-step derivation

       1. associate-*r* 29.2%

          \[\leadsto \color{blue}{\left(c \cdot y4\right) \cdot \left(y \cdot y3\right)} \]

       2. *-commutative 29.2%

          \[\leadsto \color{blue}{\left(y4 \cdot c\right)} \cdot \left(y \cdot y3\right) \]

   15. Simplified 29.2%

       \[\leadsto \color{blue}{\left(y4 \cdot c\right) \cdot \left(y \cdot y3\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 33.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -6.4 \cdot 10^{+52}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq -4.3 \cdot 10^{-281}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;y3 \leq 5.4 \cdot 10^{-131}:\\ \;\;\;\;k \cdot \left(\left(i \cdot y1\right) \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y3 \leq 8 \cdot 10^{-37}:\\ \;\;\;\;\left(i \cdot k\right) \cdot \left(y \cdot y5\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot y3\right) \cdot \left(c \cdot y4\right)\\ \end{array} \]

Alternative 33: 22.0% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+23}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;x \leq -2.35 \cdot 10^{-204}:\\ \;\;\;\;-\left(t \cdot i\right) \cdot \left(j \cdot y5\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-10}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(-t \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+166}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -3.8e+23)
   (* a (* y (* x b)))
   (if (<= x -2.35e-204)
     (- (* (* t i) (* j y5)))
     (if (<= x 1.3e-10)
       (* c (* y2 (- (* t y4))))
       (if (<= x 8.2e+166) (* k (* y (* i y5))) (* y (* b (* x a))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -3.8e+23) {
		tmp = a * (y * (x * b));
	} else if (x <= -2.35e-204) {
		tmp = -((t * i) * (j * y5));
	} else if (x <= 1.3e-10) {
		tmp = c * (y2 * -(t * y4));
	} else if (x <= 8.2e+166) {
		tmp = k * (y * (i * y5));
	} else {
		tmp = y * (b * (x * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (x <= (-3.8d+23)) then
        tmp = a * (y * (x * b))
    else if (x <= (-2.35d-204)) then
        tmp = -((t * i) * (j * y5))
    else if (x <= 1.3d-10) then
        tmp = c * (y2 * -(t * y4))
    else if (x <= 8.2d+166) then
        tmp = k * (y * (i * y5))
    else
        tmp = y * (b * (x * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -3.8e+23) {
		tmp = a * (y * (x * b));
	} else if (x <= -2.35e-204) {
		tmp = -((t * i) * (j * y5));
	} else if (x <= 1.3e-10) {
		tmp = c * (y2 * -(t * y4));
	} else if (x <= 8.2e+166) {
		tmp = k * (y * (i * y5));
	} else {
		tmp = y * (b * (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if x <= -3.8e+23:
		tmp = a * (y * (x * b))
	elif x <= -2.35e-204:
		tmp = -((t * i) * (j * y5))
	elif x <= 1.3e-10:
		tmp = c * (y2 * -(t * y4))
	elif x <= 8.2e+166:
		tmp = k * (y * (i * y5))
	else:
		tmp = y * (b * (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (x <= -3.8e+23)
		tmp = Float64(a * Float64(y * Float64(x * b)));
	elseif (x <= -2.35e-204)
		tmp = Float64(-Float64(Float64(t * i) * Float64(j * y5)));
	elseif (x <= 1.3e-10)
		tmp = Float64(c * Float64(y2 * Float64(-Float64(t * y4))));
	elseif (x <= 8.2e+166)
		tmp = Float64(k * Float64(y * Float64(i * y5)));
	else
		tmp = Float64(y * Float64(b * Float64(x * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (x <= -3.8e+23)
		tmp = a * (y * (x * b));
	elseif (x <= -2.35e-204)
		tmp = -((t * i) * (j * y5));
	elseif (x <= 1.3e-10)
		tmp = c * (y2 * -(t * y4));
	elseif (x <= 8.2e+166)
		tmp = k * (y * (i * y5));
	else
		tmp = y * (b * (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[x, -3.8e+23], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.35e-204], (-N[(N[(t * i), $MachinePrecision] * N[(j * y5), $MachinePrecision]), $MachinePrecision]), If[LessEqual[x, 1.3e-10], N[(c * N[(y2 * (-N[(t * y4), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.2e+166], N[(k * N[(y * N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(b * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -3.79999999999999975e23

   1. Initial program 22.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 32.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 41.1%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 41.1%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 41.1%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in b around inf 32.9%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 32.9%

         \[\leadsto y \cdot \left(b \cdot \left(a \cdot x - \color{blue}{y4 \cdot k}\right)\right) \]

   9. Simplified 32.9%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - y4 \cdot k\right)\right)} \]

   10. Taylor expanded in x around -inf 33.4%

       \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x\right)\right)} \]

   if -3.79999999999999975e23 < x < -2.34999999999999996e-204

   1. Initial program 27.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 35.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 35.9%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 35.9%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 35.9%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 35.9%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 35.9%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 35.9%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in i around inf 40.7%

      \[\leadsto \color{blue}{i \cdot \left(\left(k \cdot y - t \cdot j\right) \cdot y5\right)} \]

   8. Taylor expanded in k around 0 32.6%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(t \cdot \left(j \cdot y5\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 32.6%

         \[\leadsto \color{blue}{-i \cdot \left(t \cdot \left(j \cdot y5\right)\right)} \]

      2. associate-*r* 28.6%

         \[\leadsto -\color{blue}{\left(i \cdot t\right) \cdot \left(j \cdot y5\right)} \]

      3. *-commutative 28.6%

         \[\leadsto -\left(i \cdot t\right) \cdot \color{blue}{\left(y5 \cdot j\right)} \]

   10. Simplified 28.6%

       \[\leadsto \color{blue}{-\left(i \cdot t\right) \cdot \left(y5 \cdot j\right)} \]

   if -2.34999999999999996e-204 < x < 1.29999999999999991e-10

   1. Initial program 26.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 26.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 44.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 44.8%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 44.8%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 44.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in t around -inf 36.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right) \cdot t\right)} \]
   8. Step-by-step derivation

      1. *-commutative 36.0%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot \left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right)\right)} \]

      2. mul-1-neg 36.0%

         \[\leadsto c \cdot \left(t \cdot \left(i \cdot z + \color{blue}{\left(-y4 \cdot y2\right)}\right)\right) \]

      3. unsub-neg 36.0%

         \[\leadsto c \cdot \left(t \cdot \color{blue}{\left(i \cdot z - y4 \cdot y2\right)}\right) \]

   9. Simplified 36.0%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(i \cdot z - y4 \cdot y2\right)\right)} \]

   10. Taylor expanded in i around 0 27.9%

       \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 27.9%

          \[\leadsto \color{blue}{-c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)} \]

       2. distribute-rgt-neg-in 27.9%

          \[\leadsto \color{blue}{c \cdot \left(-y4 \cdot \left(t \cdot y2\right)\right)} \]

       3. associate-*r* 31.8%

          \[\leadsto c \cdot \left(-\color{blue}{\left(y4 \cdot t\right) \cdot y2}\right) \]

       4. distribute-lft-neg-in 31.8%

          \[\leadsto c \cdot \color{blue}{\left(\left(-y4 \cdot t\right) \cdot y2\right)} \]

   12. Simplified 31.8%

       \[\leadsto \color{blue}{c \cdot \left(\left(-y4 \cdot t\right) \cdot y2\right)} \]

   if 1.29999999999999991e-10 < x < 8.2000000000000005e166

   1. Initial program 13.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 18.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 45.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 45.3%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 45.3%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 45.3%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 45.3%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 45.3%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 45.3%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in i around inf 43.1%

      \[\leadsto \color{blue}{i \cdot \left(\left(k \cdot y - t \cdot j\right) \cdot y5\right)} \]

   8. Taylor expanded in k around inf 33.0%

      \[\leadsto \color{blue}{k \cdot \left(y \cdot \left(i \cdot y5\right)\right)} \]

   if 8.2000000000000005e166 < x

   1. Initial program 25.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 38.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 38.9%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 38.9%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 38.9%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in b around inf 44.1%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 44.1%

         \[\leadsto y \cdot \left(b \cdot \left(a \cdot x - \color{blue}{y4 \cdot k}\right)\right) \]

   9. Simplified 44.1%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - y4 \cdot k\right)\right)} \]

   10. Taylor expanded in a around inf 44.3%

       \[\leadsto y \cdot \left(b \cdot \color{blue}{\left(a \cdot x\right)}\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 33.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+23}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;x \leq -2.35 \cdot 10^{-204}:\\ \;\;\;\;-\left(t \cdot i\right) \cdot \left(j \cdot y5\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-10}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(-t \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+166}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a\right)\right)\\ \end{array} \]

Alternative 34: 22.1% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+29}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-217}:\\ \;\;\;\;i \cdot \left(\left(j \cdot y5\right) \cdot \left(-t\right)\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-6}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(-t \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+166}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -7.2e+29)
   (* a (* y (* x b)))
   (if (<= x -6.2e-217)
     (* i (* (* j y5) (- t)))
     (if (<= x 7.2e-6)
       (* c (* y2 (- (* t y4))))
       (if (<= x 9e+166) (* k (* y (* i y5))) (* y (* b (* x a))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -7.2e+29) {
		tmp = a * (y * (x * b));
	} else if (x <= -6.2e-217) {
		tmp = i * ((j * y5) * -t);
	} else if (x <= 7.2e-6) {
		tmp = c * (y2 * -(t * y4));
	} else if (x <= 9e+166) {
		tmp = k * (y * (i * y5));
	} else {
		tmp = y * (b * (x * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (x <= (-7.2d+29)) then
        tmp = a * (y * (x * b))
    else if (x <= (-6.2d-217)) then
        tmp = i * ((j * y5) * -t)
    else if (x <= 7.2d-6) then
        tmp = c * (y2 * -(t * y4))
    else if (x <= 9d+166) then
        tmp = k * (y * (i * y5))
    else
        tmp = y * (b * (x * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -7.2e+29) {
		tmp = a * (y * (x * b));
	} else if (x <= -6.2e-217) {
		tmp = i * ((j * y5) * -t);
	} else if (x <= 7.2e-6) {
		tmp = c * (y2 * -(t * y4));
	} else if (x <= 9e+166) {
		tmp = k * (y * (i * y5));
	} else {
		tmp = y * (b * (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if x <= -7.2e+29:
		tmp = a * (y * (x * b))
	elif x <= -6.2e-217:
		tmp = i * ((j * y5) * -t)
	elif x <= 7.2e-6:
		tmp = c * (y2 * -(t * y4))
	elif x <= 9e+166:
		tmp = k * (y * (i * y5))
	else:
		tmp = y * (b * (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (x <= -7.2e+29)
		tmp = Float64(a * Float64(y * Float64(x * b)));
	elseif (x <= -6.2e-217)
		tmp = Float64(i * Float64(Float64(j * y5) * Float64(-t)));
	elseif (x <= 7.2e-6)
		tmp = Float64(c * Float64(y2 * Float64(-Float64(t * y4))));
	elseif (x <= 9e+166)
		tmp = Float64(k * Float64(y * Float64(i * y5)));
	else
		tmp = Float64(y * Float64(b * Float64(x * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (x <= -7.2e+29)
		tmp = a * (y * (x * b));
	elseif (x <= -6.2e-217)
		tmp = i * ((j * y5) * -t);
	elseif (x <= 7.2e-6)
		tmp = c * (y2 * -(t * y4));
	elseif (x <= 9e+166)
		tmp = k * (y * (i * y5));
	else
		tmp = y * (b * (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[x, -7.2e+29], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.2e-217], N[(i * N[(N[(j * y5), $MachinePrecision] * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.2e-6], N[(c * N[(y2 * (-N[(t * y4), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9e+166], N[(k * N[(y * N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(b * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -7.19999999999999952e29

   1. Initial program 22.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 32.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 41.1%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 41.1%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 41.1%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in b around inf 32.9%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 32.9%

         \[\leadsto y \cdot \left(b \cdot \left(a \cdot x - \color{blue}{y4 \cdot k}\right)\right) \]

   9. Simplified 32.9%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - y4 \cdot k\right)\right)} \]

   10. Taylor expanded in x around -inf 33.4%

       \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x\right)\right)} \]

   if -7.19999999999999952e29 < x < -6.1999999999999997e-217

   1. Initial program 26.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 32.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 36.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 36.5%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 36.5%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 36.5%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 36.5%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 36.5%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 36.5%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in i around inf 39.1%

      \[\leadsto \color{blue}{i \cdot \left(\left(k \cdot y - t \cdot j\right) \cdot y5\right)} \]

   8. Taylor expanded in k around 0 33.3%

      \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(t \cdot \left(j \cdot y5\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 33.3%

         \[\leadsto i \cdot \color{blue}{\left(\left(-1 \cdot t\right) \cdot \left(j \cdot y5\right)\right)} \]

      2. neg-mul-1 33.3%

         \[\leadsto i \cdot \left(\color{blue}{\left(-t\right)} \cdot \left(j \cdot y5\right)\right) \]

      3. *-commutative 33.3%

         \[\leadsto i \cdot \left(\left(-t\right) \cdot \color{blue}{\left(y5 \cdot j\right)}\right) \]

   10. Simplified 33.3%

       \[\leadsto i \cdot \color{blue}{\left(\left(-t\right) \cdot \left(y5 \cdot j\right)\right)} \]

   if -6.1999999999999997e-217 < x < 7.19999999999999967e-6

   1. Initial program 27.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 27.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 44.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 44.7%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 44.7%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 44.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in t around -inf 35.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right) \cdot t\right)} \]
   8. Step-by-step derivation

      1. *-commutative 35.6%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot \left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right)\right)} \]

      2. mul-1-neg 35.6%

         \[\leadsto c \cdot \left(t \cdot \left(i \cdot z + \color{blue}{\left(-y4 \cdot y2\right)}\right)\right) \]

      3. unsub-neg 35.6%

         \[\leadsto c \cdot \left(t \cdot \color{blue}{\left(i \cdot z - y4 \cdot y2\right)}\right) \]

   9. Simplified 35.6%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(i \cdot z - y4 \cdot y2\right)\right)} \]

   10. Taylor expanded in i around 0 27.3%

       \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 27.3%

          \[\leadsto \color{blue}{-c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)} \]

       2. distribute-rgt-neg-in 27.3%

          \[\leadsto \color{blue}{c \cdot \left(-y4 \cdot \left(t \cdot y2\right)\right)} \]

       3. associate-*r* 31.3%

          \[\leadsto c \cdot \left(-\color{blue}{\left(y4 \cdot t\right) \cdot y2}\right) \]

       4. distribute-lft-neg-in 31.3%

          \[\leadsto c \cdot \color{blue}{\left(\left(-y4 \cdot t\right) \cdot y2\right)} \]

   12. Simplified 31.3%

       \[\leadsto \color{blue}{c \cdot \left(\left(-y4 \cdot t\right) \cdot y2\right)} \]

   if 7.19999999999999967e-6 < x < 9.00000000000000061e166

   1. Initial program 13.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 18.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 45.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 45.3%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 45.3%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 45.3%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 45.3%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 45.3%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 45.3%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in i around inf 43.1%

      \[\leadsto \color{blue}{i \cdot \left(\left(k \cdot y - t \cdot j\right) \cdot y5\right)} \]

   8. Taylor expanded in k around inf 33.0%

      \[\leadsto \color{blue}{k \cdot \left(y \cdot \left(i \cdot y5\right)\right)} \]

   if 9.00000000000000061e166 < x

   1. Initial program 25.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 38.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 38.9%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 38.9%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 38.9%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in b around inf 44.1%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 44.1%

         \[\leadsto y \cdot \left(b \cdot \left(a \cdot x - \color{blue}{y4 \cdot k}\right)\right) \]

   9. Simplified 44.1%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - y4 \cdot k\right)\right)} \]

   10. Taylor expanded in a around inf 44.3%

       \[\leadsto y \cdot \left(b \cdot \color{blue}{\left(a \cdot x\right)}\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 34.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+29}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-217}:\\ \;\;\;\;i \cdot \left(\left(j \cdot y5\right) \cdot \left(-t\right)\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-6}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(-t \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+166}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a\right)\right)\\ \end{array} \]

Alternative 35: 23.0% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{-10} \lor \neg \left(x \leq 7.8 \cdot 10^{-17}\right):\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= x -9.2e-10) (not (<= x 7.8e-17)))
   (* a (* y (* x b)))
   (* c (* (* z t) i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((x <= -9.2e-10) || !(x <= 7.8e-17)) {
		tmp = a * (y * (x * b));
	} else {
		tmp = c * ((z * t) * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((x <= (-9.2d-10)) .or. (.not. (x <= 7.8d-17))) then
        tmp = a * (y * (x * b))
    else
        tmp = c * ((z * t) * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((x <= -9.2e-10) || !(x <= 7.8e-17)) {
		tmp = a * (y * (x * b));
	} else {
		tmp = c * ((z * t) * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (x <= -9.2e-10) or not (x <= 7.8e-17):
		tmp = a * (y * (x * b))
	else:
		tmp = c * ((z * t) * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((x <= -9.2e-10) || !(x <= 7.8e-17))
		tmp = Float64(a * Float64(y * Float64(x * b)));
	else
		tmp = Float64(c * Float64(Float64(z * t) * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((x <= -9.2e-10) || ~((x <= 7.8e-17)))
		tmp = a * (y * (x * b));
	else
		tmp = c * ((z * t) * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[x, -9.2e-10], N[Not[LessEqual[x, 7.8e-17]], $MachinePrecision]], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(z * t), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.20000000000000028e-10 or 7.79999999999999979e-17 < x

   1. Initial program 21.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 41.8%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 41.8%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 41.8%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in b around inf 35.3%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 35.3%

         \[\leadsto y \cdot \left(b \cdot \left(a \cdot x - \color{blue}{y4 \cdot k}\right)\right) \]

   9. Simplified 35.3%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - y4 \cdot k\right)\right)} \]

   10. Taylor expanded in x around -inf 31.0%

       \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x\right)\right)} \]

   if -9.20000000000000028e-10 < x < 7.79999999999999979e-17

   1. Initial program 27.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 27.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 42.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 42.3%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 42.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 42.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in t around -inf 31.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right) \cdot t\right)} \]
   8. Step-by-step derivation

      1. *-commutative 31.0%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot \left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right)\right)} \]

      2. mul-1-neg 31.0%

         \[\leadsto c \cdot \left(t \cdot \left(i \cdot z + \color{blue}{\left(-y4 \cdot y2\right)}\right)\right) \]

      3. unsub-neg 31.0%

         \[\leadsto c \cdot \left(t \cdot \color{blue}{\left(i \cdot z - y4 \cdot y2\right)}\right) \]

   9. Simplified 31.0%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(i \cdot z - y4 \cdot y2\right)\right)} \]

   10. Taylor expanded in i around inf 20.9%

       \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(t \cdot z\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative 20.9%

          \[\leadsto c \cdot \left(i \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

   12. Simplified 20.9%

       \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(z \cdot t\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 26.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{-10} \lor \neg \left(x \leq 7.8 \cdot 10^{-17}\right):\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \end{array} \]

Alternative 36: 22.6% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{-62} \lor \neg \left(b \leq 0.009\right):\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= b -2.5e-62) (not (<= b 0.009)))
   (* a (* y (* x b)))
   (* c (* y4 (* 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 tmp;
	if ((b <= -2.5e-62) || !(b <= 0.009)) {
		tmp = a * (y * (x * b));
	} else {
		tmp = c * (y4 * (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) :: tmp
    if ((b <= (-2.5d-62)) .or. (.not. (b <= 0.009d0))) then
        tmp = a * (y * (x * b))
    else
        tmp = c * (y4 * (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 tmp;
	if ((b <= -2.5e-62) || !(b <= 0.009)) {
		tmp = a * (y * (x * b));
	} else {
		tmp = c * (y4 * (y * 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 (b <= -2.5e-62) or not (b <= 0.009):
		tmp = a * (y * (x * b))
	else:
		tmp = c * (y4 * (y * 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 ((b <= -2.5e-62) || !(b <= 0.009))
		tmp = Float64(a * Float64(y * Float64(x * b)));
	else
		tmp = Float64(c * Float64(y4 * 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)
	tmp = 0.0;
	if ((b <= -2.5e-62) || ~((b <= 0.009)))
		tmp = a * (y * (x * b));
	else
		tmp = c * (y4 * (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_] := If[Or[LessEqual[b, -2.5e-62], N[Not[LessEqual[b, 0.009]], $MachinePrecision]], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y4 * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.5000000000000001e-62 or 0.00899999999999999932 < b

   1. Initial program 21.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 40.1%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 40.1%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 40.1%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in b around inf 40.5%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 40.5%

         \[\leadsto y \cdot \left(b \cdot \left(a \cdot x - \color{blue}{y4 \cdot k}\right)\right) \]

   9. Simplified 40.5%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - y4 \cdot k\right)\right)} \]

   10. Taylor expanded in x around -inf 30.4%

       \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x\right)\right)} \]

   if -2.5000000000000001e-62 < b < 0.00899999999999999932

   1. Initial program 27.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 35.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 39.2%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 39.2%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 39.2%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in y4 around inf 26.4%

      \[\leadsto \color{blue}{y4 \cdot \left(y \cdot \left(c \cdot y3 - k \cdot b\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 26.4%

         \[\leadsto \color{blue}{\left(y4 \cdot y\right) \cdot \left(c \cdot y3 - k \cdot b\right)} \]

      2. *-commutative 26.4%

         \[\leadsto \left(y4 \cdot y\right) \cdot \left(c \cdot y3 - \color{blue}{b \cdot k}\right) \]

   9. Simplified 26.4%

      \[\leadsto \color{blue}{\left(y4 \cdot y\right) \cdot \left(c \cdot y3 - b \cdot k\right)} \]

   10. Taylor expanded in c around inf 26.3%

       \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 28.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{-62} \lor \neg \left(b \leq 0.009\right):\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \end{array} \]

Alternative 37: 22.4% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{-62} \lor \neg \left(b \leq 9.6 \cdot 10^{+61}\right):\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= b -1.9e-62) (not (<= b 9.6e+61)))
   (* a (* y (* x b)))
   (* c (* y3 (* y y4)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((b <= -1.9e-62) || !(b <= 9.6e+61)) {
		tmp = a * (y * (x * b));
	} else {
		tmp = c * (y3 * (y * y4));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((b <= (-1.9d-62)) .or. (.not. (b <= 9.6d+61))) then
        tmp = a * (y * (x * b))
    else
        tmp = c * (y3 * (y * y4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((b <= -1.9e-62) || !(b <= 9.6e+61)) {
		tmp = a * (y * (x * b));
	} else {
		tmp = c * (y3 * (y * y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (b <= -1.9e-62) or not (b <= 9.6e+61):
		tmp = a * (y * (x * b))
	else:
		tmp = c * (y3 * (y * y4))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((b <= -1.9e-62) || !(b <= 9.6e+61))
		tmp = Float64(a * Float64(y * Float64(x * b)));
	else
		tmp = Float64(c * Float64(y3 * Float64(y * y4)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((b <= -1.9e-62) || ~((b <= 9.6e+61)))
		tmp = a * (y * (x * b));
	else
		tmp = c * (y3 * (y * y4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[b, -1.9e-62], N[Not[LessEqual[b, 9.6e+61]], $MachinePrecision]], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y3 * N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.90000000000000003e-62 or 9.5999999999999995e61 < b

   1. Initial program 20.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 27.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 38.4%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 38.4%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 38.4%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in b around inf 40.4%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 40.4%

         \[\leadsto y \cdot \left(b \cdot \left(a \cdot x - \color{blue}{y4 \cdot k}\right)\right) \]

   9. Simplified 40.4%

      \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - y4 \cdot k\right)\right)} \]

   10. Taylor expanded in x around -inf 31.5%

       \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x\right)\right)} \]

   if -1.90000000000000003e-62 < b < 9.5999999999999995e61

   1. Initial program 27.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 35.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 40.9%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 40.9%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 40.9%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in y4 around inf 28.2%

      \[\leadsto \color{blue}{y4 \cdot \left(y \cdot \left(c \cdot y3 - k \cdot b\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 28.1%

         \[\leadsto \color{blue}{\left(y4 \cdot y\right) \cdot \left(c \cdot y3 - k \cdot b\right)} \]

      2. *-commutative 28.1%

         \[\leadsto \left(y4 \cdot y\right) \cdot \left(c \cdot y3 - \color{blue}{b \cdot k}\right) \]

   9. Simplified 28.1%

      \[\leadsto \color{blue}{\left(y4 \cdot y\right) \cdot \left(c \cdot y3 - b \cdot k\right)} \]

   10. Taylor expanded in c around inf 25.1%

       \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 26.6%

          \[\leadsto c \cdot \color{blue}{\left(\left(y4 \cdot y\right) \cdot y3\right)} \]

   12. Simplified 26.6%

       \[\leadsto \color{blue}{c \cdot \left(\left(y4 \cdot y\right) \cdot y3\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 29.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{-62} \lor \neg \left(b \leq 9.6 \cdot 10^{+61}\right):\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4\right)\right)\\ \end{array} \]

Alternative 38: 17.6% 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 23.7%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

3. Simplified 31.5%

   \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

4. Taylor expanded in y around inf 39.7%

   \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
5. Step-by-step derivation

   1. mul-1-neg 39.7%

      \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

6. Simplified 39.7%

   \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

7. Taylor expanded in b around inf 31.2%

   \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]
8. Step-by-step derivation

   1. *-commutative 31.2%

      \[\leadsto y \cdot \left(b \cdot \left(a \cdot x - \color{blue}{y4 \cdot k}\right)\right) \]

9. Simplified 31.2%

   \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - y4 \cdot k\right)\right)} \]

10. Taylor expanded in x around -inf 19.5%

    \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x\right)\right)} \]
11. Step-by-step derivation

    1. pow1 19.5%

       \[\leadsto a \cdot \color{blue}{{\left(y \cdot \left(b \cdot x\right)\right)}^{1}} \]

    2. *-commutative 19.5%

       \[\leadsto a \cdot {\left(y \cdot \color{blue}{\left(x \cdot b\right)}\right)}^{1} \]

12. Applied egg-rr 19.5%

    \[\leadsto a \cdot \color{blue}{{\left(y \cdot \left(x \cdot b\right)\right)}^{1}} \]
13. Step-by-step derivation

    1. unpow1 19.5%

       \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(x \cdot b\right)\right)} \]

    2. *-commutative 19.5%

       \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot b\right) \cdot y\right)} \]

    3. associate-*l* 18.7%

       \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

14. Simplified 18.7%

    \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \]

15. Final simplification 18.7%

    \[\leadsto a \cdot \left(x \cdot \left(y \cdot b\right)\right) \]

Alternative 39: 17.5% 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 23.7%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

3. Simplified 31.5%

   \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

4. Taylor expanded in y around inf 39.7%

   \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
5. Step-by-step derivation

   1. mul-1-neg 39.7%

      \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

6. Simplified 39.7%

   \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

7. Taylor expanded in b around inf 31.2%

   \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]
8. Step-by-step derivation

   1. *-commutative 31.2%

      \[\leadsto y \cdot \left(b \cdot \left(a \cdot x - \color{blue}{y4 \cdot k}\right)\right) \]

9. Simplified 31.2%

   \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(a \cdot x - y4 \cdot k\right)\right)} \]

10. Taylor expanded in x around -inf 19.5%

    \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x\right)\right)} \]

11. Final simplification 19.5%

    \[\leadsto a \cdot \left(y \cdot \left(x \cdot b\right)\right) \]

Developer target: 26.8% 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 2023230 
(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)))))