Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 29.9% → 41.9%

Time: 53.8s

Alternatives: 37

Speedup: 3.1×

• 89.1% 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: 29.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 41.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot y4 - y0 \cdot y5\\ t_2 := b \cdot y0 - i \cdot y1\\ t_3 := i \cdot y5 - b \cdot y4\\ t_4 := t \cdot \left(a \cdot y5 - c \cdot y4\right)\\ t_5 := c \cdot y0 - a \cdot y1\\ \mathbf{if}\;y2 \leq -1.35 \cdot 10^{+157}:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(x \cdot y0\right) + t\_4\right)\\ \mathbf{elif}\;y2 \leq -4.6 \cdot 10^{-20}:\\ \;\;\;\;k \cdot \left(\left(y \cdot t\_3 + y2 \cdot t\_1\right) + z \cdot t\_2\right)\\ \mathbf{elif}\;y2 \leq -1.8 \cdot 10^{-57}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 1.1 \cdot 10^{-271}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) - c \cdot \left(x \cdot y - z \cdot t\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 4.1 \cdot 10^{-92}:\\ \;\;\;\;z \cdot \left(k \cdot t\_2 + \left(t \cdot \left(c \cdot i - a \cdot b\right) - y3 \cdot t\_5\right)\right)\\ \mathbf{elif}\;y2 \leq 6.8 \cdot 10^{+49}:\\ \;\;\;\;y \cdot \left(\left(k \cdot t\_3 + x \cdot \left(a \cdot b - c \cdot i\right)\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot t\_1 + x \cdot t\_5\right) + t\_4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y1 y4) (* y0 y5)))
        (t_2 (- (* b y0) (* i y1)))
        (t_3 (- (* i y5) (* b y4)))
        (t_4 (* t (- (* a y5) (* c y4))))
        (t_5 (- (* c y0) (* a y1))))
   (if (<= y2 -1.35e+157)
     (* y2 (+ (* c (* x y0)) t_4))
     (if (<= y2 -4.6e-20)
       (* k (+ (+ (* y t_3) (* y2 t_1)) (* z t_2)))
       (if (<= y2 -1.8e-57)
         (*
          y4
          (-
           (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
           (* c (- (* t y2) (* y y3)))))
         (if (<= y2 1.1e-271)
           (*
            i
            (+
             (* y1 (- (* x j) (* z k)))
             (- (* y5 (- (* y k) (* t j))) (* c (- (* x y) (* z t))))))
           (if (<= y2 4.1e-92)
             (* z (+ (* k t_2) (- (* t (- (* c i) (* a b))) (* y3 t_5))))
             (if (<= y2 6.8e+49)
               (*
                y
                (+
                 (+ (* k t_3) (* x (- (* a b) (* c i))))
                 (* y3 (- (* c y4) (* a y5)))))
               (* y2 (+ (+ (* k t_1) (* x t_5)) t_4))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y1 * y4) - (y0 * y5);
	double t_2 = (b * y0) - (i * y1);
	double t_3 = (i * y5) - (b * y4);
	double t_4 = t * ((a * y5) - (c * y4));
	double t_5 = (c * y0) - (a * y1);
	double tmp;
	if (y2 <= -1.35e+157) {
		tmp = y2 * ((c * (x * y0)) + t_4);
	} else if (y2 <= -4.6e-20) {
		tmp = k * (((y * t_3) + (y2 * t_1)) + (z * t_2));
	} else if (y2 <= -1.8e-57) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) - (c * ((t * y2) - (y * y3))));
	} else if (y2 <= 1.1e-271) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * ((x * y) - (z * t)))));
	} else if (y2 <= 4.1e-92) {
		tmp = z * ((k * t_2) + ((t * ((c * i) - (a * b))) - (y3 * t_5)));
	} else if (y2 <= 6.8e+49) {
		tmp = y * (((k * t_3) + (x * ((a * b) - (c * i)))) + (y3 * ((c * y4) - (a * y5))));
	} else {
		tmp = y2 * (((k * t_1) + (x * t_5)) + t_4);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = (y1 * y4) - (y0 * y5)
    t_2 = (b * y0) - (i * y1)
    t_3 = (i * y5) - (b * y4)
    t_4 = t * ((a * y5) - (c * y4))
    t_5 = (c * y0) - (a * y1)
    if (y2 <= (-1.35d+157)) then
        tmp = y2 * ((c * (x * y0)) + t_4)
    else if (y2 <= (-4.6d-20)) then
        tmp = k * (((y * t_3) + (y2 * t_1)) + (z * t_2))
    else if (y2 <= (-1.8d-57)) then
        tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) - (c * ((t * y2) - (y * y3))))
    else if (y2 <= 1.1d-271) then
        tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * ((x * y) - (z * t)))))
    else if (y2 <= 4.1d-92) then
        tmp = z * ((k * t_2) + ((t * ((c * i) - (a * b))) - (y3 * t_5)))
    else if (y2 <= 6.8d+49) then
        tmp = y * (((k * t_3) + (x * ((a * b) - (c * i)))) + (y3 * ((c * y4) - (a * y5))))
    else
        tmp = y2 * (((k * t_1) + (x * t_5)) + t_4)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y1 * y4) - (y0 * y5);
	double t_2 = (b * y0) - (i * y1);
	double t_3 = (i * y5) - (b * y4);
	double t_4 = t * ((a * y5) - (c * y4));
	double t_5 = (c * y0) - (a * y1);
	double tmp;
	if (y2 <= -1.35e+157) {
		tmp = y2 * ((c * (x * y0)) + t_4);
	} else if (y2 <= -4.6e-20) {
		tmp = k * (((y * t_3) + (y2 * t_1)) + (z * t_2));
	} else if (y2 <= -1.8e-57) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) - (c * ((t * y2) - (y * y3))));
	} else if (y2 <= 1.1e-271) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * ((x * y) - (z * t)))));
	} else if (y2 <= 4.1e-92) {
		tmp = z * ((k * t_2) + ((t * ((c * i) - (a * b))) - (y3 * t_5)));
	} else if (y2 <= 6.8e+49) {
		tmp = y * (((k * t_3) + (x * ((a * b) - (c * i)))) + (y3 * ((c * y4) - (a * y5))));
	} else {
		tmp = y2 * (((k * t_1) + (x * t_5)) + t_4);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y1 * y4) - (y0 * y5)
	t_2 = (b * y0) - (i * y1)
	t_3 = (i * y5) - (b * y4)
	t_4 = t * ((a * y5) - (c * y4))
	t_5 = (c * y0) - (a * y1)
	tmp = 0
	if y2 <= -1.35e+157:
		tmp = y2 * ((c * (x * y0)) + t_4)
	elif y2 <= -4.6e-20:
		tmp = k * (((y * t_3) + (y2 * t_1)) + (z * t_2))
	elif y2 <= -1.8e-57:
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) - (c * ((t * y2) - (y * y3))))
	elif y2 <= 1.1e-271:
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * ((x * y) - (z * t)))))
	elif y2 <= 4.1e-92:
		tmp = z * ((k * t_2) + ((t * ((c * i) - (a * b))) - (y3 * t_5)))
	elif y2 <= 6.8e+49:
		tmp = y * (((k * t_3) + (x * ((a * b) - (c * i)))) + (y3 * ((c * y4) - (a * y5))))
	else:
		tmp = y2 * (((k * t_1) + (x * t_5)) + t_4)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_2 = Float64(Float64(b * y0) - Float64(i * y1))
	t_3 = Float64(Float64(i * y5) - Float64(b * y4))
	t_4 = Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))
	t_5 = Float64(Float64(c * y0) - Float64(a * y1))
	tmp = 0.0
	if (y2 <= -1.35e+157)
		tmp = Float64(y2 * Float64(Float64(c * Float64(x * y0)) + t_4));
	elseif (y2 <= -4.6e-20)
		tmp = Float64(k * Float64(Float64(Float64(y * t_3) + Float64(y2 * t_1)) + Float64(z * t_2)));
	elseif (y2 <= -1.8e-57)
		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(t * y2) - Float64(y * y3)))));
	elseif (y2 <= 1.1e-271)
		tmp = Float64(i * Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) + Float64(Float64(y5 * Float64(Float64(y * k) - Float64(t * j))) - Float64(c * Float64(Float64(x * y) - Float64(z * t))))));
	elseif (y2 <= 4.1e-92)
		tmp = Float64(z * Float64(Float64(k * t_2) + Float64(Float64(t * Float64(Float64(c * i) - Float64(a * b))) - Float64(y3 * t_5))));
	elseif (y2 <= 6.8e+49)
		tmp = Float64(y * Float64(Float64(Float64(k * t_3) + Float64(x * Float64(Float64(a * b) - Float64(c * i)))) + Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5)))));
	else
		tmp = Float64(y2 * Float64(Float64(Float64(k * t_1) + Float64(x * t_5)) + t_4));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y1 * y4) - (y0 * y5);
	t_2 = (b * y0) - (i * y1);
	t_3 = (i * y5) - (b * y4);
	t_4 = t * ((a * y5) - (c * y4));
	t_5 = (c * y0) - (a * y1);
	tmp = 0.0;
	if (y2 <= -1.35e+157)
		tmp = y2 * ((c * (x * y0)) + t_4);
	elseif (y2 <= -4.6e-20)
		tmp = k * (((y * t_3) + (y2 * t_1)) + (z * t_2));
	elseif (y2 <= -1.8e-57)
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) - (c * ((t * y2) - (y * y3))));
	elseif (y2 <= 1.1e-271)
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * ((x * y) - (z * t)))));
	elseif (y2 <= 4.1e-92)
		tmp = z * ((k * t_2) + ((t * ((c * i) - (a * b))) - (y3 * t_5)));
	elseif (y2 <= 6.8e+49)
		tmp = y * (((k * t_3) + (x * ((a * b) - (c * i)))) + (y3 * ((c * y4) - (a * y5))));
	else
		tmp = y2 * (((k * t_1) + (x * t_5)) + t_4);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -1.35e+157], N[(y2 * N[(N[(c * N[(x * y0), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -4.6e-20], N[(k * N[(N[(N[(y * t$95$3), $MachinePrecision] + N[(y2 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(z * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1.8e-57], 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[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.1e-271], N[(i * N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 4.1e-92], N[(z * N[(N[(k * t$95$2), $MachinePrecision] + N[(N[(t * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y3 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 6.8e+49], N[(y * N[(N[(N[(k * t$95$3), $MachinePrecision] + N[(x * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y2 * N[(N[(N[(k * t$95$1), $MachinePrecision] + N[(x * t$95$5), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y2 < -1.35e157

   1. Initial program 18.9%

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

   3. Taylor expanded in y2 around inf 44.8%

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

   4. Taylor expanded in c around inf 67.5%

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

   if -1.35e157 < y2 < -4.5999999999999998e-20

   1. Initial program 35.7%

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

   3. Taylor expanded in k around inf 54.9%

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

   if -4.5999999999999998e-20 < y2 < -1.8000000000000001e-57

   1. Initial program 31.3%

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

   3. Taylor expanded in y4 around inf 84.4%

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

   if -1.8000000000000001e-57 < y2 < 1.1e-271

   1. Initial program 30.6%

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

   3. Taylor expanded in i around -inf 50.9%

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

   if 1.1e-271 < y2 < 4.1000000000000002e-92

   1. Initial program 48.7%

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

   3. Taylor expanded in z around -inf 63.3%

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

   if 4.1000000000000002e-92 < y2 < 6.8000000000000001e49

   1. Initial program 26.6%

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

   3. Taylor expanded in y around inf 63.5%

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

   if 6.8000000000000001e49 < y2

   1. Initial program 25.6%

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

   3. Taylor expanded in y2 around inf 64.8%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.35 \cdot 10^{+157}:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(x \cdot y0\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -4.6 \cdot 10^{-20}:\\ \;\;\;\;k \cdot \left(\left(y \cdot \left(i \cdot y5 - b \cdot y4\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq -1.8 \cdot 10^{-57}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 1.1 \cdot 10^{-271}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) - c \cdot \left(x \cdot y - z \cdot t\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 4.1 \cdot 10^{-92}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot \left(c \cdot i - a \cdot b\right) - y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 6.8 \cdot 10^{+49}:\\ \;\;\;\;y \cdot \left(\left(k \cdot \left(i \cdot y5 - b \cdot y4\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 52.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(\left(\left(\left(a \cdot b - c \cdot i\right) \cdot \left(x \cdot y - z \cdot t\right) + \left(b \cdot y0 - i \cdot y1\right) \cdot \left(z \cdot k - x \cdot j\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(b \cdot y4 - i \cdot y5\right) \cdot \left(t \cdot j - y \cdot k\right)\right) + \left(t \cdot y2 - y \cdot y3\right) \cdot \left(a \cdot y5 - c \cdot y4\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(j \cdot \left(b \cdot \left(\frac{c \cdot y2}{b \cdot j} + -1\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (+
          (+
           (+
            (+
             (+
              (* (- (* a b) (* c i)) (- (* x y) (* z t)))
              (* (- (* b y0) (* i y1)) (- (* z k) (* x j))))
             (* (- (* x y2) (* z y3)) (- (* c y0) (* a y1))))
            (* (- (* b y4) (* i y5)) (- (* t j) (* y k))))
           (* (- (* t y2) (* y y3)) (- (* a y5) (* c y4))))
          (* (- (* k y2) (* j y3)) (- (* y1 y4) (* y0 y5))))))
   (if (<= t_1 INFINITY)
     t_1
     (* y0 (* x (* j (* b (+ (/ (* c y2) (* b j)) -1.0))))))))

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)) * ((x * y) - (z * t))) + (((b * y0) - (i * y1)) * ((z * k) - (x * j)))) + (((x * y2) - (z * y3)) * ((c * y0) - (a * y1)))) + (((b * y4) - (i * y5)) * ((t * j) - (y * k)))) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4)))) + (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = y0 * (x * (j * (b * (((c * y2) / (b * j)) + -1.0))));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (((((((a * b) - (c * i)) * ((x * y) - (z * t))) + (((b * y0) - (i * y1)) * ((z * k) - (x * j)))) + (((x * y2) - (z * y3)) * ((c * y0) - (a * y1)))) + (((b * y4) - (i * y5)) * ((t * j) - (y * k)))) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4)))) + (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5)));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = y0 * (x * (j * (b * (((c * y2) / (b * j)) + -1.0))));
	}
	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)) * ((x * y) - (z * t))) + (((b * y0) - (i * y1)) * ((z * k) - (x * j)))) + (((x * y2) - (z * y3)) * ((c * y0) - (a * y1)))) + (((b * y4) - (i * y5)) * ((t * j) - (y * k)))) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4)))) + (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5)))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = y0 * (x * (j * (b * (((c * y2) / (b * j)) + -1.0))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(a * b) - Float64(c * i)) * Float64(Float64(x * y) - Float64(z * t))) + Float64(Float64(Float64(b * y0) - Float64(i * y1)) * Float64(Float64(z * k) - Float64(x * j)))) + Float64(Float64(Float64(x * y2) - Float64(z * y3)) * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(Float64(Float64(b * y4) - Float64(i * y5)) * Float64(Float64(t * j) - Float64(y * k)))) + Float64(Float64(Float64(t * y2) - Float64(y * y3)) * Float64(Float64(a * y5) - Float64(c * y4)))) + Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y1 * y4) - Float64(y0 * y5))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(y0 * Float64(x * Float64(j * Float64(b * Float64(Float64(Float64(c * y2) / Float64(b * j)) + -1.0)))));
	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)) * ((x * y) - (z * t))) + (((b * y0) - (i * y1)) * ((z * k) - (x * j)))) + (((x * y2) - (z * y3)) * ((c * y0) - (a * y1)))) + (((b * y4) - (i * y5)) * ((t * j) - (y * k)))) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4)))) + (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = y0 * (x * (j * (b * (((c * y2) / (b * j)) + -1.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(N[(N[(N[(N[(N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision] * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision] * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(y0 * N[(x * N[(j * N[(b * N[(N[(N[(c * y2), $MachinePrecision] / N[(b * j), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 86.7%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y0 around inf 36.7%

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

   4. Taylor expanded in x around inf 37.9%

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

   5. Taylor expanded in j around inf 40.3%

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

   6. Taylor expanded in b around inf 43.6%

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

4. Final simplification 58.9%

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

Alternative 3: 41.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot y4 - y0 \cdot y5\\ t_2 := b \cdot y0 - i \cdot y1\\ t_3 := t \cdot \left(a \cdot y5 - c \cdot y4\right)\\ t_4 := c \cdot y0 - a \cdot y1\\ \mathbf{if}\;y2 \leq -1.1 \cdot 10^{+157}:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(x \cdot y0\right) + t\_3\right)\\ \mathbf{elif}\;y2 \leq -6.8 \cdot 10^{-23}:\\ \;\;\;\;k \cdot \left(\left(y \cdot \left(i \cdot y5 - b \cdot y4\right) + y2 \cdot t\_1\right) + z \cdot t\_2\right)\\ \mathbf{elif}\;y2 \leq -9 \cdot 10^{-59}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 1.5 \cdot 10^{-271}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) - c \cdot \left(x \cdot y - z \cdot t\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 4.2 \cdot 10^{-68}:\\ \;\;\;\;z \cdot \left(k \cdot t\_2 + \left(t \cdot \left(c \cdot i - a \cdot b\right) - y3 \cdot t\_4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot t\_1 + x \cdot t\_4\right) + t\_3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y1 y4) (* y0 y5)))
        (t_2 (- (* b y0) (* i y1)))
        (t_3 (* t (- (* a y5) (* c y4))))
        (t_4 (- (* c y0) (* a y1))))
   (if (<= y2 -1.1e+157)
     (* y2 (+ (* c (* x y0)) t_3))
     (if (<= y2 -6.8e-23)
       (* k (+ (+ (* y (- (* i y5) (* b y4))) (* y2 t_1)) (* z t_2)))
       (if (<= y2 -9e-59)
         (*
          y4
          (-
           (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
           (* c (- (* t y2) (* y y3)))))
         (if (<= y2 1.5e-271)
           (*
            i
            (+
             (* y1 (- (* x j) (* z k)))
             (- (* y5 (- (* y k) (* t j))) (* c (- (* x y) (* z t))))))
           (if (<= y2 4.2e-68)
             (* z (+ (* k t_2) (- (* t (- (* c i) (* a b))) (* y3 t_4))))
             (* y2 (+ (+ (* k t_1) (* x t_4)) t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y1 * y4) - (y0 * y5);
	double t_2 = (b * y0) - (i * y1);
	double t_3 = t * ((a * y5) - (c * y4));
	double t_4 = (c * y0) - (a * y1);
	double tmp;
	if (y2 <= -1.1e+157) {
		tmp = y2 * ((c * (x * y0)) + t_3);
	} else if (y2 <= -6.8e-23) {
		tmp = k * (((y * ((i * y5) - (b * y4))) + (y2 * t_1)) + (z * t_2));
	} else if (y2 <= -9e-59) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) - (c * ((t * y2) - (y * y3))));
	} else if (y2 <= 1.5e-271) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * ((x * y) - (z * t)))));
	} else if (y2 <= 4.2e-68) {
		tmp = z * ((k * t_2) + ((t * ((c * i) - (a * b))) - (y3 * t_4)));
	} else {
		tmp = y2 * (((k * t_1) + (x * t_4)) + t_3);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (y1 * y4) - (y0 * y5)
    t_2 = (b * y0) - (i * y1)
    t_3 = t * ((a * y5) - (c * y4))
    t_4 = (c * y0) - (a * y1)
    if (y2 <= (-1.1d+157)) then
        tmp = y2 * ((c * (x * y0)) + t_3)
    else if (y2 <= (-6.8d-23)) then
        tmp = k * (((y * ((i * y5) - (b * y4))) + (y2 * t_1)) + (z * t_2))
    else if (y2 <= (-9d-59)) then
        tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) - (c * ((t * y2) - (y * y3))))
    else if (y2 <= 1.5d-271) then
        tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * ((x * y) - (z * t)))))
    else if (y2 <= 4.2d-68) then
        tmp = z * ((k * t_2) + ((t * ((c * i) - (a * b))) - (y3 * t_4)))
    else
        tmp = y2 * (((k * t_1) + (x * t_4)) + t_3)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y1 * y4) - (y0 * y5);
	double t_2 = (b * y0) - (i * y1);
	double t_3 = t * ((a * y5) - (c * y4));
	double t_4 = (c * y0) - (a * y1);
	double tmp;
	if (y2 <= -1.1e+157) {
		tmp = y2 * ((c * (x * y0)) + t_3);
	} else if (y2 <= -6.8e-23) {
		tmp = k * (((y * ((i * y5) - (b * y4))) + (y2 * t_1)) + (z * t_2));
	} else if (y2 <= -9e-59) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) - (c * ((t * y2) - (y * y3))));
	} else if (y2 <= 1.5e-271) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * ((x * y) - (z * t)))));
	} else if (y2 <= 4.2e-68) {
		tmp = z * ((k * t_2) + ((t * ((c * i) - (a * b))) - (y3 * t_4)));
	} else {
		tmp = y2 * (((k * t_1) + (x * t_4)) + t_3);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y1 * y4) - (y0 * y5)
	t_2 = (b * y0) - (i * y1)
	t_3 = t * ((a * y5) - (c * y4))
	t_4 = (c * y0) - (a * y1)
	tmp = 0
	if y2 <= -1.1e+157:
		tmp = y2 * ((c * (x * y0)) + t_3)
	elif y2 <= -6.8e-23:
		tmp = k * (((y * ((i * y5) - (b * y4))) + (y2 * t_1)) + (z * t_2))
	elif y2 <= -9e-59:
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) - (c * ((t * y2) - (y * y3))))
	elif y2 <= 1.5e-271:
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * ((x * y) - (z * t)))))
	elif y2 <= 4.2e-68:
		tmp = z * ((k * t_2) + ((t * ((c * i) - (a * b))) - (y3 * t_4)))
	else:
		tmp = y2 * (((k * t_1) + (x * t_4)) + t_3)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_2 = Float64(Float64(b * y0) - Float64(i * y1))
	t_3 = Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))
	t_4 = Float64(Float64(c * y0) - Float64(a * y1))
	tmp = 0.0
	if (y2 <= -1.1e+157)
		tmp = Float64(y2 * Float64(Float64(c * Float64(x * y0)) + t_3));
	elseif (y2 <= -6.8e-23)
		tmp = Float64(k * Float64(Float64(Float64(y * Float64(Float64(i * y5) - Float64(b * y4))) + Float64(y2 * t_1)) + Float64(z * t_2)));
	elseif (y2 <= -9e-59)
		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(t * y2) - Float64(y * y3)))));
	elseif (y2 <= 1.5e-271)
		tmp = Float64(i * Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) + Float64(Float64(y5 * Float64(Float64(y * k) - Float64(t * j))) - Float64(c * Float64(Float64(x * y) - Float64(z * t))))));
	elseif (y2 <= 4.2e-68)
		tmp = Float64(z * Float64(Float64(k * t_2) + Float64(Float64(t * Float64(Float64(c * i) - Float64(a * b))) - Float64(y3 * t_4))));
	else
		tmp = Float64(y2 * Float64(Float64(Float64(k * t_1) + Float64(x * t_4)) + t_3));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y1 * y4) - (y0 * y5);
	t_2 = (b * y0) - (i * y1);
	t_3 = t * ((a * y5) - (c * y4));
	t_4 = (c * y0) - (a * y1);
	tmp = 0.0;
	if (y2 <= -1.1e+157)
		tmp = y2 * ((c * (x * y0)) + t_3);
	elseif (y2 <= -6.8e-23)
		tmp = k * (((y * ((i * y5) - (b * y4))) + (y2 * t_1)) + (z * t_2));
	elseif (y2 <= -9e-59)
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) - (c * ((t * y2) - (y * y3))));
	elseif (y2 <= 1.5e-271)
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * ((x * y) - (z * t)))));
	elseif (y2 <= 4.2e-68)
		tmp = z * ((k * t_2) + ((t * ((c * i) - (a * b))) - (y3 * t_4)));
	else
		tmp = y2 * (((k * t_1) + (x * t_4)) + t_3);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -1.1e+157], N[(y2 * N[(N[(c * N[(x * y0), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -6.8e-23], N[(k * N[(N[(N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(z * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -9e-59], 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[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.5e-271], N[(i * N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 4.2e-68], N[(z * N[(N[(k * t$95$2), $MachinePrecision] + N[(N[(t * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y3 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y2 * N[(N[(N[(k * t$95$1), $MachinePrecision] + N[(x * t$95$4), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y2 < -1.1000000000000001e157

   1. Initial program 18.9%

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

   3. Taylor expanded in y2 around inf 44.8%

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

   4. Taylor expanded in c around inf 67.5%

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

   if -1.1000000000000001e157 < y2 < -6.8000000000000001e-23

   1. Initial program 35.7%

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

   3. Taylor expanded in k around inf 54.9%

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

   if -6.8000000000000001e-23 < y2 < -9.00000000000000023e-59

   1. Initial program 31.3%

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

   3. Taylor expanded in y4 around inf 84.4%

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

   if -9.00000000000000023e-59 < y2 < 1.50000000000000001e-271

   1. Initial program 30.6%

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

   3. Taylor expanded in i around -inf 50.9%

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

   if 1.50000000000000001e-271 < y2 < 4.20000000000000016e-68

   1. Initial program 47.5%

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

   3. Taylor expanded in z around -inf 63.6%

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

   if 4.20000000000000016e-68 < y2

   1. Initial program 25.7%

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

   3. Taylor expanded in y2 around inf 58.1%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.1 \cdot 10^{+157}:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(x \cdot y0\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -6.8 \cdot 10^{-23}:\\ \;\;\;\;k \cdot \left(\left(y \cdot \left(i \cdot y5 - b \cdot y4\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq -9 \cdot 10^{-59}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 1.5 \cdot 10^{-271}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) - c \cdot \left(x \cdot y - z \cdot t\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 4.2 \cdot 10^{-68}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot \left(c \cdot i - a \cdot b\right) - y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 41.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot y0 - a \cdot y1\\ t_2 := t \cdot \left(a \cdot y5 - c \cdot y4\right)\\ t_3 := b \cdot y0 - i \cdot y1\\ \mathbf{if}\;y2 \leq -2.35 \cdot 10^{+167}:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(x \cdot y0\right) + t\_2\right)\\ \mathbf{elif}\;y2 \leq -2.4 \cdot 10^{+66}:\\ \;\;\;\;k \cdot \left(z \cdot t\_3 + y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq -1.9 \cdot 10^{-63}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 1.55 \cdot 10^{-273}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) - c \cdot \left(x \cdot y - z \cdot t\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 1.46 \cdot 10^{-67}:\\ \;\;\;\;z \cdot \left(k \cdot t\_3 + \left(t \cdot \left(c \cdot i - a \cdot b\right) - y3 \cdot t\_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot t\_1\right) + t\_2\right)\\ \end{array} \end{array} \]

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 (* t (- (* a y5) (* c y4))))
        (t_3 (- (* b y0) (* i y1))))
   (if (<= y2 -2.35e+167)
     (* y2 (+ (* c (* x y0)) t_2))
     (if (<= y2 -2.4e+66)
       (* k (+ (* z t_3) (* y4 (- (* y1 y2) (* y b)))))
       (if (<= y2 -1.9e-63)
         (*
          y4
          (-
           (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
           (* c (- (* t y2) (* y y3)))))
         (if (<= y2 1.55e-273)
           (*
            i
            (+
             (* y1 (- (* x j) (* z k)))
             (- (* y5 (- (* y k) (* t j))) (* c (- (* x y) (* z t))))))
           (if (<= y2 1.46e-67)
             (* z (+ (* k t_3) (- (* t (- (* c i) (* a b))) (* y3 t_1))))
             (* y2 (+ (+ (* k (- (* y1 y4) (* y0 y5))) (* x t_1)) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y0) - (a * y1);
	double t_2 = t * ((a * y5) - (c * y4));
	double t_3 = (b * y0) - (i * y1);
	double tmp;
	if (y2 <= -2.35e+167) {
		tmp = y2 * ((c * (x * y0)) + t_2);
	} else if (y2 <= -2.4e+66) {
		tmp = k * ((z * t_3) + (y4 * ((y1 * y2) - (y * b))));
	} else if (y2 <= -1.9e-63) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) - (c * ((t * y2) - (y * y3))));
	} else if (y2 <= 1.55e-273) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * ((x * y) - (z * t)))));
	} else if (y2 <= 1.46e-67) {
		tmp = z * ((k * t_3) + ((t * ((c * i) - (a * b))) - (y3 * t_1)));
	} else {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_1)) + t_2);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (c * y0) - (a * y1)
    t_2 = t * ((a * y5) - (c * y4))
    t_3 = (b * y0) - (i * y1)
    if (y2 <= (-2.35d+167)) then
        tmp = y2 * ((c * (x * y0)) + t_2)
    else if (y2 <= (-2.4d+66)) then
        tmp = k * ((z * t_3) + (y4 * ((y1 * y2) - (y * b))))
    else if (y2 <= (-1.9d-63)) then
        tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) - (c * ((t * y2) - (y * y3))))
    else if (y2 <= 1.55d-273) then
        tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * ((x * y) - (z * t)))))
    else if (y2 <= 1.46d-67) then
        tmp = z * ((k * t_3) + ((t * ((c * i) - (a * b))) - (y3 * t_1)))
    else
        tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_1)) + 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 = t * ((a * y5) - (c * y4));
	double t_3 = (b * y0) - (i * y1);
	double tmp;
	if (y2 <= -2.35e+167) {
		tmp = y2 * ((c * (x * y0)) + t_2);
	} else if (y2 <= -2.4e+66) {
		tmp = k * ((z * t_3) + (y4 * ((y1 * y2) - (y * b))));
	} else if (y2 <= -1.9e-63) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) - (c * ((t * y2) - (y * y3))));
	} else if (y2 <= 1.55e-273) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * ((x * y) - (z * t)))));
	} else if (y2 <= 1.46e-67) {
		tmp = z * ((k * t_3) + ((t * ((c * i) - (a * b))) - (y3 * t_1)));
	} else {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_1)) + 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 = t * ((a * y5) - (c * y4))
	t_3 = (b * y0) - (i * y1)
	tmp = 0
	if y2 <= -2.35e+167:
		tmp = y2 * ((c * (x * y0)) + t_2)
	elif y2 <= -2.4e+66:
		tmp = k * ((z * t_3) + (y4 * ((y1 * y2) - (y * b))))
	elif y2 <= -1.9e-63:
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) - (c * ((t * y2) - (y * y3))))
	elif y2 <= 1.55e-273:
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * ((x * y) - (z * t)))))
	elif y2 <= 1.46e-67:
		tmp = z * ((k * t_3) + ((t * ((c * i) - (a * b))) - (y3 * t_1)))
	else:
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_1)) + 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(t * Float64(Float64(a * y5) - Float64(c * y4)))
	t_3 = Float64(Float64(b * y0) - Float64(i * y1))
	tmp = 0.0
	if (y2 <= -2.35e+167)
		tmp = Float64(y2 * Float64(Float64(c * Float64(x * y0)) + t_2));
	elseif (y2 <= -2.4e+66)
		tmp = Float64(k * Float64(Float64(z * t_3) + Float64(y4 * Float64(Float64(y1 * y2) - Float64(y * b)))));
	elseif (y2 <= -1.9e-63)
		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(t * y2) - Float64(y * y3)))));
	elseif (y2 <= 1.55e-273)
		tmp = Float64(i * Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) + Float64(Float64(y5 * Float64(Float64(y * k) - Float64(t * j))) - Float64(c * Float64(Float64(x * y) - Float64(z * t))))));
	elseif (y2 <= 1.46e-67)
		tmp = Float64(z * Float64(Float64(k * t_3) + Float64(Float64(t * Float64(Float64(c * i) - Float64(a * b))) - Float64(y3 * t_1))));
	else
		tmp = Float64(y2 * Float64(Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(x * t_1)) + 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 = t * ((a * y5) - (c * y4));
	t_3 = (b * y0) - (i * y1);
	tmp = 0.0;
	if (y2 <= -2.35e+167)
		tmp = y2 * ((c * (x * y0)) + t_2);
	elseif (y2 <= -2.4e+66)
		tmp = k * ((z * t_3) + (y4 * ((y1 * y2) - (y * b))));
	elseif (y2 <= -1.9e-63)
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) - (c * ((t * y2) - (y * y3))));
	elseif (y2 <= 1.55e-273)
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * ((x * y) - (z * t)))));
	elseif (y2 <= 1.46e-67)
		tmp = z * ((k * t_3) + ((t * ((c * i) - (a * b))) - (y3 * t_1)));
	else
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_1)) + 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[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -2.35e+167], N[(y2 * N[(N[(c * N[(x * y0), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -2.4e+66], N[(k * N[(N[(z * t$95$3), $MachinePrecision] + N[(y4 * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1.9e-63], 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[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.55e-273], N[(i * N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.46e-67], N[(z * N[(N[(k * t$95$3), $MachinePrecision] + N[(N[(t * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y3 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y2 * N[(N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$1), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y2 < -2.35000000000000006e167

   1. Initial program 19.9%

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

   3. Taylor expanded in y2 around inf 47.3%

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

   4. Taylor expanded in c around inf 68.5%

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

   if -2.35000000000000006e167 < y2 < -2.4000000000000002e66

   1. Initial program 29.2%

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

   3. Taylor expanded in k around inf 62.9%

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

   4. Taylor expanded in y5 around 0 53.2%

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

      1. cancel-sign-sub-inv 53.2%

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

      2. mul-1-neg 53.2%

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

      3. associate-*r* 57.9%

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

      4. distribute-lft-neg-in 57.9%

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

      5. mul-1-neg 57.9%

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

      6. associate-*r* 57.9%

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

      7. distribute-rgt-in 57.9%

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

      8. +-commutative 57.9%

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

      9. mul-1-neg 57.9%

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

      10. unsub-neg 57.9%

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

      11. *-commutative 57.9%

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

      12. metadata-eval 57.9%

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

      13. *-lft-identity 57.9%

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

   6. Simplified 57.9%

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

   if -2.4000000000000002e66 < y2 < -1.90000000000000009e-63

   1. Initial program 36.2%

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

   3. Taylor expanded in y4 around inf 58.3%

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

   if -1.90000000000000009e-63 < y2 < 1.54999999999999994e-273

   1. Initial program 30.6%

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

   3. Taylor expanded in i around -inf 50.9%

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

   if 1.54999999999999994e-273 < y2 < 1.46000000000000002e-67

   1. Initial program 47.5%

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

   3. Taylor expanded in z around -inf 63.6%

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

   if 1.46000000000000002e-67 < y2

   1. Initial program 25.7%

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

   3. Taylor expanded in y2 around inf 58.1%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -2.35 \cdot 10^{+167}:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(x \cdot y0\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -2.4 \cdot 10^{+66}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right) + y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq -1.9 \cdot 10^{-63}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 1.55 \cdot 10^{-273}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) - c \cdot \left(x \cdot y - z \cdot t\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 1.46 \cdot 10^{-67}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot \left(c \cdot i - a \cdot b\right) - y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 41.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ t_2 := t \cdot \left(a \cdot y5 - c \cdot y4\right)\\ t_3 := t \cdot j - y \cdot k\\ \mathbf{if}\;y2 \leq -8.2 \cdot 10^{+167}:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(x \cdot y0\right) + t\_2\right)\\ \mathbf{elif}\;y2 \leq -2.6 \cdot 10^{+65}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right) + y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq -1.6 \cdot 10^{-56}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot t\_3 + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 2.8 \cdot 10^{-259}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) - c \cdot t\_1\right)\right)\\ \mathbf{elif}\;y2 \leq 6.2 \cdot 10^{-15}:\\ \;\;\;\;b \cdot \left(\left(a \cdot t\_1 + y4 \cdot t\_3\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t\_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t)))
        (t_2 (* t (- (* a y5) (* c y4))))
        (t_3 (- (* t j) (* y k))))
   (if (<= y2 -8.2e+167)
     (* y2 (+ (* c (* x y0)) t_2))
     (if (<= y2 -2.6e+65)
       (* k (+ (* z (- (* b y0) (* i y1))) (* y4 (- (* y1 y2) (* y b)))))
       (if (<= y2 -1.6e-56)
         (*
          y4
          (-
           (+ (* b t_3) (* y1 (- (* k y2) (* j y3))))
           (* c (- (* t y2) (* y y3)))))
         (if (<= y2 2.8e-259)
           (*
            i
            (+
             (* y1 (- (* x j) (* z k)))
             (- (* y5 (- (* y k) (* t j))) (* c t_1))))
           (if (<= y2 6.2e-15)
             (* b (+ (+ (* a t_1) (* y4 t_3)) (* y0 (- (* z k) (* x j)))))
             (*
              y2
              (+
               (+ (* k (- (* y1 y4) (* y0 y5))) (* x (- (* c y0) (* a y1))))
               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 = (x * y) - (z * t);
	double t_2 = t * ((a * y5) - (c * y4));
	double t_3 = (t * j) - (y * k);
	double tmp;
	if (y2 <= -8.2e+167) {
		tmp = y2 * ((c * (x * y0)) + t_2);
	} else if (y2 <= -2.6e+65) {
		tmp = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))));
	} else if (y2 <= -1.6e-56) {
		tmp = y4 * (((b * t_3) + (y1 * ((k * y2) - (j * y3)))) - (c * ((t * y2) - (y * y3))));
	} else if (y2 <= 2.8e-259) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * t_1)));
	} else if (y2 <= 6.2e-15) {
		tmp = b * (((a * t_1) + (y4 * t_3)) + (y0 * ((z * k) - (x * j))));
	} else {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + 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 = (x * y) - (z * t)
    t_2 = t * ((a * y5) - (c * y4))
    t_3 = (t * j) - (y * k)
    if (y2 <= (-8.2d+167)) then
        tmp = y2 * ((c * (x * y0)) + t_2)
    else if (y2 <= (-2.6d+65)) then
        tmp = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))))
    else if (y2 <= (-1.6d-56)) then
        tmp = y4 * (((b * t_3) + (y1 * ((k * y2) - (j * y3)))) - (c * ((t * y2) - (y * y3))))
    else if (y2 <= 2.8d-259) then
        tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * t_1)))
    else if (y2 <= 6.2d-15) then
        tmp = b * (((a * t_1) + (y4 * t_3)) + (y0 * ((z * k) - (x * j))))
    else
        tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + 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 = (x * y) - (z * t);
	double t_2 = t * ((a * y5) - (c * y4));
	double t_3 = (t * j) - (y * k);
	double tmp;
	if (y2 <= -8.2e+167) {
		tmp = y2 * ((c * (x * y0)) + t_2);
	} else if (y2 <= -2.6e+65) {
		tmp = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))));
	} else if (y2 <= -1.6e-56) {
		tmp = y4 * (((b * t_3) + (y1 * ((k * y2) - (j * y3)))) - (c * ((t * y2) - (y * y3))));
	} else if (y2 <= 2.8e-259) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * t_1)));
	} else if (y2 <= 6.2e-15) {
		tmp = b * (((a * t_1) + (y4 * t_3)) + (y0 * ((z * k) - (x * j))));
	} else {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + 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 = (x * y) - (z * t)
	t_2 = t * ((a * y5) - (c * y4))
	t_3 = (t * j) - (y * k)
	tmp = 0
	if y2 <= -8.2e+167:
		tmp = y2 * ((c * (x * y0)) + t_2)
	elif y2 <= -2.6e+65:
		tmp = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))))
	elif y2 <= -1.6e-56:
		tmp = y4 * (((b * t_3) + (y1 * ((k * y2) - (j * y3)))) - (c * ((t * y2) - (y * y3))))
	elif y2 <= 2.8e-259:
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * t_1)))
	elif y2 <= 6.2e-15:
		tmp = b * (((a * t_1) + (y4 * t_3)) + (y0 * ((z * k) - (x * j))))
	else:
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + 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(x * y) - Float64(z * t))
	t_2 = Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))
	t_3 = Float64(Float64(t * j) - Float64(y * k))
	tmp = 0.0
	if (y2 <= -8.2e+167)
		tmp = Float64(y2 * Float64(Float64(c * Float64(x * y0)) + t_2));
	elseif (y2 <= -2.6e+65)
		tmp = Float64(k * Float64(Float64(z * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(y4 * Float64(Float64(y1 * y2) - Float64(y * b)))));
	elseif (y2 <= -1.6e-56)
		tmp = Float64(y4 * Float64(Float64(Float64(b * t_3) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) - Float64(c * Float64(Float64(t * y2) - Float64(y * y3)))));
	elseif (y2 <= 2.8e-259)
		tmp = Float64(i * Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) + Float64(Float64(y5 * Float64(Float64(y * k) - Float64(t * j))) - Float64(c * t_1))));
	elseif (y2 <= 6.2e-15)
		tmp = Float64(b * Float64(Float64(Float64(a * t_1) + Float64(y4 * t_3)) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	else
		tmp = Float64(y2 * Float64(Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))) + 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 = (x * y) - (z * t);
	t_2 = t * ((a * y5) - (c * y4));
	t_3 = (t * j) - (y * k);
	tmp = 0.0;
	if (y2 <= -8.2e+167)
		tmp = y2 * ((c * (x * y0)) + t_2);
	elseif (y2 <= -2.6e+65)
		tmp = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))));
	elseif (y2 <= -1.6e-56)
		tmp = y4 * (((b * t_3) + (y1 * ((k * y2) - (j * y3)))) - (c * ((t * y2) - (y * y3))));
	elseif (y2 <= 2.8e-259)
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * t_1)));
	elseif (y2 <= 6.2e-15)
		tmp = b * (((a * t_1) + (y4 * t_3)) + (y0 * ((z * k) - (x * j))));
	else
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + 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[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -8.2e+167], N[(y2 * N[(N[(c * N[(x * y0), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -2.6e+65], N[(k * N[(N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1.6e-56], N[(y4 * N[(N[(N[(b * t$95$3), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.8e-259], N[(i * N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 6.2e-15], N[(b * N[(N[(N[(a * t$95$1), $MachinePrecision] + N[(y4 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y2 * N[(N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y2 < -8.2e167

   1. Initial program 19.9%

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

   3. Taylor expanded in y2 around inf 47.3%

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

   4. Taylor expanded in c around inf 68.5%

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

   if -8.2e167 < y2 < -2.60000000000000003e65

   1. Initial program 29.2%

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

   3. Taylor expanded in k around inf 62.9%

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

   4. Taylor expanded in y5 around 0 53.2%

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

      1. cancel-sign-sub-inv 53.2%

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

      2. mul-1-neg 53.2%

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

      3. associate-*r* 57.9%

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

      4. distribute-lft-neg-in 57.9%

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

      5. mul-1-neg 57.9%

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

      6. associate-*r* 57.9%

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

      7. distribute-rgt-in 57.9%

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

      8. +-commutative 57.9%

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

      9. mul-1-neg 57.9%

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

      10. unsub-neg 57.9%

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

      11. *-commutative 57.9%

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

      12. metadata-eval 57.9%

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

      13. *-lft-identity 57.9%

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

   6. Simplified 57.9%

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

   if -2.60000000000000003e65 < y2 < -1.59999999999999993e-56

   1. Initial program 36.2%

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

   3. Taylor expanded in y4 around inf 58.3%

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

   if -1.59999999999999993e-56 < y2 < 2.8e-259

   1. Initial program 30.1%

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

   3. Taylor expanded in i around -inf 51.7%

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

   if 2.8e-259 < y2 < 6.1999999999999998e-15

   1. Initial program 44.1%

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

   3. Taylor expanded in b around inf 56.6%

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

   if 6.1999999999999998e-15 < y2

   1. Initial program 24.7%

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

   3. Taylor expanded in y2 around inf 60.3%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -8.2 \cdot 10^{+167}:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(x \cdot y0\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -2.6 \cdot 10^{+65}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right) + y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq -1.6 \cdot 10^{-56}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 2.8 \cdot 10^{-259}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) - c \cdot \left(x \cdot y - z \cdot t\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 6.2 \cdot 10^{-15}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 41.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot y5 - c \cdot y4\right)\\ t_2 := t \cdot j - y \cdot k\\ \mathbf{if}\;y2 \leq -7.2 \cdot 10^{+170}:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(x \cdot y0\right) + t\_1\right)\\ \mathbf{elif}\;y2 \leq -4 \cdot 10^{+71}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right) + y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 3.05 \cdot 10^{-276}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot t\_2 + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 1.12 \cdot 10^{-15}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot t\_2\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* t (- (* a y5) (* c y4)))) (t_2 (- (* t j) (* y k))))
   (if (<= y2 -7.2e+170)
     (* y2 (+ (* c (* x y0)) t_1))
     (if (<= y2 -4e+71)
       (* k (+ (* z (- (* b y0) (* i y1))) (* y4 (- (* y1 y2) (* y b)))))
       (if (<= y2 3.05e-276)
         (*
          y4
          (-
           (+ (* b t_2) (* y1 (- (* k y2) (* j y3))))
           (* c (- (* t y2) (* y y3)))))
         (if (<= y2 1.12e-15)
           (*
            b
            (+
             (+ (* a (- (* x y) (* z t))) (* y4 t_2))
             (* y0 (- (* z k) (* x j)))))
           (*
            y2
            (+
             (+ (* k (- (* y1 y4) (* y0 y5))) (* x (- (* c y0) (* a y1))))
             t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * ((a * y5) - (c * y4));
	double t_2 = (t * j) - (y * k);
	double tmp;
	if (y2 <= -7.2e+170) {
		tmp = y2 * ((c * (x * y0)) + t_1);
	} else if (y2 <= -4e+71) {
		tmp = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))));
	} else if (y2 <= 3.05e-276) {
		tmp = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) - (c * ((t * y2) - (y * y3))));
	} else if (y2 <= 1.12e-15) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))));
	} else {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + 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 = t * ((a * y5) - (c * y4))
    t_2 = (t * j) - (y * k)
    if (y2 <= (-7.2d+170)) then
        tmp = y2 * ((c * (x * y0)) + t_1)
    else if (y2 <= (-4d+71)) then
        tmp = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))))
    else if (y2 <= 3.05d-276) then
        tmp = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) - (c * ((t * y2) - (y * y3))))
    else if (y2 <= 1.12d-15) then
        tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))))
    else
        tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * ((a * y5) - (c * y4));
	double t_2 = (t * j) - (y * k);
	double tmp;
	if (y2 <= -7.2e+170) {
		tmp = y2 * ((c * (x * y0)) + t_1);
	} else if (y2 <= -4e+71) {
		tmp = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))));
	} else if (y2 <= 3.05e-276) {
		tmp = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) - (c * ((t * y2) - (y * y3))));
	} else if (y2 <= 1.12e-15) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))));
	} else {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = t * ((a * y5) - (c * y4))
	t_2 = (t * j) - (y * k)
	tmp = 0
	if y2 <= -7.2e+170:
		tmp = y2 * ((c * (x * y0)) + t_1)
	elif y2 <= -4e+71:
		tmp = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))))
	elif y2 <= 3.05e-276:
		tmp = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) - (c * ((t * y2) - (y * y3))))
	elif y2 <= 1.12e-15:
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))))
	else:
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))
	t_2 = Float64(Float64(t * j) - Float64(y * k))
	tmp = 0.0
	if (y2 <= -7.2e+170)
		tmp = Float64(y2 * Float64(Float64(c * Float64(x * y0)) + t_1));
	elseif (y2 <= -4e+71)
		tmp = Float64(k * Float64(Float64(z * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(y4 * Float64(Float64(y1 * y2) - Float64(y * b)))));
	elseif (y2 <= 3.05e-276)
		tmp = Float64(y4 * Float64(Float64(Float64(b * t_2) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) - Float64(c * Float64(Float64(t * y2) - Float64(y * y3)))));
	elseif (y2 <= 1.12e-15)
		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)))));
	else
		tmp = Float64(y2 * Float64(Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))) + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = t * ((a * y5) - (c * y4));
	t_2 = (t * j) - (y * k);
	tmp = 0.0;
	if (y2 <= -7.2e+170)
		tmp = y2 * ((c * (x * y0)) + t_1);
	elseif (y2 <= -4e+71)
		tmp = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))));
	elseif (y2 <= 3.05e-276)
		tmp = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) - (c * ((t * y2) - (y * y3))));
	elseif (y2 <= 1.12e-15)
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))));
	else
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -7.2e+170], N[(y2 * N[(N[(c * N[(x * y0), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -4e+71], N[(k * N[(N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 3.05e-276], 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[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.12e-15], 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], N[(y2 * N[(N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y2 < -7.1999999999999999e170

   1. Initial program 19.9%

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

   3. Taylor expanded in y2 around inf 47.3%

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

   4. Taylor expanded in c around inf 68.5%

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

   if -7.1999999999999999e170 < y2 < -4.0000000000000002e71

   1. Initial program 29.2%

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

   3. Taylor expanded in k around inf 62.9%

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

   4. Taylor expanded in y5 around 0 53.2%

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

      1. cancel-sign-sub-inv 53.2%

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

      2. mul-1-neg 53.2%

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

      3. associate-*r* 57.9%

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

      4. distribute-lft-neg-in 57.9%

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

      5. mul-1-neg 57.9%

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

      6. associate-*r* 57.9%

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

      7. distribute-rgt-in 57.9%

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

      8. +-commutative 57.9%

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

      9. mul-1-neg 57.9%

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

      10. unsub-neg 57.9%

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

      11. *-commutative 57.9%

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

      12. metadata-eval 57.9%

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

      13. *-lft-identity 57.9%

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

   6. Simplified 57.9%

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

   if -4.0000000000000002e71 < y2 < 3.04999999999999989e-276

   1. Initial program 32.4%

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

   3. Taylor expanded in y4 around inf 44.1%

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

   if 3.04999999999999989e-276 < y2 < 1.1200000000000001e-15

   1. Initial program 43.2%

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

   3. Taylor expanded in b around inf 55.5%

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

   if 1.1200000000000001e-15 < y2

   1. Initial program 24.7%

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

   3. Taylor expanded in y2 around inf 60.3%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -7.2 \cdot 10^{+170}:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(x \cdot y0\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -4 \cdot 10^{+71}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right) + y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 3.05 \cdot 10^{-276}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 1.12 \cdot 10^{-15}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 37.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - y \cdot \left(c \cdot i - a \cdot b\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{if}\;x \leq -9 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-167}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right) + y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+74}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(x \cdot \left(t \cdot \frac{y5}{x} - y1\right)\right)\right)\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{+215}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(j \cdot \left(b \cdot \left(\frac{c \cdot y2}{b \cdot j} + -1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          x
          (+
           (- (* y2 (- (* c y0) (* a y1))) (* y (- (* c i) (* a b))))
           (* j (- (* i y1) (* b y0)))))))
   (if (<= x -9e+47)
     t_1
     (if (<= x -1.7e-167)
       (* k (+ (* z (- (* b y0) (* i y1))) (* y4 (- (* y1 y2) (* y b)))))
       (if (<= x 2.3e+74)
         (* a (* y2 (* x (- (* t (/ y5 x)) y1))))
         (if (<= x 7.6e+215)
           (* y0 (* x (* j (* b (+ (/ (* c y2) (* b j)) -1.0)))))
           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 = x * (((y2 * ((c * y0) - (a * y1))) - (y * ((c * i) - (a * b)))) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (x <= -9e+47) {
		tmp = t_1;
	} else if (x <= -1.7e-167) {
		tmp = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))));
	} else if (x <= 2.3e+74) {
		tmp = a * (y2 * (x * ((t * (y5 / x)) - y1)));
	} else if (x <= 7.6e+215) {
		tmp = y0 * (x * (j * (b * (((c * y2) / (b * j)) + -1.0))));
	} 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 = x * (((y2 * ((c * y0) - (a * y1))) - (y * ((c * i) - (a * b)))) + (j * ((i * y1) - (b * y0))))
    if (x <= (-9d+47)) then
        tmp = t_1
    else if (x <= (-1.7d-167)) then
        tmp = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))))
    else if (x <= 2.3d+74) then
        tmp = a * (y2 * (x * ((t * (y5 / x)) - y1)))
    else if (x <= 7.6d+215) then
        tmp = y0 * (x * (j * (b * (((c * y2) / (b * j)) + (-1.0d0)))))
    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 = x * (((y2 * ((c * y0) - (a * y1))) - (y * ((c * i) - (a * b)))) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (x <= -9e+47) {
		tmp = t_1;
	} else if (x <= -1.7e-167) {
		tmp = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))));
	} else if (x <= 2.3e+74) {
		tmp = a * (y2 * (x * ((t * (y5 / x)) - y1)));
	} else if (x <= 7.6e+215) {
		tmp = y0 * (x * (j * (b * (((c * y2) / (b * j)) + -1.0))));
	} 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 = x * (((y2 * ((c * y0) - (a * y1))) - (y * ((c * i) - (a * b)))) + (j * ((i * y1) - (b * y0))))
	tmp = 0
	if x <= -9e+47:
		tmp = t_1
	elif x <= -1.7e-167:
		tmp = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))))
	elif x <= 2.3e+74:
		tmp = a * (y2 * (x * ((t * (y5 / x)) - y1)))
	elif x <= 7.6e+215:
		tmp = y0 * (x * (j * (b * (((c * y2) / (b * j)) + -1.0))))
	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(x * Float64(Float64(Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))) - Float64(y * Float64(Float64(c * i) - Float64(a * b)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))))
	tmp = 0.0
	if (x <= -9e+47)
		tmp = t_1;
	elseif (x <= -1.7e-167)
		tmp = Float64(k * Float64(Float64(z * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(y4 * Float64(Float64(y1 * y2) - Float64(y * b)))));
	elseif (x <= 2.3e+74)
		tmp = Float64(a * Float64(y2 * Float64(x * Float64(Float64(t * Float64(y5 / x)) - y1))));
	elseif (x <= 7.6e+215)
		tmp = Float64(y0 * Float64(x * Float64(j * Float64(b * Float64(Float64(Float64(c * y2) / Float64(b * j)) + -1.0)))));
	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 = x * (((y2 * ((c * y0) - (a * y1))) - (y * ((c * i) - (a * b)))) + (j * ((i * y1) - (b * y0))));
	tmp = 0.0;
	if (x <= -9e+47)
		tmp = t_1;
	elseif (x <= -1.7e-167)
		tmp = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))));
	elseif (x <= 2.3e+74)
		tmp = a * (y2 * (x * ((t * (y5 / x)) - y1)));
	elseif (x <= 7.6e+215)
		tmp = y0 * (x * (j * (b * (((c * y2) / (b * j)) + -1.0))));
	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[(x * N[(N[(N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9e+47], t$95$1, If[LessEqual[x, -1.7e-167], N[(k * N[(N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.3e+74], N[(a * N[(y2 * N[(x * N[(N[(t * N[(y5 / x), $MachinePrecision]), $MachinePrecision] - y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.6e+215], N[(y0 * N[(x * N[(j * N[(b * N[(N[(N[(c * y2), $MachinePrecision] / N[(b * j), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -8.99999999999999958e47 or 7.59999999999999937e215 < x

   1. Initial program 18.2%

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

   3. Taylor expanded in x around inf 64.3%

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

   if -8.99999999999999958e47 < x < -1.6999999999999999e-167

   1. Initial program 31.1%

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

   3. Taylor expanded in k around inf 48.7%

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

   4. Taylor expanded in y5 around 0 48.9%

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

      1. cancel-sign-sub-inv 48.9%

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

      2. mul-1-neg 48.9%

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

      3. associate-*r* 51.1%

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

      4. distribute-lft-neg-in 51.1%

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

      5. mul-1-neg 51.1%

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

      6. associate-*r* 51.1%

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

      7. distribute-rgt-in 51.1%

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

      8. +-commutative 51.1%

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

      9. mul-1-neg 51.1%

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

      10. unsub-neg 51.1%

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

      11. *-commutative 51.1%

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

      12. metadata-eval 51.1%

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

      13. *-lft-identity 51.1%

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

   6. Simplified 51.1%

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

   if -1.6999999999999999e-167 < x < 2.2999999999999999e74

   1. Initial program 40.3%

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

   3. Taylor expanded in y2 around inf 43.7%

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

   4. Taylor expanded in a around -inf 33.8%

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

      1. associate-*r* 33.8%

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

      2. neg-mul-1 33.8%

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

   6. Simplified 33.8%

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

   7. Taylor expanded in x around inf 42.3%

      \[\leadsto \left(-a\right) \cdot \left(y2 \cdot \color{blue}{\left(x \cdot \left(y1 + -1 \cdot \frac{t \cdot y5}{x}\right)\right)}\right) \]
   8. Step-by-step derivation

      1. mul-1-neg 42.3%

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

      2. unsub-neg 42.3%

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

      3. associate-/l* 47.2%

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

   9. Simplified 47.2%

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

   if 2.2999999999999999e74 < x < 7.59999999999999937e215

   1. Initial program 34.6%

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

   3. Taylor expanded in y0 around inf 31.5%

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

   4. Taylor expanded in x around inf 50.4%

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

   5. Taylor expanded in j around inf 50.4%

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

   6. Taylor expanded in b around inf 50.6%

      \[\leadsto y0 \cdot \left(x \cdot \left(j \cdot \color{blue}{\left(b \cdot \left(\frac{c \cdot y2}{b \cdot j} - 1\right)\right)}\right)\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \left(\left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - y \cdot \left(c \cdot i - a \cdot b\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-167}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right) + y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+74}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(x \cdot \left(t \cdot \frac{y5}{x} - y1\right)\right)\right)\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{+215}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(j \cdot \left(b \cdot \left(\frac{c \cdot y2}{b \cdot j} + -1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - y \cdot \left(c \cdot i - a \cdot b\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 41.8% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot y0 - a \cdot y1\\ t_2 := t \cdot \left(a \cdot y5 - c \cdot y4\right)\\ \mathbf{if}\;y2 \leq -4 \cdot 10^{+160}:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(x \cdot y0\right) + t\_2\right)\\ \mathbf{elif}\;y2 \leq -4.1 \cdot 10^{-161}:\\ \;\;\;\;x \cdot \left(\left(y2 \cdot t\_1 - y \cdot \left(c \cdot i - a \cdot b\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 3.4 \cdot 10^{-23}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot t\_1\right) + t\_2\right)\\ \end{array} \end{array} \]

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 (* t (- (* a y5) (* c y4)))))
   (if (<= y2 -4e+160)
     (* y2 (+ (* c (* x y0)) t_2))
     (if (<= y2 -4.1e-161)
       (*
        x
        (+
         (- (* y2 t_1) (* y (- (* c i) (* a b))))
         (* j (- (* i y1) (* b y0)))))
       (if (<= y2 3.4e-23)
         (*
          b
          (+
           (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
           (* y0 (- (* z k) (* x j)))))
         (* y2 (+ (+ (* k (- (* y1 y4) (* y0 y5))) (* x t_1)) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y0) - (a * y1);
	double t_2 = t * ((a * y5) - (c * y4));
	double tmp;
	if (y2 <= -4e+160) {
		tmp = y2 * ((c * (x * y0)) + t_2);
	} else if (y2 <= -4.1e-161) {
		tmp = x * (((y2 * t_1) - (y * ((c * i) - (a * b)))) + (j * ((i * y1) - (b * y0))));
	} else if (y2 <= 3.4e-23) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_1)) + t_2);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (c * y0) - (a * y1)
    t_2 = t * ((a * y5) - (c * y4))
    if (y2 <= (-4d+160)) then
        tmp = y2 * ((c * (x * y0)) + t_2)
    else if (y2 <= (-4.1d-161)) then
        tmp = x * (((y2 * t_1) - (y * ((c * i) - (a * b)))) + (j * ((i * y1) - (b * y0))))
    else if (y2 <= 3.4d-23) then
        tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    else
        tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_1)) + 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 = t * ((a * y5) - (c * y4));
	double tmp;
	if (y2 <= -4e+160) {
		tmp = y2 * ((c * (x * y0)) + t_2);
	} else if (y2 <= -4.1e-161) {
		tmp = x * (((y2 * t_1) - (y * ((c * i) - (a * b)))) + (j * ((i * y1) - (b * y0))));
	} else if (y2 <= 3.4e-23) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_1)) + 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 = t * ((a * y5) - (c * y4))
	tmp = 0
	if y2 <= -4e+160:
		tmp = y2 * ((c * (x * y0)) + t_2)
	elif y2 <= -4.1e-161:
		tmp = x * (((y2 * t_1) - (y * ((c * i) - (a * b)))) + (j * ((i * y1) - (b * y0))))
	elif y2 <= 3.4e-23:
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	else:
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_1)) + 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(t * Float64(Float64(a * y5) - Float64(c * y4)))
	tmp = 0.0
	if (y2 <= -4e+160)
		tmp = Float64(y2 * Float64(Float64(c * Float64(x * y0)) + t_2));
	elseif (y2 <= -4.1e-161)
		tmp = Float64(x * Float64(Float64(Float64(y2 * t_1) - Float64(y * Float64(Float64(c * i) - Float64(a * b)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (y2 <= 3.4e-23)
		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)))));
	else
		tmp = Float64(y2 * Float64(Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(x * t_1)) + 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 = t * ((a * y5) - (c * y4));
	tmp = 0.0;
	if (y2 <= -4e+160)
		tmp = y2 * ((c * (x * y0)) + t_2);
	elseif (y2 <= -4.1e-161)
		tmp = x * (((y2 * t_1) - (y * ((c * i) - (a * b)))) + (j * ((i * y1) - (b * y0))));
	elseif (y2 <= 3.4e-23)
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	else
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_1)) + 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[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -4e+160], N[(y2 * N[(N[(c * N[(x * y0), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -4.1e-161], N[(x * N[(N[(N[(y2 * t$95$1), $MachinePrecision] - N[(y * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 3.4e-23], 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], N[(y2 * N[(N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$1), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y2 < -4.00000000000000003e160

   1. Initial program 18.9%

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

   3. Taylor expanded in y2 around inf 44.8%

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

   4. Taylor expanded in c around inf 67.5%

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

   if -4.00000000000000003e160 < y2 < -4.0999999999999997e-161

   1. Initial program 28.3%

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

   3. Taylor expanded in x around inf 44.9%

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

   if -4.0999999999999997e-161 < y2 < 3.4000000000000001e-23

   1. Initial program 42.2%

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

   3. Taylor expanded in b around inf 48.3%

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

   if 3.4000000000000001e-23 < y2

   1. Initial program 24.7%

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

   3. Taylor expanded in y2 around inf 60.3%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -4 \cdot 10^{+160}:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(x \cdot y0\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -4.1 \cdot 10^{-161}:\\ \;\;\;\;x \cdot \left(\left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - y \cdot \left(c \cdot i - a \cdot b\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 3.4 \cdot 10^{-23}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 33.2% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{if}\;i \leq -3.8 \cdot 10^{+161}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(j \cdot \left(b \cdot \left(\frac{c \cdot y2}{b \cdot j} + -1\right)\right)\right)\right)\\ \mathbf{elif}\;i \leq -2.9 \cdot 10^{+66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -3 \cdot 10^{-143}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(j \cdot \left(\frac{c \cdot y2}{j} - b\right)\right)\right)\\ \mathbf{elif}\;i \leq 8.8 \cdot 10^{-92}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(x \cdot \left(t \cdot \frac{y5}{x} - y1\right)\right)\right)\\ \mathbf{elif}\;i \leq 4 \cdot 10^{+74}:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(x \cdot y0\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (* i (- (* y y5) (* z y1))))))
   (if (<= i -3.8e+161)
     (* y0 (* x (* j (* b (+ (/ (* c y2) (* b j)) -1.0)))))
     (if (<= i -2.9e+66)
       t_1
       (if (<= i -3e-143)
         (* y0 (* x (* j (- (/ (* c y2) j) b))))
         (if (<= i 8.8e-92)
           (* a (* y2 (* x (- (* t (/ y5 x)) y1))))
           (if (<= i 4e+74)
             (* y2 (+ (* c (* x y0)) (* t (- (* a y5) (* 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 = k * (i * ((y * y5) - (z * y1)));
	double tmp;
	if (i <= -3.8e+161) {
		tmp = y0 * (x * (j * (b * (((c * y2) / (b * j)) + -1.0))));
	} else if (i <= -2.9e+66) {
		tmp = t_1;
	} else if (i <= -3e-143) {
		tmp = y0 * (x * (j * (((c * y2) / j) - b)));
	} else if (i <= 8.8e-92) {
		tmp = a * (y2 * (x * ((t * (y5 / x)) - y1)));
	} else if (i <= 4e+74) {
		tmp = y2 * ((c * (x * y0)) + (t * ((a * y5) - (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 = k * (i * ((y * y5) - (z * y1)))
    if (i <= (-3.8d+161)) then
        tmp = y0 * (x * (j * (b * (((c * y2) / (b * j)) + (-1.0d0)))))
    else if (i <= (-2.9d+66)) then
        tmp = t_1
    else if (i <= (-3d-143)) then
        tmp = y0 * (x * (j * (((c * y2) / j) - b)))
    else if (i <= 8.8d-92) then
        tmp = a * (y2 * (x * ((t * (y5 / x)) - y1)))
    else if (i <= 4d+74) then
        tmp = y2 * ((c * (x * y0)) + (t * ((a * y5) - (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 = k * (i * ((y * y5) - (z * y1)));
	double tmp;
	if (i <= -3.8e+161) {
		tmp = y0 * (x * (j * (b * (((c * y2) / (b * j)) + -1.0))));
	} else if (i <= -2.9e+66) {
		tmp = t_1;
	} else if (i <= -3e-143) {
		tmp = y0 * (x * (j * (((c * y2) / j) - b)));
	} else if (i <= 8.8e-92) {
		tmp = a * (y2 * (x * ((t * (y5 / x)) - y1)));
	} else if (i <= 4e+74) {
		tmp = y2 * ((c * (x * y0)) + (t * ((a * y5) - (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 = k * (i * ((y * y5) - (z * y1)))
	tmp = 0
	if i <= -3.8e+161:
		tmp = y0 * (x * (j * (b * (((c * y2) / (b * j)) + -1.0))))
	elif i <= -2.9e+66:
		tmp = t_1
	elif i <= -3e-143:
		tmp = y0 * (x * (j * (((c * y2) / j) - b)))
	elif i <= 8.8e-92:
		tmp = a * (y2 * (x * ((t * (y5 / x)) - y1)))
	elif i <= 4e+74:
		tmp = y2 * ((c * (x * y0)) + (t * ((a * y5) - (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(k * Float64(i * Float64(Float64(y * y5) - Float64(z * y1))))
	tmp = 0.0
	if (i <= -3.8e+161)
		tmp = Float64(y0 * Float64(x * Float64(j * Float64(b * Float64(Float64(Float64(c * y2) / Float64(b * j)) + -1.0)))));
	elseif (i <= -2.9e+66)
		tmp = t_1;
	elseif (i <= -3e-143)
		tmp = Float64(y0 * Float64(x * Float64(j * Float64(Float64(Float64(c * y2) / j) - b))));
	elseif (i <= 8.8e-92)
		tmp = Float64(a * Float64(y2 * Float64(x * Float64(Float64(t * Float64(y5 / x)) - y1))));
	elseif (i <= 4e+74)
		tmp = Float64(y2 * Float64(Float64(c * Float64(x * y0)) + Float64(t * Float64(Float64(a * y5) - 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 = k * (i * ((y * y5) - (z * y1)));
	tmp = 0.0;
	if (i <= -3.8e+161)
		tmp = y0 * (x * (j * (b * (((c * y2) / (b * j)) + -1.0))));
	elseif (i <= -2.9e+66)
		tmp = t_1;
	elseif (i <= -3e-143)
		tmp = y0 * (x * (j * (((c * y2) / j) - b)));
	elseif (i <= 8.8e-92)
		tmp = a * (y2 * (x * ((t * (y5 / x)) - y1)));
	elseif (i <= 4e+74)
		tmp = y2 * ((c * (x * y0)) + (t * ((a * y5) - (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[(k * N[(i * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -3.8e+161], N[(y0 * N[(x * N[(j * N[(b * N[(N[(N[(c * y2), $MachinePrecision] / N[(b * j), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -2.9e+66], t$95$1, If[LessEqual[i, -3e-143], N[(y0 * N[(x * N[(j * N[(N[(N[(c * y2), $MachinePrecision] / j), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 8.8e-92], N[(a * N[(y2 * N[(x * N[(N[(t * N[(y5 / x), $MachinePrecision]), $MachinePrecision] - y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4e+74], N[(y2 * N[(N[(c * N[(x * y0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -3.8000000000000002e161

   1. Initial program 8.1%

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

   3. Taylor expanded in y0 around inf 51.2%

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

   4. Taylor expanded in x around inf 45.1%

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

   5. Taylor expanded in j around inf 45.1%

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

   6. Taylor expanded in b around inf 57.1%

      \[\leadsto y0 \cdot \left(x \cdot \left(j \cdot \color{blue}{\left(b \cdot \left(\frac{c \cdot y2}{b \cdot j} - 1\right)\right)}\right)\right) \]

   if -3.8000000000000002e161 < i < -2.89999999999999986e66 or 3.99999999999999981e74 < i

   1. Initial program 29.5%

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

   3. Taylor expanded in k around inf 40.6%

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

   4. Taylor expanded in i around inf 55.1%

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

      1. *-commutative 55.1%

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

   6. Simplified 55.1%

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

   if -2.89999999999999986e66 < i < -2.99999999999999985e-143

   1. Initial program 37.1%

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

   3. Taylor expanded in y0 around inf 48.2%

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

   4. Taylor expanded in x around inf 43.3%

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

   5. Taylor expanded in j around inf 48.4%

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

   if -2.99999999999999985e-143 < i < 8.79999999999999949e-92

   1. Initial program 41.6%

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

   3. Taylor expanded in y2 around inf 47.0%

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

   4. Taylor expanded in a around -inf 41.0%

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

      1. associate-*r* 41.0%

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

      2. neg-mul-1 41.0%

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

   6. Simplified 41.0%

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

   7. Taylor expanded in x around inf 48.4%

      \[\leadsto \left(-a\right) \cdot \left(y2 \cdot \color{blue}{\left(x \cdot \left(y1 + -1 \cdot \frac{t \cdot y5}{x}\right)\right)}\right) \]
   8. Step-by-step derivation

      1. mul-1-neg 48.4%

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

      2. unsub-neg 48.4%

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

      3. associate-/l* 49.7%

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

   9. Simplified 49.7%

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

   if 8.79999999999999949e-92 < i < 3.99999999999999981e74

   1. Initial program 27.9%

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

   3. Taylor expanded in y2 around inf 53.4%

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

   4. Taylor expanded in c around inf 58.7%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.8 \cdot 10^{+161}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(j \cdot \left(b \cdot \left(\frac{c \cdot y2}{b \cdot j} + -1\right)\right)\right)\right)\\ \mathbf{elif}\;i \leq -2.9 \cdot 10^{+66}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;i \leq -3 \cdot 10^{-143}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(j \cdot \left(\frac{c \cdot y2}{j} - b\right)\right)\right)\\ \mathbf{elif}\;i \leq 8.8 \cdot 10^{-92}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(x \cdot \left(t \cdot \frac{y5}{x} - y1\right)\right)\right)\\ \mathbf{elif}\;i \leq 4 \cdot 10^{+74}:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(x \cdot y0\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 34.9% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y5 \leq -7 \cdot 10^{+205}:\\ \;\;\;\;k \cdot \left(y5 \cdot \left(y \cdot i - y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq -2.8 \cdot 10^{-24}:\\ \;\;\;\;y3 \cdot \left(\left(a \cdot \left(z \cdot y1\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) - a \cdot \left(y \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq -6.1 \cdot 10^{-68}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y5 \leq -1.1 \cdot 10^{-250}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq 2.12 \cdot 10^{-44}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(x \cdot \left(t \cdot \frac{y5}{x} - y1\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y5 -7e+205)
   (* k (* y5 (- (* y i) (* y0 y2))))
   (if (<= y5 -2.8e-24)
     (* y3 (- (+ (* a (* z y1)) (* j (- (* y0 y5) (* y1 y4)))) (* a (* y y5))))
     (if (<= y5 -6.1e-68)
       (* y1 (* i (- (* x j) (* z k))))
       (if (<= y5 -1.1e-250)
         (* y0 (+ (* c (- (* x y2) (* z y3))) (* b (- (* z k) (* x j)))))
         (if (<= y5 2.12e-44)
           (* j (* y1 (- (* x i) (* y3 y4))))
           (* a (* y2 (* x (- (* t (/ y5 x)) y1))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -7e+205) {
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	} else if (y5 <= -2.8e-24) {
		tmp = y3 * (((a * (z * y1)) + (j * ((y0 * y5) - (y1 * y4)))) - (a * (y * y5)));
	} else if (y5 <= -6.1e-68) {
		tmp = y1 * (i * ((x * j) - (z * k)));
	} else if (y5 <= -1.1e-250) {
		tmp = y0 * ((c * ((x * y2) - (z * y3))) + (b * ((z * k) - (x * j))));
	} else if (y5 <= 2.12e-44) {
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	} else {
		tmp = a * (y2 * (x * ((t * (y5 / x)) - y1)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y5 <= (-7d+205)) then
        tmp = k * (y5 * ((y * i) - (y0 * y2)))
    else if (y5 <= (-2.8d-24)) then
        tmp = y3 * (((a * (z * y1)) + (j * ((y0 * y5) - (y1 * y4)))) - (a * (y * y5)))
    else if (y5 <= (-6.1d-68)) then
        tmp = y1 * (i * ((x * j) - (z * k)))
    else if (y5 <= (-1.1d-250)) then
        tmp = y0 * ((c * ((x * y2) - (z * y3))) + (b * ((z * k) - (x * j))))
    else if (y5 <= 2.12d-44) then
        tmp = j * (y1 * ((x * i) - (y3 * y4)))
    else
        tmp = a * (y2 * (x * ((t * (y5 / x)) - y1)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -7e+205) {
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	} else if (y5 <= -2.8e-24) {
		tmp = y3 * (((a * (z * y1)) + (j * ((y0 * y5) - (y1 * y4)))) - (a * (y * y5)));
	} else if (y5 <= -6.1e-68) {
		tmp = y1 * (i * ((x * j) - (z * k)));
	} else if (y5 <= -1.1e-250) {
		tmp = y0 * ((c * ((x * y2) - (z * y3))) + (b * ((z * k) - (x * j))));
	} else if (y5 <= 2.12e-44) {
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	} else {
		tmp = a * (y2 * (x * ((t * (y5 / x)) - y1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y5 <= -7e+205:
		tmp = k * (y5 * ((y * i) - (y0 * y2)))
	elif y5 <= -2.8e-24:
		tmp = y3 * (((a * (z * y1)) + (j * ((y0 * y5) - (y1 * y4)))) - (a * (y * y5)))
	elif y5 <= -6.1e-68:
		tmp = y1 * (i * ((x * j) - (z * k)))
	elif y5 <= -1.1e-250:
		tmp = y0 * ((c * ((x * y2) - (z * y3))) + (b * ((z * k) - (x * j))))
	elif y5 <= 2.12e-44:
		tmp = j * (y1 * ((x * i) - (y3 * y4)))
	else:
		tmp = a * (y2 * (x * ((t * (y5 / x)) - y1)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y5 <= -7e+205)
		tmp = Float64(k * Float64(y5 * Float64(Float64(y * i) - Float64(y0 * y2))));
	elseif (y5 <= -2.8e-24)
		tmp = Float64(y3 * Float64(Float64(Float64(a * Float64(z * y1)) + Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) - Float64(a * Float64(y * y5))));
	elseif (y5 <= -6.1e-68)
		tmp = Float64(y1 * Float64(i * Float64(Float64(x * j) - Float64(z * k))));
	elseif (y5 <= -1.1e-250)
		tmp = Float64(y0 * Float64(Float64(c * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(b * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (y5 <= 2.12e-44)
		tmp = Float64(j * Float64(y1 * Float64(Float64(x * i) - Float64(y3 * y4))));
	else
		tmp = Float64(a * Float64(y2 * Float64(x * Float64(Float64(t * Float64(y5 / x)) - y1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y5 <= -7e+205)
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	elseif (y5 <= -2.8e-24)
		tmp = y3 * (((a * (z * y1)) + (j * ((y0 * y5) - (y1 * y4)))) - (a * (y * y5)));
	elseif (y5 <= -6.1e-68)
		tmp = y1 * (i * ((x * j) - (z * k)));
	elseif (y5 <= -1.1e-250)
		tmp = y0 * ((c * ((x * y2) - (z * y3))) + (b * ((z * k) - (x * j))));
	elseif (y5 <= 2.12e-44)
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	else
		tmp = a * (y2 * (x * ((t * (y5 / x)) - y1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y5, -7e+205], N[(k * N[(y5 * N[(N[(y * i), $MachinePrecision] - N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -2.8e-24], N[(y3 * N[(N[(N[(a * N[(z * y1), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -6.1e-68], N[(y1 * N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.1e-250], N[(y0 * N[(N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 2.12e-44], N[(j * N[(y1 * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y2 * N[(x * N[(N[(t * N[(y5 / x), $MachinePrecision]), $MachinePrecision] - y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y5 < -6.9999999999999996e205

   1. Initial program 18.5%

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

   3. Taylor expanded in k around inf 44.6%

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

   4. Taylor expanded in y5 around inf 59.5%

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

      1. +-commutative 59.5%

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

      2. mul-1-neg 59.5%

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

      3. unsub-neg 59.5%

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

      4. *-commutative 59.5%

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

   6. Simplified 59.5%

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

   if -6.9999999999999996e205 < y5 < -2.8000000000000002e-24

   1. Initial program 27.5%

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

   3. Taylor expanded in y3 around -inf 50.6%

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

   4. Taylor expanded in c around 0 63.4%

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

   if -2.8000000000000002e-24 < y5 < -6.1e-68

   1. Initial program 24.9%

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

   3. Taylor expanded in y1 around inf 65.3%

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

   4. Taylor expanded in i around inf 60.9%

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

   if -6.1e-68 < y5 < -1.1e-250

   1. Initial program 33.8%

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

   3. Taylor expanded in y0 around inf 47.8%

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

   4. Taylor expanded in y5 around 0 47.5%

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

   if -1.1e-250 < y5 < 2.1199999999999999e-44

   1. Initial program 43.3%

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

   3. Taylor expanded in y1 around inf 42.1%

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

   4. Taylor expanded in j around -inf 45.7%

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

      1. associate-*r* 45.7%

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

      2. neg-mul-1 45.7%

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

   6. Simplified 45.7%

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

   if 2.1199999999999999e-44 < y5

   1. Initial program 28.4%

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

   3. Taylor expanded in y2 around inf 43.6%

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

   4. Taylor expanded in a around -inf 42.4%

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

      1. associate-*r* 42.4%

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

      2. neg-mul-1 42.4%

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

   6. Simplified 42.4%

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

   7. Taylor expanded in x around inf 50.0%

      \[\leadsto \left(-a\right) \cdot \left(y2 \cdot \color{blue}{\left(x \cdot \left(y1 + -1 \cdot \frac{t \cdot y5}{x}\right)\right)}\right) \]
   8. Step-by-step derivation

      1. mul-1-neg 50.0%

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

      2. unsub-neg 50.0%

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

      3. associate-/l* 54.0%

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

   9. Simplified 54.0%

      \[\leadsto \left(-a\right) \cdot \left(y2 \cdot \color{blue}{\left(x \cdot \left(y1 - t \cdot \frac{y5}{x}\right)\right)}\right) \]
3. Recombined 6 regimes into one program.

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -7 \cdot 10^{+205}:\\ \;\;\;\;k \cdot \left(y5 \cdot \left(y \cdot i - y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq -2.8 \cdot 10^{-24}:\\ \;\;\;\;y3 \cdot \left(\left(a \cdot \left(z \cdot y1\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) - a \cdot \left(y \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq -6.1 \cdot 10^{-68}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y5 \leq -1.1 \cdot 10^{-250}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq 2.12 \cdot 10^{-44}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(x \cdot \left(t \cdot \frac{y5}{x} - y1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 33.5% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y3 \leq -3.7 \cdot 10^{+199}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;y3 \leq -1.1 \cdot 10^{+95}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right) + y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;y3 \leq 5 \cdot 10^{-102}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(x \cdot \left(t \cdot \frac{y5}{x} - y1\right)\right)\right)\\ \mathbf{elif}\;y3 \leq 4.5 \cdot 10^{+152}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y3 \cdot \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) - z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y3 -3.7e+199)
   (* y1 (* y4 (- (* k y2) (* j y3))))
   (if (<= y3 -1.1e+95)
     (* k (+ (* z (- (* b y0) (* i y1))) (* y4 (- (* y1 y2) (* y b)))))
     (if (<= y3 5e-102)
       (* a (* y2 (* x (- (* t (/ y5 x)) y1))))
       (if (<= y3 4.5e+152)
         (* b (* x (- (* y a) (* j y0))))
         (*
          y3
          (- (* j (- (* y0 y5) (* y1 y4))) (* z (- (* c y0) (* a y1))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y3 <= -3.7e+199) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else if (y3 <= -1.1e+95) {
		tmp = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))));
	} else if (y3 <= 5e-102) {
		tmp = a * (y2 * (x * ((t * (y5 / x)) - y1)));
	} else if (y3 <= 4.5e+152) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else {
		tmp = y3 * ((j * ((y0 * y5) - (y1 * y4))) - (z * ((c * y0) - (a * y1))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y3 <= (-3.7d+199)) then
        tmp = y1 * (y4 * ((k * y2) - (j * y3)))
    else if (y3 <= (-1.1d+95)) then
        tmp = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))))
    else if (y3 <= 5d-102) then
        tmp = a * (y2 * (x * ((t * (y5 / x)) - y1)))
    else if (y3 <= 4.5d+152) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else
        tmp = y3 * ((j * ((y0 * y5) - (y1 * y4))) - (z * ((c * y0) - (a * y1))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y3 <= -3.7e+199) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else if (y3 <= -1.1e+95) {
		tmp = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))));
	} else if (y3 <= 5e-102) {
		tmp = a * (y2 * (x * ((t * (y5 / x)) - y1)));
	} else if (y3 <= 4.5e+152) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else {
		tmp = y3 * ((j * ((y0 * y5) - (y1 * y4))) - (z * ((c * y0) - (a * y1))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y3 <= -3.7e+199:
		tmp = y1 * (y4 * ((k * y2) - (j * y3)))
	elif y3 <= -1.1e+95:
		tmp = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))))
	elif y3 <= 5e-102:
		tmp = a * (y2 * (x * ((t * (y5 / x)) - y1)))
	elif y3 <= 4.5e+152:
		tmp = b * (x * ((y * a) - (j * y0)))
	else:
		tmp = y3 * ((j * ((y0 * y5) - (y1 * y4))) - (z * ((c * y0) - (a * y1))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y3 <= -3.7e+199)
		tmp = Float64(y1 * Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif (y3 <= -1.1e+95)
		tmp = Float64(k * Float64(Float64(z * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(y4 * Float64(Float64(y1 * y2) - Float64(y * b)))));
	elseif (y3 <= 5e-102)
		tmp = Float64(a * Float64(y2 * Float64(x * Float64(Float64(t * Float64(y5 / x)) - y1))));
	elseif (y3 <= 4.5e+152)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	else
		tmp = Float64(y3 * Float64(Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4))) - Float64(z * Float64(Float64(c * y0) - Float64(a * y1)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y3 <= -3.7e+199)
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	elseif (y3 <= -1.1e+95)
		tmp = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))));
	elseif (y3 <= 5e-102)
		tmp = a * (y2 * (x * ((t * (y5 / x)) - y1)));
	elseif (y3 <= 4.5e+152)
		tmp = b * (x * ((y * a) - (j * y0)));
	else
		tmp = y3 * ((j * ((y0 * y5) - (y1 * y4))) - (z * ((c * y0) - (a * y1))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y3, -3.7e+199], N[(y1 * N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -1.1e+95], N[(k * N[(N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 5e-102], N[(a * N[(y2 * N[(x * N[(N[(t * N[(y5 / x), $MachinePrecision]), $MachinePrecision] - y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 4.5e+152], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y3 * N[(N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y3 < -3.70000000000000021e199

   1. Initial program 35.8%

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

   3. Taylor expanded in y1 around inf 40.0%

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

   4. Taylor expanded in y4 around inf 65.0%

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

   if -3.70000000000000021e199 < y3 < -1.0999999999999999e95

   1. Initial program 30.0%

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

   3. Taylor expanded in k around inf 60.3%

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

   4. Taylor expanded in y5 around 0 66.5%

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

      1. cancel-sign-sub-inv 66.5%

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

      2. mul-1-neg 66.5%

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

      3. associate-*r* 66.5%

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

      4. distribute-lft-neg-in 66.5%

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

      5. mul-1-neg 66.5%

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

      6. associate-*r* 66.5%

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

      7. distribute-rgt-in 66.5%

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

      8. +-commutative 66.5%

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

      9. mul-1-neg 66.5%

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

      10. unsub-neg 66.5%

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

      11. *-commutative 66.5%

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

      12. metadata-eval 66.5%

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

      13. *-lft-identity 66.5%

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

   6. Simplified 66.5%

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

   if -1.0999999999999999e95 < y3 < 5.00000000000000026e-102

   1. Initial program 33.7%

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

   3. Taylor expanded in y2 around inf 41.9%

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

   4. Taylor expanded in a around -inf 36.9%

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

      1. associate-*r* 36.9%

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

      2. neg-mul-1 36.9%

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

   6. Simplified 36.9%

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

   7. Taylor expanded in x around inf 42.1%

      \[\leadsto \left(-a\right) \cdot \left(y2 \cdot \color{blue}{\left(x \cdot \left(y1 + -1 \cdot \frac{t \cdot y5}{x}\right)\right)}\right) \]
   8. Step-by-step derivation

      1. mul-1-neg 42.1%

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

      2. unsub-neg 42.1%

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

      3. associate-/l* 44.4%

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

   9. Simplified 44.4%

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

   if 5.00000000000000026e-102 < y3 < 4.5000000000000001e152

   1. Initial program 21.9%

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

   3. Taylor expanded in b around inf 40.0%

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

   4. Taylor expanded in x around inf 45.5%

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

   if 4.5000000000000001e152 < y3

   1. Initial program 31.0%

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

   3. Taylor expanded in y3 around -inf 88.5%

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

   4. Taylor expanded in y around 0 85.0%

      \[\leadsto -1 \cdot \color{blue}{\left(y3 \cdot \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -3.7 \cdot 10^{+199}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;y3 \leq -1.1 \cdot 10^{+95}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right) + y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;y3 \leq 5 \cdot 10^{-102}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(x \cdot \left(t \cdot \frac{y5}{x} - y1\right)\right)\right)\\ \mathbf{elif}\;y3 \leq 4.5 \cdot 10^{+152}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y3 \cdot \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) - z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 34.3% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y2 \cdot \left(x \cdot \left(t \cdot \frac{y5}{x} - y1\right)\right)\right)\\ t_2 := j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{if}\;y5 \leq -4.4 \cdot 10^{+188}:\\ \;\;\;\;k \cdot \left(y5 \cdot \left(y \cdot i - y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq -1.35 \cdot 10^{+94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y5 \leq -5 \cdot 10^{-47}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y5 \leq 1.8 \cdot 10^{-275}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right) + y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;y5 \leq 1.65 \cdot 10^{-41}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y2 (* x (- (* t (/ y5 x)) y1)))))
        (t_2 (* j (* y1 (- (* x i) (* y3 y4))))))
   (if (<= y5 -4.4e+188)
     (* k (* y5 (- (* y i) (* y0 y2))))
     (if (<= y5 -1.35e+94)
       t_1
       (if (<= y5 -5e-47)
         t_2
         (if (<= y5 1.8e-275)
           (* k (+ (* z (- (* b y0) (* i y1))) (* y4 (- (* y1 y2) (* y b)))))
           (if (<= y5 1.65e-41) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y2 * (x * ((t * (y5 / x)) - y1)));
	double t_2 = j * (y1 * ((x * i) - (y3 * y4)));
	double tmp;
	if (y5 <= -4.4e+188) {
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	} else if (y5 <= -1.35e+94) {
		tmp = t_1;
	} else if (y5 <= -5e-47) {
		tmp = t_2;
	} else if (y5 <= 1.8e-275) {
		tmp = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))));
	} else if (y5 <= 1.65e-41) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (y2 * (x * ((t * (y5 / x)) - y1)))
    t_2 = j * (y1 * ((x * i) - (y3 * y4)))
    if (y5 <= (-4.4d+188)) then
        tmp = k * (y5 * ((y * i) - (y0 * y2)))
    else if (y5 <= (-1.35d+94)) then
        tmp = t_1
    else if (y5 <= (-5d-47)) then
        tmp = t_2
    else if (y5 <= 1.8d-275) then
        tmp = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))))
    else if (y5 <= 1.65d-41) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y2 * (x * ((t * (y5 / x)) - y1)));
	double t_2 = j * (y1 * ((x * i) - (y3 * y4)));
	double tmp;
	if (y5 <= -4.4e+188) {
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	} else if (y5 <= -1.35e+94) {
		tmp = t_1;
	} else if (y5 <= -5e-47) {
		tmp = t_2;
	} else if (y5 <= 1.8e-275) {
		tmp = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))));
	} else if (y5 <= 1.65e-41) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y2 * (x * ((t * (y5 / x)) - y1)))
	t_2 = j * (y1 * ((x * i) - (y3 * y4)))
	tmp = 0
	if y5 <= -4.4e+188:
		tmp = k * (y5 * ((y * i) - (y0 * y2)))
	elif y5 <= -1.35e+94:
		tmp = t_1
	elif y5 <= -5e-47:
		tmp = t_2
	elif y5 <= 1.8e-275:
		tmp = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))))
	elif y5 <= 1.65e-41:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y2 * Float64(x * Float64(Float64(t * Float64(y5 / x)) - y1))))
	t_2 = Float64(j * Float64(y1 * Float64(Float64(x * i) - Float64(y3 * y4))))
	tmp = 0.0
	if (y5 <= -4.4e+188)
		tmp = Float64(k * Float64(y5 * Float64(Float64(y * i) - Float64(y0 * y2))));
	elseif (y5 <= -1.35e+94)
		tmp = t_1;
	elseif (y5 <= -5e-47)
		tmp = t_2;
	elseif (y5 <= 1.8e-275)
		tmp = Float64(k * Float64(Float64(z * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(y4 * Float64(Float64(y1 * y2) - Float64(y * b)))));
	elseif (y5 <= 1.65e-41)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y2 * (x * ((t * (y5 / x)) - y1)));
	t_2 = j * (y1 * ((x * i) - (y3 * y4)));
	tmp = 0.0;
	if (y5 <= -4.4e+188)
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	elseif (y5 <= -1.35e+94)
		tmp = t_1;
	elseif (y5 <= -5e-47)
		tmp = t_2;
	elseif (y5 <= 1.8e-275)
		tmp = k * ((z * ((b * y0) - (i * y1))) + (y4 * ((y1 * y2) - (y * b))));
	elseif (y5 <= 1.65e-41)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y2 * N[(x * N[(N[(t * N[(y5 / x), $MachinePrecision]), $MachinePrecision] - y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(y1 * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -4.4e+188], N[(k * N[(y5 * N[(N[(y * i), $MachinePrecision] - N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.35e+94], t$95$1, If[LessEqual[y5, -5e-47], t$95$2, If[LessEqual[y5, 1.8e-275], N[(k * N[(N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.65e-41], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y5 < -4.39999999999999998e188

   1. Initial program 20.0%

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

   3. Taylor expanded in k around inf 43.6%

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

   4. Taylor expanded in y5 around inf 56.9%

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

      1. +-commutative 56.9%

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

      2. mul-1-neg 56.9%

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

      3. unsub-neg 56.9%

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

      4. *-commutative 56.9%

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

   6. Simplified 56.9%

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

   if -4.39999999999999998e188 < y5 < -1.3500000000000001e94 or 1.65000000000000012e-41 < y5

   1. Initial program 28.4%

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

   3. Taylor expanded in y2 around inf 47.8%

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

   4. Taylor expanded in a around -inf 46.0%

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

      1. associate-*r* 46.0%

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

      2. neg-mul-1 46.0%

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

   6. Simplified 46.0%

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

   7. Taylor expanded in x around inf 53.6%

      \[\leadsto \left(-a\right) \cdot \left(y2 \cdot \color{blue}{\left(x \cdot \left(y1 + -1 \cdot \frac{t \cdot y5}{x}\right)\right)}\right) \]
   8. Step-by-step derivation

      1. mul-1-neg 53.6%

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

      2. unsub-neg 53.6%

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

      3. associate-/l* 59.5%

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

   9. Simplified 59.5%

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

   if -1.3500000000000001e94 < y5 < -5.00000000000000011e-47 or 1.79999999999999985e-275 < y5 < 1.65000000000000012e-41

   1. Initial program 40.7%

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

   3. Taylor expanded in y1 around inf 36.0%

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

   4. Taylor expanded in j around -inf 55.7%

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

      1. associate-*r* 55.7%

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

      2. neg-mul-1 55.7%

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

   6. Simplified 55.7%

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

   if -5.00000000000000011e-47 < y5 < 1.79999999999999985e-275

   1. Initial program 30.8%

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

   3. Taylor expanded in k around inf 41.4%

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

   4. Taylor expanded in y5 around 0 42.9%

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

      1. cancel-sign-sub-inv 42.9%

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

      2. mul-1-neg 42.9%

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

      3. associate-*r* 41.5%

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

      4. distribute-lft-neg-in 41.5%

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

      5. mul-1-neg 41.5%

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

      6. associate-*r* 41.5%

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

      7. distribute-rgt-in 41.5%

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

      8. +-commutative 41.5%

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

      9. mul-1-neg 41.5%

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

      10. unsub-neg 41.5%

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

      11. *-commutative 41.5%

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

      12. metadata-eval 41.5%

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

      13. *-lft-identity 41.5%

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

   6. Simplified 41.5%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y2 \cdot y1 - b \cdot y\right) + z \cdot \left(y0 \cdot b - y1 \cdot i\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -4.4 \cdot 10^{+188}:\\ \;\;\;\;k \cdot \left(y5 \cdot \left(y \cdot i - y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq -1.35 \cdot 10^{+94}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(x \cdot \left(t \cdot \frac{y5}{x} - y1\right)\right)\right)\\ \mathbf{elif}\;y5 \leq -5 \cdot 10^{-47}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 1.8 \cdot 10^{-275}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right) + y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;y5 \leq 1.65 \cdot 10^{-41}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(x \cdot \left(t \cdot \frac{y5}{x} - y1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 32.5% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y2 \cdot \left(x \cdot \left(t \cdot \frac{y5}{x} - y1\right)\right)\right)\\ t_2 := j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{if}\;y5 \leq -6.6 \cdot 10^{+178}:\\ \;\;\;\;k \cdot \left(y5 \cdot \left(y \cdot i - y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq -1.05 \cdot 10^{+93}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y5 \leq -3.3 \cdot 10^{-53}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y5 \leq -1.3 \cdot 10^{-241}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;y5 \leq 1.4 \cdot 10^{-40}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y2 (* x (- (* t (/ y5 x)) y1)))))
        (t_2 (* j (* y1 (- (* x i) (* y3 y4))))))
   (if (<= y5 -6.6e+178)
     (* k (* y5 (- (* y i) (* y0 y2))))
     (if (<= y5 -1.05e+93)
       t_1
       (if (<= y5 -3.3e-53)
         t_2
         (if (<= y5 -1.3e-241)
           (* x (* y2 (- (* c y0) (* a y1))))
           (if (<= y5 1.4e-40) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y2 * (x * ((t * (y5 / x)) - y1)));
	double t_2 = j * (y1 * ((x * i) - (y3 * y4)));
	double tmp;
	if (y5 <= -6.6e+178) {
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	} else if (y5 <= -1.05e+93) {
		tmp = t_1;
	} else if (y5 <= -3.3e-53) {
		tmp = t_2;
	} else if (y5 <= -1.3e-241) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (y5 <= 1.4e-40) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (y2 * (x * ((t * (y5 / x)) - y1)))
    t_2 = j * (y1 * ((x * i) - (y3 * y4)))
    if (y5 <= (-6.6d+178)) then
        tmp = k * (y5 * ((y * i) - (y0 * y2)))
    else if (y5 <= (-1.05d+93)) then
        tmp = t_1
    else if (y5 <= (-3.3d-53)) then
        tmp = t_2
    else if (y5 <= (-1.3d-241)) then
        tmp = x * (y2 * ((c * y0) - (a * y1)))
    else if (y5 <= 1.4d-40) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y2 * (x * ((t * (y5 / x)) - y1)));
	double t_2 = j * (y1 * ((x * i) - (y3 * y4)));
	double tmp;
	if (y5 <= -6.6e+178) {
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	} else if (y5 <= -1.05e+93) {
		tmp = t_1;
	} else if (y5 <= -3.3e-53) {
		tmp = t_2;
	} else if (y5 <= -1.3e-241) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (y5 <= 1.4e-40) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y2 * (x * ((t * (y5 / x)) - y1)))
	t_2 = j * (y1 * ((x * i) - (y3 * y4)))
	tmp = 0
	if y5 <= -6.6e+178:
		tmp = k * (y5 * ((y * i) - (y0 * y2)))
	elif y5 <= -1.05e+93:
		tmp = t_1
	elif y5 <= -3.3e-53:
		tmp = t_2
	elif y5 <= -1.3e-241:
		tmp = x * (y2 * ((c * y0) - (a * y1)))
	elif y5 <= 1.4e-40:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y2 * Float64(x * Float64(Float64(t * Float64(y5 / x)) - y1))))
	t_2 = Float64(j * Float64(y1 * Float64(Float64(x * i) - Float64(y3 * y4))))
	tmp = 0.0
	if (y5 <= -6.6e+178)
		tmp = Float64(k * Float64(y5 * Float64(Float64(y * i) - Float64(y0 * y2))));
	elseif (y5 <= -1.05e+93)
		tmp = t_1;
	elseif (y5 <= -3.3e-53)
		tmp = t_2;
	elseif (y5 <= -1.3e-241)
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (y5 <= 1.4e-40)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y2 * (x * ((t * (y5 / x)) - y1)));
	t_2 = j * (y1 * ((x * i) - (y3 * y4)));
	tmp = 0.0;
	if (y5 <= -6.6e+178)
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	elseif (y5 <= -1.05e+93)
		tmp = t_1;
	elseif (y5 <= -3.3e-53)
		tmp = t_2;
	elseif (y5 <= -1.3e-241)
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	elseif (y5 <= 1.4e-40)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y2 * N[(x * N[(N[(t * N[(y5 / x), $MachinePrecision]), $MachinePrecision] - y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(y1 * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -6.6e+178], N[(k * N[(y5 * N[(N[(y * i), $MachinePrecision] - N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.05e+93], t$95$1, If[LessEqual[y5, -3.3e-53], t$95$2, If[LessEqual[y5, -1.3e-241], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.4e-40], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y5 < -6.5999999999999996e178

   1. Initial program 20.0%

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

   3. Taylor expanded in k around inf 43.6%

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

   4. Taylor expanded in y5 around inf 56.9%

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

      1. +-commutative 56.9%

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

      2. mul-1-neg 56.9%

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

      3. unsub-neg 56.9%

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

      4. *-commutative 56.9%

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

   6. Simplified 56.9%

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

   if -6.5999999999999996e178 < y5 < -1.0499999999999999e93 or 1.4e-40 < y5

   1. Initial program 28.4%

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

   3. Taylor expanded in y2 around inf 47.8%

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

   4. Taylor expanded in a around -inf 46.0%

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

      1. associate-*r* 46.0%

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

      2. neg-mul-1 46.0%

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

   6. Simplified 46.0%

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

   7. Taylor expanded in x around inf 53.6%

      \[\leadsto \left(-a\right) \cdot \left(y2 \cdot \color{blue}{\left(x \cdot \left(y1 + -1 \cdot \frac{t \cdot y5}{x}\right)\right)}\right) \]
   8. Step-by-step derivation

      1. mul-1-neg 53.6%

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

      2. unsub-neg 53.6%

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

      3. associate-/l* 59.5%

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

   9. Simplified 59.5%

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

   if -1.0499999999999999e93 < y5 < -3.30000000000000004e-53 or -1.3e-241 < y5 < 1.4e-40

   1. Initial program 38.1%

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

   3. Taylor expanded in y1 around inf 41.8%

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

   4. Taylor expanded in j around -inf 48.6%

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

      1. associate-*r* 48.6%

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

      2. neg-mul-1 48.6%

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

   6. Simplified 48.6%

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

   if -3.30000000000000004e-53 < y5 < -1.3e-241

   1. Initial program 27.6%

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

   3. Taylor expanded in y2 around inf 30.3%

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

      1. associate-*r* 30.1%

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

      2. *-commutative 30.1%

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

   5. Simplified 30.1%

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

   6. Taylor expanded in x around inf 42.0%

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

      1. *-commutative 42.0%

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

      2. *-commutative 42.0%

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

   8. Simplified 42.0%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(y0 \cdot c - y1 \cdot a\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -6.6 \cdot 10^{+178}:\\ \;\;\;\;k \cdot \left(y5 \cdot \left(y \cdot i - y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq -1.05 \cdot 10^{+93}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(x \cdot \left(t \cdot \frac{y5}{x} - y1\right)\right)\right)\\ \mathbf{elif}\;y5 \leq -3.3 \cdot 10^{-53}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -1.3 \cdot 10^{-241}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;y5 \leq 1.4 \cdot 10^{-40}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(x \cdot \left(t \cdot \frac{y5}{x} - y1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 32.0% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+76}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq -2.45 \cdot 10^{-179}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-239}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;b \leq 2.35 \cdot 10^{+33}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+152}:\\ \;\;\;\;\left(b \cdot y4\right) \cdot \left(t \cdot j - y \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= b -5e+76)
   (* a (* b (- (* x y) (* z t))))
   (if (<= b -2.45e-179)
     (* j (* y1 (- (* x i) (* y3 y4))))
     (if (<= b 3.2e-239)
       (* y2 (* y4 (- (* k y1) (* t c))))
       (if (<= b 2.35e+33)
         (* y1 (* z (- (* a y3) (* i k))))
         (if (<= b 1.8e+152)
           (* (* b y4) (- (* t j) (* y k)))
           (* j (* y0 (- (* y3 y5) (* x b))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -5e+76) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (b <= -2.45e-179) {
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	} else if (b <= 3.2e-239) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (b <= 2.35e+33) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (b <= 1.8e+152) {
		tmp = (b * y4) * ((t * j) - (y * k));
	} else {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (b <= (-5d+76)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (b <= (-2.45d-179)) then
        tmp = j * (y1 * ((x * i) - (y3 * y4)))
    else if (b <= 3.2d-239) then
        tmp = y2 * (y4 * ((k * y1) - (t * c)))
    else if (b <= 2.35d+33) then
        tmp = y1 * (z * ((a * y3) - (i * k)))
    else if (b <= 1.8d+152) then
        tmp = (b * y4) * ((t * j) - (y * k))
    else
        tmp = j * (y0 * ((y3 * y5) - (x * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -5e+76) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (b <= -2.45e-179) {
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	} else if (b <= 3.2e-239) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (b <= 2.35e+33) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (b <= 1.8e+152) {
		tmp = (b * y4) * ((t * j) - (y * k));
	} else {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if b <= -5e+76:
		tmp = a * (b * ((x * y) - (z * t)))
	elif b <= -2.45e-179:
		tmp = j * (y1 * ((x * i) - (y3 * y4)))
	elif b <= 3.2e-239:
		tmp = y2 * (y4 * ((k * y1) - (t * c)))
	elif b <= 2.35e+33:
		tmp = y1 * (z * ((a * y3) - (i * k)))
	elif b <= 1.8e+152:
		tmp = (b * y4) * ((t * j) - (y * k))
	else:
		tmp = j * (y0 * ((y3 * y5) - (x * b)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (b <= -5e+76)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (b <= -2.45e-179)
		tmp = Float64(j * Float64(y1 * Float64(Float64(x * i) - Float64(y3 * y4))));
	elseif (b <= 3.2e-239)
		tmp = Float64(y2 * Float64(y4 * Float64(Float64(k * y1) - Float64(t * c))));
	elseif (b <= 2.35e+33)
		tmp = Float64(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * k))));
	elseif (b <= 1.8e+152)
		tmp = Float64(Float64(b * y4) * Float64(Float64(t * j) - Float64(y * k)));
	else
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (b <= -5e+76)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (b <= -2.45e-179)
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	elseif (b <= 3.2e-239)
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	elseif (b <= 2.35e+33)
		tmp = y1 * (z * ((a * y3) - (i * k)));
	elseif (b <= 1.8e+152)
		tmp = (b * y4) * ((t * j) - (y * k));
	else
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[b, -5e+76], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.45e-179], N[(j * N[(y1 * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.2e-239], N[(y2 * N[(y4 * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.35e+33], N[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.8e+152], N[(N[(b * y4), $MachinePrecision] * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -4.99999999999999991e76

   1. Initial program 21.2%

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

   3. Taylor expanded in b around inf 36.3%

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

   4. Taylor expanded in a around inf 46.9%

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

   if -4.99999999999999991e76 < b < -2.45e-179

   1. Initial program 39.2%

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

   3. Taylor expanded in y1 around inf 32.7%

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

   4. Taylor expanded in j around -inf 47.0%

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

      1. associate-*r* 47.0%

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

      2. neg-mul-1 47.0%

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

   6. Simplified 47.0%

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

   if -2.45e-179 < b < 3.1999999999999999e-239

   1. Initial program 36.1%

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

   3. Taylor expanded in y2 around inf 49.4%

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

   4. Taylor expanded in y4 around inf 50.2%

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

   if 3.1999999999999999e-239 < b < 2.3499999999999999e33

   1. Initial program 40.0%

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

   3. Taylor expanded in y1 around inf 38.9%

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

   4. Taylor expanded in z around inf 41.1%

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

   if 2.3499999999999999e33 < b < 1.7999999999999999e152

   1. Initial program 10.3%

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

   3. Taylor expanded in b around inf 50.3%

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

   4. Taylor expanded in y4 around inf 65.8%

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

      1. associate-*r* 65.8%

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

   6. Simplified 65.8%

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

   if 1.7999999999999999e152 < b

   1. Initial program 17.3%

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

   3. Taylor expanded in y0 around inf 45.9%

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

   4. Taylor expanded in j around inf 66.3%

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

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+76}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq -2.45 \cdot 10^{-179}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-239}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;b \leq 2.35 \cdot 10^{+33}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+152}:\\ \;\;\;\;\left(b \cdot y4\right) \cdot \left(t \cdot j - y \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 30.7% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+35}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-123}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 1.52 \cdot 10^{-239}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+34}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;b \leq 2.35 \cdot 10^{+154}:\\ \;\;\;\;\left(b \cdot y4\right) \cdot \left(t \cdot j - y \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= b -1e+35)
   (* y0 (* x (- (* c y2) (* b j))))
   (if (<= b -2.3e-123)
     (* k (* i (- (* y y5) (* z y1))))
     (if (<= b 1.52e-239)
       (* y2 (* y4 (- (* k y1) (* t c))))
       (if (<= b 1.7e+34)
         (* y1 (* z (- (* a y3) (* i k))))
         (if (<= b 2.35e+154)
           (* (* b y4) (- (* t j) (* y k)))
           (* j (* y0 (- (* y3 y5) (* x b))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -1e+35) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else if (b <= -2.3e-123) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (b <= 1.52e-239) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (b <= 1.7e+34) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (b <= 2.35e+154) {
		tmp = (b * y4) * ((t * j) - (y * k));
	} else {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (b <= (-1d+35)) then
        tmp = y0 * (x * ((c * y2) - (b * j)))
    else if (b <= (-2.3d-123)) then
        tmp = k * (i * ((y * y5) - (z * y1)))
    else if (b <= 1.52d-239) then
        tmp = y2 * (y4 * ((k * y1) - (t * c)))
    else if (b <= 1.7d+34) then
        tmp = y1 * (z * ((a * y3) - (i * k)))
    else if (b <= 2.35d+154) then
        tmp = (b * y4) * ((t * j) - (y * k))
    else
        tmp = j * (y0 * ((y3 * y5) - (x * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -1e+35) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else if (b <= -2.3e-123) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (b <= 1.52e-239) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (b <= 1.7e+34) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (b <= 2.35e+154) {
		tmp = (b * y4) * ((t * j) - (y * k));
	} else {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if b <= -1e+35:
		tmp = y0 * (x * ((c * y2) - (b * j)))
	elif b <= -2.3e-123:
		tmp = k * (i * ((y * y5) - (z * y1)))
	elif b <= 1.52e-239:
		tmp = y2 * (y4 * ((k * y1) - (t * c)))
	elif b <= 1.7e+34:
		tmp = y1 * (z * ((a * y3) - (i * k)))
	elif b <= 2.35e+154:
		tmp = (b * y4) * ((t * j) - (y * k))
	else:
		tmp = j * (y0 * ((y3 * y5) - (x * b)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (b <= -1e+35)
		tmp = Float64(y0 * Float64(x * Float64(Float64(c * y2) - Float64(b * j))));
	elseif (b <= -2.3e-123)
		tmp = Float64(k * Float64(i * Float64(Float64(y * y5) - Float64(z * y1))));
	elseif (b <= 1.52e-239)
		tmp = Float64(y2 * Float64(y4 * Float64(Float64(k * y1) - Float64(t * c))));
	elseif (b <= 1.7e+34)
		tmp = Float64(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * k))));
	elseif (b <= 2.35e+154)
		tmp = Float64(Float64(b * y4) * Float64(Float64(t * j) - Float64(y * k)));
	else
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (b <= -1e+35)
		tmp = y0 * (x * ((c * y2) - (b * j)));
	elseif (b <= -2.3e-123)
		tmp = k * (i * ((y * y5) - (z * y1)));
	elseif (b <= 1.52e-239)
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	elseif (b <= 1.7e+34)
		tmp = y1 * (z * ((a * y3) - (i * k)));
	elseif (b <= 2.35e+154)
		tmp = (b * y4) * ((t * j) - (y * k));
	else
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[b, -1e+35], N[(y0 * N[(x * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.3e-123], N[(k * N[(i * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.52e-239], N[(y2 * N[(y4 * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.7e+34], N[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.35e+154], N[(N[(b * y4), $MachinePrecision] * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -9.9999999999999997e34

   1. Initial program 20.5%

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

   3. Taylor expanded in y0 around inf 44.6%

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

   4. Taylor expanded in x around inf 46.1%

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

   if -9.9999999999999997e34 < b < -2.29999999999999987e-123

   1. Initial program 44.2%

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

   3. Taylor expanded in k around inf 41.7%

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

   4. Taylor expanded in i around inf 44.6%

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

      1. *-commutative 44.6%

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

   6. Simplified 44.6%

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

   if -2.29999999999999987e-123 < b < 1.51999999999999995e-239

   1. Initial program 38.0%

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

   3. Taylor expanded in y2 around inf 48.3%

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

   4. Taylor expanded in y4 around inf 47.2%

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

   if 1.51999999999999995e-239 < b < 1.7e34

   1. Initial program 40.0%

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

   3. Taylor expanded in y1 around inf 38.9%

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

   4. Taylor expanded in z around inf 41.1%

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

   if 1.7e34 < b < 2.34999999999999992e154

   1. Initial program 10.3%

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

   3. Taylor expanded in b around inf 50.3%

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

   4. Taylor expanded in y4 around inf 65.8%

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

      1. associate-*r* 65.8%

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

   6. Simplified 65.8%

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

   if 2.34999999999999992e154 < b

   1. Initial program 17.3%

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

   3. Taylor expanded in y0 around inf 45.9%

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

   4. Taylor expanded in j around inf 66.3%

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

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+35}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-123}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 1.52 \cdot 10^{-239}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+34}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;b \leq 2.35 \cdot 10^{+154}:\\ \;\;\;\;\left(b \cdot y4\right) \cdot \left(t \cdot j - y \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 31.8% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{if}\;x \leq -9 \cdot 10^{+152}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-59}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-167}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+75}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+187}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y0 (* x (- (* c y2) (* b j))))))
   (if (<= x -9e+152)
     t_1
     (if (<= x -5.5e-59)
       (* x (* y2 (- (* c y0) (* a y1))))
       (if (<= x -1.35e-167)
         (* k (* y1 (- (* y2 y4) (* z i))))
         (if (<= x 2.4e+75)
           (* t (* y2 (- (* a y5) (* c y4))))
           (if (<= x 9.2e+187) t_1 (* b (* x (- (* y a) (* j y0)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * (x * ((c * y2) - (b * j)));
	double tmp;
	if (x <= -9e+152) {
		tmp = t_1;
	} else if (x <= -5.5e-59) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (x <= -1.35e-167) {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	} else if (x <= 2.4e+75) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (x <= 9.2e+187) {
		tmp = t_1;
	} else {
		tmp = b * (x * ((y * a) - (j * y0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y0 * (x * ((c * y2) - (b * j)))
    if (x <= (-9d+152)) then
        tmp = t_1
    else if (x <= (-5.5d-59)) then
        tmp = x * (y2 * ((c * y0) - (a * y1)))
    else if (x <= (-1.35d-167)) then
        tmp = k * (y1 * ((y2 * y4) - (z * i)))
    else if (x <= 2.4d+75) then
        tmp = t * (y2 * ((a * y5) - (c * y4)))
    else if (x <= 9.2d+187) then
        tmp = t_1
    else
        tmp = b * (x * ((y * a) - (j * y0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * (x * ((c * y2) - (b * j)));
	double tmp;
	if (x <= -9e+152) {
		tmp = t_1;
	} else if (x <= -5.5e-59) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (x <= -1.35e-167) {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	} else if (x <= 2.4e+75) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (x <= 9.2e+187) {
		tmp = t_1;
	} else {
		tmp = b * (x * ((y * a) - (j * y0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y0 * (x * ((c * y2) - (b * j)))
	tmp = 0
	if x <= -9e+152:
		tmp = t_1
	elif x <= -5.5e-59:
		tmp = x * (y2 * ((c * y0) - (a * y1)))
	elif x <= -1.35e-167:
		tmp = k * (y1 * ((y2 * y4) - (z * i)))
	elif x <= 2.4e+75:
		tmp = t * (y2 * ((a * y5) - (c * y4)))
	elif x <= 9.2e+187:
		tmp = t_1
	else:
		tmp = b * (x * ((y * a) - (j * y0)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y0 * Float64(x * Float64(Float64(c * y2) - Float64(b * j))))
	tmp = 0.0
	if (x <= -9e+152)
		tmp = t_1;
	elseif (x <= -5.5e-59)
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (x <= -1.35e-167)
		tmp = Float64(k * Float64(y1 * Float64(Float64(y2 * y4) - Float64(z * i))));
	elseif (x <= 2.4e+75)
		tmp = Float64(t * Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))));
	elseif (x <= 9.2e+187)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y0 * (x * ((c * y2) - (b * j)));
	tmp = 0.0;
	if (x <= -9e+152)
		tmp = t_1;
	elseif (x <= -5.5e-59)
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	elseif (x <= -1.35e-167)
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	elseif (x <= 2.4e+75)
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	elseif (x <= 9.2e+187)
		tmp = t_1;
	else
		tmp = b * (x * ((y * a) - (j * y0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y0 * N[(x * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9e+152], t$95$1, If[LessEqual[x, -5.5e-59], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.35e-167], N[(k * N[(y1 * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.4e+75], N[(t * N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.2e+187], t$95$1, N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -9.0000000000000002e152 or 2.4e75 < x < 9.20000000000000015e187

   1. Initial program 22.8%

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

   3. Taylor expanded in y0 around inf 34.1%

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

   4. Taylor expanded in x around inf 60.5%

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

   if -9.0000000000000002e152 < x < -5.50000000000000014e-59

   1. Initial program 28.5%

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

   3. Taylor expanded in y2 around inf 42.2%

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

      1. associate-*r* 42.1%

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

      2. *-commutative 42.1%

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

   5. Simplified 42.1%

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

   6. Taylor expanded in x around inf 39.3%

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

      1. *-commutative 39.3%

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

      2. *-commutative 39.3%

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

   8. Simplified 39.3%

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

   if -5.50000000000000014e-59 < x < -1.35e-167

   1. Initial program 26.9%

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

   3. Taylor expanded in y1 around inf 49.7%

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

   4. Taylor expanded in k around inf 58.0%

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

   if -1.35e-167 < x < 2.4e75

   1. Initial program 40.3%

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

   3. Taylor expanded in y2 around inf 43.7%

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

   4. Taylor expanded in t around inf 43.3%

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

   if 9.20000000000000015e187 < x

   1. Initial program 19.8%

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

   3. Taylor expanded in b around inf 35.4%

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

   4. Taylor expanded in x around inf 58.5%

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

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+152}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-59}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-167}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+75}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+187}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 32.5% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{if}\;y2 \leq -9 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq -7 \cdot 10^{-159}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 2.5 \cdot 10^{-203}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y2 \leq 3.1 \cdot 10^{-101}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 3 \cdot 10^{+67}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (* i (- (* y y5) (* z y1))))))
   (if (<= y2 -9e-28)
     (* x (* y2 (- (* c y0) (* a y1))))
     (if (<= y2 -7e-159)
       (* y0 (* c (- (* x y2) (* z y3))))
       (if (<= y2 2.5e-203)
         t_1
         (if (<= y2 3.1e-101)
           (* b (* x (- (* y a) (* j y0))))
           (if (<= y2 3e+67) t_1 (* k (* y2 (- (* y1 y4) (* y0 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 = k * (i * ((y * y5) - (z * y1)));
	double tmp;
	if (y2 <= -9e-28) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (y2 <= -7e-159) {
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	} else if (y2 <= 2.5e-203) {
		tmp = t_1;
	} else if (y2 <= 3.1e-101) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y2 <= 3e+67) {
		tmp = t_1;
	} else {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = k * (i * ((y * y5) - (z * y1)))
    if (y2 <= (-9d-28)) then
        tmp = x * (y2 * ((c * y0) - (a * y1)))
    else if (y2 <= (-7d-159)) then
        tmp = y0 * (c * ((x * y2) - (z * y3)))
    else if (y2 <= 2.5d-203) then
        tmp = t_1
    else if (y2 <= 3.1d-101) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (y2 <= 3d+67) then
        tmp = t_1
    else
        tmp = k * (y2 * ((y1 * y4) - (y0 * 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 = k * (i * ((y * y5) - (z * y1)));
	double tmp;
	if (y2 <= -9e-28) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (y2 <= -7e-159) {
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	} else if (y2 <= 2.5e-203) {
		tmp = t_1;
	} else if (y2 <= 3.1e-101) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y2 <= 3e+67) {
		tmp = t_1;
	} else {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = k * (i * ((y * y5) - (z * y1)))
	tmp = 0
	if y2 <= -9e-28:
		tmp = x * (y2 * ((c * y0) - (a * y1)))
	elif y2 <= -7e-159:
		tmp = y0 * (c * ((x * y2) - (z * y3)))
	elif y2 <= 2.5e-203:
		tmp = t_1
	elif y2 <= 3.1e-101:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif y2 <= 3e+67:
		tmp = t_1
	else:
		tmp = k * (y2 * ((y1 * y4) - (y0 * 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(k * Float64(i * Float64(Float64(y * y5) - Float64(z * y1))))
	tmp = 0.0
	if (y2 <= -9e-28)
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (y2 <= -7e-159)
		tmp = Float64(y0 * Float64(c * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (y2 <= 2.5e-203)
		tmp = t_1;
	elseif (y2 <= 3.1e-101)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (y2 <= 3e+67)
		tmp = t_1;
	else
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * 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 = k * (i * ((y * y5) - (z * y1)));
	tmp = 0.0;
	if (y2 <= -9e-28)
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	elseif (y2 <= -7e-159)
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	elseif (y2 <= 2.5e-203)
		tmp = t_1;
	elseif (y2 <= 3.1e-101)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (y2 <= 3e+67)
		tmp = t_1;
	else
		tmp = k * (y2 * ((y1 * y4) - (y0 * 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[(k * N[(i * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -9e-28], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -7e-159], N[(y0 * N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.5e-203], t$95$1, If[LessEqual[y2, 3.1e-101], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 3e+67], t$95$1, N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y2 < -8.9999999999999996e-28

   1. Initial program 27.0%

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

   3. Taylor expanded in y2 around inf 41.3%

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

      1. associate-*r* 39.9%

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

      2. *-commutative 39.9%

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

   5. Simplified 39.9%

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

   6. Taylor expanded in x around inf 48.7%

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

      1. *-commutative 48.7%

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

      2. *-commutative 48.7%

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

   8. Simplified 48.7%

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

   if -8.9999999999999996e-28 < y2 < -7.00000000000000005e-159

   1. Initial program 22.9%

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

   3. Taylor expanded in y0 around inf 31.2%

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

   4. Taylor expanded in c around inf 39.9%

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

   if -7.00000000000000005e-159 < y2 < 2.5000000000000001e-203 or 3.09999999999999973e-101 < y2 < 3.0000000000000001e67

   1. Initial program 37.7%

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

   3. Taylor expanded in k around inf 39.6%

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

   4. Taylor expanded in i around inf 44.6%

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

      1. *-commutative 44.6%

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

   6. Simplified 44.6%

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

   if 2.5000000000000001e-203 < y2 < 3.09999999999999973e-101

   1. Initial program 46.0%

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

   3. Taylor expanded in b around inf 58.9%

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

   4. Taylor expanded in x around inf 55.2%

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

   if 3.0000000000000001e67 < y2

   1. Initial program 23.1%

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

   3. Taylor expanded in y2 around inf 64.6%

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

   4. Taylor expanded in k around inf 58.6%

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

4. Final simplification 48.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -9 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq -7 \cdot 10^{-159}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 2.5 \cdot 10^{-203}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq 3.1 \cdot 10^{-101}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 3 \cdot 10^{+67}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 31.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{if}\;b \leq -3.8 \cdot 10^{+80}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq -1.02 \cdot 10^{-191}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-239}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5 \cdot 10^{+153}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (* i (- (* y y5) (* z y1))))))
   (if (<= b -3.8e+80)
     (* a (* b (- (* x y) (* z t))))
     (if (<= b -1.02e-191)
       t_1
       (if (<= b 3.4e-239)
         (* k (* y1 (- (* y2 y4) (* z i))))
         (if (<= b 2.5e+33)
           t_1
           (if (<= b 5e+153)
             (* k (* y4 (- (* y1 y2) (* y b))))
             (* j (* y0 (- (* y3 y5) (* x b)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (i * ((y * y5) - (z * y1)));
	double tmp;
	if (b <= -3.8e+80) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (b <= -1.02e-191) {
		tmp = t_1;
	} else if (b <= 3.4e-239) {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	} else if (b <= 2.5e+33) {
		tmp = t_1;
	} else if (b <= 5e+153) {
		tmp = k * (y4 * ((y1 * y2) - (y * b)));
	} else {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = k * (i * ((y * y5) - (z * y1)))
    if (b <= (-3.8d+80)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (b <= (-1.02d-191)) then
        tmp = t_1
    else if (b <= 3.4d-239) then
        tmp = k * (y1 * ((y2 * y4) - (z * i)))
    else if (b <= 2.5d+33) then
        tmp = t_1
    else if (b <= 5d+153) then
        tmp = k * (y4 * ((y1 * y2) - (y * b)))
    else
        tmp = j * (y0 * ((y3 * y5) - (x * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (i * ((y * y5) - (z * y1)));
	double tmp;
	if (b <= -3.8e+80) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (b <= -1.02e-191) {
		tmp = t_1;
	} else if (b <= 3.4e-239) {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	} else if (b <= 2.5e+33) {
		tmp = t_1;
	} else if (b <= 5e+153) {
		tmp = k * (y4 * ((y1 * y2) - (y * b)));
	} else {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = k * (i * ((y * y5) - (z * y1)))
	tmp = 0
	if b <= -3.8e+80:
		tmp = a * (b * ((x * y) - (z * t)))
	elif b <= -1.02e-191:
		tmp = t_1
	elif b <= 3.4e-239:
		tmp = k * (y1 * ((y2 * y4) - (z * i)))
	elif b <= 2.5e+33:
		tmp = t_1
	elif b <= 5e+153:
		tmp = k * (y4 * ((y1 * y2) - (y * b)))
	else:
		tmp = j * (y0 * ((y3 * y5) - (x * b)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(k * Float64(i * Float64(Float64(y * y5) - Float64(z * y1))))
	tmp = 0.0
	if (b <= -3.8e+80)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (b <= -1.02e-191)
		tmp = t_1;
	elseif (b <= 3.4e-239)
		tmp = Float64(k * Float64(y1 * Float64(Float64(y2 * y4) - Float64(z * i))));
	elseif (b <= 2.5e+33)
		tmp = t_1;
	elseif (b <= 5e+153)
		tmp = Float64(k * Float64(y4 * Float64(Float64(y1 * y2) - Float64(y * b))));
	else
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = k * (i * ((y * y5) - (z * y1)));
	tmp = 0.0;
	if (b <= -3.8e+80)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (b <= -1.02e-191)
		tmp = t_1;
	elseif (b <= 3.4e-239)
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	elseif (b <= 2.5e+33)
		tmp = t_1;
	elseif (b <= 5e+153)
		tmp = k * (y4 * ((y1 * y2) - (y * b)));
	else
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(k * N[(i * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.8e+80], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.02e-191], t$95$1, If[LessEqual[b, 3.4e-239], N[(k * N[(y1 * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.5e+33], t$95$1, If[LessEqual[b, 5e+153], N[(k * N[(y4 * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -3.79999999999999997e80

   1. Initial program 21.2%

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

   3. Taylor expanded in b around inf 36.3%

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

   4. Taylor expanded in a around inf 46.9%

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

   if -3.79999999999999997e80 < b < -1.02e-191 or 3.4e-239 < b < 2.49999999999999986e33

   1. Initial program 39.3%

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

   3. Taylor expanded in k around inf 36.7%

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

   4. Taylor expanded in i around inf 39.5%

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

      1. *-commutative 39.5%

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

   6. Simplified 39.5%

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

   if -1.02e-191 < b < 3.4e-239

   1. Initial program 36.9%

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

   3. Taylor expanded in y1 around inf 48.4%

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

   4. Taylor expanded in k around inf 44.8%

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

   if 2.49999999999999986e33 < b < 5.00000000000000018e153

   1. Initial program 10.3%

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

   3. Taylor expanded in k around inf 45.6%

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

   4. Taylor expanded in y4 around inf 60.6%

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

      1. +-commutative 60.6%

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

      2. mul-1-neg 60.6%

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

      3. unsub-neg 60.6%

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

      4. *-commutative 60.6%

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

   6. Simplified 60.6%

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

   if 5.00000000000000018e153 < b

   1. Initial program 17.3%

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

   3. Taylor expanded in y0 around inf 45.9%

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

   4. Taylor expanded in j around inf 66.3%

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

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{+80}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq -1.02 \cdot 10^{-191}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-239}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+33}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 5 \cdot 10^{+153}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 31.6% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{+151}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{-224}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+32}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+156}:\\ \;\;\;\;\left(b \cdot y4\right) \cdot \left(t \cdot j - y \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= b -3.8e+151)
   (* a (* b (- (* x y) (* z t))))
   (if (<= b 5.6e-224)
     (* a (* y2 (- (* t y5) (* x y1))))
     (if (<= b 8.5e+32)
       (* y1 (* z (- (* a y3) (* i k))))
       (if (<= b 1.05e+156)
         (* (* b y4) (- (* t j) (* y k)))
         (* j (* y0 (- (* y3 y5) (* x b)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -3.8e+151) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (b <= 5.6e-224) {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	} else if (b <= 8.5e+32) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (b <= 1.05e+156) {
		tmp = (b * y4) * ((t * j) - (y * k));
	} else {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (b <= (-3.8d+151)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (b <= 5.6d-224) then
        tmp = a * (y2 * ((t * y5) - (x * y1)))
    else if (b <= 8.5d+32) then
        tmp = y1 * (z * ((a * y3) - (i * k)))
    else if (b <= 1.05d+156) then
        tmp = (b * y4) * ((t * j) - (y * k))
    else
        tmp = j * (y0 * ((y3 * y5) - (x * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -3.8e+151) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (b <= 5.6e-224) {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	} else if (b <= 8.5e+32) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (b <= 1.05e+156) {
		tmp = (b * y4) * ((t * j) - (y * k));
	} else {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if b <= -3.8e+151:
		tmp = a * (b * ((x * y) - (z * t)))
	elif b <= 5.6e-224:
		tmp = a * (y2 * ((t * y5) - (x * y1)))
	elif b <= 8.5e+32:
		tmp = y1 * (z * ((a * y3) - (i * k)))
	elif b <= 1.05e+156:
		tmp = (b * y4) * ((t * j) - (y * k))
	else:
		tmp = j * (y0 * ((y3 * y5) - (x * b)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (b <= -3.8e+151)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (b <= 5.6e-224)
		tmp = Float64(a * Float64(y2 * Float64(Float64(t * y5) - Float64(x * y1))));
	elseif (b <= 8.5e+32)
		tmp = Float64(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * k))));
	elseif (b <= 1.05e+156)
		tmp = Float64(Float64(b * y4) * Float64(Float64(t * j) - Float64(y * k)));
	else
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (b <= -3.8e+151)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (b <= 5.6e-224)
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	elseif (b <= 8.5e+32)
		tmp = y1 * (z * ((a * y3) - (i * k)));
	elseif (b <= 1.05e+156)
		tmp = (b * y4) * ((t * j) - (y * k));
	else
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[b, -3.8e+151], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.6e-224], N[(a * N[(y2 * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.5e+32], N[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.05e+156], N[(N[(b * y4), $MachinePrecision] * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -3.8e151

   1. Initial program 17.5%

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

   3. Taylor expanded in b around inf 44.8%

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

   4. Taylor expanded in a around inf 55.8%

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

   if -3.8e151 < b < 5.5999999999999995e-224

   1. Initial program 37.2%

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

   3. Taylor expanded in y2 around inf 44.5%

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

   4. Taylor expanded in a around -inf 39.7%

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

      1. associate-*r* 39.7%

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

      2. neg-mul-1 39.7%

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

   6. Simplified 39.7%

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

   if 5.5999999999999995e-224 < b < 8.4999999999999998e32

   1. Initial program 40.4%

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

   3. Taylor expanded in y1 around inf 37.4%

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

   4. Taylor expanded in z around inf 43.2%

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

   if 8.4999999999999998e32 < b < 1.04999999999999991e156

   1. Initial program 10.3%

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

   3. Taylor expanded in b around inf 50.3%

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

   4. Taylor expanded in y4 around inf 65.8%

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

      1. associate-*r* 65.8%

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

   6. Simplified 65.8%

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

   if 1.04999999999999991e156 < b

   1. Initial program 17.3%

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

   3. Taylor expanded in y0 around inf 45.9%

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

   4. Taylor expanded in j around inf 66.3%

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

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{+151}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{-224}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+32}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+156}:\\ \;\;\;\;\left(b \cdot y4\right) \cdot \left(t \cdot j - y \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 32.3% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{if}\;y2 \leq -7.5 \cdot 10^{-94}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq 2.8 \cdot 10^{-203}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y2 \leq 4.1 \cdot 10^{-101}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 1.6 \cdot 10^{+73}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (* i (- (* y y5) (* z y1))))))
   (if (<= y2 -7.5e-94)
     (* x (* y2 (- (* c y0) (* a y1))))
     (if (<= y2 2.8e-203)
       t_1
       (if (<= y2 4.1e-101)
         (* b (* x (- (* y a) (* j y0))))
         (if (<= y2 1.6e+73) t_1 (* k (* y2 (- (* y1 y4) (* y0 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 = k * (i * ((y * y5) - (z * y1)));
	double tmp;
	if (y2 <= -7.5e-94) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (y2 <= 2.8e-203) {
		tmp = t_1;
	} else if (y2 <= 4.1e-101) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y2 <= 1.6e+73) {
		tmp = t_1;
	} else {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = k * (i * ((y * y5) - (z * y1)))
    if (y2 <= (-7.5d-94)) then
        tmp = x * (y2 * ((c * y0) - (a * y1)))
    else if (y2 <= 2.8d-203) then
        tmp = t_1
    else if (y2 <= 4.1d-101) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (y2 <= 1.6d+73) then
        tmp = t_1
    else
        tmp = k * (y2 * ((y1 * y4) - (y0 * 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 = k * (i * ((y * y5) - (z * y1)));
	double tmp;
	if (y2 <= -7.5e-94) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (y2 <= 2.8e-203) {
		tmp = t_1;
	} else if (y2 <= 4.1e-101) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y2 <= 1.6e+73) {
		tmp = t_1;
	} else {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = k * (i * ((y * y5) - (z * y1)))
	tmp = 0
	if y2 <= -7.5e-94:
		tmp = x * (y2 * ((c * y0) - (a * y1)))
	elif y2 <= 2.8e-203:
		tmp = t_1
	elif y2 <= 4.1e-101:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif y2 <= 1.6e+73:
		tmp = t_1
	else:
		tmp = k * (y2 * ((y1 * y4) - (y0 * 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(k * Float64(i * Float64(Float64(y * y5) - Float64(z * y1))))
	tmp = 0.0
	if (y2 <= -7.5e-94)
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (y2 <= 2.8e-203)
		tmp = t_1;
	elseif (y2 <= 4.1e-101)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (y2 <= 1.6e+73)
		tmp = t_1;
	else
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * 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 = k * (i * ((y * y5) - (z * y1)));
	tmp = 0.0;
	if (y2 <= -7.5e-94)
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	elseif (y2 <= 2.8e-203)
		tmp = t_1;
	elseif (y2 <= 4.1e-101)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (y2 <= 1.6e+73)
		tmp = t_1;
	else
		tmp = k * (y2 * ((y1 * y4) - (y0 * 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[(k * N[(i * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -7.5e-94], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.8e-203], t$95$1, If[LessEqual[y2, 4.1e-101], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.6e+73], t$95$1, N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y2 < -7.5000000000000003e-94

   1. Initial program 28.5%

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

   3. Taylor expanded in y2 around inf 43.2%

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

      1. associate-*r* 42.1%

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

      2. *-commutative 42.1%

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

   5. Simplified 42.1%

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

   6. Taylor expanded in x around inf 43.6%

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

      1. *-commutative 43.6%

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

      2. *-commutative 43.6%

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

   8. Simplified 43.6%

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

   if -7.5000000000000003e-94 < y2 < 2.80000000000000022e-203 or 4.10000000000000026e-101 < y2 < 1.59999999999999991e73

   1. Initial program 33.0%

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

   3. Taylor expanded in k around inf 38.4%

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

   4. Taylor expanded in i around inf 41.7%

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

      1. *-commutative 41.7%

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

   6. Simplified 41.7%

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

   if 2.80000000000000022e-203 < y2 < 4.10000000000000026e-101

   1. Initial program 46.0%

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

   3. Taylor expanded in b around inf 58.9%

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

   4. Taylor expanded in x around inf 55.2%

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

   if 1.59999999999999991e73 < y2

   1. Initial program 23.1%

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

   3. Taylor expanded in y2 around inf 64.6%

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

   4. Taylor expanded in k around inf 58.6%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -7.5 \cdot 10^{-94}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq 2.8 \cdot 10^{-203}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq 4.1 \cdot 10^{-101}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 1.6 \cdot 10^{+73}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 29.7% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.12 \cdot 10^{+34}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(b \cdot \left(-j\right)\right)\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-238}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 1.56 \cdot 10^{+32}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+154}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= b -1.12e+34)
   (* y0 (* x (* b (- j))))
   (if (<= b 6e-238)
     (* t (* y2 (- (* a y5) (* c y4))))
     (if (<= b 1.56e+32)
       (* k (* i (- (* y y5) (* z y1))))
       (if (<= b 3.5e+154)
         (* k (* y4 (- (* y1 y2) (* y b))))
         (* j (* y0 (- (* y3 y5) (* x b)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -1.12e+34) {
		tmp = y0 * (x * (b * -j));
	} else if (b <= 6e-238) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (b <= 1.56e+32) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (b <= 3.5e+154) {
		tmp = k * (y4 * ((y1 * y2) - (y * b)));
	} else {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (b <= (-1.12d+34)) then
        tmp = y0 * (x * (b * -j))
    else if (b <= 6d-238) then
        tmp = t * (y2 * ((a * y5) - (c * y4)))
    else if (b <= 1.56d+32) then
        tmp = k * (i * ((y * y5) - (z * y1)))
    else if (b <= 3.5d+154) then
        tmp = k * (y4 * ((y1 * y2) - (y * b)))
    else
        tmp = j * (y0 * ((y3 * y5) - (x * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -1.12e+34) {
		tmp = y0 * (x * (b * -j));
	} else if (b <= 6e-238) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (b <= 1.56e+32) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (b <= 3.5e+154) {
		tmp = k * (y4 * ((y1 * y2) - (y * b)));
	} else {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if b <= -1.12e+34:
		tmp = y0 * (x * (b * -j))
	elif b <= 6e-238:
		tmp = t * (y2 * ((a * y5) - (c * y4)))
	elif b <= 1.56e+32:
		tmp = k * (i * ((y * y5) - (z * y1)))
	elif b <= 3.5e+154:
		tmp = k * (y4 * ((y1 * y2) - (y * b)))
	else:
		tmp = j * (y0 * ((y3 * y5) - (x * b)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (b <= -1.12e+34)
		tmp = Float64(y0 * Float64(x * Float64(b * Float64(-j))));
	elseif (b <= 6e-238)
		tmp = Float64(t * Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))));
	elseif (b <= 1.56e+32)
		tmp = Float64(k * Float64(i * Float64(Float64(y * y5) - Float64(z * y1))));
	elseif (b <= 3.5e+154)
		tmp = Float64(k * Float64(y4 * Float64(Float64(y1 * y2) - Float64(y * b))));
	else
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (b <= -1.12e+34)
		tmp = y0 * (x * (b * -j));
	elseif (b <= 6e-238)
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	elseif (b <= 1.56e+32)
		tmp = k * (i * ((y * y5) - (z * y1)));
	elseif (b <= 3.5e+154)
		tmp = k * (y4 * ((y1 * y2) - (y * b)));
	else
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[b, -1.12e+34], N[(y0 * N[(x * N[(b * (-j)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6e-238], N[(t * N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.56e+32], N[(k * N[(i * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.5e+154], N[(k * N[(y4 * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.12e34

   1. Initial program 20.1%

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

   3. Taylor expanded in y0 around inf 45.7%

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

   4. Taylor expanded in x around inf 45.3%

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

   5. Taylor expanded in c around 0 42.4%

      \[\leadsto y0 \cdot \left(x \cdot \color{blue}{\left(-1 \cdot \left(b \cdot j\right)\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 42.4%

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

      2. distribute-lft-neg-out 42.4%

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

      3. *-commutative 42.4%

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

   7. Simplified 42.4%

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

   if -1.12e34 < b < 5.9999999999999999e-238

   1. Initial program 40.1%

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

   3. Taylor expanded in y2 around inf 47.1%

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

   4. Taylor expanded in t around inf 41.0%

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

   if 5.9999999999999999e-238 < b < 1.56e32

   1. Initial program 40.7%

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

   3. Taylor expanded in k around inf 39.3%

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

   4. Taylor expanded in i around inf 41.5%

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

      1. *-commutative 41.5%

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

   6. Simplified 41.5%

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

   if 1.56e32 < b < 3.5000000000000002e154

   1. Initial program 10.3%

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

   3. Taylor expanded in k around inf 45.6%

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

   4. Taylor expanded in y4 around inf 60.6%

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

      1. +-commutative 60.6%

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

      2. mul-1-neg 60.6%

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

      3. unsub-neg 60.6%

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

      4. *-commutative 60.6%

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

   6. Simplified 60.6%

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

   if 3.5000000000000002e154 < b

   1. Initial program 17.3%

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

   3. Taylor expanded in y0 around inf 45.9%

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

   4. Taylor expanded in j around inf 66.3%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.12 \cdot 10^{+34}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(b \cdot \left(-j\right)\right)\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-238}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 1.56 \cdot 10^{+32}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+154}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 31.4% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{if}\;y2 \leq -2.55 \cdot 10^{+176}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 2.4 \cdot 10^{-203}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y2 \leq 2.05 \cdot 10^{-101}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 3.2 \cdot 10^{+67}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (* i (- (* y y5) (* z y1))))))
   (if (<= y2 -2.55e+176)
     (* c (* x (* y0 y2)))
     (if (<= y2 2.4e-203)
       t_1
       (if (<= y2 2.05e-101)
         (* b (* x (- (* y a) (* j y0))))
         (if (<= y2 3.2e+67) t_1 (* k (* y2 (- (* y1 y4) (* y0 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 = k * (i * ((y * y5) - (z * y1)));
	double tmp;
	if (y2 <= -2.55e+176) {
		tmp = c * (x * (y0 * y2));
	} else if (y2 <= 2.4e-203) {
		tmp = t_1;
	} else if (y2 <= 2.05e-101) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y2 <= 3.2e+67) {
		tmp = t_1;
	} else {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = k * (i * ((y * y5) - (z * y1)))
    if (y2 <= (-2.55d+176)) then
        tmp = c * (x * (y0 * y2))
    else if (y2 <= 2.4d-203) then
        tmp = t_1
    else if (y2 <= 2.05d-101) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (y2 <= 3.2d+67) then
        tmp = t_1
    else
        tmp = k * (y2 * ((y1 * y4) - (y0 * 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 = k * (i * ((y * y5) - (z * y1)));
	double tmp;
	if (y2 <= -2.55e+176) {
		tmp = c * (x * (y0 * y2));
	} else if (y2 <= 2.4e-203) {
		tmp = t_1;
	} else if (y2 <= 2.05e-101) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y2 <= 3.2e+67) {
		tmp = t_1;
	} else {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = k * (i * ((y * y5) - (z * y1)))
	tmp = 0
	if y2 <= -2.55e+176:
		tmp = c * (x * (y0 * y2))
	elif y2 <= 2.4e-203:
		tmp = t_1
	elif y2 <= 2.05e-101:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif y2 <= 3.2e+67:
		tmp = t_1
	else:
		tmp = k * (y2 * ((y1 * y4) - (y0 * 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(k * Float64(i * Float64(Float64(y * y5) - Float64(z * y1))))
	tmp = 0.0
	if (y2 <= -2.55e+176)
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	elseif (y2 <= 2.4e-203)
		tmp = t_1;
	elseif (y2 <= 2.05e-101)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (y2 <= 3.2e+67)
		tmp = t_1;
	else
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * 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 = k * (i * ((y * y5) - (z * y1)));
	tmp = 0.0;
	if (y2 <= -2.55e+176)
		tmp = c * (x * (y0 * y2));
	elseif (y2 <= 2.4e-203)
		tmp = t_1;
	elseif (y2 <= 2.05e-101)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (y2 <= 3.2e+67)
		tmp = t_1;
	else
		tmp = k * (y2 * ((y1 * y4) - (y0 * 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[(k * N[(i * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -2.55e+176], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.4e-203], t$95$1, If[LessEqual[y2, 2.05e-101], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 3.2e+67], t$95$1, N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y2 < -2.55e176

   1. Initial program 14.8%

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

   3. Taylor expanded in y0 around inf 46.9%

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

   4. Taylor expanded in x around inf 50.8%

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

   5. Taylor expanded in j around inf 54.2%

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

   6. Taylor expanded in j around 0 57.8%

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

   if -2.55e176 < y2 < 2.3999999999999999e-203 or 2.05000000000000013e-101 < y2 < 3.19999999999999983e67

   1. Initial program 33.7%

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

   3. Taylor expanded in k around inf 40.8%

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

   4. Taylor expanded in i around inf 37.2%

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

      1. *-commutative 37.2%

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

   6. Simplified 37.2%

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

   if 2.3999999999999999e-203 < y2 < 2.05000000000000013e-101

   1. Initial program 46.0%

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

   3. Taylor expanded in b around inf 58.9%

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

   4. Taylor expanded in x around inf 55.2%

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

   if 3.19999999999999983e67 < y2

   1. Initial program 23.1%

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

   3. Taylor expanded in y2 around inf 64.6%

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

   4. Taylor expanded in k around inf 58.6%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -2.55 \cdot 10^{+176}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 2.4 \cdot 10^{-203}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq 2.05 \cdot 10^{-101}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 3.2 \cdot 10^{+67}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 31.7% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{if}\;b \leq -1.02 \cdot 10^{+79}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq -5.9 \cdot 10^{-192}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{-239}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{+151}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (* i (- (* y y5) (* z y1))))))
   (if (<= b -1.02e+79)
     (* a (* b (- (* x y) (* z t))))
     (if (<= b -5.9e-192)
       t_1
       (if (<= b 7.8e-239)
         (* k (* y1 (- (* y2 y4) (* z i))))
         (if (<= b 2.25e+151) t_1 (* j (* y0 (- (* y3 y5) (* x b))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (i * ((y * y5) - (z * y1)));
	double tmp;
	if (b <= -1.02e+79) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (b <= -5.9e-192) {
		tmp = t_1;
	} else if (b <= 7.8e-239) {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	} else if (b <= 2.25e+151) {
		tmp = t_1;
	} else {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = k * (i * ((y * y5) - (z * y1)))
    if (b <= (-1.02d+79)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (b <= (-5.9d-192)) then
        tmp = t_1
    else if (b <= 7.8d-239) then
        tmp = k * (y1 * ((y2 * y4) - (z * i)))
    else if (b <= 2.25d+151) then
        tmp = t_1
    else
        tmp = j * (y0 * ((y3 * y5) - (x * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (i * ((y * y5) - (z * y1)));
	double tmp;
	if (b <= -1.02e+79) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (b <= -5.9e-192) {
		tmp = t_1;
	} else if (b <= 7.8e-239) {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	} else if (b <= 2.25e+151) {
		tmp = t_1;
	} else {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = k * (i * ((y * y5) - (z * y1)))
	tmp = 0
	if b <= -1.02e+79:
		tmp = a * (b * ((x * y) - (z * t)))
	elif b <= -5.9e-192:
		tmp = t_1
	elif b <= 7.8e-239:
		tmp = k * (y1 * ((y2 * y4) - (z * i)))
	elif b <= 2.25e+151:
		tmp = t_1
	else:
		tmp = j * (y0 * ((y3 * y5) - (x * b)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(k * Float64(i * Float64(Float64(y * y5) - Float64(z * y1))))
	tmp = 0.0
	if (b <= -1.02e+79)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (b <= -5.9e-192)
		tmp = t_1;
	elseif (b <= 7.8e-239)
		tmp = Float64(k * Float64(y1 * Float64(Float64(y2 * y4) - Float64(z * i))));
	elseif (b <= 2.25e+151)
		tmp = t_1;
	else
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = k * (i * ((y * y5) - (z * y1)));
	tmp = 0.0;
	if (b <= -1.02e+79)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (b <= -5.9e-192)
		tmp = t_1;
	elseif (b <= 7.8e-239)
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	elseif (b <= 2.25e+151)
		tmp = t_1;
	else
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(k * N[(i * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.02e+79], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -5.9e-192], t$95$1, If[LessEqual[b, 7.8e-239], N[(k * N[(y1 * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.25e+151], t$95$1, N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.02000000000000006e79

   1. Initial program 21.2%

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

   3. Taylor expanded in b around inf 36.3%

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

   4. Taylor expanded in a around inf 46.9%

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

   if -1.02000000000000006e79 < b < -5.8999999999999997e-192 or 7.8e-239 < b < 2.2499999999999999e151

   1. Initial program 35.3%

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

   3. Taylor expanded in k around inf 38.3%

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

   4. Taylor expanded in i around inf 38.5%

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

      1. *-commutative 38.5%

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

   6. Simplified 38.5%

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

   if -5.8999999999999997e-192 < b < 7.8e-239

   1. Initial program 36.9%

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

   3. Taylor expanded in y1 around inf 48.4%

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

   4. Taylor expanded in k around inf 44.8%

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

   if 2.2499999999999999e151 < b

   1. Initial program 16.8%

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

   3. Taylor expanded in y0 around inf 44.7%

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

   4. Taylor expanded in j around inf 64.5%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 44.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.02 \cdot 10^{+79}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq -5.9 \cdot 10^{-192}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{-239}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{+151}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 30.8% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{if}\;b \leq -4.8 \cdot 10^{+76}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq -5.4 \cdot 10^{-275}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-239}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+151}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (* i (- (* y y5) (* z y1))))))
   (if (<= b -4.8e+76)
     (* a (* b (- (* x y) (* z t))))
     (if (<= b -5.4e-275)
       t_1
       (if (<= b 5.5e-239)
         (* a (* t (* y2 y5)))
         (if (<= b 1.2e+151) t_1 (* j (* y0 (- (* y3 y5) (* x b))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (i * ((y * y5) - (z * y1)));
	double tmp;
	if (b <= -4.8e+76) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (b <= -5.4e-275) {
		tmp = t_1;
	} else if (b <= 5.5e-239) {
		tmp = a * (t * (y2 * y5));
	} else if (b <= 1.2e+151) {
		tmp = t_1;
	} else {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = k * (i * ((y * y5) - (z * y1)))
    if (b <= (-4.8d+76)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (b <= (-5.4d-275)) then
        tmp = t_1
    else if (b <= 5.5d-239) then
        tmp = a * (t * (y2 * y5))
    else if (b <= 1.2d+151) then
        tmp = t_1
    else
        tmp = j * (y0 * ((y3 * y5) - (x * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (i * ((y * y5) - (z * y1)));
	double tmp;
	if (b <= -4.8e+76) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (b <= -5.4e-275) {
		tmp = t_1;
	} else if (b <= 5.5e-239) {
		tmp = a * (t * (y2 * y5));
	} else if (b <= 1.2e+151) {
		tmp = t_1;
	} else {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = k * (i * ((y * y5) - (z * y1)))
	tmp = 0
	if b <= -4.8e+76:
		tmp = a * (b * ((x * y) - (z * t)))
	elif b <= -5.4e-275:
		tmp = t_1
	elif b <= 5.5e-239:
		tmp = a * (t * (y2 * y5))
	elif b <= 1.2e+151:
		tmp = t_1
	else:
		tmp = j * (y0 * ((y3 * y5) - (x * b)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(k * Float64(i * Float64(Float64(y * y5) - Float64(z * y1))))
	tmp = 0.0
	if (b <= -4.8e+76)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (b <= -5.4e-275)
		tmp = t_1;
	elseif (b <= 5.5e-239)
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	elseif (b <= 1.2e+151)
		tmp = t_1;
	else
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = k * (i * ((y * y5) - (z * y1)));
	tmp = 0.0;
	if (b <= -4.8e+76)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (b <= -5.4e-275)
		tmp = t_1;
	elseif (b <= 5.5e-239)
		tmp = a * (t * (y2 * y5));
	elseif (b <= 1.2e+151)
		tmp = t_1;
	else
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(k * N[(i * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.8e+76], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -5.4e-275], t$95$1, If[LessEqual[b, 5.5e-239], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.2e+151], t$95$1, N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -4.8e76

   1. Initial program 21.2%

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

   3. Taylor expanded in b around inf 36.3%

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

   4. Taylor expanded in a around inf 46.9%

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

   if -4.8e76 < b < -5.39999999999999987e-275 or 5.49999999999999978e-239 < b < 1.20000000000000005e151

   1. Initial program 35.9%

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

   3. Taylor expanded in k around inf 39.3%

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

   4. Taylor expanded in i around inf 37.5%

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

      1. *-commutative 37.5%

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

   6. Simplified 37.5%

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

   if -5.39999999999999987e-275 < b < 5.49999999999999978e-239

   1. Initial program 34.5%

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

   3. Taylor expanded in y2 around inf 58.0%

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

   4. Taylor expanded in a around -inf 54.8%

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

      1. associate-*r* 54.8%

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

      2. neg-mul-1 54.8%

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

   6. Simplified 54.8%

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

   7. Taylor expanded in x around 0 47.3%

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

   if 1.20000000000000005e151 < b

   1. Initial program 16.8%

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

   3. Taylor expanded in y0 around inf 44.7%

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

   4. Taylor expanded in j around inf 64.5%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{+76}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq -5.4 \cdot 10^{-275}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-239}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+151}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 28.7% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y2 \cdot \left(x \cdot \left(-y1\right)\right)\right)\\ \mathbf{if}\;y1 \leq -5.2 \cdot 10^{+138}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq 8.5 \cdot 10^{-294}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 4.8 \cdot 10^{-115}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y1 \leq 7 \cdot 10^{+29}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y2 (* x (- y1))))))
   (if (<= y1 -5.2e+138)
     t_1
     (if (<= y1 8.5e-294)
       (* b (* j (- (* t y4) (* x y0))))
       (if (<= y1 4.8e-115)
         (* j (* y0 (- (* y3 y5) (* x b))))
         (if (<= y1 7e+29) (* a (* b (- (* x y) (* z t)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y2 * (x * -y1));
	double tmp;
	if (y1 <= -5.2e+138) {
		tmp = t_1;
	} else if (y1 <= 8.5e-294) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y1 <= 4.8e-115) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else if (y1 <= 7e+29) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (y2 * (x * -y1))
    if (y1 <= (-5.2d+138)) then
        tmp = t_1
    else if (y1 <= 8.5d-294) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (y1 <= 4.8d-115) then
        tmp = j * (y0 * ((y3 * y5) - (x * b)))
    else if (y1 <= 7d+29) then
        tmp = a * (b * ((x * y) - (z * t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y2 * (x * -y1));
	double tmp;
	if (y1 <= -5.2e+138) {
		tmp = t_1;
	} else if (y1 <= 8.5e-294) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y1 <= 4.8e-115) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else if (y1 <= 7e+29) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y2 * (x * -y1))
	tmp = 0
	if y1 <= -5.2e+138:
		tmp = t_1
	elif y1 <= 8.5e-294:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif y1 <= 4.8e-115:
		tmp = j * (y0 * ((y3 * y5) - (x * b)))
	elif y1 <= 7e+29:
		tmp = a * (b * ((x * y) - (z * t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y2 * Float64(x * Float64(-y1))))
	tmp = 0.0
	if (y1 <= -5.2e+138)
		tmp = t_1;
	elseif (y1 <= 8.5e-294)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (y1 <= 4.8e-115)
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))));
	elseif (y1 <= 7e+29)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y2 * (x * -y1));
	tmp = 0.0;
	if (y1 <= -5.2e+138)
		tmp = t_1;
	elseif (y1 <= 8.5e-294)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (y1 <= 4.8e-115)
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	elseif (y1 <= 7e+29)
		tmp = a * (b * ((x * y) - (z * t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y2 * N[(x * (-y1)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -5.2e+138], t$95$1, If[LessEqual[y1, 8.5e-294], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 4.8e-115], N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 7e+29], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y1 < -5.2000000000000002e138 or 6.99999999999999958e29 < y1

   1. Initial program 27.5%

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

   3. Taylor expanded in y2 around inf 40.4%

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

   4. Taylor expanded in a around -inf 42.7%

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

      1. associate-*r* 42.7%

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

      2. neg-mul-1 42.7%

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

   6. Simplified 42.7%

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

   7. Taylor expanded in x around inf 40.9%

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

      1. *-commutative 40.9%

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

   9. Simplified 40.9%

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

   if -5.2000000000000002e138 < y1 < 8.4999999999999999e-294

   1. Initial program 30.3%

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

   3. Taylor expanded in b around inf 39.7%

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

   4. Taylor expanded in j around inf 39.6%

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

   if 8.4999999999999999e-294 < y1 < 4.80000000000000042e-115

   1. Initial program 30.9%

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

   3. Taylor expanded in y0 around inf 44.1%

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

   4. Taylor expanded in j around inf 49.4%

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

   if 4.80000000000000042e-115 < y1 < 6.99999999999999958e29

   1. Initial program 43.7%

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

   3. Taylor expanded in b around inf 37.2%

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

   4. Taylor expanded in a around inf 37.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -5.2 \cdot 10^{+138}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(x \cdot \left(-y1\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 8.5 \cdot 10^{-294}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 4.8 \cdot 10^{-115}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y1 \leq 7 \cdot 10^{+29}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(x \cdot \left(-y1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 22.3% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(x \cdot \left(b \cdot \left(-j\right)\right)\right)\\ \mathbf{if}\;b \leq -3.4 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.12 \cdot 10^{-203}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+108}:\\ \;\;\;\;\left(-i\right) \cdot \left(k \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{+170}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y0 (* x (* b (- j))))))
   (if (<= b -3.4e+32)
     t_1
     (if (<= b 1.12e-203)
       (* a (* y2 (* t y5)))
       (if (<= b 1.4e+108)
         (* (- i) (* k (* z y1)))
         (if (<= b 4.4e+170) (* a (* t (* y2 y5))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * (x * (b * -j));
	double tmp;
	if (b <= -3.4e+32) {
		tmp = t_1;
	} else if (b <= 1.12e-203) {
		tmp = a * (y2 * (t * y5));
	} else if (b <= 1.4e+108) {
		tmp = -i * (k * (z * y1));
	} else if (b <= 4.4e+170) {
		tmp = a * (t * (y2 * y5));
	} 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 = y0 * (x * (b * -j))
    if (b <= (-3.4d+32)) then
        tmp = t_1
    else if (b <= 1.12d-203) then
        tmp = a * (y2 * (t * y5))
    else if (b <= 1.4d+108) then
        tmp = -i * (k * (z * y1))
    else if (b <= 4.4d+170) then
        tmp = a * (t * (y2 * y5))
    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 = y0 * (x * (b * -j));
	double tmp;
	if (b <= -3.4e+32) {
		tmp = t_1;
	} else if (b <= 1.12e-203) {
		tmp = a * (y2 * (t * y5));
	} else if (b <= 1.4e+108) {
		tmp = -i * (k * (z * y1));
	} else if (b <= 4.4e+170) {
		tmp = a * (t * (y2 * y5));
	} 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 = y0 * (x * (b * -j))
	tmp = 0
	if b <= -3.4e+32:
		tmp = t_1
	elif b <= 1.12e-203:
		tmp = a * (y2 * (t * y5))
	elif b <= 1.4e+108:
		tmp = -i * (k * (z * y1))
	elif b <= 4.4e+170:
		tmp = a * (t * (y2 * y5))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y0 * Float64(x * Float64(b * Float64(-j))))
	tmp = 0.0
	if (b <= -3.4e+32)
		tmp = t_1;
	elseif (b <= 1.12e-203)
		tmp = Float64(a * Float64(y2 * Float64(t * y5)));
	elseif (b <= 1.4e+108)
		tmp = Float64(Float64(-i) * Float64(k * Float64(z * y1)));
	elseif (b <= 4.4e+170)
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	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 = y0 * (x * (b * -j));
	tmp = 0.0;
	if (b <= -3.4e+32)
		tmp = t_1;
	elseif (b <= 1.12e-203)
		tmp = a * (y2 * (t * y5));
	elseif (b <= 1.4e+108)
		tmp = -i * (k * (z * y1));
	elseif (b <= 4.4e+170)
		tmp = a * (t * (y2 * y5));
	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[(y0 * N[(x * N[(b * (-j)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.4e+32], t$95$1, If[LessEqual[b, 1.12e-203], N[(a * N[(y2 * N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.4e+108], N[((-i) * N[(k * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.4e+170], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.39999999999999979e32 or 4.39999999999999978e170 < b

   1. Initial program 18.5%

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

   3. Taylor expanded in y0 around inf 43.8%

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

   4. Taylor expanded in x around inf 48.7%

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

   5. Taylor expanded in c around 0 43.5%

      \[\leadsto y0 \cdot \left(x \cdot \color{blue}{\left(-1 \cdot \left(b \cdot j\right)\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 43.5%

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

      2. distribute-lft-neg-out 43.5%

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

      3. *-commutative 43.5%

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

   7. Simplified 43.5%

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

   if -3.39999999999999979e32 < b < 1.12e-203

   1. Initial program 41.3%

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

   3. Taylor expanded in y2 around inf 47.7%

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

   4. Taylor expanded in a around -inf 37.1%

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

      1. associate-*r* 37.1%

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

      2. neg-mul-1 37.1%

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

   6. Simplified 37.1%

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

   7. Taylor expanded in x around 0 29.4%

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

      1. neg-mul-1 29.4%

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

      2. distribute-lft-neg-in 29.4%

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

      3. *-commutative 29.4%

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

   9. Simplified 29.4%

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

   if 1.12e-203 < b < 1.3999999999999999e108

   1. Initial program 33.6%

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

   3. Taylor expanded in y1 around inf 34.2%

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

   4. Taylor expanded in z around inf 42.9%

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

   5. Taylor expanded in a around 0 33.3%

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

      1. associate-*r* 33.3%

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

      2. neg-mul-1 33.3%

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

   7. Simplified 33.3%

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

   if 1.3999999999999999e108 < b < 4.39999999999999978e170

   1. Initial program 15.9%

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

   3. Taylor expanded in y2 around inf 69.9%

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

   4. Taylor expanded in a around -inf 39.4%

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

      1. associate-*r* 39.4%

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

      2. neg-mul-1 39.4%

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

   6. Simplified 39.4%

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

   7. Taylor expanded in x around 0 47.1%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 35.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{+32}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(b \cdot \left(-j\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.12 \cdot 10^{-203}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+108}:\\ \;\;\;\;\left(-i\right) \cdot \left(k \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{+170}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(b \cdot \left(-j\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 22.3% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(x \cdot \left(b \cdot \left(-j\right)\right)\right)\\ t_2 := a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{if}\;b \leq -2.05 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-204}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+100}:\\ \;\;\;\;\left(-i\right) \cdot \left(k \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 5.1 \cdot 10^{+172}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y0 (* x (* b (- j))))) (t_2 (* a (* t (* y2 y5)))))
   (if (<= b -2.05e+33)
     t_1
     (if (<= b 4.5e-204)
       t_2
       (if (<= b 1.6e+100)
         (* (- i) (* k (* z y1)))
         (if (<= b 5.1e+172) 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 = y0 * (x * (b * -j));
	double t_2 = a * (t * (y2 * y5));
	double tmp;
	if (b <= -2.05e+33) {
		tmp = t_1;
	} else if (b <= 4.5e-204) {
		tmp = t_2;
	} else if (b <= 1.6e+100) {
		tmp = -i * (k * (z * y1));
	} else if (b <= 5.1e+172) {
		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 = y0 * (x * (b * -j))
    t_2 = a * (t * (y2 * y5))
    if (b <= (-2.05d+33)) then
        tmp = t_1
    else if (b <= 4.5d-204) then
        tmp = t_2
    else if (b <= 1.6d+100) then
        tmp = -i * (k * (z * y1))
    else if (b <= 5.1d+172) 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 = y0 * (x * (b * -j));
	double t_2 = a * (t * (y2 * y5));
	double tmp;
	if (b <= -2.05e+33) {
		tmp = t_1;
	} else if (b <= 4.5e-204) {
		tmp = t_2;
	} else if (b <= 1.6e+100) {
		tmp = -i * (k * (z * y1));
	} else if (b <= 5.1e+172) {
		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 = y0 * (x * (b * -j))
	t_2 = a * (t * (y2 * y5))
	tmp = 0
	if b <= -2.05e+33:
		tmp = t_1
	elif b <= 4.5e-204:
		tmp = t_2
	elif b <= 1.6e+100:
		tmp = -i * (k * (z * y1))
	elif b <= 5.1e+172:
		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(y0 * Float64(x * Float64(b * Float64(-j))))
	t_2 = Float64(a * Float64(t * Float64(y2 * y5)))
	tmp = 0.0
	if (b <= -2.05e+33)
		tmp = t_1;
	elseif (b <= 4.5e-204)
		tmp = t_2;
	elseif (b <= 1.6e+100)
		tmp = Float64(Float64(-i) * Float64(k * Float64(z * y1)));
	elseif (b <= 5.1e+172)
		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 = y0 * (x * (b * -j));
	t_2 = a * (t * (y2 * y5));
	tmp = 0.0;
	if (b <= -2.05e+33)
		tmp = t_1;
	elseif (b <= 4.5e-204)
		tmp = t_2;
	elseif (b <= 1.6e+100)
		tmp = -i * (k * (z * y1));
	elseif (b <= 5.1e+172)
		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[(y0 * N[(x * N[(b * (-j)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.05e+33], t$95$1, If[LessEqual[b, 4.5e-204], t$95$2, If[LessEqual[b, 1.6e+100], N[((-i) * N[(k * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.1e+172], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.04999999999999997e33 or 5.1e172 < b

   1. Initial program 18.6%

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

   3. Taylor expanded in y0 around inf 44.4%

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

   4. Taylor expanded in x around inf 49.2%

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

   5. Taylor expanded in c around 0 44.0%

      \[\leadsto y0 \cdot \left(x \cdot \color{blue}{\left(-1 \cdot \left(b \cdot j\right)\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 44.0%

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

      2. distribute-lft-neg-out 44.0%

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

      3. *-commutative 44.0%

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

   7. Simplified 44.0%

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

   if -2.04999999999999997e33 < b < 4.49999999999999974e-204 or 1.5999999999999999e100 < b < 5.1e172

   1. Initial program 38.1%

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

   3. Taylor expanded in y2 around inf 49.9%

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

   4. Taylor expanded in a around -inf 37.1%

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

      1. associate-*r* 37.1%

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

      2. neg-mul-1 37.1%

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

   6. Simplified 37.1%

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

   7. Taylor expanded in x around 0 31.1%

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

   if 4.49999999999999974e-204 < b < 1.5999999999999999e100

   1. Initial program 33.6%

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

   3. Taylor expanded in y1 around inf 34.2%

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

   4. Taylor expanded in z around inf 42.9%

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

   5. Taylor expanded in a around 0 33.3%

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

      1. associate-*r* 33.3%

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

      2. neg-mul-1 33.3%

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

   7. Simplified 33.3%

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

4. Final simplification 35.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.05 \cdot 10^{+33}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(b \cdot \left(-j\right)\right)\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-204}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+100}:\\ \;\;\;\;\left(-i\right) \cdot \left(k \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 5.1 \cdot 10^{+172}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(b \cdot \left(-j\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 22.2% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(x \cdot \left(b \cdot \left(-j\right)\right)\right)\\ t_2 := a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{if}\;b \leq -4.8 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-233}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{+95}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(i \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{+171}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y0 (* x (* b (- j))))) (t_2 (* a (* t (* y2 y5)))))
   (if (<= b -4.8e+33)
     t_1
     (if (<= b 3.5e-233)
       t_2
       (if (<= b 2.25e+95)
         (* y1 (* z (* i (- k))))
         (if (<= b 3.4e+171) 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 = y0 * (x * (b * -j));
	double t_2 = a * (t * (y2 * y5));
	double tmp;
	if (b <= -4.8e+33) {
		tmp = t_1;
	} else if (b <= 3.5e-233) {
		tmp = t_2;
	} else if (b <= 2.25e+95) {
		tmp = y1 * (z * (i * -k));
	} else if (b <= 3.4e+171) {
		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 = y0 * (x * (b * -j))
    t_2 = a * (t * (y2 * y5))
    if (b <= (-4.8d+33)) then
        tmp = t_1
    else if (b <= 3.5d-233) then
        tmp = t_2
    else if (b <= 2.25d+95) then
        tmp = y1 * (z * (i * -k))
    else if (b <= 3.4d+171) 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 = y0 * (x * (b * -j));
	double t_2 = a * (t * (y2 * y5));
	double tmp;
	if (b <= -4.8e+33) {
		tmp = t_1;
	} else if (b <= 3.5e-233) {
		tmp = t_2;
	} else if (b <= 2.25e+95) {
		tmp = y1 * (z * (i * -k));
	} else if (b <= 3.4e+171) {
		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 = y0 * (x * (b * -j))
	t_2 = a * (t * (y2 * y5))
	tmp = 0
	if b <= -4.8e+33:
		tmp = t_1
	elif b <= 3.5e-233:
		tmp = t_2
	elif b <= 2.25e+95:
		tmp = y1 * (z * (i * -k))
	elif b <= 3.4e+171:
		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(y0 * Float64(x * Float64(b * Float64(-j))))
	t_2 = Float64(a * Float64(t * Float64(y2 * y5)))
	tmp = 0.0
	if (b <= -4.8e+33)
		tmp = t_1;
	elseif (b <= 3.5e-233)
		tmp = t_2;
	elseif (b <= 2.25e+95)
		tmp = Float64(y1 * Float64(z * Float64(i * Float64(-k))));
	elseif (b <= 3.4e+171)
		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 = y0 * (x * (b * -j));
	t_2 = a * (t * (y2 * y5));
	tmp = 0.0;
	if (b <= -4.8e+33)
		tmp = t_1;
	elseif (b <= 3.5e-233)
		tmp = t_2;
	elseif (b <= 2.25e+95)
		tmp = y1 * (z * (i * -k));
	elseif (b <= 3.4e+171)
		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[(y0 * N[(x * N[(b * (-j)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.8e+33], t$95$1, If[LessEqual[b, 3.5e-233], t$95$2, If[LessEqual[b, 2.25e+95], N[(y1 * N[(z * N[(i * (-k)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.4e+171], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.8e33 or 3.4000000000000001e171 < b

   1. Initial program 18.6%

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

   3. Taylor expanded in y0 around inf 44.4%

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

   4. Taylor expanded in x around inf 49.2%

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

   5. Taylor expanded in c around 0 44.0%

      \[\leadsto y0 \cdot \left(x \cdot \color{blue}{\left(-1 \cdot \left(b \cdot j\right)\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 44.0%

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

      2. distribute-lft-neg-out 44.0%

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

      3. *-commutative 44.0%

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

   7. Simplified 44.0%

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

   if -4.8e33 < b < 3.49999999999999991e-233 or 2.25000000000000008e95 < b < 3.4000000000000001e171

   1. Initial program 37.1%

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

   3. Taylor expanded in y2 around inf 50.3%

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

   4. Taylor expanded in a around -inf 38.7%

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

      1. associate-*r* 38.7%

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

      2. neg-mul-1 38.7%

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

   6. Simplified 38.7%

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

   7. Taylor expanded in x around 0 31.6%

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

   if 3.49999999999999991e-233 < b < 2.25000000000000008e95

   1. Initial program 35.7%

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

   3. Taylor expanded in y1 around inf 36.3%

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

   4. Taylor expanded in z around inf 44.3%

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

   5. Taylor expanded in a around 0 32.3%

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

      1. mul-1-neg 32.3%

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

      2. distribute-lft-neg-out 32.3%

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

      3. *-commutative 32.3%

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

   7. Simplified 32.3%

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

4. Final simplification 35.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{+33}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(b \cdot \left(-j\right)\right)\right)\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-233}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{+95}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(i \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{+171}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(b \cdot \left(-j\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 21.4% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{if}\;y5 \leq -1.9 \cdot 10^{+115}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y5 \leq -7 \cdot 10^{-75}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq 3.9 \cdot 10^{-178}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y5 \leq 5 \cdot 10^{-41}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* t (* y2 y5)))))
   (if (<= y5 -1.9e+115)
     t_1
     (if (<= y5 -7e-75)
       (* y1 (* z (* a y3)))
       (if (<= y5 3.9e-178)
         (* a (* (* x y) b))
         (if (<= y5 5e-41) (* y1 (* a (* z y3))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (t * (y2 * y5));
	double tmp;
	if (y5 <= -1.9e+115) {
		tmp = t_1;
	} else if (y5 <= -7e-75) {
		tmp = y1 * (z * (a * y3));
	} else if (y5 <= 3.9e-178) {
		tmp = a * ((x * y) * b);
	} else if (y5 <= 5e-41) {
		tmp = y1 * (a * (z * y3));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (t * (y2 * y5))
    if (y5 <= (-1.9d+115)) then
        tmp = t_1
    else if (y5 <= (-7d-75)) then
        tmp = y1 * (z * (a * y3))
    else if (y5 <= 3.9d-178) then
        tmp = a * ((x * y) * b)
    else if (y5 <= 5d-41) then
        tmp = y1 * (a * (z * y3))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (t * (y2 * y5));
	double tmp;
	if (y5 <= -1.9e+115) {
		tmp = t_1;
	} else if (y5 <= -7e-75) {
		tmp = y1 * (z * (a * y3));
	} else if (y5 <= 3.9e-178) {
		tmp = a * ((x * y) * b);
	} else if (y5 <= 5e-41) {
		tmp = y1 * (a * (z * y3));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (t * (y2 * y5))
	tmp = 0
	if y5 <= -1.9e+115:
		tmp = t_1
	elif y5 <= -7e-75:
		tmp = y1 * (z * (a * y3))
	elif y5 <= 3.9e-178:
		tmp = a * ((x * y) * b)
	elif y5 <= 5e-41:
		tmp = y1 * (a * (z * y3))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(t * Float64(y2 * y5)))
	tmp = 0.0
	if (y5 <= -1.9e+115)
		tmp = t_1;
	elseif (y5 <= -7e-75)
		tmp = Float64(y1 * Float64(z * Float64(a * y3)));
	elseif (y5 <= 3.9e-178)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	elseif (y5 <= 5e-41)
		tmp = Float64(y1 * Float64(a * Float64(z * y3)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (t * (y2 * y5));
	tmp = 0.0;
	if (y5 <= -1.9e+115)
		tmp = t_1;
	elseif (y5 <= -7e-75)
		tmp = y1 * (z * (a * y3));
	elseif (y5 <= 3.9e-178)
		tmp = a * ((x * y) * b);
	elseif (y5 <= 5e-41)
		tmp = y1 * (a * (z * y3));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -1.9e+115], t$95$1, If[LessEqual[y5, -7e-75], N[(y1 * N[(z * N[(a * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 3.9e-178], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 5e-41], N[(y1 * N[(a * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y5 < -1.9e115 or 4.9999999999999996e-41 < y5

   1. Initial program 27.7%

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

   3. Taylor expanded in y2 around inf 45.1%

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

   4. Taylor expanded in a around -inf 44.4%

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

      1. associate-*r* 44.4%

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

      2. neg-mul-1 44.4%

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

   6. Simplified 44.4%

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

   7. Taylor expanded in x around 0 36.7%

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

   if -1.9e115 < y5 < -6.9999999999999997e-75

   1. Initial program 21.2%

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

   3. Taylor expanded in y1 around inf 40.2%

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

   4. Taylor expanded in z around inf 43.2%

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

   5. Taylor expanded in a around inf 34.7%

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

      1. associate-*r* 36.6%

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

   7. Simplified 36.6%

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

   if -6.9999999999999997e-75 < y5 < 3.90000000000000025e-178

   1. Initial program 38.5%

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

   3. Taylor expanded in b around inf 36.5%

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

   4. Taylor expanded in a around inf 30.3%

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

   5. Taylor expanded in x around inf 23.6%

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

      1. *-commutative 23.6%

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

   7. Simplified 23.6%

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

   if 3.90000000000000025e-178 < y5 < 4.9999999999999996e-41

   1. Initial program 49.9%

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

   3. Taylor expanded in y1 around inf 50.3%

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

   4. Taylor expanded in z around inf 35.0%

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

   5. Taylor expanded in a around inf 45.6%

      \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(y3 \cdot z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 33.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -1.9 \cdot 10^{+115}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq -7 \cdot 10^{-75}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq 3.9 \cdot 10^{-178}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y5 \leq 5 \cdot 10^{-41}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 21.5% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ t_2 := y1 \cdot \left(a \cdot \left(z \cdot y3\right)\right)\\ \mathbf{if}\;y5 \leq -8.5 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y5 \leq -5.4 \cdot 10^{-79}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y5 \leq 5.1 \cdot 10^{-179}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y5 \leq 9.8 \cdot 10^{-42}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* t (* y2 y5)))) (t_2 (* y1 (* a (* z y3)))))
   (if (<= y5 -8.5e+46)
     t_1
     (if (<= y5 -5.4e-79)
       t_2
       (if (<= y5 5.1e-179)
         (* a (* (* x y) b))
         (if (<= y5 9.8e-42) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (t * (y2 * y5));
	double t_2 = y1 * (a * (z * y3));
	double tmp;
	if (y5 <= -8.5e+46) {
		tmp = t_1;
	} else if (y5 <= -5.4e-79) {
		tmp = t_2;
	} else if (y5 <= 5.1e-179) {
		tmp = a * ((x * y) * b);
	} else if (y5 <= 9.8e-42) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (t * (y2 * y5))
    t_2 = y1 * (a * (z * y3))
    if (y5 <= (-8.5d+46)) then
        tmp = t_1
    else if (y5 <= (-5.4d-79)) then
        tmp = t_2
    else if (y5 <= 5.1d-179) then
        tmp = a * ((x * y) * b)
    else if (y5 <= 9.8d-42) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (t * (y2 * y5));
	double t_2 = y1 * (a * (z * y3));
	double tmp;
	if (y5 <= -8.5e+46) {
		tmp = t_1;
	} else if (y5 <= -5.4e-79) {
		tmp = t_2;
	} else if (y5 <= 5.1e-179) {
		tmp = a * ((x * y) * b);
	} else if (y5 <= 9.8e-42) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (t * (y2 * y5))
	t_2 = y1 * (a * (z * y3))
	tmp = 0
	if y5 <= -8.5e+46:
		tmp = t_1
	elif y5 <= -5.4e-79:
		tmp = t_2
	elif y5 <= 5.1e-179:
		tmp = a * ((x * y) * b)
	elif y5 <= 9.8e-42:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(t * Float64(y2 * y5)))
	t_2 = Float64(y1 * Float64(a * Float64(z * y3)))
	tmp = 0.0
	if (y5 <= -8.5e+46)
		tmp = t_1;
	elseif (y5 <= -5.4e-79)
		tmp = t_2;
	elseif (y5 <= 5.1e-179)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	elseif (y5 <= 9.8e-42)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (t * (y2 * y5));
	t_2 = y1 * (a * (z * y3));
	tmp = 0.0;
	if (y5 <= -8.5e+46)
		tmp = t_1;
	elseif (y5 <= -5.4e-79)
		tmp = t_2;
	elseif (y5 <= 5.1e-179)
		tmp = a * ((x * y) * b);
	elseif (y5 <= 9.8e-42)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y1 * N[(a * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -8.5e+46], t$95$1, If[LessEqual[y5, -5.4e-79], t$95$2, If[LessEqual[y5, 5.1e-179], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 9.8e-42], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y5 < -8.4999999999999996e46 or 9.8000000000000001e-42 < y5

   1. Initial program 26.0%

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

   3. Taylor expanded in y2 around inf 47.0%

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

   4. Taylor expanded in a around -inf 42.1%

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

      1. associate-*r* 42.1%

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

      2. neg-mul-1 42.1%

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

   6. Simplified 42.1%

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

   7. Taylor expanded in x around 0 35.9%

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

   if -8.4999999999999996e46 < y5 < -5.4000000000000004e-79 or 5.10000000000000028e-179 < y5 < 9.8000000000000001e-42

   1. Initial program 33.5%

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

   3. Taylor expanded in y1 around inf 48.6%

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

   4. Taylor expanded in z around inf 42.5%

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

   5. Taylor expanded in a around inf 40.1%

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

   if -5.4000000000000004e-79 < y5 < 5.10000000000000028e-179

   1. Initial program 38.5%

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

   3. Taylor expanded in b around inf 36.5%

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

   4. Taylor expanded in a around inf 30.3%

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

   5. Taylor expanded in x around inf 23.6%

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

      1. *-commutative 23.6%

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

   7. Simplified 23.6%

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

4. Final simplification 33.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -8.5 \cdot 10^{+46}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq -5.4 \cdot 10^{-79}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq 5.1 \cdot 10^{-179}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y5 \leq 9.8 \cdot 10^{-42}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 31: 21.4% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ t_2 := a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{if}\;y5 \leq -8 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y5 \leq -6 \cdot 10^{-75}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y5 \leq 9.8 \cdot 10^{-178}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y5 \leq 3.8 \cdot 10^{-44}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* t (* y2 y5)))) (t_2 (* a (* y1 (* z y3)))))
   (if (<= y5 -8e+17)
     t_1
     (if (<= y5 -6e-75)
       t_2
       (if (<= y5 9.8e-178)
         (* a (* (* x y) b))
         (if (<= y5 3.8e-44) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (t * (y2 * y5));
	double t_2 = a * (y1 * (z * y3));
	double tmp;
	if (y5 <= -8e+17) {
		tmp = t_1;
	} else if (y5 <= -6e-75) {
		tmp = t_2;
	} else if (y5 <= 9.8e-178) {
		tmp = a * ((x * y) * b);
	} else if (y5 <= 3.8e-44) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (t * (y2 * y5))
    t_2 = a * (y1 * (z * y3))
    if (y5 <= (-8d+17)) then
        tmp = t_1
    else if (y5 <= (-6d-75)) then
        tmp = t_2
    else if (y5 <= 9.8d-178) then
        tmp = a * ((x * y) * b)
    else if (y5 <= 3.8d-44) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (t * (y2 * y5));
	double t_2 = a * (y1 * (z * y3));
	double tmp;
	if (y5 <= -8e+17) {
		tmp = t_1;
	} else if (y5 <= -6e-75) {
		tmp = t_2;
	} else if (y5 <= 9.8e-178) {
		tmp = a * ((x * y) * b);
	} else if (y5 <= 3.8e-44) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (t * (y2 * y5))
	t_2 = a * (y1 * (z * y3))
	tmp = 0
	if y5 <= -8e+17:
		tmp = t_1
	elif y5 <= -6e-75:
		tmp = t_2
	elif y5 <= 9.8e-178:
		tmp = a * ((x * y) * b)
	elif y5 <= 3.8e-44:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(t * Float64(y2 * y5)))
	t_2 = Float64(a * Float64(y1 * Float64(z * y3)))
	tmp = 0.0
	if (y5 <= -8e+17)
		tmp = t_1;
	elseif (y5 <= -6e-75)
		tmp = t_2;
	elseif (y5 <= 9.8e-178)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	elseif (y5 <= 3.8e-44)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (t * (y2 * y5));
	t_2 = a * (y1 * (z * y3));
	tmp = 0.0;
	if (y5 <= -8e+17)
		tmp = t_1;
	elseif (y5 <= -6e-75)
		tmp = t_2;
	elseif (y5 <= 9.8e-178)
		tmp = a * ((x * y) * b);
	elseif (y5 <= 3.8e-44)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(y1 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -8e+17], t$95$1, If[LessEqual[y5, -6e-75], t$95$2, If[LessEqual[y5, 9.8e-178], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 3.8e-44], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y5 < -8e17 or 3.8000000000000001e-44 < y5

   1. Initial program 26.2%

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

   3. Taylor expanded in y2 around inf 46.8%

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

   4. Taylor expanded in a around -inf 41.2%

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

      1. associate-*r* 41.2%

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

      2. neg-mul-1 41.2%

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

   6. Simplified 41.2%

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

   7. Taylor expanded in x around 0 35.2%

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

   if -8e17 < y5 < -5.9999999999999997e-75 or 9.80000000000000041e-178 < y5 < 3.8000000000000001e-44

   1. Initial program 32.0%

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

   3. Taylor expanded in y1 around inf 48.4%

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

   4. Taylor expanded in z around inf 41.9%

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

   5. Taylor expanded in a around inf 37.7%

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

      1. *-commutative 37.7%

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

   7. Simplified 37.7%

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

   if -5.9999999999999997e-75 < y5 < 9.80000000000000041e-178

   1. Initial program 39.4%

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

   3. Taylor expanded in b around inf 36.0%

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

   4. Taylor expanded in a around inf 29.9%

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

   5. Taylor expanded in x around inf 23.3%

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

      1. *-commutative 23.3%

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

   7. Simplified 23.3%

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

4. Final simplification 32.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -8 \cdot 10^{+17}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq -6 \cdot 10^{-75}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq 9.8 \cdot 10^{-178}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y5 \leq 3.8 \cdot 10^{-44}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 32: 28.9% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y2 \cdot \left(x \cdot \left(-y1\right)\right)\right)\\ \mathbf{if}\;y1 \leq -1.2 \cdot 10^{+137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq 2 \cdot 10^{-169}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 1.25 \cdot 10^{+27}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y2 (* x (- y1))))))
   (if (<= y1 -1.2e+137)
     t_1
     (if (<= y1 2e-169)
       (* b (* j (- (* t y4) (* x y0))))
       (if (<= y1 1.25e+27) (* a (* b (- (* x y) (* z t)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y2 * (x * -y1));
	double tmp;
	if (y1 <= -1.2e+137) {
		tmp = t_1;
	} else if (y1 <= 2e-169) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y1 <= 1.25e+27) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (y2 * (x * -y1))
    if (y1 <= (-1.2d+137)) then
        tmp = t_1
    else if (y1 <= 2d-169) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (y1 <= 1.25d+27) then
        tmp = a * (b * ((x * y) - (z * t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y2 * (x * -y1));
	double tmp;
	if (y1 <= -1.2e+137) {
		tmp = t_1;
	} else if (y1 <= 2e-169) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y1 <= 1.25e+27) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y2 * (x * -y1))
	tmp = 0
	if y1 <= -1.2e+137:
		tmp = t_1
	elif y1 <= 2e-169:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif y1 <= 1.25e+27:
		tmp = a * (b * ((x * y) - (z * t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y2 * Float64(x * Float64(-y1))))
	tmp = 0.0
	if (y1 <= -1.2e+137)
		tmp = t_1;
	elseif (y1 <= 2e-169)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (y1 <= 1.25e+27)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y2 * (x * -y1));
	tmp = 0.0;
	if (y1 <= -1.2e+137)
		tmp = t_1;
	elseif (y1 <= 2e-169)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (y1 <= 1.25e+27)
		tmp = a * (b * ((x * y) - (z * t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y2 * N[(x * (-y1)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -1.2e+137], t$95$1, If[LessEqual[y1, 2e-169], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.25e+27], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y1 < -1.19999999999999992e137 or 1.24999999999999995e27 < y1

   1. Initial program 27.5%

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

   3. Taylor expanded in y2 around inf 40.4%

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

   4. Taylor expanded in a around -inf 42.7%

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

      1. associate-*r* 42.7%

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

      2. neg-mul-1 42.7%

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

   6. Simplified 42.7%

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

   7. Taylor expanded in x around inf 40.9%

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

      1. *-commutative 40.9%

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

   9. Simplified 40.9%

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

   if -1.19999999999999992e137 < y1 < 2.00000000000000004e-169

   1. Initial program 31.1%

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

   3. Taylor expanded in b around inf 44.3%

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

   4. Taylor expanded in j around inf 38.9%

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

   if 2.00000000000000004e-169 < y1 < 1.24999999999999995e27

   1. Initial program 38.3%

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

   3. Taylor expanded in b around inf 34.0%

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

   4. Taylor expanded in a around inf 36.9%

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

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -1.2 \cdot 10^{+137}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(x \cdot \left(-y1\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 2 \cdot 10^{-169}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 1.25 \cdot 10^{+27}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(x \cdot \left(-y1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 33: 21.7% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(x \cdot \left(b \cdot \left(-j\right)\right)\right)\\ \mathbf{if}\;b \leq -1.95 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-243}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{+174}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y0 (* x (* b (- j))))))
   (if (<= b -1.95e+33)
     t_1
     (if (<= b 3.2e-243)
       (* a (* t (* y2 y5)))
       (if (<= b 2.6e+174) (* y0 (* x (* c y2))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * (x * (b * -j));
	double tmp;
	if (b <= -1.95e+33) {
		tmp = t_1;
	} else if (b <= 3.2e-243) {
		tmp = a * (t * (y2 * y5));
	} else if (b <= 2.6e+174) {
		tmp = y0 * (x * (c * y2));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y0 * (x * (b * -j))
    if (b <= (-1.95d+33)) then
        tmp = t_1
    else if (b <= 3.2d-243) then
        tmp = a * (t * (y2 * y5))
    else if (b <= 2.6d+174) then
        tmp = y0 * (x * (c * y2))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * (x * (b * -j));
	double tmp;
	if (b <= -1.95e+33) {
		tmp = t_1;
	} else if (b <= 3.2e-243) {
		tmp = a * (t * (y2 * y5));
	} else if (b <= 2.6e+174) {
		tmp = y0 * (x * (c * y2));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y0 * (x * (b * -j))
	tmp = 0
	if b <= -1.95e+33:
		tmp = t_1
	elif b <= 3.2e-243:
		tmp = a * (t * (y2 * y5))
	elif b <= 2.6e+174:
		tmp = y0 * (x * (c * y2))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y0 * Float64(x * Float64(b * Float64(-j))))
	tmp = 0.0
	if (b <= -1.95e+33)
		tmp = t_1;
	elseif (b <= 3.2e-243)
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	elseif (b <= 2.6e+174)
		tmp = Float64(y0 * Float64(x * Float64(c * y2)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y0 * (x * (b * -j));
	tmp = 0.0;
	if (b <= -1.95e+33)
		tmp = t_1;
	elseif (b <= 3.2e-243)
		tmp = a * (t * (y2 * y5));
	elseif (b <= 2.6e+174)
		tmp = y0 * (x * (c * y2));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y0 * N[(x * N[(b * (-j)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.95e+33], t$95$1, If[LessEqual[b, 3.2e-243], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.6e+174], N[(y0 * N[(x * N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.9500000000000001e33 or 2.5999999999999999e174 < b

   1. Initial program 18.9%

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

   3. Taylor expanded in y0 around inf 44.9%

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

   4. Taylor expanded in x around inf 49.8%

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

   5. Taylor expanded in c around 0 44.5%

      \[\leadsto y0 \cdot \left(x \cdot \color{blue}{\left(-1 \cdot \left(b \cdot j\right)\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 44.5%

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

      2. distribute-lft-neg-out 44.5%

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

      3. *-commutative 44.5%

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

   7. Simplified 44.5%

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

   if -1.9500000000000001e33 < b < 3.1999999999999998e-243

   1. Initial program 41.5%

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

   3. Taylor expanded in y2 around inf 47.5%

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

   4. Taylor expanded in a around -inf 39.0%

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

      1. associate-*r* 39.0%

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

      2. neg-mul-1 39.0%

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

   6. Simplified 39.0%

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

   7. Taylor expanded in x around 0 29.1%

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

   if 3.1999999999999998e-243 < b < 2.5999999999999999e174

   1. Initial program 30.9%

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

   3. Taylor expanded in y0 around inf 31.2%

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

   4. Taylor expanded in x around inf 34.0%

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

   5. Taylor expanded in c around inf 29.6%

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

4. Final simplification 34.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.95 \cdot 10^{+33}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(b \cdot \left(-j\right)\right)\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-243}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{+174}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(b \cdot \left(-j\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 34: 27.2% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -1.15 \cdot 10^{-76}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 2.35 \cdot 10^{+157}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -1.15e-76)
   (* c (* x (* y0 y2)))
   (if (<= y2 2.35e+157)
     (* a (* b (- (* x y) (* z t))))
     (* a (* t (* y2 y5))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -1.15e-76) {
		tmp = c * (x * (y0 * y2));
	} else if (y2 <= 2.35e+157) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = a * (t * (y2 * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y2 <= (-1.15d-76)) then
        tmp = c * (x * (y0 * y2))
    else if (y2 <= 2.35d+157) then
        tmp = a * (b * ((x * y) - (z * t)))
    else
        tmp = a * (t * (y2 * y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -1.15e-76) {
		tmp = c * (x * (y0 * y2));
	} else if (y2 <= 2.35e+157) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = a * (t * (y2 * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y2 <= -1.15e-76:
		tmp = c * (x * (y0 * y2))
	elif y2 <= 2.35e+157:
		tmp = a * (b * ((x * y) - (z * t)))
	else:
		tmp = a * (t * (y2 * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y2 <= -1.15e-76)
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	elseif (y2 <= 2.35e+157)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	else
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y2 <= -1.15e-76)
		tmp = c * (x * (y0 * y2));
	elseif (y2 <= 2.35e+157)
		tmp = a * (b * ((x * y) - (z * t)));
	else
		tmp = a * (t * (y2 * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y2, -1.15e-76], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.35e+157], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y2 < -1.15000000000000003e-76

   1. Initial program 28.3%

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

   3. Taylor expanded in y0 around inf 37.0%

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

   4. Taylor expanded in x around inf 36.7%

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

   5. Taylor expanded in j around inf 40.2%

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

   6. Taylor expanded in j around 0 32.0%

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

   if -1.15000000000000003e-76 < y2 < 2.35000000000000015e157

   1. Initial program 34.8%

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

   3. Taylor expanded in b around inf 38.7%

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

   4. Taylor expanded in a around inf 34.4%

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

   if 2.35000000000000015e157 < y2

   1. Initial program 19.6%

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

   3. Taylor expanded in y2 around inf 74.1%

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

   4. Taylor expanded in a around -inf 58.4%

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

      1. associate-*r* 58.4%

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

      2. neg-mul-1 58.4%

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

   6. Simplified 58.4%

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

   7. Taylor expanded in x around 0 52.6%

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

4. Final simplification 35.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.15 \cdot 10^{-76}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 2.35 \cdot 10^{+157}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 35: 20.6% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+28} \lor \neg \left(x \leq 8.5 \cdot 10^{+230}\right):\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= x -1.65e+28) (not (<= x 8.5e+230)))
   (* a (* (* x y) b))
   (* a (* t (* y2 y5)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((x <= -1.65e+28) || !(x <= 8.5e+230)) {
		tmp = a * ((x * y) * b);
	} else {
		tmp = a * (t * (y2 * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((x <= (-1.65d+28)) .or. (.not. (x <= 8.5d+230))) then
        tmp = a * ((x * y) * b)
    else
        tmp = a * (t * (y2 * y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((x <= -1.65e+28) || !(x <= 8.5e+230)) {
		tmp = a * ((x * y) * b);
	} else {
		tmp = a * (t * (y2 * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (x <= -1.65e+28) or not (x <= 8.5e+230):
		tmp = a * ((x * y) * b)
	else:
		tmp = a * (t * (y2 * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((x <= -1.65e+28) || !(x <= 8.5e+230))
		tmp = Float64(a * Float64(Float64(x * y) * b));
	else
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((x <= -1.65e+28) || ~((x <= 8.5e+230)))
		tmp = a * ((x * y) * b);
	else
		tmp = a * (t * (y2 * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[x, -1.65e+28], N[Not[LessEqual[x, 8.5e+230]], $MachinePrecision]], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.65e28 or 8.499999999999999e230 < x

   1. Initial program 19.4%

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

   3. Taylor expanded in b around inf 41.5%

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

   4. Taylor expanded in a around inf 45.4%

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

   5. Taylor expanded in x around inf 39.6%

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

      1. *-commutative 39.6%

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

   7. Simplified 39.6%

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

   if -1.65e28 < x < 8.499999999999999e230

   1. Initial program 36.3%

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

   3. Taylor expanded in y2 around inf 40.4%

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

   4. Taylor expanded in a around -inf 29.3%

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

      1. associate-*r* 29.3%

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

      2. neg-mul-1 29.3%

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

   6. Simplified 29.3%

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

   7. Taylor expanded in x around 0 24.1%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 29.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+28} \lor \neg \left(x \leq 8.5 \cdot 10^{+230}\right):\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 36: 21.8% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -5.2 \cdot 10^{-53}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 1.45 \cdot 10^{-19}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -5.2e-53)
   (* c (* x (* y0 y2)))
   (if (<= y2 1.45e-19) (* a (* (* x y) b)) (* a (* t (* y2 y5))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -5.2e-53) {
		tmp = c * (x * (y0 * y2));
	} else if (y2 <= 1.45e-19) {
		tmp = a * ((x * y) * b);
	} else {
		tmp = a * (t * (y2 * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y2 <= (-5.2d-53)) then
        tmp = c * (x * (y0 * y2))
    else if (y2 <= 1.45d-19) then
        tmp = a * ((x * y) * b)
    else
        tmp = a * (t * (y2 * y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -5.2e-53) {
		tmp = c * (x * (y0 * y2));
	} else if (y2 <= 1.45e-19) {
		tmp = a * ((x * y) * b);
	} else {
		tmp = a * (t * (y2 * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y2 <= -5.2e-53:
		tmp = c * (x * (y0 * y2))
	elif y2 <= 1.45e-19:
		tmp = a * ((x * y) * b)
	else:
		tmp = a * (t * (y2 * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y2 <= -5.2e-53)
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	elseif (y2 <= 1.45e-19)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	else
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y2 <= -5.2e-53)
		tmp = c * (x * (y0 * y2));
	elseif (y2 <= 1.45e-19)
		tmp = a * ((x * y) * b);
	else
		tmp = a * (t * (y2 * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y2, -5.2e-53], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.45e-19], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y2 < -5.19999999999999993e-53

   1. Initial program 28.4%

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

   3. Taylor expanded in y0 around inf 37.6%

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

   4. Taylor expanded in x around inf 36.0%

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

   5. Taylor expanded in j around inf 39.6%

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

   6. Taylor expanded in j around 0 33.5%

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

   if -5.19999999999999993e-53 < y2 < 1.45e-19

   1. Initial program 36.1%

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

   3. Taylor expanded in b around inf 42.6%

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

   4. Taylor expanded in a around inf 33.5%

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

   5. Taylor expanded in x around inf 21.5%

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

      1. *-commutative 21.5%

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

   7. Simplified 21.5%

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

   if 1.45e-19 < y2

   1. Initial program 24.7%

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

   3. Taylor expanded in y2 around inf 60.3%

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

   4. Taylor expanded in a around -inf 49.9%

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

      1. associate-*r* 49.9%

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

      2. neg-mul-1 49.9%

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

   6. Simplified 49.9%

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

   7. Taylor expanded in x around 0 41.3%

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

4. Final simplification 30.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -5.2 \cdot 10^{-53}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 1.45 \cdot 10^{-19}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 37: 16.9% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(\left(x \cdot y\right) \cdot b\right) \end{array} \]

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(Float64(x * 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[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 30.8%

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

3. Taylor expanded in b around inf 33.9%

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

4. Taylor expanded in a around inf 27.8%

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

5. Taylor expanded in x around inf 17.3%

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

   1. *-commutative 17.3%

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

7. Simplified 17.3%

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

8. Final simplification 17.3%

   \[\leadsto a \cdot \left(\left(x \cdot y\right) \cdot b\right) \]
9. Add Preprocessing

Developer Target 1: 27.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot c - y5 \cdot a\\ t_2 := x \cdot y2 - z \cdot y3\\ t_3 := y2 \cdot t - y3 \cdot y\\ t_4 := k \cdot y2 - j \cdot y3\\ t_5 := y4 \cdot b - y5 \cdot i\\ t_6 := \left(j \cdot t - k \cdot y\right) \cdot t\_5\\ t_7 := b \cdot a - i \cdot c\\ t_8 := t\_7 \cdot \left(y \cdot x - t \cdot z\right)\\ t_9 := j \cdot x - k \cdot z\\ t_10 := \left(b \cdot y0 - i \cdot y1\right) \cdot t\_9\\ t_11 := t\_9 \cdot \left(y0 \cdot b - i \cdot y1\right)\\ t_12 := y4 \cdot y1 - y5 \cdot y0\\ t_13 := t\_4 \cdot t\_12\\ t_14 := \left(y2 \cdot k - y3 \cdot j\right) \cdot t\_12\\ t_15 := \left(\left(\left(\left(k \cdot y\right) \cdot \left(y5 \cdot i\right) - \left(y \cdot b\right) \cdot \left(y4 \cdot k\right)\right) - \left(y5 \cdot t\right) \cdot \left(i \cdot j\right)\right) - \left(t\_3 \cdot t\_1 - t\_14\right)\right) + \left(t\_8 - \left(t\_11 - \left(y2 \cdot x - y3 \cdot z\right) \cdot \left(c \cdot y0 - y1 \cdot a\right)\right)\right)\\ t_16 := \left(\left(t\_6 - \left(y3 \cdot y\right) \cdot \left(y5 \cdot a - y4 \cdot c\right)\right) + \left(\left(y5 \cdot a\right) \cdot \left(t \cdot y2\right) + t\_13\right)\right) + \left(t\_2 \cdot \left(c \cdot y0 - a \cdot y1\right) - \left(t\_10 - \left(y \cdot x - z \cdot t\right) \cdot t\_7\right)\right)\\ t_17 := t \cdot y2 - y \cdot y3\\ \mathbf{if}\;y4 < -7.206256231996481 \cdot 10^{+60}:\\ \;\;\;\;\left(t\_8 - \left(t\_11 - t\_6\right)\right) - \left(\frac{t\_3}{\frac{1}{t\_1}} - t\_14\right)\\ \mathbf{elif}\;y4 < -3.364603505246317 \cdot 10^{-66}:\\ \;\;\;\;\left(\left(\left(\left(t \cdot c\right) \cdot \left(i \cdot z\right) - \left(a \cdot t\right) \cdot \left(b \cdot z\right)\right) - \left(y \cdot c\right) \cdot \left(i \cdot x\right)\right) - t\_10\right) + \left(\left(y0 \cdot c - a \cdot y1\right) \cdot t\_2 - \left(t\_17 \cdot \left(y4 \cdot c - a \cdot y5\right) - \left(y1 \cdot y4 - y5 \cdot y0\right) \cdot t\_4\right)\right)\\ \mathbf{elif}\;y4 < -1.2000065055686116 \cdot 10^{-105}:\\ \;\;\;\;t\_16\\ \mathbf{elif}\;y4 < 6.718963124057495 \cdot 10^{-279}:\\ \;\;\;\;t\_15\\ \mathbf{elif}\;y4 < 4.77962681403792 \cdot 10^{-222}:\\ \;\;\;\;t\_16\\ \mathbf{elif}\;y4 < 2.2852241541266835 \cdot 10^{-175}:\\ \;\;\;\;t\_15\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(k \cdot \left(i \cdot \left(z \cdot y1\right)\right) - \left(j \cdot \left(i \cdot \left(x \cdot y1\right)\right) + y0 \cdot \left(k \cdot \left(z \cdot b\right)\right)\right)\right)\right) + \left(z \cdot \left(y3 \cdot \left(a \cdot y1\right)\right) - \left(y2 \cdot \left(x \cdot \left(a \cdot y1\right)\right) + y0 \cdot \left(z \cdot \left(c \cdot y3\right)\right)\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot t\_5\right) - t\_17 \cdot t\_1\right) + t\_13\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y4 c) (* y5 a)))
        (t_2 (- (* x y2) (* z y3)))
        (t_3 (- (* y2 t) (* y3 y)))
        (t_4 (- (* k y2) (* j y3)))
        (t_5 (- (* y4 b) (* y5 i)))
        (t_6 (* (- (* j t) (* k y)) t_5))
        (t_7 (- (* b a) (* i c)))
        (t_8 (* t_7 (- (* y x) (* t z))))
        (t_9 (- (* j x) (* k z)))
        (t_10 (* (- (* b y0) (* i y1)) t_9))
        (t_11 (* t_9 (- (* y0 b) (* i y1))))
        (t_12 (- (* y4 y1) (* y5 y0)))
        (t_13 (* t_4 t_12))
        (t_14 (* (- (* y2 k) (* y3 j)) t_12))
        (t_15
         (+
          (-
           (-
            (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k)))
            (* (* y5 t) (* i j)))
           (- (* t_3 t_1) t_14))
          (- t_8 (- t_11 (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))))
        (t_16
         (+
          (+
           (- t_6 (* (* y3 y) (- (* y5 a) (* y4 c))))
           (+ (* (* y5 a) (* t y2)) t_13))
          (-
           (* t_2 (- (* c y0) (* a y1)))
           (- t_10 (* (- (* y x) (* z t)) t_7)))))
        (t_17 (- (* t y2) (* y y3))))
   (if (< y4 -7.206256231996481e+60)
     (- (- t_8 (- t_11 t_6)) (- (/ t_3 (/ 1.0 t_1)) t_14))
     (if (< y4 -3.364603505246317e-66)
       (+
        (-
         (- (- (* (* t c) (* i z)) (* (* a t) (* b z))) (* (* y c) (* i x)))
         t_10)
        (-
         (* (- (* y0 c) (* a y1)) t_2)
         (- (* t_17 (- (* y4 c) (* a y5))) (* (- (* y1 y4) (* y5 y0)) t_4))))
       (if (< y4 -1.2000065055686116e-105)
         t_16
         (if (< y4 6.718963124057495e-279)
           t_15
           (if (< y4 4.77962681403792e-222)
             t_16
             (if (< y4 2.2852241541266835e-175)
               t_15
               (+
                (-
                 (+
                  (+
                   (-
                    (* (- (* x y) (* z t)) (- (* a b) (* c i)))
                    (-
                     (* k (* i (* z y1)))
                     (+ (* j (* i (* x y1))) (* y0 (* k (* z b))))))
                   (-
                    (* z (* y3 (* a y1)))
                    (+ (* y2 (* x (* a y1))) (* y0 (* z (* c y3))))))
                  (* (- (* t j) (* y k)) t_5))
                 (* t_17 t_1))
                t_13)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y4 * c) - (y5 * a);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (y2 * t) - (y3 * y);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = (y4 * b) - (y5 * i);
	double t_6 = ((j * t) - (k * y)) * t_5;
	double t_7 = (b * a) - (i * c);
	double t_8 = t_7 * ((y * x) - (t * z));
	double t_9 = (j * x) - (k * z);
	double t_10 = ((b * y0) - (i * y1)) * t_9;
	double t_11 = t_9 * ((y0 * b) - (i * y1));
	double t_12 = (y4 * y1) - (y5 * y0);
	double t_13 = t_4 * t_12;
	double t_14 = ((y2 * k) - (y3 * j)) * t_12;
	double t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	double t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	double t_17 = (t * y2) - (y * y3);
	double tmp;
	if (y4 < -7.206256231996481e+60) {
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	} else if (y4 < -3.364603505246317e-66) {
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	} else if (y4 < -1.2000065055686116e-105) {
		tmp = t_16;
	} else if (y4 < 6.718963124057495e-279) {
		tmp = t_15;
	} else if (y4 < 4.77962681403792e-222) {
		tmp = t_16;
	} else if (y4 < 2.2852241541266835e-175) {
		tmp = t_15;
	} else {
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_10
    real(8) :: t_11
    real(8) :: t_12
    real(8) :: t_13
    real(8) :: t_14
    real(8) :: t_15
    real(8) :: t_16
    real(8) :: t_17
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = (y4 * c) - (y5 * a)
    t_2 = (x * y2) - (z * y3)
    t_3 = (y2 * t) - (y3 * y)
    t_4 = (k * y2) - (j * y3)
    t_5 = (y4 * b) - (y5 * i)
    t_6 = ((j * t) - (k * y)) * t_5
    t_7 = (b * a) - (i * c)
    t_8 = t_7 * ((y * x) - (t * z))
    t_9 = (j * x) - (k * z)
    t_10 = ((b * y0) - (i * y1)) * t_9
    t_11 = t_9 * ((y0 * b) - (i * y1))
    t_12 = (y4 * y1) - (y5 * y0)
    t_13 = t_4 * t_12
    t_14 = ((y2 * k) - (y3 * j)) * t_12
    t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))))
    t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)))
    t_17 = (t * y2) - (y * y3)
    if (y4 < (-7.206256231996481d+60)) then
        tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0d0 / t_1)) - t_14)
    else if (y4 < (-3.364603505246317d-66)) then
        tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)))
    else if (y4 < (-1.2000065055686116d-105)) then
        tmp = t_16
    else if (y4 < 6.718963124057495d-279) then
        tmp = t_15
    else if (y4 < 4.77962681403792d-222) then
        tmp = t_16
    else if (y4 < 2.2852241541266835d-175) then
        tmp = t_15
    else
        tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y4 * c) - (y5 * a);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (y2 * t) - (y3 * y);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = (y4 * b) - (y5 * i);
	double t_6 = ((j * t) - (k * y)) * t_5;
	double t_7 = (b * a) - (i * c);
	double t_8 = t_7 * ((y * x) - (t * z));
	double t_9 = (j * x) - (k * z);
	double t_10 = ((b * y0) - (i * y1)) * t_9;
	double t_11 = t_9 * ((y0 * b) - (i * y1));
	double t_12 = (y4 * y1) - (y5 * y0);
	double t_13 = t_4 * t_12;
	double t_14 = ((y2 * k) - (y3 * j)) * t_12;
	double t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	double t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	double t_17 = (t * y2) - (y * y3);
	double tmp;
	if (y4 < -7.206256231996481e+60) {
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	} else if (y4 < -3.364603505246317e-66) {
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	} else if (y4 < -1.2000065055686116e-105) {
		tmp = t_16;
	} else if (y4 < 6.718963124057495e-279) {
		tmp = t_15;
	} else if (y4 < 4.77962681403792e-222) {
		tmp = t_16;
	} else if (y4 < 2.2852241541266835e-175) {
		tmp = t_15;
	} else {
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y4 * c) - (y5 * a)
	t_2 = (x * y2) - (z * y3)
	t_3 = (y2 * t) - (y3 * y)
	t_4 = (k * y2) - (j * y3)
	t_5 = (y4 * b) - (y5 * i)
	t_6 = ((j * t) - (k * y)) * t_5
	t_7 = (b * a) - (i * c)
	t_8 = t_7 * ((y * x) - (t * z))
	t_9 = (j * x) - (k * z)
	t_10 = ((b * y0) - (i * y1)) * t_9
	t_11 = t_9 * ((y0 * b) - (i * y1))
	t_12 = (y4 * y1) - (y5 * y0)
	t_13 = t_4 * t_12
	t_14 = ((y2 * k) - (y3 * j)) * t_12
	t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))))
	t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)))
	t_17 = (t * y2) - (y * y3)
	tmp = 0
	if y4 < -7.206256231996481e+60:
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14)
	elif y4 < -3.364603505246317e-66:
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)))
	elif y4 < -1.2000065055686116e-105:
		tmp = t_16
	elif y4 < 6.718963124057495e-279:
		tmp = t_15
	elif y4 < 4.77962681403792e-222:
		tmp = t_16
	elif y4 < 2.2852241541266835e-175:
		tmp = t_15
	else:
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y4 * c) - Float64(y5 * a))
	t_2 = Float64(Float64(x * y2) - Float64(z * y3))
	t_3 = Float64(Float64(y2 * t) - Float64(y3 * y))
	t_4 = Float64(Float64(k * y2) - Float64(j * y3))
	t_5 = Float64(Float64(y4 * b) - Float64(y5 * i))
	t_6 = Float64(Float64(Float64(j * t) - Float64(k * y)) * t_5)
	t_7 = Float64(Float64(b * a) - Float64(i * c))
	t_8 = Float64(t_7 * Float64(Float64(y * x) - Float64(t * z)))
	t_9 = Float64(Float64(j * x) - Float64(k * z))
	t_10 = Float64(Float64(Float64(b * y0) - Float64(i * y1)) * t_9)
	t_11 = Float64(t_9 * Float64(Float64(y0 * b) - Float64(i * y1)))
	t_12 = Float64(Float64(y4 * y1) - Float64(y5 * y0))
	t_13 = Float64(t_4 * t_12)
	t_14 = Float64(Float64(Float64(y2 * k) - Float64(y3 * j)) * t_12)
	t_15 = Float64(Float64(Float64(Float64(Float64(Float64(k * y) * Float64(y5 * i)) - Float64(Float64(y * b) * Float64(y4 * k))) - Float64(Float64(y5 * t) * Float64(i * j))) - Float64(Float64(t_3 * t_1) - t_14)) + Float64(t_8 - Float64(t_11 - Float64(Float64(Float64(y2 * x) - Float64(y3 * z)) * Float64(Float64(c * y0) - Float64(y1 * a))))))
	t_16 = Float64(Float64(Float64(t_6 - Float64(Float64(y3 * y) * Float64(Float64(y5 * a) - Float64(y4 * c)))) + Float64(Float64(Float64(y5 * a) * Float64(t * y2)) + t_13)) + Float64(Float64(t_2 * Float64(Float64(c * y0) - Float64(a * y1))) - Float64(t_10 - Float64(Float64(Float64(y * x) - Float64(z * t)) * t_7))))
	t_17 = Float64(Float64(t * y2) - Float64(y * y3))
	tmp = 0.0
	if (y4 < -7.206256231996481e+60)
		tmp = Float64(Float64(t_8 - Float64(t_11 - t_6)) - Float64(Float64(t_3 / Float64(1.0 / t_1)) - t_14));
	elseif (y4 < -3.364603505246317e-66)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(t * c) * Float64(i * z)) - Float64(Float64(a * t) * Float64(b * z))) - Float64(Float64(y * c) * Float64(i * x))) - t_10) + Float64(Float64(Float64(Float64(y0 * c) - Float64(a * y1)) * t_2) - Float64(Float64(t_17 * Float64(Float64(y4 * c) - Float64(a * y5))) - Float64(Float64(Float64(y1 * y4) - Float64(y5 * y0)) * t_4))));
	elseif (y4 < -1.2000065055686116e-105)
		tmp = t_16;
	elseif (y4 < 6.718963124057495e-279)
		tmp = t_15;
	elseif (y4 < 4.77962681403792e-222)
		tmp = t_16;
	elseif (y4 < 2.2852241541266835e-175)
		tmp = t_15;
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) - Float64(z * t)) * Float64(Float64(a * b) - Float64(c * i))) - Float64(Float64(k * Float64(i * Float64(z * y1))) - Float64(Float64(j * Float64(i * Float64(x * y1))) + Float64(y0 * Float64(k * Float64(z * b)))))) + Float64(Float64(z * Float64(y3 * Float64(a * y1))) - Float64(Float64(y2 * Float64(x * Float64(a * y1))) + Float64(y0 * Float64(z * Float64(c * y3)))))) + Float64(Float64(Float64(t * j) - Float64(y * k)) * t_5)) - Float64(t_17 * t_1)) + t_13);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y4 * c) - (y5 * a);
	t_2 = (x * y2) - (z * y3);
	t_3 = (y2 * t) - (y3 * y);
	t_4 = (k * y2) - (j * y3);
	t_5 = (y4 * b) - (y5 * i);
	t_6 = ((j * t) - (k * y)) * t_5;
	t_7 = (b * a) - (i * c);
	t_8 = t_7 * ((y * x) - (t * z));
	t_9 = (j * x) - (k * z);
	t_10 = ((b * y0) - (i * y1)) * t_9;
	t_11 = t_9 * ((y0 * b) - (i * y1));
	t_12 = (y4 * y1) - (y5 * y0);
	t_13 = t_4 * t_12;
	t_14 = ((y2 * k) - (y3 * j)) * t_12;
	t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	t_17 = (t * y2) - (y * y3);
	tmp = 0.0;
	if (y4 < -7.206256231996481e+60)
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	elseif (y4 < -3.364603505246317e-66)
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	elseif (y4 < -1.2000065055686116e-105)
		tmp = t_16;
	elseif (y4 < 6.718963124057495e-279)
		tmp = t_15;
	elseif (y4 < 4.77962681403792e-222)
		tmp = t_16;
	elseif (y4 < 2.2852241541266835e-175)
		tmp = t_15;
	else
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y4 * c), $MachinePrecision] - N[(y5 * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y2 * t), $MachinePrecision] - N[(y3 * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(y4 * b), $MachinePrecision] - N[(y5 * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision] * t$95$5), $MachinePrecision]}, Block[{t$95$7 = N[(N[(b * a), $MachinePrecision] - N[(i * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(t$95$7 * N[(N[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$10 = N[(N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision] * t$95$9), $MachinePrecision]}, Block[{t$95$11 = N[(t$95$9 * N[(N[(y0 * b), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$12 = N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$13 = N[(t$95$4 * t$95$12), $MachinePrecision]}, Block[{t$95$14 = N[(N[(N[(y2 * k), $MachinePrecision] - N[(y3 * j), $MachinePrecision]), $MachinePrecision] * t$95$12), $MachinePrecision]}, Block[{t$95$15 = N[(N[(N[(N[(N[(N[(k * y), $MachinePrecision] * N[(y5 * i), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] * N[(y4 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y5 * t), $MachinePrecision] * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$3 * t$95$1), $MachinePrecision] - t$95$14), $MachinePrecision]), $MachinePrecision] + N[(t$95$8 - N[(t$95$11 - N[(N[(N[(y2 * x), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision] * N[(N[(c * y0), $MachinePrecision] - N[(y1 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$16 = N[(N[(N[(t$95$6 - N[(N[(y3 * y), $MachinePrecision] * N[(N[(y5 * a), $MachinePrecision] - N[(y4 * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y5 * a), $MachinePrecision] * N[(t * y2), $MachinePrecision]), $MachinePrecision] + t$95$13), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$10 - N[(N[(N[(y * x), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$17 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, If[Less[y4, -7.206256231996481e+60], N[(N[(t$95$8 - N[(t$95$11 - t$95$6), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$3 / N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision] - t$95$14), $MachinePrecision]), $MachinePrecision], If[Less[y4, -3.364603505246317e-66], N[(N[(N[(N[(N[(N[(t * c), $MachinePrecision] * N[(i * z), $MachinePrecision]), $MachinePrecision] - N[(N[(a * t), $MachinePrecision] * N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * c), $MachinePrecision] * N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$10), $MachinePrecision] + N[(N[(N[(N[(y0 * c), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision] - N[(N[(t$95$17 * N[(N[(y4 * c), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(y1 * y4), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision] * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[y4, -1.2000065055686116e-105], t$95$16, If[Less[y4, 6.718963124057495e-279], t$95$15, If[Less[y4, 4.77962681403792e-222], t$95$16, If[Less[y4, 2.2852241541266835e-175], t$95$15, N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(k * N[(i * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * N[(i * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(k * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(y3 * N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y2 * N[(x * N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(z * N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * t$95$5), $MachinePrecision]), $MachinePrecision] - N[(t$95$17 * t$95$1), $MachinePrecision]), $MachinePrecision] + t$95$13), $MachinePrecision]]]]]]]]]]]]]]]]]]]]]]]]

Reproduce

herbie shell --seed 2024139 
(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :name "Linear.Matrix:det44 from linear-1.19.1.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y4 -7206256231996481000000000000000000000000000000000000000000000) (- (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))))) (- (/ (- (* y2 t) (* y3 y)) (/ 1 (- (* y4 c) (* y5 a)))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (if (< y4 -3364603505246317/1000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (- (- (* (* t c) (* i z)) (* (* a t) (* b z))) (* (* y c) (* i x))) (* (- (* b y0) (* i y1)) (- (* j x) (* k z)))) (- (* (- (* y0 c) (* a y1)) (- (* x y2) (* z y3))) (- (* (- (* t y2) (* y y3)) (- (* y4 c) (* a y5))) (* (- (* y1 y4) (* y5 y0)) (- (* k y2) (* j y3)))))) (if (< y4 -3000016263921529/2500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (+ (- (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))) (* (* y3 y) (- (* y5 a) (* y4 c)))) (+ (* (* y5 a) (* t y2)) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* x y2) (* z y3)) (- (* c y0) (* a y1))) (- (* (- (* b y0) (* i y1)) (- (* j x) (* k z))) (* (- (* y x) (* z t)) (- (* b a) (* i c)))))) (if (< y4 1343792624811499/200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (- (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k))) (* (* y5 t) (* i j))) (- (* (- (* y2 t) (* y3 y)) (- (* y4 c) (* y5 a))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))) (if (< y4 29872667587737/6250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (+ (- (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))) (* (* y3 y) (- (* y5 a) (* y4 c)))) (+ (* (* y5 a) (* t y2)) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* x y2) (* z y3)) (- (* c y0) (* a y1))) (- (* (- (* b y0) (* i y1)) (- (* j x) (* k z))) (* (- (* y x) (* z t)) (- (* b a) (* i c)))))) (if (< y4 4570448308253367/20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (- (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k))) (* (* y5 t) (* i j))) (- (* (- (* y2 t) (* y3 y)) (- (* y4 c) (* y5 a))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))) (+ (- (+ (+ (- (* (- (* x y) (* z t)) (- (* a b) (* c i))) (- (* k (* i (* z y1))) (+ (* j (* i (* x y1))) (* y0 (* k (* z b)))))) (- (* z (* y3 (* a y1))) (+ (* y2 (* x (* a y1))) (* y0 (* z (* c y3)))))) (* (- (* t j) (* y k)) (- (* y4 b) (* y5 i)))) (* (- (* t y2) (* y y3)) (- (* y4 c) (* y5 a)))) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0)))))))))))

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