Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 30.6% → 54.0%

Time: 45.2s

Alternatives: 37

Speedup: 3.1×

• 89.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 30.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 54.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision] * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision] * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, Infinity], t$95$2, N[(i * N[(N[(y1 * t$95$1), $MachinePrecision] + N[(N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $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 93.3%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in i around -inf 41.8%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.3%

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

Alternative 2: 40.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot \left(x \cdot j - z \cdot k\right)\\ t_2 := y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;i \leq -2.6 \cdot 10^{+33}:\\ \;\;\;\;i \cdot \left(t\_1 + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) + c \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{-181}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 1.7 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq 1.35 \cdot 10^{+70}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{+191}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;i \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y1 (- (* x j) (* z k))))
        (t_2
         (*
          y4
          (+
           (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
           (* c (- (* y y3) (* t y2)))))))
   (if (<= i -2.6e+33)
     (* i (+ t_1 (+ (* y5 (- (* y k) (* t j))) (* c (- (* z t) (* x y))))))
     (if (<= i 2.2e-181)
       t_2
       (if (<= i 1.7e+42)
         (*
          x
          (+
           (+ (* y (- (* a b) (* c i))) (* y2 (- (* c y0) (* a y1))))
           (* j (- (* i y1) (* b y0)))))
         (if (<= i 1.35e+70)
           (* t (* y5 (- (* a y2) (* i j))))
           (if (<= i 1.3e+191) t_2 (* i t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * ((x * j) - (z * k));
	double t_2 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double tmp;
	if (i <= -2.6e+33) {
		tmp = i * (t_1 + ((y5 * ((y * k) - (t * j))) + (c * ((z * t) - (x * y)))));
	} else if (i <= 2.2e-181) {
		tmp = t_2;
	} else if (i <= 1.7e+42) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	} else if (i <= 1.35e+70) {
		tmp = t * (y5 * ((a * y2) - (i * j)));
	} else if (i <= 1.3e+191) {
		tmp = t_2;
	} else {
		tmp = i * 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 = y1 * ((x * j) - (z * k))
    t_2 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    if (i <= (-2.6d+33)) then
        tmp = i * (t_1 + ((y5 * ((y * k) - (t * j))) + (c * ((z * t) - (x * y)))))
    else if (i <= 2.2d-181) then
        tmp = t_2
    else if (i <= 1.7d+42) then
        tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
    else if (i <= 1.35d+70) then
        tmp = t * (y5 * ((a * y2) - (i * j)))
    else if (i <= 1.3d+191) then
        tmp = t_2
    else
        tmp = i * 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 = y1 * ((x * j) - (z * k));
	double t_2 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double tmp;
	if (i <= -2.6e+33) {
		tmp = i * (t_1 + ((y5 * ((y * k) - (t * j))) + (c * ((z * t) - (x * y)))));
	} else if (i <= 2.2e-181) {
		tmp = t_2;
	} else if (i <= 1.7e+42) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	} else if (i <= 1.35e+70) {
		tmp = t * (y5 * ((a * y2) - (i * j)));
	} else if (i <= 1.3e+191) {
		tmp = t_2;
	} else {
		tmp = i * 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 = y1 * ((x * j) - (z * k))
	t_2 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	tmp = 0
	if i <= -2.6e+33:
		tmp = i * (t_1 + ((y5 * ((y * k) - (t * j))) + (c * ((z * t) - (x * y)))))
	elif i <= 2.2e-181:
		tmp = t_2
	elif i <= 1.7e+42:
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
	elif i <= 1.35e+70:
		tmp = t * (y5 * ((a * y2) - (i * j)))
	elif i <= 1.3e+191:
		tmp = t_2
	else:
		tmp = i * 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(y1 * Float64(Float64(x * j) - Float64(z * k)))
	t_2 = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))))
	tmp = 0.0
	if (i <= -2.6e+33)
		tmp = Float64(i * Float64(t_1 + Float64(Float64(y5 * Float64(Float64(y * k) - Float64(t * j))) + Float64(c * Float64(Float64(z * t) - Float64(x * y))))));
	elseif (i <= 2.2e-181)
		tmp = t_2;
	elseif (i <= 1.7e+42)
		tmp = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (i <= 1.35e+70)
		tmp = Float64(t * Float64(y5 * Float64(Float64(a * y2) - Float64(i * j))));
	elseif (i <= 1.3e+191)
		tmp = t_2;
	else
		tmp = Float64(i * 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 = y1 * ((x * j) - (z * k));
	t_2 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	tmp = 0.0;
	if (i <= -2.6e+33)
		tmp = i * (t_1 + ((y5 * ((y * k) - (t * j))) + (c * ((z * t) - (x * y)))));
	elseif (i <= 2.2e-181)
		tmp = t_2;
	elseif (i <= 1.7e+42)
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	elseif (i <= 1.35e+70)
		tmp = t * (y5 * ((a * y2) - (i * j)));
	elseif (i <= 1.3e+191)
		tmp = t_2;
	else
		tmp = i * 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[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.6e+33], N[(i * N[(t$95$1 + N[(N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.2e-181], t$95$2, If[LessEqual[i, 1.7e+42], N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.35e+70], N[(t * N[(y5 * N[(N[(a * y2), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.3e+191], t$95$2, N[(i * t$95$1), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -2.5999999999999997e33

   1. Initial program 24.0%

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

   3. Taylor expanded in i around -inf 59.9%

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

   if -2.5999999999999997e33 < i < 2.19999999999999997e-181 or 1.35e70 < i < 1.3e191

   1. Initial program 37.0%

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

   3. Taylor expanded in y4 around inf 52.2%

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

   if 2.19999999999999997e-181 < i < 1.69999999999999988e42

   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 x around inf 47.1%

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

   if 1.69999999999999988e42 < i < 1.35e70

   1. Initial program 11.1%

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

   3. Taylor expanded in y5 around -inf 66.7%

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

   4. Taylor expanded in t around inf 100.0%

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

   if 1.3e191 < i

   1. Initial program 21.1%

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

   3. Taylor expanded in y1 around inf 53.4%

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

   4. Taylor expanded in i around inf 69.6%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.6 \cdot 10^{+33}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) + c \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{-181}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq 1.7 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq 1.35 \cdot 10^{+70}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{+191}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 42.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y2 - z \cdot y3\\ t_2 := c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot t\_1\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ t_3 := j \cdot y3 - k \cdot y2\\ \mathbf{if}\;c \leq -7 \cdot 10^{-30}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -5.5 \cdot 10^{-289}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) - \left(a \cdot t\_1 + y4 \cdot t\_3\right)\right)\\ \mathbf{elif}\;c \leq 2 \cdot 10^{-70}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot t\_3\right)\\ \mathbf{elif}\;c \leq 10^{+130}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* x y2) (* z y3)))
        (t_2
         (*
          c
          (+
           (+ (* i (- (* z t) (* x y))) (* y0 t_1))
           (* y4 (- (* y y3) (* t y2))))))
        (t_3 (- (* j y3) (* k y2))))
   (if (<= c -7e-30)
     t_2
     (if (<= c -5.5e-289)
       (* y1 (- (* i (- (* x j) (* z k))) (+ (* a t_1) (* y4 t_3))))
       (if (<= c 2e-70)
         (* y5 (+ (* a (- (* t y2) (* y y3))) (* y0 t_3)))
         (if (<= c 1e+130)
           (*
            x
            (+
             (+ (* y (- (* a b) (* c i))) (* y2 (- (* c y0) (* a y1))))
             (* j (- (* i y1) (* b y0)))))
           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 * y2) - (z * y3);
	double t_2 = c * (((i * ((z * t) - (x * y))) + (y0 * t_1)) + (y4 * ((y * y3) - (t * y2))));
	double t_3 = (j * y3) - (k * y2);
	double tmp;
	if (c <= -7e-30) {
		tmp = t_2;
	} else if (c <= -5.5e-289) {
		tmp = y1 * ((i * ((x * j) - (z * k))) - ((a * t_1) + (y4 * t_3)));
	} else if (c <= 2e-70) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + (y0 * t_3));
	} else if (c <= 1e+130) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (x * y2) - (z * y3)
    t_2 = c * (((i * ((z * t) - (x * y))) + (y0 * t_1)) + (y4 * ((y * y3) - (t * y2))))
    t_3 = (j * y3) - (k * y2)
    if (c <= (-7d-30)) then
        tmp = t_2
    else if (c <= (-5.5d-289)) then
        tmp = y1 * ((i * ((x * j) - (z * k))) - ((a * t_1) + (y4 * t_3)))
    else if (c <= 2d-70) then
        tmp = y5 * ((a * ((t * y2) - (y * y3))) + (y0 * t_3))
    else if (c <= 1d+130) then
        tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (x * y2) - (z * y3);
	double t_2 = c * (((i * ((z * t) - (x * y))) + (y0 * t_1)) + (y4 * ((y * y3) - (t * y2))));
	double t_3 = (j * y3) - (k * y2);
	double tmp;
	if (c <= -7e-30) {
		tmp = t_2;
	} else if (c <= -5.5e-289) {
		tmp = y1 * ((i * ((x * j) - (z * k))) - ((a * t_1) + (y4 * t_3)));
	} else if (c <= 2e-70) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + (y0 * t_3));
	} else if (c <= 1e+130) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (x * y2) - (z * y3)
	t_2 = c * (((i * ((z * t) - (x * y))) + (y0 * t_1)) + (y4 * ((y * y3) - (t * y2))))
	t_3 = (j * y3) - (k * y2)
	tmp = 0
	if c <= -7e-30:
		tmp = t_2
	elif c <= -5.5e-289:
		tmp = y1 * ((i * ((x * j) - (z * k))) - ((a * t_1) + (y4 * t_3)))
	elif c <= 2e-70:
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + (y0 * t_3))
	elif c <= 1e+130:
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(x * y2) - Float64(z * y3))
	t_2 = Float64(c * Float64(Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(y0 * t_1)) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))))
	t_3 = Float64(Float64(j * y3) - Float64(k * y2))
	tmp = 0.0
	if (c <= -7e-30)
		tmp = t_2;
	elseif (c <= -5.5e-289)
		tmp = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) - Float64(Float64(a * t_1) + Float64(y4 * t_3))));
	elseif (c <= 2e-70)
		tmp = Float64(y5 * Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(y0 * t_3)));
	elseif (c <= 1e+130)
		tmp = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (x * y2) - (z * y3);
	t_2 = c * (((i * ((z * t) - (x * y))) + (y0 * t_1)) + (y4 * ((y * y3) - (t * y2))));
	t_3 = (j * y3) - (k * y2);
	tmp = 0.0;
	if (c <= -7e-30)
		tmp = t_2;
	elseif (c <= -5.5e-289)
		tmp = y1 * ((i * ((x * j) - (z * k))) - ((a * t_1) + (y4 * t_3)));
	elseif (c <= 2e-70)
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + (y0 * t_3));
	elseif (c <= 1e+130)
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -7e-30], t$95$2, If[LessEqual[c, -5.5e-289], N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(a * t$95$1), $MachinePrecision] + N[(y4 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2e-70], N[(y5 * N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1e+130], N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -7.0000000000000006e-30 or 1.0000000000000001e130 < c

   1. Initial program 27.3%

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

   3. Taylor expanded in c around inf 59.9%

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

   if -7.0000000000000006e-30 < c < -5.5000000000000004e-289

   1. Initial program 42.0%

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

   3. Taylor expanded in y1 around inf 57.1%

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

   if -5.5000000000000004e-289 < c < 1.99999999999999999e-70

   1. Initial program 29.4%

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

   3. Taylor expanded in y5 around -inf 43.4%

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

   4. Taylor expanded in i around 0 57.7%

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

   if 1.99999999999999999e-70 < c < 1.0000000000000001e130

   1. Initial program 31.9%

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

   3. Taylor expanded in x around inf 50.7%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7 \cdot 10^{-30}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -5.5 \cdot 10^{-289}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) - \left(a \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;c \leq 2 \cdot 10^{-70}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq 10^{+130}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 43.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x \cdot y\\ t_2 := i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) + c \cdot t\_1\right)\right)\\ t_3 := y \cdot y3 - t \cdot y2\\ \mathbf{if}\;i \leq -1.05 \cdot 10^{+33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -8 \cdot 10^{-224}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot t\_3\right)\\ \mathbf{elif}\;i \leq 5.8 \cdot 10^{-25}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;i \leq 2.9 \cdot 10^{+121}:\\ \;\;\;\;c \cdot \left(\left(i \cdot t\_1 + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot t\_3\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* z t) (* x y)))
        (t_2
         (*
          i
          (+
           (* y1 (- (* x j) (* z k)))
           (+ (* y5 (- (* y k) (* t j))) (* c t_1)))))
        (t_3 (- (* y y3) (* t y2))))
   (if (<= i -1.05e+33)
     t_2
     (if (<= i -8e-224)
       (*
        y4
        (+
         (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
         (* c t_3)))
       (if (<= i 5.8e-25)
         (*
          y3
          (+
           (* y (- (* c y4) (* a y5)))
           (+ (* j (- (* y0 y5) (* y1 y4))) (* z (- (* a y1) (* c y0))))))
         (if (<= i 2.9e+121)
           (* c (+ (+ (* i t_1) (* y0 (- (* x y2) (* z y3)))) (* y4 t_3)))
           t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (z * t) - (x * y);
	double t_2 = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) + (c * t_1)));
	double t_3 = (y * y3) - (t * y2);
	double tmp;
	if (i <= -1.05e+33) {
		tmp = t_2;
	} else if (i <= -8e-224) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_3));
	} else if (i <= 5.8e-25) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	} else if (i <= 2.9e+121) {
		tmp = c * (((i * t_1) + (y0 * ((x * y2) - (z * y3)))) + (y4 * t_3));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (z * t) - (x * y)
    t_2 = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) + (c * t_1)))
    t_3 = (y * y3) - (t * y2)
    if (i <= (-1.05d+33)) then
        tmp = t_2
    else if (i <= (-8d-224)) then
        tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_3))
    else if (i <= 5.8d-25) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))))
    else if (i <= 2.9d+121) then
        tmp = c * (((i * t_1) + (y0 * ((x * y2) - (z * y3)))) + (y4 * t_3))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (z * t) - (x * y);
	double t_2 = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) + (c * t_1)));
	double t_3 = (y * y3) - (t * y2);
	double tmp;
	if (i <= -1.05e+33) {
		tmp = t_2;
	} else if (i <= -8e-224) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_3));
	} else if (i <= 5.8e-25) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	} else if (i <= 2.9e+121) {
		tmp = c * (((i * t_1) + (y0 * ((x * y2) - (z * y3)))) + (y4 * t_3));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (z * t) - (x * y)
	t_2 = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) + (c * t_1)))
	t_3 = (y * y3) - (t * y2)
	tmp = 0
	if i <= -1.05e+33:
		tmp = t_2
	elif i <= -8e-224:
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_3))
	elif i <= 5.8e-25:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))))
	elif i <= 2.9e+121:
		tmp = c * (((i * t_1) + (y0 * ((x * y2) - (z * y3)))) + (y4 * t_3))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(z * t) - Float64(x * y))
	t_2 = 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))))
	t_3 = Float64(Float64(y * y3) - Float64(t * y2))
	tmp = 0.0
	if (i <= -1.05e+33)
		tmp = t_2;
	elseif (i <= -8e-224)
		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 * t_3)));
	elseif (i <= 5.8e-25)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(z * Float64(Float64(a * y1) - Float64(c * y0))))));
	elseif (i <= 2.9e+121)
		tmp = Float64(c * Float64(Float64(Float64(i * t_1) + Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3)))) + Float64(y4 * t_3)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (z * t) - (x * y);
	t_2 = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) + (c * t_1)));
	t_3 = (y * y3) - (t * y2);
	tmp = 0.0;
	if (i <= -1.05e+33)
		tmp = t_2;
	elseif (i <= -8e-224)
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_3));
	elseif (i <= 5.8e-25)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	elseif (i <= 2.9e+121)
		tmp = c * (((i * t_1) + (y0 * ((x * y2) - (z * y3)))) + (y4 * t_3));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = 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]}, Block[{t$95$3 = N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.05e+33], t$95$2, If[LessEqual[i, -8e-224], 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 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.8e-25], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.9e+121], N[(c * N[(N[(N[(i * t$95$1), $MachinePrecision] + N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -1.05e33 or 2.8999999999999999e121 < i

   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 i around -inf 62.7%

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

   if -1.05e33 < i < -8.0000000000000002e-224

   1. Initial program 37.0%

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

   3. Taylor expanded in y4 around inf 59.7%

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

   if -8.0000000000000002e-224 < i < 5.8000000000000001e-25

   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 y3 around -inf 45.9%

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

   if 5.8000000000000001e-25 < i < 2.8999999999999999e121

   1. Initial program 33.3%

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

   3. Taylor expanded in c around inf 59.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.05 \cdot 10^{+33}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) + c \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \mathbf{elif}\;i \leq -8 \cdot 10^{-224}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq 5.8 \cdot 10^{-25}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;i \leq 2.9 \cdot 10^{+121}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) + c \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 39.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot y0 - a \cdot y1\\ \mathbf{if}\;y \leq -6 \cdot 10^{+200}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{-17}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot t\_1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-267}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-80}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot t\_1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+147}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* c y0) (* a y1))))
   (if (<= y -6e+200)
     (* b (* y (- (* x a) (* k y4))))
     (if (<= y -8.8e-17)
       (*
        x
        (+
         (+ (* y (- (* a b) (* c i))) (* y2 t_1))
         (* j (- (* i y1) (* b y0)))))
       (if (<= y 4.2e-267)
         (* y1 (+ (* y4 (- (* k y2) (* j y3))) (* a (- (* z y3) (* x y2)))))
         (if (<= y 4.5e-80)
           (*
            y2
            (+
             (+ (* k (- (* y1 y4) (* y0 y5))) (* x t_1))
             (* t (- (* a y5) (* c y4)))))
           (if (<= y 2.7e+147)
             (*
              y5
              (+ (* a (- (* t y2) (* y y3))) (* y0 (- (* j y3) (* k y2)))))
             (* i (* y (- (* k y5) (* x c)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y0) - (a * y1);
	double tmp;
	if (y <= -6e+200) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (y <= -8.8e-17) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * ((i * y1) - (b * y0))));
	} else if (y <= 4.2e-267) {
		tmp = y1 * ((y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2))));
	} else if (y <= 4.5e-80) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_1)) + (t * ((a * y5) - (c * y4))));
	} else if (y <= 2.7e+147) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2))));
	} else {
		tmp = i * (y * ((k * y5) - (x * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (c * y0) - (a * y1)
    if (y <= (-6d+200)) then
        tmp = b * (y * ((x * a) - (k * y4)))
    else if (y <= (-8.8d-17)) then
        tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * ((i * y1) - (b * y0))))
    else if (y <= 4.2d-267) then
        tmp = y1 * ((y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2))))
    else if (y <= 4.5d-80) then
        tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_1)) + (t * ((a * y5) - (c * y4))))
    else if (y <= 2.7d+147) then
        tmp = y5 * ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2))))
    else
        tmp = i * (y * ((k * y5) - (x * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y0) - (a * y1);
	double tmp;
	if (y <= -6e+200) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (y <= -8.8e-17) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * ((i * y1) - (b * y0))));
	} else if (y <= 4.2e-267) {
		tmp = y1 * ((y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2))));
	} else if (y <= 4.5e-80) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_1)) + (t * ((a * y5) - (c * y4))));
	} else if (y <= 2.7e+147) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2))));
	} else {
		tmp = i * (y * ((k * y5) - (x * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (c * y0) - (a * y1)
	tmp = 0
	if y <= -6e+200:
		tmp = b * (y * ((x * a) - (k * y4)))
	elif y <= -8.8e-17:
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * ((i * y1) - (b * y0))))
	elif y <= 4.2e-267:
		tmp = y1 * ((y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2))))
	elif y <= 4.5e-80:
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_1)) + (t * ((a * y5) - (c * y4))))
	elif y <= 2.7e+147:
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2))))
	else:
		tmp = i * (y * ((k * y5) - (x * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(c * y0) - Float64(a * y1))
	tmp = 0.0
	if (y <= -6e+200)
		tmp = Float64(b * Float64(y * Float64(Float64(x * a) - Float64(k * y4))));
	elseif (y <= -8.8e-17)
		tmp = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * t_1)) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (y <= 4.2e-267)
		tmp = Float64(y1 * Float64(Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))) + Float64(a * Float64(Float64(z * y3) - Float64(x * y2)))));
	elseif (y <= 4.5e-80)
		tmp = Float64(y2 * Float64(Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(x * t_1)) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y <= 2.7e+147)
		tmp = Float64(y5 * Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2)))));
	else
		tmp = Float64(i * Float64(y * Float64(Float64(k * y5) - Float64(x * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (c * y0) - (a * y1);
	tmp = 0.0;
	if (y <= -6e+200)
		tmp = b * (y * ((x * a) - (k * y4)));
	elseif (y <= -8.8e-17)
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * ((i * y1) - (b * y0))));
	elseif (y <= 4.2e-267)
		tmp = y1 * ((y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2))));
	elseif (y <= 4.5e-80)
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_1)) + (t * ((a * y5) - (c * y4))));
	elseif (y <= 2.7e+147)
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2))));
	else
		tmp = i * (y * ((k * y5) - (x * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6e+200], N[(b * N[(y * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8.8e-17], N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e-267], N[(y1 * N[(N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e-80], N[(y2 * N[(N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e+147], N[(y5 * N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(y * N[(N[(k * y5), $MachinePrecision] - N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -5.99999999999999982e200

   1. Initial program 23.0%

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

   3. Taylor expanded in b around inf 38.6%

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

   4. Taylor expanded in y around inf 62.1%

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

      1. +-commutative 62.1%

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

      2. mul-1-neg 62.1%

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

      3. unsub-neg 62.1%

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

   6. Simplified 62.1%

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

   if -5.99999999999999982e200 < y < -8.8e-17

   1. Initial program 27.8%

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

   3. Taylor expanded in x around inf 53.2%

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

   if -8.8e-17 < y < 4.2000000000000003e-267

   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 y1 around inf 51.0%

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

   4. Taylor expanded in i around 0 48.1%

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

      1. +-commutative 48.1%

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

      2. mul-1-neg 48.1%

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

      3. unsub-neg 48.1%

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

   6. Simplified 48.1%

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

   if 4.2000000000000003e-267 < y < 4.5000000000000003e-80

   1. Initial program 50.1%

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

   3. Taylor expanded in y2 around inf 50.7%

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

   if 4.5000000000000003e-80 < y < 2.69999999999999998e147

   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 y5 around -inf 53.5%

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

   4. Taylor expanded in i around 0 53.6%

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

   if 2.69999999999999998e147 < y

   1. Initial program 26.3%

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

   3. Taylor expanded in i around -inf 50.3%

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

   4. Taylor expanded in y around inf 68.8%

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

      1. +-commutative 68.8%

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

      2. mul-1-neg 68.8%

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

      3. unsub-neg 68.8%

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

   6. Simplified 68.8%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(y \cdot \left(c \cdot x - k \cdot y5\right)\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+200}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{-17}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-267}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-80}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+147}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 31.4% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ t_2 := i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{if}\;y1 \leq -8.5 \cdot 10^{+224}:\\ \;\;\;\;y1 \cdot \left(k \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq -6.5 \cdot 10^{+43}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y1 \leq -125000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq -1.1 \cdot 10^{-116}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -1 \cdot 10^{-254}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq 6.6 \cdot 10^{-126}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y1 \leq 1.15 \cdot 10^{-9}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* x (- (* y0 y2) (* y i)))))
        (t_2 (* i (* y1 (- (* x j) (* z k))))))
   (if (<= y1 -8.5e+224)
     (* y1 (* k (* y2 y4)))
     (if (<= y1 -6.5e+43)
       t_2
       (if (<= y1 -125000.0)
         t_1
         (if (<= y1 -1.1e-116)
           (* c (* y4 (- (* y y3) (* t y2))))
           (if (<= y1 -1e-254)
             t_1
             (if (<= y1 6.6e-126)
               (* a (* b (- (* x y) (* z t))))
               (if (<= y1 1.15e-9)
                 (* c (* z (- (* t i) (* y0 y3))))
                 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 * (x * ((y0 * y2) - (y * i)));
	double t_2 = i * (y1 * ((x * j) - (z * k)));
	double tmp;
	if (y1 <= -8.5e+224) {
		tmp = y1 * (k * (y2 * y4));
	} else if (y1 <= -6.5e+43) {
		tmp = t_2;
	} else if (y1 <= -125000.0) {
		tmp = t_1;
	} else if (y1 <= -1.1e-116) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (y1 <= -1e-254) {
		tmp = t_1;
	} else if (y1 <= 6.6e-126) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y1 <= 1.15e-9) {
		tmp = c * (z * ((t * i) - (y0 * y3)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * (x * ((y0 * y2) - (y * i)))
    t_2 = i * (y1 * ((x * j) - (z * k)))
    if (y1 <= (-8.5d+224)) then
        tmp = y1 * (k * (y2 * y4))
    else if (y1 <= (-6.5d+43)) then
        tmp = t_2
    else if (y1 <= (-125000.0d0)) then
        tmp = t_1
    else if (y1 <= (-1.1d-116)) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else if (y1 <= (-1d-254)) then
        tmp = t_1
    else if (y1 <= 6.6d-126) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (y1 <= 1.15d-9) then
        tmp = c * (z * ((t * i) - (y0 * y3)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (x * ((y0 * y2) - (y * i)));
	double t_2 = i * (y1 * ((x * j) - (z * k)));
	double tmp;
	if (y1 <= -8.5e+224) {
		tmp = y1 * (k * (y2 * y4));
	} else if (y1 <= -6.5e+43) {
		tmp = t_2;
	} else if (y1 <= -125000.0) {
		tmp = t_1;
	} else if (y1 <= -1.1e-116) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (y1 <= -1e-254) {
		tmp = t_1;
	} else if (y1 <= 6.6e-126) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y1 <= 1.15e-9) {
		tmp = c * (z * ((t * i) - (y0 * y3)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (x * ((y0 * y2) - (y * i)))
	t_2 = i * (y1 * ((x * j) - (z * k)))
	tmp = 0
	if y1 <= -8.5e+224:
		tmp = y1 * (k * (y2 * y4))
	elif y1 <= -6.5e+43:
		tmp = t_2
	elif y1 <= -125000.0:
		tmp = t_1
	elif y1 <= -1.1e-116:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	elif y1 <= -1e-254:
		tmp = t_1
	elif y1 <= 6.6e-126:
		tmp = a * (b * ((x * y) - (z * t)))
	elif y1 <= 1.15e-9:
		tmp = c * (z * ((t * i) - (y0 * y3)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(x * Float64(Float64(y0 * y2) - Float64(y * i))))
	t_2 = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))))
	tmp = 0.0
	if (y1 <= -8.5e+224)
		tmp = Float64(y1 * Float64(k * Float64(y2 * y4)));
	elseif (y1 <= -6.5e+43)
		tmp = t_2;
	elseif (y1 <= -125000.0)
		tmp = t_1;
	elseif (y1 <= -1.1e-116)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (y1 <= -1e-254)
		tmp = t_1;
	elseif (y1 <= 6.6e-126)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y1 <= 1.15e-9)
		tmp = Float64(c * Float64(z * Float64(Float64(t * i) - Float64(y0 * y3))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (x * ((y0 * y2) - (y * i)));
	t_2 = i * (y1 * ((x * j) - (z * k)));
	tmp = 0.0;
	if (y1 <= -8.5e+224)
		tmp = y1 * (k * (y2 * y4));
	elseif (y1 <= -6.5e+43)
		tmp = t_2;
	elseif (y1 <= -125000.0)
		tmp = t_1;
	elseif (y1 <= -1.1e-116)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	elseif (y1 <= -1e-254)
		tmp = t_1;
	elseif (y1 <= 6.6e-126)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (y1 <= 1.15e-9)
		tmp = c * (z * ((t * i) - (y0 * y3)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(x * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -8.5e+224], N[(y1 * N[(k * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -6.5e+43], t$95$2, If[LessEqual[y1, -125000.0], t$95$1, If[LessEqual[y1, -1.1e-116], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -1e-254], t$95$1, If[LessEqual[y1, 6.6e-126], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.15e-9], N[(c * N[(z * N[(N[(t * i), $MachinePrecision] - N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y1 < -8.50000000000000046e224

   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 66.5%

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

   4. Taylor expanded in y2 around inf 55.1%

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

      1. +-commutative 55.1%

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

      2. mul-1-neg 55.1%

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

      3. unsub-neg 55.1%

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

   6. Simplified 55.1%

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

   7. Taylor expanded in k around inf 54.6%

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

   if -8.50000000000000046e224 < y1 < -6.4999999999999998e43 or 1.15e-9 < y1

   1. Initial program 25.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 i around inf 43.4%

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

   if -6.4999999999999998e43 < y1 < -125000 or -1.10000000000000005e-116 < y1 < -9.9999999999999991e-255

   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 c around inf 54.0%

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

   4. Taylor expanded in x around inf 73.4%

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

      1. +-commutative 73.4%

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

      2. mul-1-neg 73.4%

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

      3. unsub-neg 73.4%

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

   6. Simplified 73.4%

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

   if -125000 < y1 < -1.10000000000000005e-116

   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 y4 around inf 35.3%

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

   4. Taylor expanded in c around inf 45.9%

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

   if -9.9999999999999991e-255 < y1 < 6.6000000000000001e-126

   1. Initial program 42.8%

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

   3. Taylor expanded in b around inf 48.6%

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

   4. Taylor expanded in a around inf 42.3%

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

   if 6.6000000000000001e-126 < y1 < 1.15e-9

   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 c around inf 71.4%

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

   4. Taylor expanded in z around inf 52.9%

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

      1. +-commutative 52.9%

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

      2. mul-1-neg 52.9%

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

      3. unsub-neg 52.9%

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

   6. Simplified 52.9%

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

4. Final simplification 48.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -8.5 \cdot 10^{+224}:\\ \;\;\;\;y1 \cdot \left(k \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq -6.5 \cdot 10^{+43}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y1 \leq -125000:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;y1 \leq -1.1 \cdot 10^{-116}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -1 \cdot 10^{-254}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;y1 \leq 6.6 \cdot 10^{-126}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y1 \leq 1.15 \cdot 10^{-9}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 43.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) + c \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \mathbf{if}\;i \leq -7.4 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -1.35 \cdot 10^{-223}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq 1.85 \cdot 10^{-42}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          i
          (+
           (* y1 (- (* x j) (* z k)))
           (+ (* y5 (- (* y k) (* t j))) (* c (- (* z t) (* x y))))))))
   (if (<= i -7.4e+30)
     t_1
     (if (<= i -1.35e-223)
       (*
        y4
        (+
         (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
         (* c (- (* y y3) (* t y2)))))
       (if (<= i 1.85e-42)
         (*
          y3
          (+
           (* y (- (* c y4) (* a y5)))
           (+ (* j (- (* y0 y5) (* y1 y4))) (* z (- (* a y1) (* c y0))))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) + (c * ((z * t) - (x * y)))));
	double tmp;
	if (i <= -7.4e+30) {
		tmp = t_1;
	} else if (i <= -1.35e-223) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (i <= 1.85e-42) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	} 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 = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) + (c * ((z * t) - (x * y)))))
    if (i <= (-7.4d+30)) then
        tmp = t_1
    else if (i <= (-1.35d-223)) then
        tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    else if (i <= 1.85d-42) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))))
    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 = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) + (c * ((z * t) - (x * y)))));
	double tmp;
	if (i <= -7.4e+30) {
		tmp = t_1;
	} else if (i <= -1.35e-223) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (i <= 1.85e-42) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	} 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 = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) + (c * ((z * t) - (x * y)))))
	tmp = 0
	if i <= -7.4e+30:
		tmp = t_1
	elif i <= -1.35e-223:
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	elif i <= 1.85e-42:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))))
	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(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(z * t) - Float64(x * y))))))
	tmp = 0.0
	if (i <= -7.4e+30)
		tmp = t_1;
	elseif (i <= -1.35e-223)
		tmp = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (i <= 1.85e-42)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(z * Float64(Float64(a * y1) - Float64(c * y0))))));
	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 = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) + (c * ((z * t) - (x * y)))));
	tmp = 0.0;
	if (i <= -7.4e+30)
		tmp = t_1;
	elseif (i <= -1.35e-223)
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	elseif (i <= 1.85e-42)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	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[(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[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -7.4e+30], t$95$1, If[LessEqual[i, -1.35e-223], N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.85e-42], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -7.40000000000000032e30 or 1.8500000000000001e-42 < i

   1. Initial program 27.3%

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

   3. Taylor expanded in i around -inf 55.2%

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

   if -7.40000000000000032e30 < i < -1.34999999999999994e-223

   1. Initial program 37.0%

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

   3. Taylor expanded in y4 around inf 59.7%

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

   if -1.34999999999999994e-223 < i < 1.8500000000000001e-42

   1. Initial program 35.5%

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

   3. Taylor expanded in y3 around -inf 46.9%

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

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -7.4 \cdot 10^{+30}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) + c \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \mathbf{elif}\;i \leq -1.35 \cdot 10^{-223}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq 1.85 \cdot 10^{-42}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) + c \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 40.4% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-6}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{+133}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+235}:\\ \;\;\;\;y1 \cdot \left(\left(k \cdot \left(y2 \cdot y4\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right) - i \cdot \left(z \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -2.25e+65)
   (*
    x
    (+
     (+ (* y (- (* a b) (* c i))) (* y2 (- (* c y0) (* a y1))))
     (* j (- (* i y1) (* b y0)))))
   (if (<= x -5.2e-6)
     (* i (* y (- (* k y5) (* x c))))
     (if (<= x 1.12e+133)
       (*
        y4
        (+
         (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
         (* c (- (* y y3) (* t y2)))))
       (if (<= x 2.4e+235)
         (*
          y1
          (- (+ (* k (* y2 y4)) (* a (- (* z y3) (* x y2)))) (* i (* z k))))
         (* b (* x (- (* y a) (* j y0)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -2.25e+65) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	} else if (x <= -5.2e-6) {
		tmp = i * (y * ((k * y5) - (x * c)));
	} else if (x <= 1.12e+133) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (x <= 2.4e+235) {
		tmp = y1 * (((k * (y2 * y4)) + (a * ((z * y3) - (x * y2)))) - (i * (z * k)));
	} else {
		tmp = b * (x * ((y * a) - (j * y0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (x <= (-2.25d+65)) then
        tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
    else if (x <= (-5.2d-6)) then
        tmp = i * (y * ((k * y5) - (x * c)))
    else if (x <= 1.12d+133) then
        tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    else if (x <= 2.4d+235) then
        tmp = y1 * (((k * (y2 * y4)) + (a * ((z * y3) - (x * y2)))) - (i * (z * k)))
    else
        tmp = b * (x * ((y * a) - (j * y0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -2.25e+65) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	} else if (x <= -5.2e-6) {
		tmp = i * (y * ((k * y5) - (x * c)));
	} else if (x <= 1.12e+133) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (x <= 2.4e+235) {
		tmp = y1 * (((k * (y2 * y4)) + (a * ((z * y3) - (x * y2)))) - (i * (z * k)));
	} else {
		tmp = b * (x * ((y * a) - (j * y0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if x <= -2.25e+65:
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
	elif x <= -5.2e-6:
		tmp = i * (y * ((k * y5) - (x * c)))
	elif x <= 1.12e+133:
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	elif x <= 2.4e+235:
		tmp = y1 * (((k * (y2 * y4)) + (a * ((z * y3) - (x * y2)))) - (i * (z * k)))
	else:
		tmp = b * (x * ((y * a) - (j * y0)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (x <= -2.25e+65)
		tmp = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (x <= -5.2e-6)
		tmp = Float64(i * Float64(y * Float64(Float64(k * y5) - Float64(x * c))));
	elseif (x <= 1.12e+133)
		tmp = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (x <= 2.4e+235)
		tmp = Float64(y1 * Float64(Float64(Float64(k * Float64(y2 * y4)) + Float64(a * Float64(Float64(z * y3) - Float64(x * y2)))) - Float64(i * Float64(z * k))));
	else
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (x <= -2.25e+65)
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	elseif (x <= -5.2e-6)
		tmp = i * (y * ((k * y5) - (x * c)));
	elseif (x <= 1.12e+133)
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	elseif (x <= 2.4e+235)
		tmp = y1 * (((k * (y2 * y4)) + (a * ((z * y3) - (x * y2)))) - (i * (z * k)));
	else
		tmp = b * (x * ((y * a) - (j * y0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[x, -2.25e+65], N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.2e-6], N[(i * N[(y * N[(N[(k * y5), $MachinePrecision] - N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.12e+133], N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.4e+235], N[(y1 * N[(N[(N[(k * N[(y2 * y4), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(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 < -2.25e65

   1. Initial program 36.8%

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

   3. Taylor expanded in x around inf 68.2%

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

   if -2.25e65 < x < -5.20000000000000019e-6

   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 i around -inf 46.4%

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

   4. Taylor expanded in y around inf 77.5%

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

      1. +-commutative 77.5%

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

      2. mul-1-neg 77.5%

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

      3. unsub-neg 77.5%

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

   6. Simplified 77.5%

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

   if -5.20000000000000019e-6 < x < 1.12e133

   1. Initial program 31.5%

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

   3. Taylor expanded in y4 around inf 44.0%

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

   if 1.12e133 < x < 2.3999999999999999e235

   1. Initial program 36.4%

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

   3. Taylor expanded in y1 around inf 63.6%

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

   4. Taylor expanded in j around 0 68.5%

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

      1. +-commutative 68.5%

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

      2. mul-1-neg 68.5%

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

      3. unsub-neg 68.5%

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

   6. Simplified 68.5%

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

   if 2.3999999999999999e235 < x

   1. Initial program 15.4%

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

   3. Taylor expanded in b around inf 46.2%

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

   4. Taylor expanded in x around inf 77.0%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-6}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{+133}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+235}:\\ \;\;\;\;y1 \cdot \left(\left(k \cdot \left(y2 \cdot y4\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right) - i \cdot \left(z \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 38.3% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+200}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-17}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-159}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+141}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y -6.4e+200)
   (* b (* y (- (* x a) (* k y4))))
   (if (<= y -4.2e-17)
     (*
      x
      (+
       (+ (* y (- (* a b) (* c i))) (* y2 (- (* c y0) (* a y1))))
       (* j (- (* i y1) (* b y0)))))
     (if (<= y 5e-159)
       (* y1 (+ (* y4 (- (* k y2) (* j y3))) (* a (- (* z y3) (* x y2)))))
       (if (<= y 2e+141)
         (* y5 (+ (* a (- (* t y2) (* y y3))) (* y0 (- (* j y3) (* k y2)))))
         (* i (* y (- (* k y5) (* x c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -6.4e+200) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (y <= -4.2e-17) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	} else if (y <= 5e-159) {
		tmp = y1 * ((y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2))));
	} else if (y <= 2e+141) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2))));
	} else {
		tmp = i * (y * ((k * y5) - (x * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y <= (-6.4d+200)) then
        tmp = b * (y * ((x * a) - (k * y4)))
    else if (y <= (-4.2d-17)) then
        tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
    else if (y <= 5d-159) then
        tmp = y1 * ((y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2))))
    else if (y <= 2d+141) then
        tmp = y5 * ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2))))
    else
        tmp = i * (y * ((k * y5) - (x * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -6.4e+200) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (y <= -4.2e-17) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	} else if (y <= 5e-159) {
		tmp = y1 * ((y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2))));
	} else if (y <= 2e+141) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2))));
	} else {
		tmp = i * (y * ((k * y5) - (x * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y <= -6.4e+200:
		tmp = b * (y * ((x * a) - (k * y4)))
	elif y <= -4.2e-17:
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
	elif y <= 5e-159:
		tmp = y1 * ((y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2))))
	elif y <= 2e+141:
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2))))
	else:
		tmp = i * (y * ((k * y5) - (x * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y <= -6.4e+200)
		tmp = Float64(b * Float64(y * Float64(Float64(x * a) - Float64(k * y4))));
	elseif (y <= -4.2e-17)
		tmp = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (y <= 5e-159)
		tmp = Float64(y1 * Float64(Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))) + Float64(a * Float64(Float64(z * y3) - Float64(x * y2)))));
	elseif (y <= 2e+141)
		tmp = Float64(y5 * Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2)))));
	else
		tmp = Float64(i * Float64(y * Float64(Float64(k * y5) - Float64(x * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y <= -6.4e+200)
		tmp = b * (y * ((x * a) - (k * y4)));
	elseif (y <= -4.2e-17)
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	elseif (y <= 5e-159)
		tmp = y1 * ((y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2))));
	elseif (y <= 2e+141)
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2))));
	else
		tmp = i * (y * ((k * y5) - (x * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y, -6.4e+200], N[(b * N[(y * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.2e-17], N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e-159], N[(y1 * N[(N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e+141], N[(y5 * N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(y * N[(N[(k * y5), $MachinePrecision] - N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -6.40000000000000062e200

   1. Initial program 23.0%

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

   3. Taylor expanded in b around inf 38.6%

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

   4. Taylor expanded in y around inf 62.1%

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

      1. +-commutative 62.1%

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

      2. mul-1-neg 62.1%

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

      3. unsub-neg 62.1%

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

   6. Simplified 62.1%

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

   if -6.40000000000000062e200 < y < -4.19999999999999984e-17

   1. Initial program 27.8%

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

   3. Taylor expanded in x around inf 53.2%

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

   if -4.19999999999999984e-17 < y < 5.00000000000000032e-159

   1. Initial program 35.0%

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

   3. Taylor expanded in y1 around inf 48.9%

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

   4. Taylor expanded in i around 0 45.6%

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

      1. +-commutative 45.6%

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

      2. mul-1-neg 45.6%

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

      3. unsub-neg 45.6%

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

   6. Simplified 45.6%

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

   if 5.00000000000000032e-159 < y < 2.00000000000000003e141

   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 y5 around -inf 52.8%

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

   4. Taylor expanded in i around 0 48.4%

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

   if 2.00000000000000003e141 < y

   1. Initial program 26.3%

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

   3. Taylor expanded in i around -inf 50.3%

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

   4. Taylor expanded in y around inf 68.8%

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

      1. +-commutative 68.8%

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

      2. mul-1-neg 68.8%

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

      3. unsub-neg 68.8%

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

   6. Simplified 68.8%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(y \cdot \left(c \cdot x - k \cdot y5\right)\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+200}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-17}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-159}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+141}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 34.3% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -1.04 \cdot 10^{+95}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -5.6 \cdot 10^{-93}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq -7.6 \cdot 10^{-247}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y2 \leq 3.35 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 1.35 \cdot 10^{+118}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -1.04e+95)
   (* c (* y4 (- (* y y3) (* t y2))))
   (if (<= y2 -5.6e-93)
     (* j (* y4 (- (* t b) (* y1 y3))))
     (if (<= y2 -7.6e-247)
       (* a (* b (- (* x y) (* z t))))
       (if (<= y2 3.35e+41)
         (* x (+ (* y (- (* a b) (* c i))) (* j (- (* i y1) (* b y0)))))
         (if (<= y2 1.35e+118)
           (* y2 (* y4 (- (* k y1) (* t c))))
           (* y1 (* y2 (- (* k y4) (* x a))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -1.04e+95) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (y2 <= -5.6e-93) {
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	} else if (y2 <= -7.6e-247) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y2 <= 3.35e+41) {
		tmp = x * ((y * ((a * b) - (c * i))) + (j * ((i * y1) - (b * y0))));
	} else if (y2 <= 1.35e+118) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else {
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y2 <= (-1.04d+95)) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else if (y2 <= (-5.6d-93)) then
        tmp = j * (y4 * ((t * b) - (y1 * y3)))
    else if (y2 <= (-7.6d-247)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (y2 <= 3.35d+41) then
        tmp = x * ((y * ((a * b) - (c * i))) + (j * ((i * y1) - (b * y0))))
    else if (y2 <= 1.35d+118) then
        tmp = y2 * (y4 * ((k * y1) - (t * c)))
    else
        tmp = y1 * (y2 * ((k * y4) - (x * a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -1.04e+95) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (y2 <= -5.6e-93) {
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	} else if (y2 <= -7.6e-247) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y2 <= 3.35e+41) {
		tmp = x * ((y * ((a * b) - (c * i))) + (j * ((i * y1) - (b * y0))));
	} else if (y2 <= 1.35e+118) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else {
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y2 <= -1.04e+95:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	elif y2 <= -5.6e-93:
		tmp = j * (y4 * ((t * b) - (y1 * y3)))
	elif y2 <= -7.6e-247:
		tmp = a * (b * ((x * y) - (z * t)))
	elif y2 <= 3.35e+41:
		tmp = x * ((y * ((a * b) - (c * i))) + (j * ((i * y1) - (b * y0))))
	elif y2 <= 1.35e+118:
		tmp = y2 * (y4 * ((k * y1) - (t * c)))
	else:
		tmp = y1 * (y2 * ((k * y4) - (x * a)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y2 <= -1.04e+95)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (y2 <= -5.6e-93)
		tmp = Float64(j * Float64(y4 * Float64(Float64(t * b) - Float64(y1 * y3))));
	elseif (y2 <= -7.6e-247)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y2 <= 3.35e+41)
		tmp = Float64(x * Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (y2 <= 1.35e+118)
		tmp = Float64(y2 * Float64(y4 * Float64(Float64(k * y1) - Float64(t * c))));
	else
		tmp = Float64(y1 * Float64(y2 * Float64(Float64(k * y4) - Float64(x * a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y2 <= -1.04e+95)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	elseif (y2 <= -5.6e-93)
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	elseif (y2 <= -7.6e-247)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (y2 <= 3.35e+41)
		tmp = x * ((y * ((a * b) - (c * i))) + (j * ((i * y1) - (b * y0))));
	elseif (y2 <= 1.35e+118)
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	else
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y2, -1.04e+95], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -5.6e-93], N[(j * N[(y4 * N[(N[(t * b), $MachinePrecision] - N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -7.6e-247], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 3.35e+41], N[(x * N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.35e+118], N[(y2 * N[(y4 * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(y2 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y2 < -1.04e95

   1. Initial program 33.3%

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

   3. Taylor expanded in y4 around inf 41.9%

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

   4. Taylor expanded in c around inf 48.3%

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

   if -1.04e95 < y2 < -5.59999999999999997e-93

   1. Initial program 23.5%

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

   3. Taylor expanded in y4 around inf 41.5%

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

   4. Taylor expanded in j around inf 50.9%

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

      1. +-commutative 50.9%

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

      2. mul-1-neg 50.9%

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

      3. unsub-neg 50.9%

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

   6. Simplified 50.9%

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

   if -5.59999999999999997e-93 < y2 < -7.59999999999999977e-247

   1. Initial program 30.4%

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

   3. Taylor expanded in b around inf 40.1%

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

   4. Taylor expanded in a around inf 56.1%

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

   if -7.59999999999999977e-247 < y2 < 3.3499999999999998e41

   1. Initial program 35.2%

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

   3. Taylor expanded in x around inf 42.9%

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

   4. Taylor expanded in y2 around 0 41.9%

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

   if 3.3499999999999998e41 < y2 < 1.35e118

   1. Initial program 37.4%

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

   3. Taylor expanded in y4 around inf 50.8%

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

   4. Taylor expanded in y2 around inf 63.5%

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

   if 1.35e118 < y2

   1. Initial program 27.8%

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

   3. Taylor expanded in y1 around inf 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 y2 around inf 62.1%

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

      1. +-commutative 62.1%

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

      2. mul-1-neg 62.1%

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

      3. unsub-neg 62.1%

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

   6. Simplified 62.1%

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

4. Final simplification 50.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.04 \cdot 10^{+95}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -5.6 \cdot 10^{-93}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq -7.6 \cdot 10^{-247}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y2 \leq 3.35 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 1.35 \cdot 10^{+118}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 31.2% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y5 \leq -1.45 \cdot 10^{+161}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq -3.2 \cdot 10^{-121}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq -2.6 \cdot 10^{-238}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 2.8 \cdot 10^{-284}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 1.02 \cdot 10^{+140}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y5 -1.45e+161)
   (* y5 (* a (- (* t y2) (* y y3))))
   (if (<= y5 -3.2e-121)
     (* c (* y4 (- (* y y3) (* t y2))))
     (if (<= y5 -2.6e-238)
       (* b (* y (- (* x a) (* k y4))))
       (if (<= y5 2.8e-284)
         (* a (* y1 (- (* z y3) (* x y2))))
         (if (<= y5 1.02e+140)
           (* i (* y1 (- (* x j) (* z k))))
           (* i (* y5 (- (* y k) (* t j))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -1.45e+161) {
		tmp = y5 * (a * ((t * y2) - (y * y3)));
	} else if (y5 <= -3.2e-121) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (y5 <= -2.6e-238) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (y5 <= 2.8e-284) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (y5 <= 1.02e+140) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else {
		tmp = i * (y5 * ((y * k) - (t * j)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y5 <= (-1.45d+161)) then
        tmp = y5 * (a * ((t * y2) - (y * y3)))
    else if (y5 <= (-3.2d-121)) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else if (y5 <= (-2.6d-238)) then
        tmp = b * (y * ((x * a) - (k * y4)))
    else if (y5 <= 2.8d-284) then
        tmp = a * (y1 * ((z * y3) - (x * y2)))
    else if (y5 <= 1.02d+140) then
        tmp = i * (y1 * ((x * j) - (z * k)))
    else
        tmp = i * (y5 * ((y * k) - (t * j)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -1.45e+161) {
		tmp = y5 * (a * ((t * y2) - (y * y3)));
	} else if (y5 <= -3.2e-121) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (y5 <= -2.6e-238) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (y5 <= 2.8e-284) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (y5 <= 1.02e+140) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else {
		tmp = i * (y5 * ((y * k) - (t * j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y5 <= -1.45e+161:
		tmp = y5 * (a * ((t * y2) - (y * y3)))
	elif y5 <= -3.2e-121:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	elif y5 <= -2.6e-238:
		tmp = b * (y * ((x * a) - (k * y4)))
	elif y5 <= 2.8e-284:
		tmp = a * (y1 * ((z * y3) - (x * y2)))
	elif y5 <= 1.02e+140:
		tmp = i * (y1 * ((x * j) - (z * k)))
	else:
		tmp = i * (y5 * ((y * k) - (t * j)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y5 <= -1.45e+161)
		tmp = Float64(y5 * Float64(a * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (y5 <= -3.2e-121)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (y5 <= -2.6e-238)
		tmp = Float64(b * Float64(y * Float64(Float64(x * a) - Float64(k * y4))));
	elseif (y5 <= 2.8e-284)
		tmp = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))));
	elseif (y5 <= 1.02e+140)
		tmp = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))));
	else
		tmp = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y5 <= -1.45e+161)
		tmp = y5 * (a * ((t * y2) - (y * y3)));
	elseif (y5 <= -3.2e-121)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	elseif (y5 <= -2.6e-238)
		tmp = b * (y * ((x * a) - (k * y4)));
	elseif (y5 <= 2.8e-284)
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	elseif (y5 <= 1.02e+140)
		tmp = i * (y1 * ((x * j) - (z * k)));
	else
		tmp = i * (y5 * ((y * k) - (t * j)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y5, -1.45e+161], N[(y5 * N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -3.2e-121], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -2.6e-238], N[(b * N[(y * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 2.8e-284], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.02e+140], N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y5 < -1.45000000000000008e161

   1. Initial program 25.0%

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

   3. Taylor expanded in y5 around -inf 67.3%

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

   4. Taylor expanded in a around inf 67.5%

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

   if -1.45000000000000008e161 < y5 < -3.20000000000000019e-121

   1. Initial program 22.1%

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

   3. Taylor expanded in y4 around inf 39.4%

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

   4. Taylor expanded in c around inf 39.9%

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

   if -3.20000000000000019e-121 < y5 < -2.6000000000000001e-238

   1. Initial program 45.5%

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

   3. Taylor expanded in b around inf 51.2%

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

   4. Taylor expanded in y around inf 55.8%

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

      1. +-commutative 55.8%

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

      2. mul-1-neg 55.8%

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

      3. unsub-neg 55.8%

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

   6. Simplified 55.8%

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

   if -2.6000000000000001e-238 < y5 < 2.8000000000000003e-284

   1. Initial program 46.2%

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

   3. Taylor expanded in y1 around inf 61.7%

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

   4. Taylor expanded in a around inf 51.4%

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

      1. mul-1-neg 51.4%

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

   6. Simplified 51.4%

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

   if 2.8000000000000003e-284 < y5 < 1.02000000000000007e140

   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 y1 around inf 46.8%

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

   4. Taylor expanded in i around inf 39.1%

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

   if 1.02000000000000007e140 < y5

   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 i around -inf 43.7%

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

   4. Taylor expanded in y5 around inf 65.5%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -1.45 \cdot 10^{+161}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq -3.2 \cdot 10^{-121}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq -2.6 \cdot 10^{-238}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 2.8 \cdot 10^{-284}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 1.02 \cdot 10^{+140}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 29.1% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{if}\;i \leq -1.06 \cdot 10^{+241}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq -8 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -6 \cdot 10^{-169}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;i \leq 2.1 \cdot 10^{+30}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq 1.02 \cdot 10^{+107}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* x (- (* y0 y2) (* y i))))))
   (if (<= i -1.06e+241)
     (* b (* j (- (* t y4) (* x y0))))
     (if (<= i -8e+49)
       t_1
       (if (<= i -6e-169)
         (* a (* b (- (* x y) (* z t))))
         (if (<= i 2.1e+30)
           (* b (* x (- (* y a) (* j y0))))
           (if (<= i 1.02e+107) (* c (* y2 (- (* x y0) (* t y4)))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (x * ((y0 * y2) - (y * i)));
	double tmp;
	if (i <= -1.06e+241) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (i <= -8e+49) {
		tmp = t_1;
	} else if (i <= -6e-169) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (i <= 2.1e+30) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (i <= 1.02e+107) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (x * ((y0 * y2) - (y * i)))
    if (i <= (-1.06d+241)) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (i <= (-8d+49)) then
        tmp = t_1
    else if (i <= (-6d-169)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (i <= 2.1d+30) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (i <= 1.02d+107) then
        tmp = c * (y2 * ((x * y0) - (t * y4)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (x * ((y0 * y2) - (y * i)));
	double tmp;
	if (i <= -1.06e+241) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (i <= -8e+49) {
		tmp = t_1;
	} else if (i <= -6e-169) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (i <= 2.1e+30) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (i <= 1.02e+107) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (x * ((y0 * y2) - (y * i)))
	tmp = 0
	if i <= -1.06e+241:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif i <= -8e+49:
		tmp = t_1
	elif i <= -6e-169:
		tmp = a * (b * ((x * y) - (z * t)))
	elif i <= 2.1e+30:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif i <= 1.02e+107:
		tmp = c * (y2 * ((x * y0) - (t * y4)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(x * Float64(Float64(y0 * y2) - Float64(y * i))))
	tmp = 0.0
	if (i <= -1.06e+241)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (i <= -8e+49)
		tmp = t_1;
	elseif (i <= -6e-169)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (i <= 2.1e+30)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (i <= 1.02e+107)
		tmp = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (x * ((y0 * y2) - (y * i)));
	tmp = 0.0;
	if (i <= -1.06e+241)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (i <= -8e+49)
		tmp = t_1;
	elseif (i <= -6e-169)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (i <= 2.1e+30)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (i <= 1.02e+107)
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(x * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.06e+241], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -8e+49], t$95$1, If[LessEqual[i, -6e-169], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.1e+30], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.02e+107], N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -1.06000000000000005e241

   1. Initial program 14.3%

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

   3. Taylor expanded in b around inf 57.9%

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

   4. Taylor expanded in j around inf 51.4%

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

   if -1.06000000000000005e241 < i < -7.99999999999999957e49 or 1.01999999999999994e107 < i

   1. Initial program 26.1%

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

   3. Taylor expanded in c around inf 45.4%

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

   4. Taylor expanded in x around inf 47.5%

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

      1. +-commutative 47.5%

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

      2. mul-1-neg 47.5%

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

      3. unsub-neg 47.5%

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

   6. Simplified 47.5%

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

   if -7.99999999999999957e49 < i < -5.9999999999999998e-169

   1. Initial program 37.9%

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

   3. Taylor expanded in b around inf 42.5%

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

   4. Taylor expanded in a around inf 35.2%

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

   if -5.9999999999999998e-169 < i < 2.1e30

   1. Initial program 37.0%

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

   3. Taylor expanded in b around inf 36.9%

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

   4. Taylor expanded in x around inf 38.8%

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

   if 2.1e30 < i < 1.01999999999999994e107

   1. Initial program 17.6%

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

   3. Taylor expanded in c around inf 47.3%

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

   4. Taylor expanded in y2 around inf 65.6%

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

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.06 \cdot 10^{+241}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq -8 \cdot 10^{+49}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;i \leq -6 \cdot 10^{-169}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;i \leq 2.1 \cdot 10^{+30}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq 1.02 \cdot 10^{+107}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 37.5% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-13}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-155}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+146}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y -1.9e-13)
   (* b (* y (- (* x a) (* k y4))))
   (if (<= y 1.3e-155)
     (* y1 (+ (* y4 (- (* k y2) (* j y3))) (* a (- (* z y3) (* x y2)))))
     (if (<= y 8e+146)
       (* y5 (+ (* a (- (* t y2) (* y y3))) (* y0 (- (* j y3) (* k y2)))))
       (* i (* y (- (* k y5) (* x c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -1.9e-13) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (y <= 1.3e-155) {
		tmp = y1 * ((y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2))));
	} else if (y <= 8e+146) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2))));
	} else {
		tmp = i * (y * ((k * y5) - (x * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y <= (-1.9d-13)) then
        tmp = b * (y * ((x * a) - (k * y4)))
    else if (y <= 1.3d-155) then
        tmp = y1 * ((y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2))))
    else if (y <= 8d+146) then
        tmp = y5 * ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2))))
    else
        tmp = i * (y * ((k * y5) - (x * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -1.9e-13) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (y <= 1.3e-155) {
		tmp = y1 * ((y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2))));
	} else if (y <= 8e+146) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2))));
	} else {
		tmp = i * (y * ((k * y5) - (x * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y <= -1.9e-13:
		tmp = b * (y * ((x * a) - (k * y4)))
	elif y <= 1.3e-155:
		tmp = y1 * ((y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2))))
	elif y <= 8e+146:
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2))))
	else:
		tmp = i * (y * ((k * y5) - (x * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y <= -1.9e-13)
		tmp = Float64(b * Float64(y * Float64(Float64(x * a) - Float64(k * y4))));
	elseif (y <= 1.3e-155)
		tmp = Float64(y1 * Float64(Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))) + Float64(a * Float64(Float64(z * y3) - Float64(x * y2)))));
	elseif (y <= 8e+146)
		tmp = Float64(y5 * Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2)))));
	else
		tmp = Float64(i * Float64(y * Float64(Float64(k * y5) - Float64(x * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y <= -1.9e-13)
		tmp = b * (y * ((x * a) - (k * y4)));
	elseif (y <= 1.3e-155)
		tmp = y1 * ((y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2))));
	elseif (y <= 8e+146)
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2))));
	else
		tmp = i * (y * ((k * y5) - (x * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y, -1.9e-13], N[(b * N[(y * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e-155], N[(y1 * N[(N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e+146], N[(y5 * N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(y * N[(N[(k * y5), $MachinePrecision] - N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.9e-13

   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 b around inf 41.9%

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

   4. Taylor expanded in y around inf 47.2%

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

      1. +-commutative 47.2%

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

      2. mul-1-neg 47.2%

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

      3. unsub-neg 47.2%

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

   6. Simplified 47.2%

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

   if -1.9e-13 < y < 1.30000000000000004e-155

   1. Initial program 34.6%

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

   3. Taylor expanded in y1 around inf 49.4%

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

   4. Taylor expanded in i around 0 45.1%

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

      1. +-commutative 45.1%

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

      2. mul-1-neg 45.1%

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

      3. unsub-neg 45.1%

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

   6. Simplified 45.1%

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

   if 1.30000000000000004e-155 < y < 7.99999999999999947e146

   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 y5 around -inf 52.8%

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

   4. Taylor expanded in i around 0 48.4%

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

   if 7.99999999999999947e146 < y

   1. Initial program 26.3%

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

   3. Taylor expanded in i around -inf 50.3%

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

   4. Taylor expanded in y around inf 68.8%

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

      1. +-commutative 68.8%

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

      2. mul-1-neg 68.8%

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

      3. unsub-neg 68.8%

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

   6. Simplified 68.8%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(y \cdot \left(c \cdot x - k \cdot y5\right)\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-13}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-155}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+146}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 22.1% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot \left(z \cdot \left(-t\right)\right)\right)\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{+222}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{+16}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(-z \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-138}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-136}:\\ \;\;\;\;j \cdot \left(\left(y1 \cdot y3\right) \cdot \left(-y4\right)\right)\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{+27}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* b (* z (- t))))))
   (if (<= z -1.65e+222)
     t_1
     (if (<= z -6.5e+16)
       (* c (* y0 (- (* z y3))))
       (if (<= z -1.35e-138)
         (* y1 (* y2 (* k y4)))
         (if (<= z 6.5e-136)
           (* j (* (* y1 y3) (- y4)))
           (if (<= z 1.08e+27) (* t (* a (* 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 = a * (b * (z * -t));
	double tmp;
	if (z <= -1.65e+222) {
		tmp = t_1;
	} else if (z <= -6.5e+16) {
		tmp = c * (y0 * -(z * y3));
	} else if (z <= -1.35e-138) {
		tmp = y1 * (y2 * (k * y4));
	} else if (z <= 6.5e-136) {
		tmp = j * ((y1 * y3) * -y4);
	} else if (z <= 1.08e+27) {
		tmp = t * (a * (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 = a * (b * (z * -t))
    if (z <= (-1.65d+222)) then
        tmp = t_1
    else if (z <= (-6.5d+16)) then
        tmp = c * (y0 * -(z * y3))
    else if (z <= (-1.35d-138)) then
        tmp = y1 * (y2 * (k * y4))
    else if (z <= 6.5d-136) then
        tmp = j * ((y1 * y3) * -y4)
    else if (z <= 1.08d+27) then
        tmp = t * (a * (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 = a * (b * (z * -t));
	double tmp;
	if (z <= -1.65e+222) {
		tmp = t_1;
	} else if (z <= -6.5e+16) {
		tmp = c * (y0 * -(z * y3));
	} else if (z <= -1.35e-138) {
		tmp = y1 * (y2 * (k * y4));
	} else if (z <= 6.5e-136) {
		tmp = j * ((y1 * y3) * -y4);
	} else if (z <= 1.08e+27) {
		tmp = t * (a * (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 = a * (b * (z * -t))
	tmp = 0
	if z <= -1.65e+222:
		tmp = t_1
	elif z <= -6.5e+16:
		tmp = c * (y0 * -(z * y3))
	elif z <= -1.35e-138:
		tmp = y1 * (y2 * (k * y4))
	elif z <= 6.5e-136:
		tmp = j * ((y1 * y3) * -y4)
	elif z <= 1.08e+27:
		tmp = t * (a * (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(a * Float64(b * Float64(z * Float64(-t))))
	tmp = 0.0
	if (z <= -1.65e+222)
		tmp = t_1;
	elseif (z <= -6.5e+16)
		tmp = Float64(c * Float64(y0 * Float64(-Float64(z * y3))));
	elseif (z <= -1.35e-138)
		tmp = Float64(y1 * Float64(y2 * Float64(k * y4)));
	elseif (z <= 6.5e-136)
		tmp = Float64(j * Float64(Float64(y1 * y3) * Float64(-y4)));
	elseif (z <= 1.08e+27)
		tmp = Float64(t * Float64(a * 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 = a * (b * (z * -t));
	tmp = 0.0;
	if (z <= -1.65e+222)
		tmp = t_1;
	elseif (z <= -6.5e+16)
		tmp = c * (y0 * -(z * y3));
	elseif (z <= -1.35e-138)
		tmp = y1 * (y2 * (k * y4));
	elseif (z <= 6.5e-136)
		tmp = j * ((y1 * y3) * -y4);
	elseif (z <= 1.08e+27)
		tmp = t * (a * (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[(a * N[(b * N[(z * (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.65e+222], t$95$1, If[LessEqual[z, -6.5e+16], N[(c * N[(y0 * (-N[(z * y3), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.35e-138], N[(y1 * N[(y2 * N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e-136], N[(j * N[(N[(y1 * y3), $MachinePrecision] * (-y4)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.08e+27], N[(t * N[(a * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.64999999999999992e222 or 1.08e27 < z

   1. Initial program 27.2%

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

   3. Taylor expanded in b around inf 43.3%

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

   4. Taylor expanded in a around inf 47.9%

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

   5. Taylor expanded in x around 0 43.7%

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

      1. mul-1-neg 43.7%

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

      2. *-commutative 43.7%

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

      3. distribute-lft-neg-in 43.7%

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

      4. *-commutative 43.7%

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

      5. distribute-lft-neg-in 43.7%

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

      6. distribute-rgt-neg-in 43.7%

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

   7. Simplified 43.7%

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

   if -1.64999999999999992e222 < z < -6.5e16

   1. Initial program 37.9%

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

   3. Taylor expanded in c around inf 38.0%

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

   4. Taylor expanded in z around inf 36.7%

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

      1. +-commutative 36.7%

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

      2. mul-1-neg 36.7%

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

      3. unsub-neg 36.7%

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

   6. Simplified 36.7%

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

   7. Taylor expanded in i around 0 36.3%

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

      1. mul-1-neg 36.3%

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

      2. *-commutative 36.3%

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

      3. distribute-lft-neg-in 36.3%

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

      4. *-commutative 36.3%

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

      5. distribute-lft-neg-in 36.3%

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

      6. *-commutative 36.3%

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

      7. distribute-lft-neg-in 36.3%

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

   9. Simplified 36.3%

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

   if -6.5e16 < z < -1.35000000000000014e-138

   1. Initial program 35.5%

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

   3. Taylor expanded in y1 around inf 41.0%

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

   4. Taylor expanded in y2 around inf 46.0%

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

      1. +-commutative 46.0%

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

      2. mul-1-neg 46.0%

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

      3. unsub-neg 46.0%

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

   6. Simplified 46.0%

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

   7. Taylor expanded in k around inf 36.5%

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

   if -1.35000000000000014e-138 < z < 6.50000000000000011e-136

   1. Initial program 29.9%

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

   3. Taylor expanded in y1 around inf 40.6%

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

   4. Taylor expanded in j around -inf 33.5%

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

      1. associate-*r* 33.5%

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

      2. mul-1-neg 33.5%

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

   6. Simplified 33.5%

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

   7. Taylor expanded in y3 around inf 21.1%

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

      1. associate-*r* 21.1%

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

      2. neg-mul-1 21.1%

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

      3. associate-*r* 26.0%

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

      4. *-commutative 26.0%

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

   9. Simplified 26.0%

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

   if 6.50000000000000011e-136 < z < 1.08e27

   1. Initial program 33.4%

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

   3. Taylor expanded in y5 around -inf 40.2%

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

   4. Taylor expanded in t around inf 37.8%

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

   5. Taylor expanded in i around 0 28.7%

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

      1. associate-*r* 28.7%

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

      2. neg-mul-1 28.7%

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

   7. Simplified 28.7%

      \[\leadsto -1 \cdot \left(t \cdot \color{blue}{\left(\left(-a\right) \cdot \left(y2 \cdot y5\right)\right)}\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 34.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+222}:\\ \;\;\;\;a \cdot \left(b \cdot \left(z \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{+16}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(-z \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-138}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-136}:\\ \;\;\;\;j \cdot \left(\left(y1 \cdot y3\right) \cdot \left(-y4\right)\right)\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{+27}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(z \cdot \left(-t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 22.1% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot \left(z \cdot \left(-t\right)\right)\right)\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{+222}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{+16}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(-z \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-135}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-140}:\\ \;\;\;\;j \cdot \left(\left(y1 \cdot y3\right) \cdot \left(-y4\right)\right)\\ \mathbf{elif}\;z \leq 1.92 \cdot 10^{+28}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* b (* z (- t))))))
   (if (<= z -1.3e+222)
     t_1
     (if (<= z -6.4e+16)
       (* c (* y0 (- (* z y3))))
       (if (<= z -3.8e-135)
         (* y1 (* y2 (* k y4)))
         (if (<= z 6.8e-140)
           (* j (* (* y1 y3) (- y4)))
           (if (<= z 1.92e+28) (* 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 = a * (b * (z * -t));
	double tmp;
	if (z <= -1.3e+222) {
		tmp = t_1;
	} else if (z <= -6.4e+16) {
		tmp = c * (y0 * -(z * y3));
	} else if (z <= -3.8e-135) {
		tmp = y1 * (y2 * (k * y4));
	} else if (z <= 6.8e-140) {
		tmp = j * ((y1 * y3) * -y4);
	} else if (z <= 1.92e+28) {
		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 = a * (b * (z * -t))
    if (z <= (-1.3d+222)) then
        tmp = t_1
    else if (z <= (-6.4d+16)) then
        tmp = c * (y0 * -(z * y3))
    else if (z <= (-3.8d-135)) then
        tmp = y1 * (y2 * (k * y4))
    else if (z <= 6.8d-140) then
        tmp = j * ((y1 * y3) * -y4)
    else if (z <= 1.92d+28) 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 = a * (b * (z * -t));
	double tmp;
	if (z <= -1.3e+222) {
		tmp = t_1;
	} else if (z <= -6.4e+16) {
		tmp = c * (y0 * -(z * y3));
	} else if (z <= -3.8e-135) {
		tmp = y1 * (y2 * (k * y4));
	} else if (z <= 6.8e-140) {
		tmp = j * ((y1 * y3) * -y4);
	} else if (z <= 1.92e+28) {
		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 = a * (b * (z * -t))
	tmp = 0
	if z <= -1.3e+222:
		tmp = t_1
	elif z <= -6.4e+16:
		tmp = c * (y0 * -(z * y3))
	elif z <= -3.8e-135:
		tmp = y1 * (y2 * (k * y4))
	elif z <= 6.8e-140:
		tmp = j * ((y1 * y3) * -y4)
	elif z <= 1.92e+28:
		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(a * Float64(b * Float64(z * Float64(-t))))
	tmp = 0.0
	if (z <= -1.3e+222)
		tmp = t_1;
	elseif (z <= -6.4e+16)
		tmp = Float64(c * Float64(y0 * Float64(-Float64(z * y3))));
	elseif (z <= -3.8e-135)
		tmp = Float64(y1 * Float64(y2 * Float64(k * y4)));
	elseif (z <= 6.8e-140)
		tmp = Float64(j * Float64(Float64(y1 * y3) * Float64(-y4)));
	elseif (z <= 1.92e+28)
		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 = a * (b * (z * -t));
	tmp = 0.0;
	if (z <= -1.3e+222)
		tmp = t_1;
	elseif (z <= -6.4e+16)
		tmp = c * (y0 * -(z * y3));
	elseif (z <= -3.8e-135)
		tmp = y1 * (y2 * (k * y4));
	elseif (z <= 6.8e-140)
		tmp = j * ((y1 * y3) * -y4);
	elseif (z <= 1.92e+28)
		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[(a * N[(b * N[(z * (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.3e+222], t$95$1, If[LessEqual[z, -6.4e+16], N[(c * N[(y0 * (-N[(z * y3), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.8e-135], N[(y1 * N[(y2 * N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e-140], N[(j * N[(N[(y1 * y3), $MachinePrecision] * (-y4)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.92e+28], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.3000000000000001e222 or 1.91999999999999998e28 < z

   1. Initial program 27.2%

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

   3. Taylor expanded in b around inf 43.3%

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

   4. Taylor expanded in a around inf 47.9%

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

   5. Taylor expanded in x around 0 43.7%

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

      1. mul-1-neg 43.7%

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

      2. *-commutative 43.7%

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

      3. distribute-lft-neg-in 43.7%

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

      4. *-commutative 43.7%

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

      5. distribute-lft-neg-in 43.7%

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

      6. distribute-rgt-neg-in 43.7%

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

   7. Simplified 43.7%

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

   if -1.3000000000000001e222 < z < -6.4e16

   1. Initial program 37.9%

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

   3. Taylor expanded in c around inf 38.0%

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

   4. Taylor expanded in z around inf 36.7%

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

      1. +-commutative 36.7%

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

      2. mul-1-neg 36.7%

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

      3. unsub-neg 36.7%

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

   6. Simplified 36.7%

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

   7. Taylor expanded in i around 0 36.3%

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

      1. mul-1-neg 36.3%

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

      2. *-commutative 36.3%

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

      3. distribute-lft-neg-in 36.3%

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

      4. *-commutative 36.3%

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

      5. distribute-lft-neg-in 36.3%

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

      6. *-commutative 36.3%

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

      7. distribute-lft-neg-in 36.3%

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

   9. Simplified 36.3%

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

   if -6.4e16 < z < -3.8000000000000003e-135

   1. Initial program 35.5%

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

   3. Taylor expanded in y1 around inf 41.0%

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

   4. Taylor expanded in y2 around inf 46.0%

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

      1. +-commutative 46.0%

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

      2. mul-1-neg 46.0%

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

      3. unsub-neg 46.0%

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

   6. Simplified 46.0%

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

   7. Taylor expanded in k around inf 36.5%

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

   if -3.8000000000000003e-135 < z < 6.80000000000000017e-140

   1. Initial program 29.9%

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

   3. Taylor expanded in y1 around inf 40.6%

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

   4. Taylor expanded in j around -inf 33.5%

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

      1. associate-*r* 33.5%

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

      2. mul-1-neg 33.5%

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

   6. Simplified 33.5%

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

   7. Taylor expanded in y3 around inf 21.1%

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

      1. associate-*r* 21.1%

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

      2. neg-mul-1 21.1%

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

      3. associate-*r* 26.0%

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

      4. *-commutative 26.0%

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

   9. Simplified 26.0%

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

   if 6.80000000000000017e-140 < z < 1.91999999999999998e28

   1. Initial program 33.4%

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

   3. Taylor expanded in y5 around -inf 40.2%

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

   4. Taylor expanded in t around inf 37.8%

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

   5. Taylor expanded in i around 0 28.7%

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

4. Final simplification 34.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+222}:\\ \;\;\;\;a \cdot \left(b \cdot \left(z \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{+16}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(-z \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-135}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-140}:\\ \;\;\;\;j \cdot \left(\left(y1 \cdot y3\right) \cdot \left(-y4\right)\right)\\ \mathbf{elif}\;z \leq 1.92 \cdot 10^{+28}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(z \cdot \left(-t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 22.1% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{if}\;y5 \leq -1.1 \cdot 10^{+128}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y5 \leq -9 \cdot 10^{-266}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y5 \leq 3.25 \cdot 10^{-193}:\\ \;\;\;\;-c \cdot \left(z \cdot \left(y0 \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq 4.6 \cdot 10^{-119}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq 2.9 \cdot 10^{-25}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* t (* y2 y5)))))
   (if (<= y5 -1.1e+128)
     t_1
     (if (<= y5 -9e-266)
       (* a (* (* x y) b))
       (if (<= y5 3.25e-193)
         (- (* c (* z (* y0 y3))))
         (if (<= y5 4.6e-119)
           (* i (* y1 (* x j)))
           (if (<= y5 2.9e-25) (* c (* z (* t i))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (t * (y2 * y5));
	double tmp;
	if (y5 <= -1.1e+128) {
		tmp = t_1;
	} else if (y5 <= -9e-266) {
		tmp = a * ((x * y) * b);
	} else if (y5 <= 3.25e-193) {
		tmp = -(c * (z * (y0 * y3)));
	} else if (y5 <= 4.6e-119) {
		tmp = i * (y1 * (x * j));
	} else if (y5 <= 2.9e-25) {
		tmp = c * (z * (t * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (t * (y2 * y5))
    if (y5 <= (-1.1d+128)) then
        tmp = t_1
    else if (y5 <= (-9d-266)) then
        tmp = a * ((x * y) * b)
    else if (y5 <= 3.25d-193) then
        tmp = -(c * (z * (y0 * y3)))
    else if (y5 <= 4.6d-119) then
        tmp = i * (y1 * (x * j))
    else if (y5 <= 2.9d-25) then
        tmp = c * (z * (t * i))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (t * (y2 * y5));
	double tmp;
	if (y5 <= -1.1e+128) {
		tmp = t_1;
	} else if (y5 <= -9e-266) {
		tmp = a * ((x * y) * b);
	} else if (y5 <= 3.25e-193) {
		tmp = -(c * (z * (y0 * y3)));
	} else if (y5 <= 4.6e-119) {
		tmp = i * (y1 * (x * j));
	} else if (y5 <= 2.9e-25) {
		tmp = c * (z * (t * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (t * (y2 * y5))
	tmp = 0
	if y5 <= -1.1e+128:
		tmp = t_1
	elif y5 <= -9e-266:
		tmp = a * ((x * y) * b)
	elif y5 <= 3.25e-193:
		tmp = -(c * (z * (y0 * y3)))
	elif y5 <= 4.6e-119:
		tmp = i * (y1 * (x * j))
	elif y5 <= 2.9e-25:
		tmp = c * (z * (t * i))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(t * Float64(y2 * y5)))
	tmp = 0.0
	if (y5 <= -1.1e+128)
		tmp = t_1;
	elseif (y5 <= -9e-266)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	elseif (y5 <= 3.25e-193)
		tmp = Float64(-Float64(c * Float64(z * Float64(y0 * y3))));
	elseif (y5 <= 4.6e-119)
		tmp = Float64(i * Float64(y1 * Float64(x * j)));
	elseif (y5 <= 2.9e-25)
		tmp = Float64(c * Float64(z * Float64(t * i)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (t * (y2 * y5));
	tmp = 0.0;
	if (y5 <= -1.1e+128)
		tmp = t_1;
	elseif (y5 <= -9e-266)
		tmp = a * ((x * y) * b);
	elseif (y5 <= 3.25e-193)
		tmp = -(c * (z * (y0 * y3)));
	elseif (y5 <= 4.6e-119)
		tmp = i * (y1 * (x * j));
	elseif (y5 <= 2.9e-25)
		tmp = c * (z * (t * i));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -1.1e+128], t$95$1, If[LessEqual[y5, -9e-266], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 3.25e-193], (-N[(c * N[(z * N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), If[LessEqual[y5, 4.6e-119], N[(i * N[(y1 * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 2.9e-25], N[(c * N[(z * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y5 < -1.10000000000000008e128 or 2.9000000000000001e-25 < y5

   1. Initial program 28.2%

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

   3. Taylor expanded in y5 around -inf 53.7%

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

   4. Taylor expanded in t around inf 41.7%

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

   5. Taylor expanded in i around 0 37.2%

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

   if -1.10000000000000008e128 < y5 < -9.0000000000000006e-266

   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 b around inf 38.5%

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

   4. Taylor expanded in a around inf 34.0%

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

   5. Taylor expanded in x around inf 23.7%

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

   if -9.0000000000000006e-266 < y5 < 3.2500000000000002e-193

   1. Initial program 51.6%

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

   3. Taylor expanded in c around inf 59.2%

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

   4. Taylor expanded in z around inf 30.0%

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

      1. +-commutative 30.0%

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

      2. mul-1-neg 30.0%

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

      3. unsub-neg 30.0%

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

   6. Simplified 30.0%

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

   7. Taylor expanded in i around 0 30.0%

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

      1. neg-mul-1 30.0%

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

      2. distribute-rgt-neg-in 30.0%

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

   9. Simplified 30.0%

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

   if 3.2500000000000002e-193 < y5 < 4.59999999999999987e-119

   1. Initial program 27.3%

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

   3. Taylor expanded in y1 around inf 64.2%

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

   4. Taylor expanded in j around -inf 42.6%

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

      1. associate-*r* 42.6%

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

      2. mul-1-neg 42.6%

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

   6. Simplified 42.6%

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

   7. Taylor expanded in y3 around 0 38.3%

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

      1. associate-*r* 42.8%

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

   9. Simplified 42.8%

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

   if 4.59999999999999987e-119 < y5 < 2.9000000000000001e-25

   1. Initial program 36.4%

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

   3. Taylor expanded in c around inf 37.6%

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

   4. Taylor expanded in z around inf 37.5%

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

      1. +-commutative 37.5%

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

      2. mul-1-neg 37.5%

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

      3. unsub-neg 37.5%

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

   6. Simplified 37.5%

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

   7. Taylor expanded in i around inf 33.5%

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

      1. associate-*r* 37.8%

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

      2. *-commutative 37.8%

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

   9. Simplified 37.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(t \cdot i\right) \cdot z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 32.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -1.1 \cdot 10^{+128}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq -9 \cdot 10^{-266}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y5 \leq 3.25 \cdot 10^{-193}:\\ \;\;\;\;-c \cdot \left(z \cdot \left(y0 \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq 4.6 \cdot 10^{-119}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq 2.9 \cdot 10^{-25}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 29.5% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y5 \leq -4.8 \cdot 10^{-118}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq -1.7 \cdot 10^{-233}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 10^{-284}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 1.15 \cdot 10^{+140}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y5 -4.8e-118)
   (* c (* y4 (- (* y y3) (* t y2))))
   (if (<= y5 -1.7e-233)
     (* b (* y (- (* x a) (* k y4))))
     (if (<= y5 1e-284)
       (* a (* y1 (- (* z y3) (* x y2))))
       (if (<= y5 1.15e+140)
         (* i (* y1 (- (* x j) (* z k))))
         (* i (* y5 (- (* y k) (* t j)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -4.8e-118) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (y5 <= -1.7e-233) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (y5 <= 1e-284) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (y5 <= 1.15e+140) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else {
		tmp = i * (y5 * ((y * k) - (t * j)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y5 <= (-4.8d-118)) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else if (y5 <= (-1.7d-233)) then
        tmp = b * (y * ((x * a) - (k * y4)))
    else if (y5 <= 1d-284) then
        tmp = a * (y1 * ((z * y3) - (x * y2)))
    else if (y5 <= 1.15d+140) then
        tmp = i * (y1 * ((x * j) - (z * k)))
    else
        tmp = i * (y5 * ((y * k) - (t * j)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -4.8e-118) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (y5 <= -1.7e-233) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (y5 <= 1e-284) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (y5 <= 1.15e+140) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else {
		tmp = i * (y5 * ((y * k) - (t * j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y5 <= -4.8e-118:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	elif y5 <= -1.7e-233:
		tmp = b * (y * ((x * a) - (k * y4)))
	elif y5 <= 1e-284:
		tmp = a * (y1 * ((z * y3) - (x * y2)))
	elif y5 <= 1.15e+140:
		tmp = i * (y1 * ((x * j) - (z * k)))
	else:
		tmp = i * (y5 * ((y * k) - (t * j)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y5 <= -4.8e-118)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (y5 <= -1.7e-233)
		tmp = Float64(b * Float64(y * Float64(Float64(x * a) - Float64(k * y4))));
	elseif (y5 <= 1e-284)
		tmp = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))));
	elseif (y5 <= 1.15e+140)
		tmp = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))));
	else
		tmp = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y5 <= -4.8e-118)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	elseif (y5 <= -1.7e-233)
		tmp = b * (y * ((x * a) - (k * y4)));
	elseif (y5 <= 1e-284)
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	elseif (y5 <= 1.15e+140)
		tmp = i * (y1 * ((x * j) - (z * k)));
	else
		tmp = i * (y5 * ((y * k) - (t * j)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y5, -4.8e-118], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.7e-233], N[(b * N[(y * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1e-284], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.15e+140], N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y5 < -4.8000000000000003e-118

   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 y4 around inf 39.1%

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

   4. Taylor expanded in c around inf 40.6%

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

   if -4.8000000000000003e-118 < y5 < -1.7000000000000001e-233

   1. Initial program 45.5%

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

   3. Taylor expanded in b around inf 51.2%

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

   4. Taylor expanded in y around inf 55.8%

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

      1. +-commutative 55.8%

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

      2. mul-1-neg 55.8%

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

      3. unsub-neg 55.8%

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

   6. Simplified 55.8%

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

   if -1.7000000000000001e-233 < y5 < 1.00000000000000004e-284

   1. Initial program 46.2%

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

   3. Taylor expanded in y1 around inf 61.7%

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

   4. Taylor expanded in a around inf 51.4%

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

      1. mul-1-neg 51.4%

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

   6. Simplified 51.4%

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

   if 1.00000000000000004e-284 < y5 < 1.14999999999999995e140

   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 y1 around inf 46.8%

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

   4. Taylor expanded in i around inf 39.1%

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

   if 1.14999999999999995e140 < y5

   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 i around -inf 43.7%

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

   4. Taylor expanded in y5 around inf 65.5%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 46.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -4.8 \cdot 10^{-118}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq -1.7 \cdot 10^{-233}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 10^{-284}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 1.15 \cdot 10^{+140}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 28.5% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y5 \leq -1.45 \cdot 10^{-120}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq -1.35 \cdot 10^{-238}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 6.5 \cdot 10^{-285}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 4.6 \cdot 10^{+112}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y5 -1.45e-120)
   (* c (* y4 (- (* y y3) (* t y2))))
   (if (<= y5 -1.35e-238)
     (* b (* y (- (* x a) (* k y4))))
     (if (<= y5 6.5e-285)
       (* a (* y1 (- (* z y3) (* x y2))))
       (if (<= y5 4.6e+112)
         (* i (* y1 (- (* x j) (* z k))))
         (* i (* y (- (* k y5) (* x c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -1.45e-120) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (y5 <= -1.35e-238) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (y5 <= 6.5e-285) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (y5 <= 4.6e+112) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else {
		tmp = i * (y * ((k * y5) - (x * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y5 <= (-1.45d-120)) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else if (y5 <= (-1.35d-238)) then
        tmp = b * (y * ((x * a) - (k * y4)))
    else if (y5 <= 6.5d-285) then
        tmp = a * (y1 * ((z * y3) - (x * y2)))
    else if (y5 <= 4.6d+112) then
        tmp = i * (y1 * ((x * j) - (z * k)))
    else
        tmp = i * (y * ((k * y5) - (x * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -1.45e-120) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (y5 <= -1.35e-238) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (y5 <= 6.5e-285) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (y5 <= 4.6e+112) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else {
		tmp = i * (y * ((k * y5) - (x * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y5 <= -1.45e-120:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	elif y5 <= -1.35e-238:
		tmp = b * (y * ((x * a) - (k * y4)))
	elif y5 <= 6.5e-285:
		tmp = a * (y1 * ((z * y3) - (x * y2)))
	elif y5 <= 4.6e+112:
		tmp = i * (y1 * ((x * j) - (z * k)))
	else:
		tmp = i * (y * ((k * y5) - (x * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y5 <= -1.45e-120)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (y5 <= -1.35e-238)
		tmp = Float64(b * Float64(y * Float64(Float64(x * a) - Float64(k * y4))));
	elseif (y5 <= 6.5e-285)
		tmp = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))));
	elseif (y5 <= 4.6e+112)
		tmp = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))));
	else
		tmp = Float64(i * Float64(y * Float64(Float64(k * y5) - Float64(x * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y5 <= -1.45e-120)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	elseif (y5 <= -1.35e-238)
		tmp = b * (y * ((x * a) - (k * y4)));
	elseif (y5 <= 6.5e-285)
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	elseif (y5 <= 4.6e+112)
		tmp = i * (y1 * ((x * j) - (z * k)));
	else
		tmp = i * (y * ((k * y5) - (x * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y5, -1.45e-120], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.35e-238], N[(b * N[(y * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 6.5e-285], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 4.6e+112], N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(y * N[(N[(k * y5), $MachinePrecision] - N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y5 < -1.45e-120

   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 y4 around inf 39.1%

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

   4. Taylor expanded in c around inf 40.6%

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

   if -1.45e-120 < y5 < -1.34999999999999995e-238

   1. Initial program 45.5%

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

   3. Taylor expanded in b around inf 51.2%

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

   4. Taylor expanded in y around inf 55.8%

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

      1. +-commutative 55.8%

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

      2. mul-1-neg 55.8%

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

      3. unsub-neg 55.8%

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

   6. Simplified 55.8%

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

   if -1.34999999999999995e-238 < y5 < 6.5e-285

   1. Initial program 46.2%

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

   3. Taylor expanded in y1 around inf 61.7%

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

   4. Taylor expanded in a around inf 51.4%

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

      1. mul-1-neg 51.4%

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

   6. Simplified 51.4%

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

   if 6.5e-285 < y5 < 4.5999999999999999e112

   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 46.1%

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

   4. Taylor expanded in i around inf 39.3%

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

   if 4.5999999999999999e112 < y5

   1. Initial program 25.0%

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

   3. Taylor expanded in i around -inf 45.5%

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

   4. Taylor expanded in y around inf 60.4%

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

      1. +-commutative 60.4%

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

      2. mul-1-neg 60.4%

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

      3. unsub-neg 60.4%

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

   6. Simplified 60.4%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(y \cdot \left(c \cdot x - k \cdot y5\right)\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -1.45 \cdot 10^{-120}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq -1.35 \cdot 10^{-238}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 6.5 \cdot 10^{-285}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 4.6 \cdot 10^{+112}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 31.4% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -4.3 \cdot 10^{+95}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -9.5 \cdot 10^{-90}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 4.1 \cdot 10^{-14}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y2 \leq 2.25 \cdot 10^{+89}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -4.3e+95)
   (* c (* y4 (- (* y y3) (* t y2))))
   (if (<= y2 -9.5e-90)
     (* j (* y4 (- (* t b) (* y1 y3))))
     (if (<= y2 4.1e-14)
       (* a (* b (- (* x y) (* z t))))
       (if (<= y2 2.25e+89)
         (* c (* x (- (* y0 y2) (* y i))))
         (* y1 (* y2 (- (* k y4) (* x a)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -4.3e+95) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (y2 <= -9.5e-90) {
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	} else if (y2 <= 4.1e-14) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y2 <= 2.25e+89) {
		tmp = c * (x * ((y0 * y2) - (y * i)));
	} else {
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y2 <= (-4.3d+95)) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else if (y2 <= (-9.5d-90)) then
        tmp = j * (y4 * ((t * b) - (y1 * y3)))
    else if (y2 <= 4.1d-14) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (y2 <= 2.25d+89) then
        tmp = c * (x * ((y0 * y2) - (y * i)))
    else
        tmp = y1 * (y2 * ((k * y4) - (x * a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -4.3e+95) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (y2 <= -9.5e-90) {
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	} else if (y2 <= 4.1e-14) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y2 <= 2.25e+89) {
		tmp = c * (x * ((y0 * y2) - (y * i)));
	} else {
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y2 <= -4.3e+95:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	elif y2 <= -9.5e-90:
		tmp = j * (y4 * ((t * b) - (y1 * y3)))
	elif y2 <= 4.1e-14:
		tmp = a * (b * ((x * y) - (z * t)))
	elif y2 <= 2.25e+89:
		tmp = c * (x * ((y0 * y2) - (y * i)))
	else:
		tmp = y1 * (y2 * ((k * y4) - (x * a)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y2 <= -4.3e+95)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (y2 <= -9.5e-90)
		tmp = Float64(j * Float64(y4 * Float64(Float64(t * b) - Float64(y1 * y3))));
	elseif (y2 <= 4.1e-14)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y2 <= 2.25e+89)
		tmp = Float64(c * Float64(x * Float64(Float64(y0 * y2) - Float64(y * i))));
	else
		tmp = Float64(y1 * Float64(y2 * Float64(Float64(k * y4) - Float64(x * a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y2 <= -4.3e+95)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	elseif (y2 <= -9.5e-90)
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	elseif (y2 <= 4.1e-14)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (y2 <= 2.25e+89)
		tmp = c * (x * ((y0 * y2) - (y * i)));
	else
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y2, -4.3e+95], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -9.5e-90], N[(j * N[(y4 * N[(N[(t * b), $MachinePrecision] - N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 4.1e-14], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.25e+89], N[(c * N[(x * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(y2 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y2 < -4.3e95

   1. Initial program 33.3%

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

   3. Taylor expanded in y4 around inf 41.9%

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

   4. Taylor expanded in c around inf 48.3%

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

   if -4.3e95 < y2 < -9.5000000000000003e-90

   1. Initial program 23.5%

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

   3. Taylor expanded in y4 around inf 41.5%

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

   4. Taylor expanded in j around inf 50.9%

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

      1. +-commutative 50.9%

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

      2. mul-1-neg 50.9%

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

      3. unsub-neg 50.9%

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

   6. Simplified 50.9%

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

   if -9.5000000000000003e-90 < y2 < 4.1000000000000002e-14

   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 b around inf 33.8%

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

   4. Taylor expanded in a around inf 36.1%

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

   if 4.1000000000000002e-14 < y2 < 2.25e89

   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 c around inf 46.9%

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

   4. Taylor expanded in x around inf 41.9%

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

      1. +-commutative 41.9%

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

      2. mul-1-neg 41.9%

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

      3. unsub-neg 41.9%

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

   6. Simplified 41.9%

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

   if 2.25e89 < y2

   1. Initial program 32.8%

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

   3. Taylor expanded in y1 around inf 47.7%

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

   4. Taylor expanded in y2 around inf 58.5%

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

      1. +-commutative 58.5%

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

      2. mul-1-neg 58.5%

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

      3. unsub-neg 58.5%

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

   6. Simplified 58.5%

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

4. Final simplification 44.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -4.3 \cdot 10^{+95}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -9.5 \cdot 10^{-90}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 4.1 \cdot 10^{-14}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y2 \leq 2.25 \cdot 10^{+89}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 30.6% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;y2 \leq -1.12 \cdot 10^{+94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y2 \leq -2.6 \cdot 10^{-89}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 2.6 \cdot 10^{-10}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y2 \leq 4 \cdot 10^{+159}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y4 (- (* y y3) (* t y2))))))
   (if (<= y2 -1.12e+94)
     t_1
     (if (<= y2 -2.6e-89)
       (* j (* y4 (- (* t b) (* y1 y3))))
       (if (<= y2 2.6e-10)
         (* a (* b (- (* x y) (* z t))))
         (if (<= y2 4e+159) t_1 (* x (* y2 (- (* 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 t_1 = c * (y4 * ((y * y3) - (t * y2)));
	double tmp;
	if (y2 <= -1.12e+94) {
		tmp = t_1;
	} else if (y2 <= -2.6e-89) {
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	} else if (y2 <= 2.6e-10) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y2 <= 4e+159) {
		tmp = t_1;
	} else {
		tmp = x * (y2 * ((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) :: t_1
    real(8) :: tmp
    t_1 = c * (y4 * ((y * y3) - (t * y2)))
    if (y2 <= (-1.12d+94)) then
        tmp = t_1
    else if (y2 <= (-2.6d-89)) then
        tmp = j * (y4 * ((t * b) - (y1 * y3)))
    else if (y2 <= 2.6d-10) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (y2 <= 4d+159) then
        tmp = t_1
    else
        tmp = x * (y2 * ((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 t_1 = c * (y4 * ((y * y3) - (t * y2)));
	double tmp;
	if (y2 <= -1.12e+94) {
		tmp = t_1;
	} else if (y2 <= -2.6e-89) {
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	} else if (y2 <= 2.6e-10) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y2 <= 4e+159) {
		tmp = t_1;
	} else {
		tmp = x * (y2 * ((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):
	t_1 = c * (y4 * ((y * y3) - (t * y2)))
	tmp = 0
	if y2 <= -1.12e+94:
		tmp = t_1
	elif y2 <= -2.6e-89:
		tmp = j * (y4 * ((t * b) - (y1 * y3)))
	elif y2 <= 2.6e-10:
		tmp = a * (b * ((x * y) - (z * t)))
	elif y2 <= 4e+159:
		tmp = t_1
	else:
		tmp = x * (y2 * ((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)
	t_1 = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))))
	tmp = 0.0
	if (y2 <= -1.12e+94)
		tmp = t_1;
	elseif (y2 <= -2.6e-89)
		tmp = Float64(j * Float64(y4 * Float64(Float64(t * b) - Float64(y1 * y3))));
	elseif (y2 <= 2.6e-10)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y2 <= 4e+159)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(y2 * 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)
	t_1 = c * (y4 * ((y * y3) - (t * y2)));
	tmp = 0.0;
	if (y2 <= -1.12e+94)
		tmp = t_1;
	elseif (y2 <= -2.6e-89)
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	elseif (y2 <= 2.6e-10)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (y2 <= 4e+159)
		tmp = t_1;
	else
		tmp = x * (y2 * ((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_] := Block[{t$95$1 = N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -1.12e+94], t$95$1, If[LessEqual[y2, -2.6e-89], N[(j * N[(y4 * N[(N[(t * b), $MachinePrecision] - N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.6e-10], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 4e+159], t$95$1, N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y2 < -1.11999999999999996e94 or 2.59999999999999981e-10 < y2 < 3.9999999999999997e159

   1. Initial program 35.0%

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

   3. Taylor expanded in y4 around inf 42.9%

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

   4. Taylor expanded in c around inf 44.9%

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

   if -1.11999999999999996e94 < y2 < -2.5999999999999999e-89

   1. Initial program 23.5%

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

   3. Taylor expanded in y4 around inf 41.5%

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

   4. Taylor expanded in j around inf 50.9%

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

      1. +-commutative 50.9%

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

      2. mul-1-neg 50.9%

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

      3. unsub-neg 50.9%

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

   6. Simplified 50.9%

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

   if -2.5999999999999999e-89 < y2 < 2.59999999999999981e-10

   1. Initial program 34.0%

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

   3. Taylor expanded in b around inf 35.0%

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

   4. Taylor expanded in a around inf 36.4%

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

   if 3.9999999999999997e159 < y2

   1. Initial program 23.7%

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

   3. Taylor expanded in x around inf 57.5%

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

   4. Taylor expanded in y2 around inf 64.4%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.12 \cdot 10^{+94}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -2.6 \cdot 10^{-89}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 2.6 \cdot 10^{-10}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y2 \leq 4 \cdot 10^{+159}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 29.3% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;y2 \leq -6.8 \cdot 10^{+94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y2 \leq -5.8 \cdot 10^{-95}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 1.15 \cdot 10^{-10}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y2 \leq 1.9 \cdot 10^{+132}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y1 \cdot \left(-y2\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y4 (- (* y y3) (* t y2))))))
   (if (<= y2 -6.8e+94)
     t_1
     (if (<= y2 -5.8e-95)
       (* j (* y4 (- (* t b) (* y1 y3))))
       (if (<= y2 1.15e-10)
         (* a (* b (- (* x y) (* z t))))
         (if (<= y2 1.9e+132) t_1 (* a (* x (* y1 (- y2))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y4 * ((y * y3) - (t * y2)));
	double tmp;
	if (y2 <= -6.8e+94) {
		tmp = t_1;
	} else if (y2 <= -5.8e-95) {
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	} else if (y2 <= 1.15e-10) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y2 <= 1.9e+132) {
		tmp = t_1;
	} else {
		tmp = a * (x * (y1 * -y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (y4 * ((y * y3) - (t * y2)))
    if (y2 <= (-6.8d+94)) then
        tmp = t_1
    else if (y2 <= (-5.8d-95)) then
        tmp = j * (y4 * ((t * b) - (y1 * y3)))
    else if (y2 <= 1.15d-10) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (y2 <= 1.9d+132) then
        tmp = t_1
    else
        tmp = a * (x * (y1 * -y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y4 * ((y * y3) - (t * y2)));
	double tmp;
	if (y2 <= -6.8e+94) {
		tmp = t_1;
	} else if (y2 <= -5.8e-95) {
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	} else if (y2 <= 1.15e-10) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y2 <= 1.9e+132) {
		tmp = t_1;
	} else {
		tmp = a * (x * (y1 * -y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (y4 * ((y * y3) - (t * y2)))
	tmp = 0
	if y2 <= -6.8e+94:
		tmp = t_1
	elif y2 <= -5.8e-95:
		tmp = j * (y4 * ((t * b) - (y1 * y3)))
	elif y2 <= 1.15e-10:
		tmp = a * (b * ((x * y) - (z * t)))
	elif y2 <= 1.9e+132:
		tmp = t_1
	else:
		tmp = a * (x * (y1 * -y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))))
	tmp = 0.0
	if (y2 <= -6.8e+94)
		tmp = t_1;
	elseif (y2 <= -5.8e-95)
		tmp = Float64(j * Float64(y4 * Float64(Float64(t * b) - Float64(y1 * y3))));
	elseif (y2 <= 1.15e-10)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y2 <= 1.9e+132)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(x * Float64(y1 * Float64(-y2))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (y4 * ((y * y3) - (t * y2)));
	tmp = 0.0;
	if (y2 <= -6.8e+94)
		tmp = t_1;
	elseif (y2 <= -5.8e-95)
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	elseif (y2 <= 1.15e-10)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (y2 <= 1.9e+132)
		tmp = t_1;
	else
		tmp = a * (x * (y1 * -y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -6.8e+94], t$95$1, If[LessEqual[y2, -5.8e-95], N[(j * N[(y4 * N[(N[(t * b), $MachinePrecision] - N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.15e-10], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.9e+132], t$95$1, N[(a * N[(x * N[(y1 * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y2 < -6.8000000000000004e94 or 1.15000000000000004e-10 < y2 < 1.90000000000000003e132

   1. Initial program 35.2%

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

   3. Taylor expanded in y4 around inf 42.6%

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

   4. Taylor expanded in c around inf 43.5%

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

   if -6.8000000000000004e94 < y2 < -5.80000000000000004e-95

   1. Initial program 23.5%

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

   3. Taylor expanded in y4 around inf 41.5%

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

   4. Taylor expanded in j around inf 50.9%

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

      1. +-commutative 50.9%

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

      2. mul-1-neg 50.9%

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

      3. unsub-neg 50.9%

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

   6. Simplified 50.9%

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

   if -5.80000000000000004e-95 < y2 < 1.15000000000000004e-10

   1. Initial program 34.0%

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

   3. Taylor expanded in b around inf 35.0%

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

   4. Taylor expanded in a around inf 36.4%

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

   if 1.90000000000000003e132 < y2

   1. Initial program 25.9%

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

   3. Taylor expanded in y1 around inf 51.0%

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

   4. Taylor expanded in y2 around inf 61.1%

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

      1. +-commutative 61.1%

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

      2. mul-1-neg 61.1%

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

      3. unsub-neg 61.1%

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

   6. Simplified 61.1%

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

   7. Taylor expanded in k around 0 57.4%

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

      1. mul-1-neg 57.4%

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

      2. *-commutative 57.4%

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

      3. distribute-rgt-neg-in 57.4%

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

   9. Simplified 57.4%

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

4. Final simplification 43.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -6.8 \cdot 10^{+94}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -5.8 \cdot 10^{-95}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 1.15 \cdot 10^{-10}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y2 \leq 1.9 \cdot 10^{+132}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y1 \cdot \left(-y2\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 29.2% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{if}\;i \leq -2.9 \cdot 10^{+242}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq -8.5 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -4.8 \cdot 10^{-168}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;i \leq 6.2 \cdot 10^{+46}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* x (- (* y0 y2) (* y i))))))
   (if (<= i -2.9e+242)
     (* b (* j (- (* t y4) (* x y0))))
     (if (<= i -8.5e+49)
       t_1
       (if (<= i -4.8e-168)
         (* a (* b (- (* x y) (* z t))))
         (if (<= i 6.2e+46) (* b (* x (- (* y a) (* j y0)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (x * ((y0 * y2) - (y * i)));
	double tmp;
	if (i <= -2.9e+242) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (i <= -8.5e+49) {
		tmp = t_1;
	} else if (i <= -4.8e-168) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (i <= 6.2e+46) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (x * ((y0 * y2) - (y * i)))
    if (i <= (-2.9d+242)) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (i <= (-8.5d+49)) then
        tmp = t_1
    else if (i <= (-4.8d-168)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (i <= 6.2d+46) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (x * ((y0 * y2) - (y * i)));
	double tmp;
	if (i <= -2.9e+242) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (i <= -8.5e+49) {
		tmp = t_1;
	} else if (i <= -4.8e-168) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (i <= 6.2e+46) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (x * ((y0 * y2) - (y * i)))
	tmp = 0
	if i <= -2.9e+242:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif i <= -8.5e+49:
		tmp = t_1
	elif i <= -4.8e-168:
		tmp = a * (b * ((x * y) - (z * t)))
	elif i <= 6.2e+46:
		tmp = b * (x * ((y * a) - (j * y0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(x * Float64(Float64(y0 * y2) - Float64(y * i))))
	tmp = 0.0
	if (i <= -2.9e+242)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (i <= -8.5e+49)
		tmp = t_1;
	elseif (i <= -4.8e-168)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (i <= 6.2e+46)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (x * ((y0 * y2) - (y * i)));
	tmp = 0.0;
	if (i <= -2.9e+242)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (i <= -8.5e+49)
		tmp = t_1;
	elseif (i <= -4.8e-168)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (i <= 6.2e+46)
		tmp = b * (x * ((y * a) - (j * y0)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(x * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.9e+242], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -8.5e+49], t$95$1, If[LessEqual[i, -4.8e-168], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 6.2e+46], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -2.89999999999999997e242

   1. Initial program 14.3%

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

   3. Taylor expanded in b around inf 57.9%

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

   4. Taylor expanded in j around inf 51.4%

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

   if -2.89999999999999997e242 < i < -8.4999999999999996e49 or 6.1999999999999995e46 < i

   1. Initial program 23.8%

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

   3. Taylor expanded in c around inf 44.4%

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

   4. Taylor expanded in x around inf 45.3%

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

      1. +-commutative 45.3%

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

      2. mul-1-neg 45.3%

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

      3. unsub-neg 45.3%

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

   6. Simplified 45.3%

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

   if -8.4999999999999996e49 < i < -4.7999999999999999e-168

   1. Initial program 37.9%

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

   3. Taylor expanded in b around inf 42.5%

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

   4. Taylor expanded in a around inf 35.2%

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

   if -4.7999999999999999e-168 < i < 6.1999999999999995e46

   1. Initial program 37.3%

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

   3. Taylor expanded in b around inf 36.2%

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

   4. Taylor expanded in x around inf 39.0%

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

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.9 \cdot 10^{+242}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq -8.5 \cdot 10^{+49}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;i \leq -4.8 \cdot 10^{-168}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;i \leq 6.2 \cdot 10^{+46}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 28.0% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.1 \cdot 10^{+54}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq -1.3 \cdot 10^{-116}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 1.9 \cdot 10^{+17}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 5.8 \cdot 10^{+142}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -1.1e+54)
   (* b (* j (- (* t y4) (* x y0))))
   (if (<= j -1.3e-116)
     (* a (* t (* y2 y5)))
     (if (<= j 1.9e+17)
       (* b (* y (- (* x a) (* k y4))))
       (if (<= j 5.8e+142)
         (* b (* y0 (- (* z k) (* x j))))
         (* a (* b (- (* x y) (* z t)))))))))

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 (j <= -1.1e+54) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (j <= -1.3e-116) {
		tmp = a * (t * (y2 * y5));
	} else if (j <= 1.9e+17) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (j <= 5.8e+142) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else {
		tmp = a * (b * ((x * y) - (z * t)));
	}
	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 (j <= (-1.1d+54)) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (j <= (-1.3d-116)) then
        tmp = a * (t * (y2 * y5))
    else if (j <= 1.9d+17) then
        tmp = b * (y * ((x * a) - (k * y4)))
    else if (j <= 5.8d+142) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else
        tmp = a * (b * ((x * y) - (z * t)))
    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 (j <= -1.1e+54) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (j <= -1.3e-116) {
		tmp = a * (t * (y2 * y5));
	} else if (j <= 1.9e+17) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (j <= 5.8e+142) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else {
		tmp = a * (b * ((x * y) - (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if j <= -1.1e+54:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif j <= -1.3e-116:
		tmp = a * (t * (y2 * y5))
	elif j <= 1.9e+17:
		tmp = b * (y * ((x * a) - (k * y4)))
	elif j <= 5.8e+142:
		tmp = b * (y0 * ((z * k) - (x * j)))
	else:
		tmp = a * (b * ((x * y) - (z * t)))
	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 (j <= -1.1e+54)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (j <= -1.3e-116)
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	elseif (j <= 1.9e+17)
		tmp = Float64(b * Float64(y * Float64(Float64(x * a) - Float64(k * y4))));
	elseif (j <= 5.8e+142)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	else
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	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 (j <= -1.1e+54)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (j <= -1.3e-116)
		tmp = a * (t * (y2 * y5));
	elseif (j <= 1.9e+17)
		tmp = b * (y * ((x * a) - (k * y4)));
	elseif (j <= 5.8e+142)
		tmp = b * (y0 * ((z * k) - (x * j)));
	else
		tmp = a * (b * ((x * y) - (z * t)));
	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[j, -1.1e+54], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.3e-116], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.9e+17], N[(b * N[(y * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.8e+142], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -1.09999999999999995e54

   1. Initial program 16.2%

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

   3. Taylor expanded in b around inf 44.4%

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

   4. Taylor expanded in j around inf 44.5%

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

   if -1.09999999999999995e54 < j < -1.3e-116

   1. Initial program 35.6%

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

   3. Taylor expanded in y5 around -inf 52.0%

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

   4. Taylor expanded in t around inf 46.7%

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

   5. Taylor expanded in i around 0 40.2%

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

   if -1.3e-116 < j < 1.9e17

   1. Initial program 44.6%

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

   3. Taylor expanded in b around inf 30.3%

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

   4. Taylor expanded in y around inf 35.3%

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

      1. +-commutative 35.3%

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

      2. mul-1-neg 35.3%

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

      3. unsub-neg 35.3%

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

   6. Simplified 35.3%

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

   if 1.9e17 < j < 5.80000000000000027e142

   1. Initial program 33.3%

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

   3. Taylor expanded in b around inf 52.8%

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

   4. Taylor expanded in y0 around inf 56.5%

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

   if 5.80000000000000027e142 < j

   1. Initial program 15.8%

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

   3. Taylor expanded in b around inf 27.1%

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

   4. Taylor expanded in a around inf 38.1%

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

4. Final simplification 40.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.1 \cdot 10^{+54}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq -1.3 \cdot 10^{-116}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 1.9 \cdot 10^{+17}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 5.8 \cdot 10^{+142}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 28.1% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{if}\;y0 \leq -1.6 \cdot 10^{+160}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y0 \leq -1.45 \cdot 10^{+56}:\\ \;\;\;\;j \cdot \left(\left(y1 \cdot y3\right) \cdot \left(-y4\right)\right)\\ \mathbf{elif}\;y0 \leq -6.7 \cdot 10^{-245}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 9.5 \cdot 10^{+208}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* j (- (* t y4) (* x y0))))))
   (if (<= y0 -1.6e+160)
     t_1
     (if (<= y0 -1.45e+56)
       (* j (* (* y1 y3) (- y4)))
       (if (<= y0 -6.7e-245)
         (* b (* y (- (* x a) (* k y4))))
         (if (<= y0 9.5e+208) (* 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 = b * (j * ((t * y4) - (x * y0)));
	double tmp;
	if (y0 <= -1.6e+160) {
		tmp = t_1;
	} else if (y0 <= -1.45e+56) {
		tmp = j * ((y1 * y3) * -y4);
	} else if (y0 <= -6.7e-245) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (y0 <= 9.5e+208) {
		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 = b * (j * ((t * y4) - (x * y0)))
    if (y0 <= (-1.6d+160)) then
        tmp = t_1
    else if (y0 <= (-1.45d+56)) then
        tmp = j * ((y1 * y3) * -y4)
    else if (y0 <= (-6.7d-245)) then
        tmp = b * (y * ((x * a) - (k * y4)))
    else if (y0 <= 9.5d+208) 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 = b * (j * ((t * y4) - (x * y0)));
	double tmp;
	if (y0 <= -1.6e+160) {
		tmp = t_1;
	} else if (y0 <= -1.45e+56) {
		tmp = j * ((y1 * y3) * -y4);
	} else if (y0 <= -6.7e-245) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (y0 <= 9.5e+208) {
		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 = b * (j * ((t * y4) - (x * y0)))
	tmp = 0
	if y0 <= -1.6e+160:
		tmp = t_1
	elif y0 <= -1.45e+56:
		tmp = j * ((y1 * y3) * -y4)
	elif y0 <= -6.7e-245:
		tmp = b * (y * ((x * a) - (k * y4)))
	elif y0 <= 9.5e+208:
		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(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))))
	tmp = 0.0
	if (y0 <= -1.6e+160)
		tmp = t_1;
	elseif (y0 <= -1.45e+56)
		tmp = Float64(j * Float64(Float64(y1 * y3) * Float64(-y4)));
	elseif (y0 <= -6.7e-245)
		tmp = Float64(b * Float64(y * Float64(Float64(x * a) - Float64(k * y4))));
	elseif (y0 <= 9.5e+208)
		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 = b * (j * ((t * y4) - (x * y0)));
	tmp = 0.0;
	if (y0 <= -1.6e+160)
		tmp = t_1;
	elseif (y0 <= -1.45e+56)
		tmp = j * ((y1 * y3) * -y4);
	elseif (y0 <= -6.7e-245)
		tmp = b * (y * ((x * a) - (k * y4)));
	elseif (y0 <= 9.5e+208)
		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[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -1.6e+160], t$95$1, If[LessEqual[y0, -1.45e+56], N[(j * N[(N[(y1 * y3), $MachinePrecision] * (-y4)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -6.7e-245], N[(b * N[(y * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 9.5e+208], 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 y0 < -1.5999999999999999e160 or 9.4999999999999996e208 < y0

   1. Initial program 31.9%

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

   3. Taylor expanded in b around inf 36.7%

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

   4. Taylor expanded in j around inf 49.6%

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

   if -1.5999999999999999e160 < y0 < -1.45000000000000004e56

   1. Initial program 31.9%

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

   3. Taylor expanded in y1 around inf 48.7%

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

   4. Taylor expanded in j around -inf 57.1%

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

      1. associate-*r* 57.1%

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

      2. mul-1-neg 57.1%

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

   6. Simplified 57.1%

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

   7. Taylor expanded in y3 around inf 53.0%

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

      1. associate-*r* 53.0%

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

      2. neg-mul-1 53.0%

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

      3. associate-*r* 53.1%

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

      4. *-commutative 53.1%

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

   9. Simplified 53.1%

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

   if -1.45000000000000004e56 < y0 < -6.7e-245

   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 b around inf 42.0%

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

   4. Taylor expanded in y around inf 39.5%

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

      1. +-commutative 39.5%

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

      2. mul-1-neg 39.5%

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

      3. unsub-neg 39.5%

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

   6. Simplified 39.5%

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

   if -6.7e-245 < y0 < 9.4999999999999996e208

   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 36.1%

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

   4. Taylor expanded in a around inf 34.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 40.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -1.6 \cdot 10^{+160}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -1.45 \cdot 10^{+56}:\\ \;\;\;\;j \cdot \left(\left(y1 \cdot y3\right) \cdot \left(-y4\right)\right)\\ \mathbf{elif}\;y0 \leq -6.7 \cdot 10^{-245}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 9.5 \cdot 10^{+208}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 22.5% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{+33}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-82}:\\ \;\;\;\;c \cdot \left(z \cdot \left(y0 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-278}:\\ \;\;\;\;i \cdot \left(j \cdot \left(t \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;x \leq 0.2:\\ \;\;\;\;j \cdot \left(\left(y1 \cdot y3\right) \cdot \left(-y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(x \cdot \left(-y2\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -7.8e+33)
   (* a (* y (* x b)))
   (if (<= x -1.7e-82)
     (* c (* z (* y0 (- y3))))
     (if (<= x -1.35e-278)
       (* i (* j (* t (- y5))))
       (if (<= x 0.2) (* j (* (* y1 y3) (- y4))) (* y1 (* a (* x (- y2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -7.8e+33) {
		tmp = a * (y * (x * b));
	} else if (x <= -1.7e-82) {
		tmp = c * (z * (y0 * -y3));
	} else if (x <= -1.35e-278) {
		tmp = i * (j * (t * -y5));
	} else if (x <= 0.2) {
		tmp = j * ((y1 * y3) * -y4);
	} else {
		tmp = y1 * (a * (x * -y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (x <= (-7.8d+33)) then
        tmp = a * (y * (x * b))
    else if (x <= (-1.7d-82)) then
        tmp = c * (z * (y0 * -y3))
    else if (x <= (-1.35d-278)) then
        tmp = i * (j * (t * -y5))
    else if (x <= 0.2d0) then
        tmp = j * ((y1 * y3) * -y4)
    else
        tmp = y1 * (a * (x * -y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -7.8e+33) {
		tmp = a * (y * (x * b));
	} else if (x <= -1.7e-82) {
		tmp = c * (z * (y0 * -y3));
	} else if (x <= -1.35e-278) {
		tmp = i * (j * (t * -y5));
	} else if (x <= 0.2) {
		tmp = j * ((y1 * y3) * -y4);
	} else {
		tmp = y1 * (a * (x * -y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if x <= -7.8e+33:
		tmp = a * (y * (x * b))
	elif x <= -1.7e-82:
		tmp = c * (z * (y0 * -y3))
	elif x <= -1.35e-278:
		tmp = i * (j * (t * -y5))
	elif x <= 0.2:
		tmp = j * ((y1 * y3) * -y4)
	else:
		tmp = y1 * (a * (x * -y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (x <= -7.8e+33)
		tmp = Float64(a * Float64(y * Float64(x * b)));
	elseif (x <= -1.7e-82)
		tmp = Float64(c * Float64(z * Float64(y0 * Float64(-y3))));
	elseif (x <= -1.35e-278)
		tmp = Float64(i * Float64(j * Float64(t * Float64(-y5))));
	elseif (x <= 0.2)
		tmp = Float64(j * Float64(Float64(y1 * y3) * Float64(-y4)));
	else
		tmp = Float64(y1 * Float64(a * Float64(x * Float64(-y2))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (x <= -7.8e+33)
		tmp = a * (y * (x * b));
	elseif (x <= -1.7e-82)
		tmp = c * (z * (y0 * -y3));
	elseif (x <= -1.35e-278)
		tmp = i * (j * (t * -y5));
	elseif (x <= 0.2)
		tmp = j * ((y1 * y3) * -y4);
	else
		tmp = y1 * (a * (x * -y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[x, -7.8e+33], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.7e-82], N[(c * N[(z * N[(y0 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.35e-278], N[(i * N[(j * N[(t * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.2], N[(j * N[(N[(y1 * y3), $MachinePrecision] * (-y4)), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(a * N[(x * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -7.8000000000000004e33

   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 b around inf 41.2%

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

   4. Taylor expanded in a around inf 38.0%

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

   5. Taylor expanded in x around inf 30.8%

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

      1. associate-*r* 34.7%

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

   7. Simplified 34.7%

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

   if -7.8000000000000004e33 < x < -1.69999999999999988e-82

   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 c around inf 42.8%

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

   4. Taylor expanded in z around inf 31.5%

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

      1. +-commutative 31.5%

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

      2. mul-1-neg 31.5%

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

      3. unsub-neg 31.5%

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

   6. Simplified 31.5%

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

   7. Taylor expanded in i around 0 25.5%

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

      1. neg-mul-1 25.5%

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

      2. distribute-rgt-neg-in 25.5%

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

   9. Simplified 25.5%

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

   if -1.69999999999999988e-82 < x < -1.3500000000000001e-278

   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 y5 around -inf 28.2%

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

   4. Taylor expanded in t around inf 29.3%

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

   5. Taylor expanded in i around inf 33.7%

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

      1. associate-*r* 33.7%

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

      2. mul-1-neg 33.7%

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

   7. Simplified 33.7%

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

   if -1.3500000000000001e-278 < x < 0.20000000000000001

   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 y1 around inf 35.6%

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

   4. Taylor expanded in j around -inf 23.2%

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

      1. associate-*r* 23.2%

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

      2. mul-1-neg 23.2%

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

   6. Simplified 23.2%

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

   7. Taylor expanded in y3 around inf 20.6%

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

      1. associate-*r* 20.6%

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

      2. neg-mul-1 20.6%

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

      3. associate-*r* 24.7%

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

      4. *-commutative 24.7%

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

   9. Simplified 24.7%

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

   if 0.20000000000000001 < x

   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 51.1%

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

   4. Taylor expanded in y2 around inf 41.1%

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

      1. +-commutative 41.1%

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

      2. mul-1-neg 41.1%

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

      3. unsub-neg 41.1%

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

   6. Simplified 41.1%

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

   7. Taylor expanded in k around 0 37.8%

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

      1. mul-1-neg 37.8%

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

      2. *-commutative 37.8%

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

      3. distribute-rgt-neg-in 37.8%

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

   9. Simplified 37.8%

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

4. Final simplification 31.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{+33}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-82}:\\ \;\;\;\;c \cdot \left(z \cdot \left(y0 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-278}:\\ \;\;\;\;i \cdot \left(j \cdot \left(t \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;x \leq 0.2:\\ \;\;\;\;j \cdot \left(\left(y1 \cdot y3\right) \cdot \left(-y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(x \cdot \left(-y2\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 21.9% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{if}\;y5 \leq -1.9 \cdot 10^{+129}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y5 \leq -1 \cdot 10^{-238}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y5 \leq 4.7 \cdot 10^{-120}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq 10^{-21}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* t (* y2 y5)))))
   (if (<= y5 -1.9e+129)
     t_1
     (if (<= y5 -1e-238)
       (* a (* (* x y) b))
       (if (<= y5 4.7e-120)
         (* i (* y1 (* x j)))
         (if (<= y5 1e-21) (* c (* z (* t i))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (t * (y2 * y5));
	double tmp;
	if (y5 <= -1.9e+129) {
		tmp = t_1;
	} else if (y5 <= -1e-238) {
		tmp = a * ((x * y) * b);
	} else if (y5 <= 4.7e-120) {
		tmp = i * (y1 * (x * j));
	} else if (y5 <= 1e-21) {
		tmp = c * (z * (t * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (t * (y2 * y5))
    if (y5 <= (-1.9d+129)) then
        tmp = t_1
    else if (y5 <= (-1d-238)) then
        tmp = a * ((x * y) * b)
    else if (y5 <= 4.7d-120) then
        tmp = i * (y1 * (x * j))
    else if (y5 <= 1d-21) then
        tmp = c * (z * (t * i))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (t * (y2 * y5));
	double tmp;
	if (y5 <= -1.9e+129) {
		tmp = t_1;
	} else if (y5 <= -1e-238) {
		tmp = a * ((x * y) * b);
	} else if (y5 <= 4.7e-120) {
		tmp = i * (y1 * (x * j));
	} else if (y5 <= 1e-21) {
		tmp = c * (z * (t * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (t * (y2 * y5))
	tmp = 0
	if y5 <= -1.9e+129:
		tmp = t_1
	elif y5 <= -1e-238:
		tmp = a * ((x * y) * b)
	elif y5 <= 4.7e-120:
		tmp = i * (y1 * (x * j))
	elif y5 <= 1e-21:
		tmp = c * (z * (t * i))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(t * Float64(y2 * y5)))
	tmp = 0.0
	if (y5 <= -1.9e+129)
		tmp = t_1;
	elseif (y5 <= -1e-238)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	elseif (y5 <= 4.7e-120)
		tmp = Float64(i * Float64(y1 * Float64(x * j)));
	elseif (y5 <= 1e-21)
		tmp = Float64(c * Float64(z * Float64(t * i)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (t * (y2 * y5));
	tmp = 0.0;
	if (y5 <= -1.9e+129)
		tmp = t_1;
	elseif (y5 <= -1e-238)
		tmp = a * ((x * y) * b);
	elseif (y5 <= 4.7e-120)
		tmp = i * (y1 * (x * j));
	elseif (y5 <= 1e-21)
		tmp = c * (z * (t * i));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -1.9e+129], t$95$1, If[LessEqual[y5, -1e-238], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 4.7e-120], N[(i * N[(y1 * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1e-21], N[(c * N[(z * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y5 < -1.90000000000000003e129 or 9.99999999999999908e-22 < y5

   1. Initial program 28.2%

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

   3. Taylor expanded in y5 around -inf 53.7%

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

   4. Taylor expanded in t around inf 41.7%

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

   5. Taylor expanded in i around 0 37.2%

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

   if -1.90000000000000003e129 < y5 < -9.9999999999999999e-239

   1. Initial program 27.1%

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

   3. Taylor expanded in b around inf 37.4%

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

   4. Taylor expanded in a around inf 34.0%

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

   5. Taylor expanded in x around inf 24.6%

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

   if -9.9999999999999999e-239 < y5 < 4.70000000000000016e-120

   1. Initial program 40.8%

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

   3. Taylor expanded in y1 around inf 53.3%

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

   4. Taylor expanded in j around -inf 32.9%

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

      1. associate-*r* 32.9%

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

      2. mul-1-neg 32.9%

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

   6. Simplified 32.9%

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

   7. Taylor expanded in y3 around 0 22.3%

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

      1. associate-*r* 25.1%

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

   9. Simplified 25.1%

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

   if 4.70000000000000016e-120 < y5 < 9.99999999999999908e-22

   1. Initial program 36.4%

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

   3. Taylor expanded in c around inf 37.6%

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

   4. Taylor expanded in z around inf 37.5%

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

      1. +-commutative 37.5%

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

      2. mul-1-neg 37.5%

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

      3. unsub-neg 37.5%

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

   6. Simplified 37.5%

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

   7. Taylor expanded in i around inf 33.5%

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

      1. associate-*r* 37.8%

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

      2. *-commutative 37.8%

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

   9. Simplified 37.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(t \cdot i\right) \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 30.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -1.9 \cdot 10^{+129}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq -1 \cdot 10^{-238}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y5 \leq 4.7 \cdot 10^{-120}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq 10^{-21}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 22.0% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{if}\;y5 \leq -2 \cdot 10^{+129}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y5 \leq -6.5 \cdot 10^{-239}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y5 \leq 2.1 \cdot 10^{-119}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y5 \leq 1.12 \cdot 10^{-12}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* t (* y2 y5)))))
   (if (<= y5 -2e+129)
     t_1
     (if (<= y5 -6.5e-239)
       (* a (* (* x y) b))
       (if (<= y5 2.1e-119)
         (* i (* j (* x y1)))
         (if (<= y5 1.12e-12) (* c (* z (* t i))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (t * (y2 * y5));
	double tmp;
	if (y5 <= -2e+129) {
		tmp = t_1;
	} else if (y5 <= -6.5e-239) {
		tmp = a * ((x * y) * b);
	} else if (y5 <= 2.1e-119) {
		tmp = i * (j * (x * y1));
	} else if (y5 <= 1.12e-12) {
		tmp = c * (z * (t * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (t * (y2 * y5))
    if (y5 <= (-2d+129)) then
        tmp = t_1
    else if (y5 <= (-6.5d-239)) then
        tmp = a * ((x * y) * b)
    else if (y5 <= 2.1d-119) then
        tmp = i * (j * (x * y1))
    else if (y5 <= 1.12d-12) then
        tmp = c * (z * (t * i))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (t * (y2 * y5));
	double tmp;
	if (y5 <= -2e+129) {
		tmp = t_1;
	} else if (y5 <= -6.5e-239) {
		tmp = a * ((x * y) * b);
	} else if (y5 <= 2.1e-119) {
		tmp = i * (j * (x * y1));
	} else if (y5 <= 1.12e-12) {
		tmp = c * (z * (t * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (t * (y2 * y5))
	tmp = 0
	if y5 <= -2e+129:
		tmp = t_1
	elif y5 <= -6.5e-239:
		tmp = a * ((x * y) * b)
	elif y5 <= 2.1e-119:
		tmp = i * (j * (x * y1))
	elif y5 <= 1.12e-12:
		tmp = c * (z * (t * i))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(t * Float64(y2 * y5)))
	tmp = 0.0
	if (y5 <= -2e+129)
		tmp = t_1;
	elseif (y5 <= -6.5e-239)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	elseif (y5 <= 2.1e-119)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (y5 <= 1.12e-12)
		tmp = Float64(c * Float64(z * Float64(t * i)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (t * (y2 * y5));
	tmp = 0.0;
	if (y5 <= -2e+129)
		tmp = t_1;
	elseif (y5 <= -6.5e-239)
		tmp = a * ((x * y) * b);
	elseif (y5 <= 2.1e-119)
		tmp = i * (j * (x * y1));
	elseif (y5 <= 1.12e-12)
		tmp = c * (z * (t * i));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -2e+129], t$95$1, If[LessEqual[y5, -6.5e-239], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 2.1e-119], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.12e-12], N[(c * N[(z * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y5 < -2e129 or 1.1200000000000001e-12 < y5

   1. Initial program 28.2%

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

   3. Taylor expanded in y5 around -inf 53.7%

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

   4. Taylor expanded in t around inf 41.7%

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

   5. Taylor expanded in i around 0 37.2%

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

   if -2e129 < y5 < -6.5000000000000003e-239

   1. Initial program 27.1%

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

   3. Taylor expanded in b around inf 37.4%

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

   4. Taylor expanded in a around inf 34.0%

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

   5. Taylor expanded in x around inf 24.6%

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

   if -6.5000000000000003e-239 < y5 < 2.1e-119

   1. Initial program 40.8%

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

   3. Taylor expanded in y1 around inf 53.3%

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

   4. Taylor expanded in j around -inf 32.9%

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

      1. associate-*r* 32.9%

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

      2. mul-1-neg 32.9%

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

   6. Simplified 32.9%

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

   7. Taylor expanded in y3 around 0 22.3%

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

   if 2.1e-119 < y5 < 1.1200000000000001e-12

   1. Initial program 36.4%

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

   3. Taylor expanded in c around inf 37.6%

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

   4. Taylor expanded in z around inf 37.5%

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

      1. +-commutative 37.5%

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

      2. mul-1-neg 37.5%

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

      3. unsub-neg 37.5%

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

   6. Simplified 37.5%

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

   7. Taylor expanded in i around inf 33.5%

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

      1. associate-*r* 37.8%

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

      2. *-commutative 37.8%

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

   9. Simplified 37.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(t \cdot i\right) \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 29.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -2 \cdot 10^{+129}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq -6.5 \cdot 10^{-239}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y5 \leq 2.1 \cdot 10^{-119}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y5 \leq 1.12 \cdot 10^{-12}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 29.5% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;y2 \leq -6.2 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y2 \leq 2.2 \cdot 10^{-10}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y2 \leq 4.4 \cdot 10^{+119}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y1 \cdot \left(-y2\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y4 (- (* y y3) (* t y2))))))
   (if (<= y2 -6.2e-22)
     t_1
     (if (<= y2 2.2e-10)
       (* a (* b (- (* x y) (* z t))))
       (if (<= y2 4.4e+119) t_1 (* a (* x (* y1 (- y2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y4 * ((y * y3) - (t * y2)));
	double tmp;
	if (y2 <= -6.2e-22) {
		tmp = t_1;
	} else if (y2 <= 2.2e-10) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y2 <= 4.4e+119) {
		tmp = t_1;
	} else {
		tmp = a * (x * (y1 * -y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (y4 * ((y * y3) - (t * y2)))
    if (y2 <= (-6.2d-22)) then
        tmp = t_1
    else if (y2 <= 2.2d-10) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (y2 <= 4.4d+119) then
        tmp = t_1
    else
        tmp = a * (x * (y1 * -y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y4 * ((y * y3) - (t * y2)));
	double tmp;
	if (y2 <= -6.2e-22) {
		tmp = t_1;
	} else if (y2 <= 2.2e-10) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y2 <= 4.4e+119) {
		tmp = t_1;
	} else {
		tmp = a * (x * (y1 * -y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (y4 * ((y * y3) - (t * y2)))
	tmp = 0
	if y2 <= -6.2e-22:
		tmp = t_1
	elif y2 <= 2.2e-10:
		tmp = a * (b * ((x * y) - (z * t)))
	elif y2 <= 4.4e+119:
		tmp = t_1
	else:
		tmp = a * (x * (y1 * -y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))))
	tmp = 0.0
	if (y2 <= -6.2e-22)
		tmp = t_1;
	elseif (y2 <= 2.2e-10)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y2 <= 4.4e+119)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(x * Float64(y1 * Float64(-y2))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (y4 * ((y * y3) - (t * y2)));
	tmp = 0.0;
	if (y2 <= -6.2e-22)
		tmp = t_1;
	elseif (y2 <= 2.2e-10)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (y2 <= 4.4e+119)
		tmp = t_1;
	else
		tmp = a * (x * (y1 * -y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -6.2e-22], t$95$1, If[LessEqual[y2, 2.2e-10], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 4.4e+119], t$95$1, N[(a * N[(x * N[(y1 * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y2 < -6.20000000000000025e-22 or 2.1999999999999999e-10 < y2 < 4.4000000000000003e119

   1. Initial program 31.5%

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

   3. Taylor expanded in y4 around inf 42.7%

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

   4. Taylor expanded in c around inf 42.5%

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

   if -6.20000000000000025e-22 < y2 < 2.1999999999999999e-10

   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 b around inf 34.6%

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

   4. Taylor expanded in a around inf 35.1%

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

   if 4.4000000000000003e119 < y2

   1. Initial program 25.9%

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

   3. Taylor expanded in y1 around inf 51.0%

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

   4. Taylor expanded in y2 around inf 61.1%

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

      1. +-commutative 61.1%

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

      2. mul-1-neg 61.1%

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

      3. unsub-neg 61.1%

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

   6. Simplified 61.1%

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

   7. Taylor expanded in k around 0 57.4%

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

      1. mul-1-neg 57.4%

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

      2. *-commutative 57.4%

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

      3. distribute-rgt-neg-in 57.4%

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

   9. Simplified 57.4%

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

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -6.2 \cdot 10^{-22}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 2.2 \cdot 10^{-10}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y2 \leq 4.4 \cdot 10^{+119}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y1 \cdot \left(-y2\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 28.0% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{if}\;y0 \leq -1.2 \cdot 10^{+163}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y0 \leq -1.85 \cdot 10^{+50}:\\ \;\;\;\;j \cdot \left(\left(y1 \cdot y3\right) \cdot \left(-y4\right)\right)\\ \mathbf{elif}\;y0 \leq 4.7 \cdot 10^{+209}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* j (- (* t y4) (* x y0))))))
   (if (<= y0 -1.2e+163)
     t_1
     (if (<= y0 -1.85e+50)
       (* j (* (* y1 y3) (- y4)))
       (if (<= y0 4.7e+209) (* 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 = b * (j * ((t * y4) - (x * y0)));
	double tmp;
	if (y0 <= -1.2e+163) {
		tmp = t_1;
	} else if (y0 <= -1.85e+50) {
		tmp = j * ((y1 * y3) * -y4);
	} else if (y0 <= 4.7e+209) {
		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 = b * (j * ((t * y4) - (x * y0)))
    if (y0 <= (-1.2d+163)) then
        tmp = t_1
    else if (y0 <= (-1.85d+50)) then
        tmp = j * ((y1 * y3) * -y4)
    else if (y0 <= 4.7d+209) 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 = b * (j * ((t * y4) - (x * y0)));
	double tmp;
	if (y0 <= -1.2e+163) {
		tmp = t_1;
	} else if (y0 <= -1.85e+50) {
		tmp = j * ((y1 * y3) * -y4);
	} else if (y0 <= 4.7e+209) {
		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 = b * (j * ((t * y4) - (x * y0)))
	tmp = 0
	if y0 <= -1.2e+163:
		tmp = t_1
	elif y0 <= -1.85e+50:
		tmp = j * ((y1 * y3) * -y4)
	elif y0 <= 4.7e+209:
		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(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))))
	tmp = 0.0
	if (y0 <= -1.2e+163)
		tmp = t_1;
	elseif (y0 <= -1.85e+50)
		tmp = Float64(j * Float64(Float64(y1 * y3) * Float64(-y4)));
	elseif (y0 <= 4.7e+209)
		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 = b * (j * ((t * y4) - (x * y0)));
	tmp = 0.0;
	if (y0 <= -1.2e+163)
		tmp = t_1;
	elseif (y0 <= -1.85e+50)
		tmp = j * ((y1 * y3) * -y4);
	elseif (y0 <= 4.7e+209)
		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[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -1.2e+163], t$95$1, If[LessEqual[y0, -1.85e+50], N[(j * N[(N[(y1 * y3), $MachinePrecision] * (-y4)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 4.7e+209], 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 y0 < -1.1999999999999999e163 or 4.7000000000000001e209 < y0

   1. Initial program 31.9%

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

   3. Taylor expanded in b around inf 36.7%

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

   4. Taylor expanded in j around inf 49.6%

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

   if -1.1999999999999999e163 < y0 < -1.85e50

   1. Initial program 34.6%

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

   3. Taylor expanded in y1 around inf 47.0%

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

   4. Taylor expanded in j around -inf 55.0%

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

      1. associate-*r* 55.0%

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

      2. mul-1-neg 55.0%

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

   6. Simplified 55.0%

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

   7. Taylor expanded in y3 around inf 51.1%

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

      1. associate-*r* 51.1%

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

      2. neg-mul-1 51.1%

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

      3. associate-*r* 51.1%

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

      4. *-commutative 51.1%

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

   9. Simplified 51.1%

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

   if -1.85e50 < y0 < 4.7000000000000001e209

   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 b around inf 38.2%

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

   4. Taylor expanded in a around inf 33.7%

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

4. Final simplification 38.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -1.2 \cdot 10^{+163}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -1.85 \cdot 10^{+50}:\\ \;\;\;\;j \cdot \left(\left(y1 \cdot y3\right) \cdot \left(-y4\right)\right)\\ \mathbf{elif}\;y0 \leq 4.7 \cdot 10^{+209}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 28.4% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{if}\;y2 \leq -3.35 \cdot 10^{+158}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y2 \leq 122000:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y2 \leq 1.7 \cdot 10^{+125}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y1 \cdot \left(-y2\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* t (* y2 y5)))))
   (if (<= y2 -3.35e+158)
     t_1
     (if (<= y2 122000.0)
       (* a (* b (- (* x y) (* z t))))
       (if (<= y2 1.7e+125) t_1 (* a (* x (* y1 (- y2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (t * (y2 * y5));
	double tmp;
	if (y2 <= -3.35e+158) {
		tmp = t_1;
	} else if (y2 <= 122000.0) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y2 <= 1.7e+125) {
		tmp = t_1;
	} else {
		tmp = a * (x * (y1 * -y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (t * (y2 * y5))
    if (y2 <= (-3.35d+158)) then
        tmp = t_1
    else if (y2 <= 122000.0d0) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (y2 <= 1.7d+125) then
        tmp = t_1
    else
        tmp = a * (x * (y1 * -y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (t * (y2 * y5));
	double tmp;
	if (y2 <= -3.35e+158) {
		tmp = t_1;
	} else if (y2 <= 122000.0) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y2 <= 1.7e+125) {
		tmp = t_1;
	} else {
		tmp = a * (x * (y1 * -y2));
	}
	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 y2 <= -3.35e+158:
		tmp = t_1
	elif y2 <= 122000.0:
		tmp = a * (b * ((x * y) - (z * t)))
	elif y2 <= 1.7e+125:
		tmp = t_1
	else:
		tmp = a * (x * (y1 * -y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(t * Float64(y2 * y5)))
	tmp = 0.0
	if (y2 <= -3.35e+158)
		tmp = t_1;
	elseif (y2 <= 122000.0)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y2 <= 1.7e+125)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(x * Float64(y1 * Float64(-y2))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (t * (y2 * y5));
	tmp = 0.0;
	if (y2 <= -3.35e+158)
		tmp = t_1;
	elseif (y2 <= 122000.0)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (y2 <= 1.7e+125)
		tmp = t_1;
	else
		tmp = a * (x * (y1 * -y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -3.35e+158], t$95$1, If[LessEqual[y2, 122000.0], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.7e+125], t$95$1, N[(a * N[(x * N[(y1 * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y2 < -3.3499999999999998e158 or 122000 < y2 < 1.6999999999999999e125

   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 y5 around -inf 39.7%

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

   4. Taylor expanded in t around inf 36.8%

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

   5. Taylor expanded in i around 0 36.3%

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

   if -3.3499999999999998e158 < y2 < 122000

   1. Initial program 31.4%

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

   3. Taylor expanded in b around inf 37.0%

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

   4. Taylor expanded in a around inf 33.3%

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

   if 1.6999999999999999e125 < y2

   1. Initial program 25.9%

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

   3. Taylor expanded in y1 around inf 51.0%

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

   4. Taylor expanded in y2 around inf 61.1%

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

      1. +-commutative 61.1%

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

      2. mul-1-neg 61.1%

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

      3. unsub-neg 61.1%

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

   6. Simplified 61.1%

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

   7. Taylor expanded in k around 0 57.4%

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

      1. mul-1-neg 57.4%

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

      2. *-commutative 57.4%

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

      3. distribute-rgt-neg-in 57.4%

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

   9. Simplified 57.4%

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

4. Final simplification 37.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -3.35 \cdot 10^{+158}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 122000:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y2 \leq 1.7 \cdot 10^{+125}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y1 \cdot \left(-y2\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 31: 22.9% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+32}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-63}:\\ \;\;\;\;c \cdot \left(z \cdot \left(y0 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;x \leq 0.175:\\ \;\;\;\;a \cdot \left(b \cdot \left(z \cdot \left(-t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(x \cdot \left(-y2\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -1.8e+32)
   (* a (* y (* x b)))
   (if (<= x -4e-63)
     (* c (* z (* y0 (- y3))))
     (if (<= x 0.175) (* a (* b (* z (- t)))) (* y1 (* a (* x (- y2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -1.8e+32) {
		tmp = a * (y * (x * b));
	} else if (x <= -4e-63) {
		tmp = c * (z * (y0 * -y3));
	} else if (x <= 0.175) {
		tmp = a * (b * (z * -t));
	} else {
		tmp = y1 * (a * (x * -y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (x <= (-1.8d+32)) then
        tmp = a * (y * (x * b))
    else if (x <= (-4d-63)) then
        tmp = c * (z * (y0 * -y3))
    else if (x <= 0.175d0) then
        tmp = a * (b * (z * -t))
    else
        tmp = y1 * (a * (x * -y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -1.8e+32) {
		tmp = a * (y * (x * b));
	} else if (x <= -4e-63) {
		tmp = c * (z * (y0 * -y3));
	} else if (x <= 0.175) {
		tmp = a * (b * (z * -t));
	} else {
		tmp = y1 * (a * (x * -y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if x <= -1.8e+32:
		tmp = a * (y * (x * b))
	elif x <= -4e-63:
		tmp = c * (z * (y0 * -y3))
	elif x <= 0.175:
		tmp = a * (b * (z * -t))
	else:
		tmp = y1 * (a * (x * -y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (x <= -1.8e+32)
		tmp = Float64(a * Float64(y * Float64(x * b)));
	elseif (x <= -4e-63)
		tmp = Float64(c * Float64(z * Float64(y0 * Float64(-y3))));
	elseif (x <= 0.175)
		tmp = Float64(a * Float64(b * Float64(z * Float64(-t))));
	else
		tmp = Float64(y1 * Float64(a * Float64(x * Float64(-y2))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (x <= -1.8e+32)
		tmp = a * (y * (x * b));
	elseif (x <= -4e-63)
		tmp = c * (z * (y0 * -y3));
	elseif (x <= 0.175)
		tmp = a * (b * (z * -t));
	else
		tmp = y1 * (a * (x * -y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[x, -1.8e+32], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4e-63], N[(c * N[(z * N[(y0 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.175], N[(a * N[(b * N[(z * (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(a * N[(x * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.7999999999999998e32

   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 b around inf 41.2%

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

   4. Taylor expanded in a around inf 38.0%

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

   5. Taylor expanded in x around inf 30.8%

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

      1. associate-*r* 34.7%

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

   7. Simplified 34.7%

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

   if -1.7999999999999998e32 < x < -4.00000000000000027e-63

   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 c around inf 44.3%

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

   4. Taylor expanded in z around inf 29.4%

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

      1. +-commutative 29.4%

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

      2. mul-1-neg 29.4%

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

      3. unsub-neg 29.4%

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

   6. Simplified 29.4%

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

   7. Taylor expanded in i around 0 29.4%

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

      1. neg-mul-1 29.4%

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

      2. distribute-rgt-neg-in 29.4%

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

   9. Simplified 29.4%

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

   if -4.00000000000000027e-63 < x < 0.17499999999999999

   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 b around inf 32.0%

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

   4. Taylor expanded in a around inf 28.3%

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

   5. Taylor expanded in x around 0 26.7%

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

      1. mul-1-neg 26.7%

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

      2. *-commutative 26.7%

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

      3. distribute-lft-neg-in 26.7%

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

      4. *-commutative 26.7%

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

      5. distribute-lft-neg-in 26.7%

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

      6. distribute-rgt-neg-in 26.7%

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

   7. Simplified 26.7%

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

   if 0.17499999999999999 < x

   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 51.1%

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

   4. Taylor expanded in y2 around inf 41.1%

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

      1. +-commutative 41.1%

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

      2. mul-1-neg 41.1%

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

      3. unsub-neg 41.1%

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

   6. Simplified 41.1%

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

   7. Taylor expanded in k around 0 37.8%

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

      1. mul-1-neg 37.8%

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

      2. *-commutative 37.8%

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

      3. distribute-rgt-neg-in 37.8%

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

   9. Simplified 37.8%

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

4. Final simplification 31.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+32}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-63}:\\ \;\;\;\;c \cdot \left(z \cdot \left(y0 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;x \leq 0.175:\\ \;\;\;\;a \cdot \left(b \cdot \left(z \cdot \left(-t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(x \cdot \left(-y2\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 32: 21.4% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{if}\;y2 \leq -1.3 \cdot 10^{+151}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y2 \leq 4.5 \cdot 10^{-20}:\\ \;\;\;\;j \cdot \left(\left(y1 \cdot y3\right) \cdot \left(-y4\right)\right)\\ \mathbf{elif}\;y2 \leq 5 \cdot 10^{+118}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y1 \cdot \left(-y2\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* t (* y2 y5)))))
   (if (<= y2 -1.3e+151)
     t_1
     (if (<= y2 4.5e-20)
       (* j (* (* y1 y3) (- y4)))
       (if (<= y2 5e+118) t_1 (* a (* x (* y1 (- y2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (t * (y2 * y5));
	double tmp;
	if (y2 <= -1.3e+151) {
		tmp = t_1;
	} else if (y2 <= 4.5e-20) {
		tmp = j * ((y1 * y3) * -y4);
	} else if (y2 <= 5e+118) {
		tmp = t_1;
	} else {
		tmp = a * (x * (y1 * -y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (t * (y2 * y5))
    if (y2 <= (-1.3d+151)) then
        tmp = t_1
    else if (y2 <= 4.5d-20) then
        tmp = j * ((y1 * y3) * -y4)
    else if (y2 <= 5d+118) then
        tmp = t_1
    else
        tmp = a * (x * (y1 * -y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (t * (y2 * y5));
	double tmp;
	if (y2 <= -1.3e+151) {
		tmp = t_1;
	} else if (y2 <= 4.5e-20) {
		tmp = j * ((y1 * y3) * -y4);
	} else if (y2 <= 5e+118) {
		tmp = t_1;
	} else {
		tmp = a * (x * (y1 * -y2));
	}
	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 y2 <= -1.3e+151:
		tmp = t_1
	elif y2 <= 4.5e-20:
		tmp = j * ((y1 * y3) * -y4)
	elif y2 <= 5e+118:
		tmp = t_1
	else:
		tmp = a * (x * (y1 * -y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(t * Float64(y2 * y5)))
	tmp = 0.0
	if (y2 <= -1.3e+151)
		tmp = t_1;
	elseif (y2 <= 4.5e-20)
		tmp = Float64(j * Float64(Float64(y1 * y3) * Float64(-y4)));
	elseif (y2 <= 5e+118)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(x * Float64(y1 * Float64(-y2))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (t * (y2 * y5));
	tmp = 0.0;
	if (y2 <= -1.3e+151)
		tmp = t_1;
	elseif (y2 <= 4.5e-20)
		tmp = j * ((y1 * y3) * -y4);
	elseif (y2 <= 5e+118)
		tmp = t_1;
	else
		tmp = a * (x * (y1 * -y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -1.3e+151], t$95$1, If[LessEqual[y2, 4.5e-20], N[(j * N[(N[(y1 * y3), $MachinePrecision] * (-y4)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 5e+118], t$95$1, N[(a * N[(x * N[(y1 * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y2 < -1.30000000000000007e151 or 4.5000000000000001e-20 < y2 < 4.99999999999999972e118

   1. Initial program 34.4%

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

   3. Taylor expanded in y5 around -inf 40.9%

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

   4. Taylor expanded in t around inf 35.7%

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

   5. Taylor expanded in i around 0 33.8%

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

   if -1.30000000000000007e151 < y2 < 4.5000000000000001e-20

   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 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 j around -inf 26.6%

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

      1. associate-*r* 26.6%

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

      2. mul-1-neg 26.6%

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

   6. Simplified 26.6%

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

   7. Taylor expanded in y3 around inf 18.2%

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

      1. associate-*r* 18.2%

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

      2. neg-mul-1 18.2%

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

      3. associate-*r* 20.7%

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

      4. *-commutative 20.7%

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

   9. Simplified 20.7%

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

   if 4.99999999999999972e118 < y2

   1. Initial program 25.9%

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

   3. Taylor expanded in y1 around inf 51.0%

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

   4. Taylor expanded in y2 around inf 61.1%

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

      1. +-commutative 61.1%

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

      2. mul-1-neg 61.1%

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

      3. unsub-neg 61.1%

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

   6. Simplified 61.1%

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

   7. Taylor expanded in k around 0 57.4%

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

      1. mul-1-neg 57.4%

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

      2. *-commutative 57.4%

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

      3. distribute-rgt-neg-in 57.4%

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

   9. Simplified 57.4%

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

4. Final simplification 29.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.3 \cdot 10^{+151}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 4.5 \cdot 10^{-20}:\\ \;\;\;\;j \cdot \left(\left(y1 \cdot y3\right) \cdot \left(-y4\right)\right)\\ \mathbf{elif}\;y2 \leq 5 \cdot 10^{+118}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y1 \cdot \left(-y2\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 33: 21.9% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{if}\;y5 \leq -1.1 \cdot 10^{+128}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y5 \leq 4.9 \cdot 10^{-126}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;y5 \leq 6 \cdot 10^{-19}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* t (* y2 y5)))))
   (if (<= y5 -1.1e+128)
     t_1
     (if (<= y5 4.9e-126)
       (* a (* y (* x b)))
       (if (<= y5 6e-19) (* c (* z (* t i))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (t * (y2 * y5));
	double tmp;
	if (y5 <= -1.1e+128) {
		tmp = t_1;
	} else if (y5 <= 4.9e-126) {
		tmp = a * (y * (x * b));
	} else if (y5 <= 6e-19) {
		tmp = c * (z * (t * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (t * (y2 * y5))
    if (y5 <= (-1.1d+128)) then
        tmp = t_1
    else if (y5 <= 4.9d-126) then
        tmp = a * (y * (x * b))
    else if (y5 <= 6d-19) then
        tmp = c * (z * (t * i))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (t * (y2 * y5));
	double tmp;
	if (y5 <= -1.1e+128) {
		tmp = t_1;
	} else if (y5 <= 4.9e-126) {
		tmp = a * (y * (x * b));
	} else if (y5 <= 6e-19) {
		tmp = c * (z * (t * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (t * (y2 * y5))
	tmp = 0
	if y5 <= -1.1e+128:
		tmp = t_1
	elif y5 <= 4.9e-126:
		tmp = a * (y * (x * b))
	elif y5 <= 6e-19:
		tmp = c * (z * (t * i))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(t * Float64(y2 * y5)))
	tmp = 0.0
	if (y5 <= -1.1e+128)
		tmp = t_1;
	elseif (y5 <= 4.9e-126)
		tmp = Float64(a * Float64(y * Float64(x * b)));
	elseif (y5 <= 6e-19)
		tmp = Float64(c * Float64(z * Float64(t * i)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (t * (y2 * y5));
	tmp = 0.0;
	if (y5 <= -1.1e+128)
		tmp = t_1;
	elseif (y5 <= 4.9e-126)
		tmp = a * (y * (x * b));
	elseif (y5 <= 6e-19)
		tmp = c * (z * (t * i));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -1.1e+128], t$95$1, If[LessEqual[y5, 4.9e-126], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 6e-19], N[(c * N[(z * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y5 < -1.10000000000000008e128 or 5.99999999999999985e-19 < y5

   1. Initial program 28.2%

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

   3. Taylor expanded in y5 around -inf 53.7%

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

   4. Taylor expanded in t around inf 41.7%

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

   5. Taylor expanded in i around 0 37.2%

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

   if -1.10000000000000008e128 < y5 < 4.9000000000000001e-126

   1. Initial program 32.9%

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

   3. Taylor expanded in b around inf 34.6%

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

   4. Taylor expanded in a around inf 31.5%

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

   5. Taylor expanded in x around inf 19.6%

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

      1. associate-*r* 19.7%

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

   7. Simplified 19.7%

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

   if 4.9000000000000001e-126 < y5 < 5.99999999999999985e-19

   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 c around inf 35.9%

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

   4. Taylor expanded in z around inf 32.1%

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

      1. +-commutative 32.1%

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

      2. mul-1-neg 32.1%

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

      3. unsub-neg 32.1%

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

   6. Simplified 32.1%

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

   7. Taylor expanded in i around inf 28.7%

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

      1. associate-*r* 32.4%

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

      2. *-commutative 32.4%

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

   9. Simplified 32.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(t \cdot i\right) \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 27.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -1.1 \cdot 10^{+128}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq 4.9 \cdot 10^{-126}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;y5 \leq 6 \cdot 10^{-19}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 34: 22.1% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{if}\;y5 \leq -2.6 \cdot 10^{+128}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y5 \leq -1.25 \cdot 10^{-202}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y5 \leq 7.5 \cdot 10^{-11}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* t (* y2 y5)))))
   (if (<= y5 -2.6e+128)
     t_1
     (if (<= y5 -1.25e-202)
       (* a (* (* x y) b))
       (if (<= y5 7.5e-11) (* c (* i (* 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 * (t * (y2 * y5));
	double tmp;
	if (y5 <= -2.6e+128) {
		tmp = t_1;
	} else if (y5 <= -1.25e-202) {
		tmp = a * ((x * y) * b);
	} else if (y5 <= 7.5e-11) {
		tmp = c * (i * (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 * (t * (y2 * y5))
    if (y5 <= (-2.6d+128)) then
        tmp = t_1
    else if (y5 <= (-1.25d-202)) then
        tmp = a * ((x * y) * b)
    else if (y5 <= 7.5d-11) then
        tmp = c * (i * (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 * (t * (y2 * y5));
	double tmp;
	if (y5 <= -2.6e+128) {
		tmp = t_1;
	} else if (y5 <= -1.25e-202) {
		tmp = a * ((x * y) * b);
	} else if (y5 <= 7.5e-11) {
		tmp = c * (i * (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 * (t * (y2 * y5))
	tmp = 0
	if y5 <= -2.6e+128:
		tmp = t_1
	elif y5 <= -1.25e-202:
		tmp = a * ((x * y) * b)
	elif y5 <= 7.5e-11:
		tmp = c * (i * (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(t * Float64(y2 * y5)))
	tmp = 0.0
	if (y5 <= -2.6e+128)
		tmp = t_1;
	elseif (y5 <= -1.25e-202)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	elseif (y5 <= 7.5e-11)
		tmp = Float64(c * Float64(i * 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 * (t * (y2 * y5));
	tmp = 0.0;
	if (y5 <= -2.6e+128)
		tmp = t_1;
	elseif (y5 <= -1.25e-202)
		tmp = a * ((x * y) * b);
	elseif (y5 <= 7.5e-11)
		tmp = c * (i * (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[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -2.6e+128], t$95$1, If[LessEqual[y5, -1.25e-202], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 7.5e-11], N[(c * N[(i * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y5 < -2.6e128 or 7.5e-11 < y5

   1. Initial program 28.2%

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

   3. Taylor expanded in y5 around -inf 53.7%

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

   4. Taylor expanded in t around inf 41.7%

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

   5. Taylor expanded in i around 0 37.2%

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

   if -2.6e128 < y5 < -1.24999999999999993e-202

   1. Initial program 25.4%

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

   3. Taylor expanded in b around inf 33.8%

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

   4. Taylor expanded in a around inf 33.0%

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

   5. Taylor expanded in x around inf 24.1%

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

   if -1.24999999999999993e-202 < y5 < 7.5e-11

   1. Initial program 39.9%

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

   3. Taylor expanded in c around inf 45.7%

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

   4. Taylor expanded in z around inf 29.4%

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

      1. +-commutative 29.4%

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

      2. mul-1-neg 29.4%

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

      3. unsub-neg 29.4%

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

   6. Simplified 29.4%

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

   7. Taylor expanded in i around inf 19.8%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 27.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -2.6 \cdot 10^{+128}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq -1.25 \cdot 10^{-202}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y5 \leq 7.5 \cdot 10^{-11}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 35: 21.2% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y5 \leq -1.05 \cdot 10^{+128} \lor \neg \left(y5 \leq 2.2 \cdot 10^{-125}\right):\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= y5 -1.05e+128) (not (<= y5 2.2e-125)))
   (* a (* t (* y2 y5)))
   (* a (* y (* x b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y5 <= -1.05e+128) || !(y5 <= 2.2e-125)) {
		tmp = a * (t * (y2 * y5));
	} else {
		tmp = a * (y * (x * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((y5 <= (-1.05d+128)) .or. (.not. (y5 <= 2.2d-125))) then
        tmp = a * (t * (y2 * y5))
    else
        tmp = a * (y * (x * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y5 <= -1.05e+128) || !(y5 <= 2.2e-125)) {
		tmp = a * (t * (y2 * y5));
	} else {
		tmp = a * (y * (x * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (y5 <= -1.05e+128) or not (y5 <= 2.2e-125):
		tmp = a * (t * (y2 * y5))
	else:
		tmp = a * (y * (x * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((y5 <= -1.05e+128) || !(y5 <= 2.2e-125))
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	else
		tmp = Float64(a * Float64(y * Float64(x * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((y5 <= -1.05e+128) || ~((y5 <= 2.2e-125)))
		tmp = a * (t * (y2 * y5));
	else
		tmp = a * (y * (x * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[y5, -1.05e+128], N[Not[LessEqual[y5, 2.2e-125]], $MachinePrecision]], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y5 < -1.05e128 or 2.19999999999999995e-125 < y5

   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 y5 around -inf 46.1%

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

   4. Taylor expanded in t around inf 35.0%

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

   5. Taylor expanded in i around 0 31.4%

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

   if -1.05e128 < y5 < 2.19999999999999995e-125

   1. Initial program 32.7%

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

   3. Taylor expanded in b around inf 34.4%

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

   4. Taylor expanded in a around inf 31.3%

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

   5. Taylor expanded in x around inf 19.5%

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

      1. associate-*r* 19.5%

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

   7. Simplified 19.5%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot x\right) \cdot y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 25.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -1.05 \cdot 10^{+128} \lor \neg \left(y5 \leq 2.2 \cdot 10^{-125}\right):\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 36: 21.4% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y5 \leq -2.8 \cdot 10^{+128} \lor \neg \left(y5 \leq 1.9 \cdot 10^{-125}\right):\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= y5 -2.8e+128) (not (<= y5 1.9e-125)))
   (* a (* t (* y2 y5)))
   (* a (* (* x y) b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y5 <= -2.8e+128) || !(y5 <= 1.9e-125)) {
		tmp = a * (t * (y2 * y5));
	} else {
		tmp = a * ((x * y) * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((y5 <= (-2.8d+128)) .or. (.not. (y5 <= 1.9d-125))) then
        tmp = a * (t * (y2 * y5))
    else
        tmp = a * ((x * y) * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y5 <= -2.8e+128) || !(y5 <= 1.9e-125)) {
		tmp = a * (t * (y2 * y5));
	} else {
		tmp = a * ((x * y) * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (y5 <= -2.8e+128) or not (y5 <= 1.9e-125):
		tmp = a * (t * (y2 * y5))
	else:
		tmp = a * ((x * y) * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((y5 <= -2.8e+128) || !(y5 <= 1.9e-125))
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	else
		tmp = Float64(a * Float64(Float64(x * y) * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((y5 <= -2.8e+128) || ~((y5 <= 1.9e-125)))
		tmp = a * (t * (y2 * y5));
	else
		tmp = a * ((x * y) * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[y5, -2.8e+128], N[Not[LessEqual[y5, 1.9e-125]], $MachinePrecision]], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y5 < -2.79999999999999983e128 or 1.9000000000000001e-125 < y5

   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 y5 around -inf 46.1%

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

   4. Taylor expanded in t around inf 35.0%

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

   5. Taylor expanded in i around 0 31.4%

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

   if -2.79999999999999983e128 < y5 < 1.9000000000000001e-125

   1. Initial program 32.7%

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

   3. Taylor expanded in b around inf 34.4%

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

   4. Taylor expanded in a around inf 31.3%

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

   5. Taylor expanded in x around inf 19.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 25.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -2.8 \cdot 10^{+128} \lor \neg \left(y5 \leq 1.9 \cdot 10^{-125}\right):\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 37: 17.6% 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 31.7%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
2. Add Preprocessing

3. Taylor expanded in b around inf 36.4%

   \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

4. Taylor expanded in a around inf 28.7%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

5. Taylor expanded in x around inf 15.8%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]

6. Final simplification 15.8%

   \[\leadsto a \cdot \left(\left(x \cdot y\right) \cdot b\right) \]
7. Add Preprocessing

Developer Target 1: 28.7% 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 2024180 
(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)))))