Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 30.5% → 42.9%

Time: 46.3s

Alternatives: 32

Speedup: 4.5×

• 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: 30.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 42.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y2 - z \cdot y3\\ t_2 := c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot t\_1\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ t_3 := y0 \cdot y5 - y1 \cdot y4\\ t_4 := y1 \cdot y4 - y0 \cdot y5\\ t_5 := \left(k \cdot y2 - j \cdot y3\right) \cdot t\_4\\ t_6 := t \cdot y2 - y \cdot y3\\ \mathbf{if}\;c \leq -4.2 \cdot 10^{+136}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -3 \cdot 10^{-46}:\\ \;\;\;\;j \cdot \left(i \cdot \left(\left(x \cdot y1 - t \cdot y5\right) - y3 \cdot \frac{t\_4}{i}\right)\right)\\ \mathbf{elif}\;c \leq -3.9 \cdot 10^{-286}:\\ \;\;\;\;a \cdot \left(\left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right) + b \cdot \left(x \cdot y - z \cdot t\right)\right) + y5 \cdot t\_6\right)\\ \mathbf{elif}\;c \leq 8.8 \cdot 10^{-218}:\\ \;\;\;\;t\_5 + \left(x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t\_6 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq 5.4 \cdot 10^{-167}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot t\_3 + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{-55}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(y \cdot \left(b \cdot y4 - i \cdot y5\right) + y2 \cdot t\_3\right)\right)\\ \mathbf{elif}\;c \leq 1.65 \cdot 10^{+83}:\\ \;\;\;\;t\_5 + y0 \cdot \left(c \cdot t\_1 + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (- (* y0 y5) (* y1 y4)))
        (t_4 (- (* y1 y4) (* y0 y5)))
        (t_5 (* (- (* k y2) (* j y3)) t_4))
        (t_6 (- (* t y2) (* y y3))))
   (if (<= c -4.2e+136)
     t_2
     (if (<= c -3e-46)
       (* j (* i (- (- (* x y1) (* t y5)) (* y3 (/ t_4 i)))))
       (if (<= c -3.9e-286)
         (*
          a
          (+
           (+ (* y1 (- (* z y3) (* x y2))) (* b (- (* x y) (* z t))))
           (* y5 t_6)))
         (if (<= c 8.8e-218)
           (+
            t_5
            (+
             (* x (* y2 (- (* c y0) (* a y1))))
             (* t_6 (- (* a y5) (* c y4)))))
           (if (<= c 5.4e-167)
             (*
              y3
              (+
               (* y (- (* c y4) (* a y5)))
               (+ (* j t_3) (* z (- (* a y1) (* c y0))))))
             (if (<= c 6.5e-55)
               (*
                k
                (-
                 (* z (- (* b y0) (* i y1)))
                 (+ (* y (- (* b y4) (* i y5))) (* y2 t_3))))
               (if (<= c 1.65e+83)
                 (+ t_5 (* y0 (+ (* c t_1) (* b (- (* z k) (* x j))))))
                 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 = (y0 * y5) - (y1 * y4);
	double t_4 = (y1 * y4) - (y0 * y5);
	double t_5 = ((k * y2) - (j * y3)) * t_4;
	double t_6 = (t * y2) - (y * y3);
	double tmp;
	if (c <= -4.2e+136) {
		tmp = t_2;
	} else if (c <= -3e-46) {
		tmp = j * (i * (((x * y1) - (t * y5)) - (y3 * (t_4 / i))));
	} else if (c <= -3.9e-286) {
		tmp = a * (((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t)))) + (y5 * t_6));
	} else if (c <= 8.8e-218) {
		tmp = t_5 + ((x * (y2 * ((c * y0) - (a * y1)))) + (t_6 * ((a * y5) - (c * y4))));
	} else if (c <= 5.4e-167) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_3) + (z * ((a * y1) - (c * y0)))));
	} else if (c <= 6.5e-55) {
		tmp = k * ((z * ((b * y0) - (i * y1))) - ((y * ((b * y4) - (i * y5))) + (y2 * t_3)));
	} else if (c <= 1.65e+83) {
		tmp = t_5 + (y0 * ((c * t_1) + (b * ((z * k) - (x * j)))));
	} 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) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    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 = (y0 * y5) - (y1 * y4)
    t_4 = (y1 * y4) - (y0 * y5)
    t_5 = ((k * y2) - (j * y3)) * t_4
    t_6 = (t * y2) - (y * y3)
    if (c <= (-4.2d+136)) then
        tmp = t_2
    else if (c <= (-3d-46)) then
        tmp = j * (i * (((x * y1) - (t * y5)) - (y3 * (t_4 / i))))
    else if (c <= (-3.9d-286)) then
        tmp = a * (((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t)))) + (y5 * t_6))
    else if (c <= 8.8d-218) then
        tmp = t_5 + ((x * (y2 * ((c * y0) - (a * y1)))) + (t_6 * ((a * y5) - (c * y4))))
    else if (c <= 5.4d-167) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_3) + (z * ((a * y1) - (c * y0)))))
    else if (c <= 6.5d-55) then
        tmp = k * ((z * ((b * y0) - (i * y1))) - ((y * ((b * y4) - (i * y5))) + (y2 * t_3)))
    else if (c <= 1.65d+83) then
        tmp = t_5 + (y0 * ((c * t_1) + (b * ((z * k) - (x * j)))))
    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 = (y0 * y5) - (y1 * y4);
	double t_4 = (y1 * y4) - (y0 * y5);
	double t_5 = ((k * y2) - (j * y3)) * t_4;
	double t_6 = (t * y2) - (y * y3);
	double tmp;
	if (c <= -4.2e+136) {
		tmp = t_2;
	} else if (c <= -3e-46) {
		tmp = j * (i * (((x * y1) - (t * y5)) - (y3 * (t_4 / i))));
	} else if (c <= -3.9e-286) {
		tmp = a * (((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t)))) + (y5 * t_6));
	} else if (c <= 8.8e-218) {
		tmp = t_5 + ((x * (y2 * ((c * y0) - (a * y1)))) + (t_6 * ((a * y5) - (c * y4))));
	} else if (c <= 5.4e-167) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_3) + (z * ((a * y1) - (c * y0)))));
	} else if (c <= 6.5e-55) {
		tmp = k * ((z * ((b * y0) - (i * y1))) - ((y * ((b * y4) - (i * y5))) + (y2 * t_3)));
	} else if (c <= 1.65e+83) {
		tmp = t_5 + (y0 * ((c * t_1) + (b * ((z * k) - (x * j)))));
	} 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 = (y0 * y5) - (y1 * y4)
	t_4 = (y1 * y4) - (y0 * y5)
	t_5 = ((k * y2) - (j * y3)) * t_4
	t_6 = (t * y2) - (y * y3)
	tmp = 0
	if c <= -4.2e+136:
		tmp = t_2
	elif c <= -3e-46:
		tmp = j * (i * (((x * y1) - (t * y5)) - (y3 * (t_4 / i))))
	elif c <= -3.9e-286:
		tmp = a * (((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t)))) + (y5 * t_6))
	elif c <= 8.8e-218:
		tmp = t_5 + ((x * (y2 * ((c * y0) - (a * y1)))) + (t_6 * ((a * y5) - (c * y4))))
	elif c <= 5.4e-167:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_3) + (z * ((a * y1) - (c * y0)))))
	elif c <= 6.5e-55:
		tmp = k * ((z * ((b * y0) - (i * y1))) - ((y * ((b * y4) - (i * y5))) + (y2 * t_3)))
	elif c <= 1.65e+83:
		tmp = t_5 + (y0 * ((c * t_1) + (b * ((z * k) - (x * j)))))
	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(y0 * y5) - Float64(y1 * y4))
	t_4 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_5 = Float64(Float64(Float64(k * y2) - Float64(j * y3)) * t_4)
	t_6 = Float64(Float64(t * y2) - Float64(y * y3))
	tmp = 0.0
	if (c <= -4.2e+136)
		tmp = t_2;
	elseif (c <= -3e-46)
		tmp = Float64(j * Float64(i * Float64(Float64(Float64(x * y1) - Float64(t * y5)) - Float64(y3 * Float64(t_4 / i)))));
	elseif (c <= -3.9e-286)
		tmp = Float64(a * Float64(Float64(Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))) + Float64(b * Float64(Float64(x * y) - Float64(z * t)))) + Float64(y5 * t_6)));
	elseif (c <= 8.8e-218)
		tmp = Float64(t_5 + Float64(Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(t_6 * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (c <= 5.4e-167)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(j * t_3) + Float64(z * Float64(Float64(a * y1) - Float64(c * y0))))));
	elseif (c <= 6.5e-55)
		tmp = Float64(k * Float64(Float64(z * Float64(Float64(b * y0) - Float64(i * y1))) - Float64(Float64(y * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(y2 * t_3))));
	elseif (c <= 1.65e+83)
		tmp = Float64(t_5 + Float64(y0 * Float64(Float64(c * t_1) + Float64(b * Float64(Float64(z * k) - Float64(x * j))))));
	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 = (y0 * y5) - (y1 * y4);
	t_4 = (y1 * y4) - (y0 * y5);
	t_5 = ((k * y2) - (j * y3)) * t_4;
	t_6 = (t * y2) - (y * y3);
	tmp = 0.0;
	if (c <= -4.2e+136)
		tmp = t_2;
	elseif (c <= -3e-46)
		tmp = j * (i * (((x * y1) - (t * y5)) - (y3 * (t_4 / i))));
	elseif (c <= -3.9e-286)
		tmp = a * (((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t)))) + (y5 * t_6));
	elseif (c <= 8.8e-218)
		tmp = t_5 + ((x * (y2 * ((c * y0) - (a * y1)))) + (t_6 * ((a * y5) - (c * y4))));
	elseif (c <= 5.4e-167)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_3) + (z * ((a * y1) - (c * y0)))));
	elseif (c <= 6.5e-55)
		tmp = k * ((z * ((b * y0) - (i * y1))) - ((y * ((b * y4) - (i * y5))) + (y2 * t_3)));
	elseif (c <= 1.65e+83)
		tmp = t_5 + (y0 * ((c * t_1) + (b * ((z * k) - (x * j)))));
	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[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * t$95$4), $MachinePrecision]}, Block[{t$95$6 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4.2e+136], t$95$2, If[LessEqual[c, -3e-46], N[(j * N[(i * N[(N[(N[(x * y1), $MachinePrecision] - N[(t * y5), $MachinePrecision]), $MachinePrecision] - N[(y3 * N[(t$95$4 / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3.9e-286], N[(a * N[(N[(N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 8.8e-218], N[(t$95$5 + N[(N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$6 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.4e-167], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * t$95$3), $MachinePrecision] + N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.5e-55], N[(k * N[(N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.65e+83], N[(t$95$5 + N[(y0 * N[(N[(c * t$95$1), $MachinePrecision] + N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if c < -4.1999999999999998e136 or 1.64999999999999992e83 < c

   1. Initial program 37.8%

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

   3. Simplified 37.8%

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

   5. Taylor expanded in c around inf 65.4%

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

   if -4.1999999999999998e136 < c < -2.99999999999999987e-46

   1. Initial program 28.7%

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

   3. Taylor expanded in i around -inf 51.8%

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

   4. Taylor expanded in j around inf 58.1%

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

   5. Taylor expanded in i around inf 60.9%

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

      1. fma-define 60.9%

         \[\leadsto j \cdot \left(i \cdot \color{blue}{\mathsf{fma}\left(-1, t \cdot y5 - x \cdot y1, -1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{i}\right)}\right) \]

      2. mul-1-neg 60.9%

         \[\leadsto j \cdot \left(i \cdot \mathsf{fma}\left(-1, t \cdot y5 - x \cdot y1, \color{blue}{-\frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{i}}\right)\right) \]

      3. fmm-undef 60.9%

         \[\leadsto j \cdot \left(i \cdot \color{blue}{\left(-1 \cdot \left(t \cdot y5 - x \cdot y1\right) - \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{i}\right)}\right) \]

      4. mul-1-neg 60.9%

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

      5. *-commutative 60.9%

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

      6. associate-/l* 60.8%

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

      7. *-commutative 60.8%

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

   7. Simplified 60.8%

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

   if -2.99999999999999987e-46 < c < -3.89999999999999995e-286

   1. Initial program 39.0%

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

   3. Simplified 39.0%

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

   5. Taylor expanded in a around inf 63.3%

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

   if -3.89999999999999995e-286 < c < 8.80000000000000028e-218

   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 y2 around inf 68.4%

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

   if 8.80000000000000028e-218 < c < 5.4000000000000001e-167

   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 y3 around -inf 86.0%

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

   if 5.4000000000000001e-167 < c < 6.50000000000000006e-55

   1. Initial program 23.4%

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

   3. Taylor expanded in k around inf 65.9%

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

   if 6.50000000000000006e-55 < c < 1.64999999999999992e83

   1. Initial program 38.7%

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

   3. Taylor expanded in y0 around inf 58.3%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
3. Recombined 7 regimes into one program.

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.2 \cdot 10^{+136}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -3 \cdot 10^{-46}:\\ \;\;\;\;j \cdot \left(i \cdot \left(\left(x \cdot y1 - t \cdot y5\right) - y3 \cdot \frac{y1 \cdot y4 - y0 \cdot y5}{i}\right)\right)\\ \mathbf{elif}\;c \leq -3.9 \cdot 10^{-286}:\\ \;\;\;\;a \cdot \left(\left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right) + b \cdot \left(x \cdot y - z \cdot t\right)\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;c \leq 8.8 \cdot 10^{-218}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot y2 - y \cdot y3\right) \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq 5.4 \cdot 10^{-167}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{-55}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(y \cdot \left(b \cdot y4 - i \cdot y5\right) + y2 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.65 \cdot 10^{+83}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 57.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision] * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision] * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision] * N[(N[(a * b), $MachinePrecision] - N[(c * i), $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] * t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, Infinity], t$95$2, N[(j * N[(i * N[(N[(N[(x * y1), $MachinePrecision] - N[(t * y5), $MachinePrecision]), $MachinePrecision] - N[(y3 * N[(t$95$1 / i), $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 93.4%

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

   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 32.7%

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

   4. Taylor expanded in j around inf 43.4%

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

   5. Taylor expanded in i around inf 45.3%

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

      1. fma-define 45.3%

         \[\leadsto j \cdot \left(i \cdot \color{blue}{\mathsf{fma}\left(-1, t \cdot y5 - x \cdot y1, -1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{i}\right)}\right) \]

      2. mul-1-neg 45.3%

         \[\leadsto j \cdot \left(i \cdot \mathsf{fma}\left(-1, t \cdot y5 - x \cdot y1, \color{blue}{-\frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{i}}\right)\right) \]

      3. fmm-undef 45.3%

         \[\leadsto j \cdot \left(i \cdot \color{blue}{\left(-1 \cdot \left(t \cdot y5 - x \cdot y1\right) - \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{i}\right)}\right) \]

      4. mul-1-neg 45.3%

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

      5. *-commutative 45.3%

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

      6. associate-/l* 45.8%

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

      7. *-commutative 45.8%

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

   7. Simplified 45.8%

      \[\leadsto j \cdot \color{blue}{\left(i \cdot \left(\left(-\left(t \cdot y5 - y1 \cdot x\right)\right) - y3 \cdot \frac{y1 \cdot y4 - y5 \cdot y0}{i}\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 64.2%

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

Alternative 3: 42.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot y4 - y0 \cdot y5\\ t_2 := t \cdot y2 - y \cdot y3\\ t_3 := y5 \cdot \left(\left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + a \cdot t\_2\right)\\ \mathbf{if}\;y5 \leq -3.5 \cdot 10^{+115}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y5 \leq -1.45 \cdot 10^{-59}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot t\_1 + i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(c \cdot \left(z \cdot t - x \cdot y\right) - y5 \cdot \left(t \cdot j - y \cdot k\right)\right)\right)\\ \mathbf{elif}\;y5 \leq -2.05 \cdot 10^{-109}:\\ \;\;\;\;a \cdot \left(\left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right) + b \cdot \left(x \cdot y - z \cdot t\right)\right) + y5 \cdot t\_2\right)\\ \mathbf{elif}\;y5 \leq 2.9 \cdot 10^{+67}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot t\_1 + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y1 y4) (* y0 y5)))
        (t_2 (- (* t y2) (* y y3)))
        (t_3
         (*
          y5
          (+
           (+ (* i (- (* y k) (* t j))) (* y0 (- (* j y3) (* k y2))))
           (* a t_2)))))
   (if (<= y5 -3.5e+115)
     t_3
     (if (<= y5 -1.45e-59)
       (+
        (* (- (* k y2) (* j y3)) t_1)
        (*
         i
         (+
          (* y1 (- (* x j) (* z k)))
          (- (* c (- (* z t) (* x y))) (* y5 (- (* t j) (* y k)))))))
       (if (<= y5 -2.05e-109)
         (*
          a
          (+
           (+ (* y1 (- (* z y3) (* x y2))) (* b (- (* x y) (* z t))))
           (* y5 t_2)))
         (if (<= y5 2.9e+67)
           (*
            y2
            (+
             (+ (* k t_1) (* x (- (* c y0) (* a y1))))
             (* t (- (* a y5) (* c y4)))))
           t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y1 * y4) - (y0 * y5);
	double t_2 = (t * y2) - (y * y3);
	double t_3 = y5 * (((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))) + (a * t_2));
	double tmp;
	if (y5 <= -3.5e+115) {
		tmp = t_3;
	} else if (y5 <= -1.45e-59) {
		tmp = (((k * y2) - (j * y3)) * t_1) + (i * ((y1 * ((x * j) - (z * k))) + ((c * ((z * t) - (x * y))) - (y5 * ((t * j) - (y * k))))));
	} else if (y5 <= -2.05e-109) {
		tmp = a * (((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t)))) + (y5 * t_2));
	} else if (y5 <= 2.9e+67) {
		tmp = y2 * (((k * t_1) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (y1 * y4) - (y0 * y5)
    t_2 = (t * y2) - (y * y3)
    t_3 = y5 * (((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))) + (a * t_2))
    if (y5 <= (-3.5d+115)) then
        tmp = t_3
    else if (y5 <= (-1.45d-59)) then
        tmp = (((k * y2) - (j * y3)) * t_1) + (i * ((y1 * ((x * j) - (z * k))) + ((c * ((z * t) - (x * y))) - (y5 * ((t * j) - (y * k))))))
    else if (y5 <= (-2.05d-109)) then
        tmp = a * (((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t)))) + (y5 * t_2))
    else if (y5 <= 2.9d+67) then
        tmp = y2 * (((k * t_1) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y1 * y4) - (y0 * y5);
	double t_2 = (t * y2) - (y * y3);
	double t_3 = y5 * (((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))) + (a * t_2));
	double tmp;
	if (y5 <= -3.5e+115) {
		tmp = t_3;
	} else if (y5 <= -1.45e-59) {
		tmp = (((k * y2) - (j * y3)) * t_1) + (i * ((y1 * ((x * j) - (z * k))) + ((c * ((z * t) - (x * y))) - (y5 * ((t * j) - (y * k))))));
	} else if (y5 <= -2.05e-109) {
		tmp = a * (((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t)))) + (y5 * t_2));
	} else if (y5 <= 2.9e+67) {
		tmp = y2 * (((k * t_1) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y1 * y4) - (y0 * y5)
	t_2 = (t * y2) - (y * y3)
	t_3 = y5 * (((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))) + (a * t_2))
	tmp = 0
	if y5 <= -3.5e+115:
		tmp = t_3
	elif y5 <= -1.45e-59:
		tmp = (((k * y2) - (j * y3)) * t_1) + (i * ((y1 * ((x * j) - (z * k))) + ((c * ((z * t) - (x * y))) - (y5 * ((t * j) - (y * k))))))
	elif y5 <= -2.05e-109:
		tmp = a * (((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t)))) + (y5 * t_2))
	elif y5 <= 2.9e+67:
		tmp = y2 * (((k * t_1) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_2 = Float64(Float64(t * y2) - Float64(y * y3))
	t_3 = Float64(y5 * Float64(Float64(Float64(i * Float64(Float64(y * k) - Float64(t * j))) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2)))) + Float64(a * t_2)))
	tmp = 0.0
	if (y5 <= -3.5e+115)
		tmp = t_3;
	elseif (y5 <= -1.45e-59)
		tmp = Float64(Float64(Float64(Float64(k * y2) - Float64(j * y3)) * t_1) + Float64(i * Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) + Float64(Float64(c * Float64(Float64(z * t) - Float64(x * y))) - Float64(y5 * Float64(Float64(t * j) - Float64(y * k)))))));
	elseif (y5 <= -2.05e-109)
		tmp = Float64(a * Float64(Float64(Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))) + Float64(b * Float64(Float64(x * y) - Float64(z * t)))) + Float64(y5 * t_2)));
	elseif (y5 <= 2.9e+67)
		tmp = Float64(y2 * Float64(Float64(Float64(k * t_1) + Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y1 * y4) - (y0 * y5);
	t_2 = (t * y2) - (y * y3);
	t_3 = y5 * (((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))) + (a * t_2));
	tmp = 0.0;
	if (y5 <= -3.5e+115)
		tmp = t_3;
	elseif (y5 <= -1.45e-59)
		tmp = (((k * y2) - (j * y3)) * t_1) + (i * ((y1 * ((x * j) - (z * k))) + ((c * ((z * t) - (x * y))) - (y5 * ((t * j) - (y * k))))));
	elseif (y5 <= -2.05e-109)
		tmp = a * (((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t)))) + (y5 * t_2));
	elseif (y5 <= 2.9e+67)
		tmp = y2 * (((k * t_1) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y5 * N[(N[(N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -3.5e+115], t$95$3, If[LessEqual[y5, -1.45e-59], N[(N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision] + N[(i * N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(c * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y5 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -2.05e-109], N[(a * N[(N[(N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 2.9e+67], N[(y2 * N[(N[(N[(k * t$95$1), $MachinePrecision] + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y5 < -3.50000000000000005e115 or 2.90000000000000023e67 < y5

   1. Initial program 28.9%

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

   3. Taylor expanded in y5 around -inf 68.0%

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

   if -3.50000000000000005e115 < y5 < -1.45000000000000008e-59

   1. Initial program 48.0%

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

   3. Taylor expanded in i around -inf 67.7%

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

   if -1.45000000000000008e-59 < y5 < -2.0500000000000001e-109

   1. Initial program 50.0%

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

   3. Simplified 50.0%

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

   5. Taylor expanded in a around inf 99.8%

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

   if -2.0500000000000001e-109 < y5 < 2.90000000000000023e67

   1. Initial program 36.0%

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

   3. Taylor expanded in y2 around inf 50.8%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -3.5 \cdot 10^{+115}:\\ \;\;\;\;y5 \cdot \left(\left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq -1.45 \cdot 10^{-59}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(c \cdot \left(z \cdot t - x \cdot y\right) - y5 \cdot \left(t \cdot j - y \cdot k\right)\right)\right)\\ \mathbf{elif}\;y5 \leq -2.05 \cdot 10^{-109}:\\ \;\;\;\;a \cdot \left(\left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right) + b \cdot \left(x \cdot y - z \cdot t\right)\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq 2.9 \cdot 10^{+67}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(\left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 42.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot y4 - y0 \cdot y5\\ t_2 := t \cdot y2 - y \cdot y3\\ t_3 := y5 \cdot \left(\left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + a \cdot t\_2\right)\\ \mathbf{if}\;y5 \leq -2.05 \cdot 10^{+117}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y5 \leq -4200000:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot t\_1 + x \cdot \left(i \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;y5 \leq -9.5 \cdot 10^{-61}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq -1.7 \cdot 10^{-109}:\\ \;\;\;\;a \cdot \left(\left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right) + b \cdot \left(x \cdot y - z \cdot t\right)\right) + y5 \cdot t\_2\right)\\ \mathbf{elif}\;y5 \leq 2.25 \cdot 10^{+67}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot t\_1 + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y1 y4) (* y0 y5)))
        (t_2 (- (* t y2) (* y y3)))
        (t_3
         (*
          y5
          (+
           (+ (* i (- (* y k) (* t j))) (* y0 (- (* j y3) (* k y2))))
           (* a t_2)))))
   (if (<= y5 -2.05e+117)
     t_3
     (if (<= y5 -4200000.0)
       (+ (* (- (* k y2) (* j y3)) t_1) (* x (* i (- (* j y1) (* y c)))))
       (if (<= y5 -9.5e-61)
         (*
          c
          (+
           (+ (* i (- (* z t) (* x y))) (* y0 (- (* x y2) (* z y3))))
           (* y4 (- (* y y3) (* t y2)))))
         (if (<= y5 -1.7e-109)
           (*
            a
            (+
             (+ (* y1 (- (* z y3) (* x y2))) (* b (- (* x y) (* z t))))
             (* y5 t_2)))
           (if (<= y5 2.25e+67)
             (*
              y2
              (+
               (+ (* k t_1) (* x (- (* c y0) (* a y1))))
               (* t (- (* a y5) (* c y4)))))
             t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y1 * y4) - (y0 * y5);
	double t_2 = (t * y2) - (y * y3);
	double t_3 = y5 * (((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))) + (a * t_2));
	double tmp;
	if (y5 <= -2.05e+117) {
		tmp = t_3;
	} else if (y5 <= -4200000.0) {
		tmp = (((k * y2) - (j * y3)) * t_1) + (x * (i * ((j * y1) - (y * c))));
	} else if (y5 <= -9.5e-61) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (y5 <= -1.7e-109) {
		tmp = a * (((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t)))) + (y5 * t_2));
	} else if (y5 <= 2.25e+67) {
		tmp = y2 * (((k * t_1) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (y1 * y4) - (y0 * y5)
    t_2 = (t * y2) - (y * y3)
    t_3 = y5 * (((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))) + (a * t_2))
    if (y5 <= (-2.05d+117)) then
        tmp = t_3
    else if (y5 <= (-4200000.0d0)) then
        tmp = (((k * y2) - (j * y3)) * t_1) + (x * (i * ((j * y1) - (y * c))))
    else if (y5 <= (-9.5d-61)) then
        tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))))
    else if (y5 <= (-1.7d-109)) then
        tmp = a * (((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t)))) + (y5 * t_2))
    else if (y5 <= 2.25d+67) then
        tmp = y2 * (((k * t_1) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y1 * y4) - (y0 * y5);
	double t_2 = (t * y2) - (y * y3);
	double t_3 = y5 * (((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))) + (a * t_2));
	double tmp;
	if (y5 <= -2.05e+117) {
		tmp = t_3;
	} else if (y5 <= -4200000.0) {
		tmp = (((k * y2) - (j * y3)) * t_1) + (x * (i * ((j * y1) - (y * c))));
	} else if (y5 <= -9.5e-61) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (y5 <= -1.7e-109) {
		tmp = a * (((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t)))) + (y5 * t_2));
	} else if (y5 <= 2.25e+67) {
		tmp = y2 * (((k * t_1) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y1 * y4) - (y0 * y5)
	t_2 = (t * y2) - (y * y3)
	t_3 = y5 * (((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))) + (a * t_2))
	tmp = 0
	if y5 <= -2.05e+117:
		tmp = t_3
	elif y5 <= -4200000.0:
		tmp = (((k * y2) - (j * y3)) * t_1) + (x * (i * ((j * y1) - (y * c))))
	elif y5 <= -9.5e-61:
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))))
	elif y5 <= -1.7e-109:
		tmp = a * (((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t)))) + (y5 * t_2))
	elif y5 <= 2.25e+67:
		tmp = y2 * (((k * t_1) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_2 = Float64(Float64(t * y2) - Float64(y * y3))
	t_3 = Float64(y5 * Float64(Float64(Float64(i * Float64(Float64(y * k) - Float64(t * j))) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2)))) + Float64(a * t_2)))
	tmp = 0.0
	if (y5 <= -2.05e+117)
		tmp = t_3;
	elseif (y5 <= -4200000.0)
		tmp = Float64(Float64(Float64(Float64(k * y2) - Float64(j * y3)) * t_1) + Float64(x * Float64(i * Float64(Float64(j * y1) - Float64(y * c)))));
	elseif (y5 <= -9.5e-61)
		tmp = Float64(c * Float64(Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3)))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (y5 <= -1.7e-109)
		tmp = Float64(a * Float64(Float64(Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))) + Float64(b * Float64(Float64(x * y) - Float64(z * t)))) + Float64(y5 * t_2)));
	elseif (y5 <= 2.25e+67)
		tmp = Float64(y2 * Float64(Float64(Float64(k * t_1) + Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y1 * y4) - (y0 * y5);
	t_2 = (t * y2) - (y * y3);
	t_3 = y5 * (((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))) + (a * t_2));
	tmp = 0.0;
	if (y5 <= -2.05e+117)
		tmp = t_3;
	elseif (y5 <= -4200000.0)
		tmp = (((k * y2) - (j * y3)) * t_1) + (x * (i * ((j * y1) - (y * c))));
	elseif (y5 <= -9.5e-61)
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	elseif (y5 <= -1.7e-109)
		tmp = a * (((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t)))) + (y5 * t_2));
	elseif (y5 <= 2.25e+67)
		tmp = y2 * (((k * t_1) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y5 * N[(N[(N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -2.05e+117], t$95$3, If[LessEqual[y5, -4200000.0], N[(N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision] + N[(x * N[(i * N[(N[(j * y1), $MachinePrecision] - N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -9.5e-61], N[(c * N[(N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.7e-109], N[(a * N[(N[(N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 2.25e+67], N[(y2 * N[(N[(N[(k * t$95$1), $MachinePrecision] + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y5 < -2.05e117 or 2.2499999999999999e67 < y5

   1. Initial program 29.6%

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

   3. Taylor expanded in y5 around -inf 68.4%

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

   if -2.05e117 < y5 < -4.2e6

   1. Initial program 40.9%

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

   3. Taylor expanded in i around -inf 63.6%

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

   4. Taylor expanded in x around inf 67.0%

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

      1. fma-define 67.0%

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

      2. associate-/l* 70.7%

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

      3. fma-define 70.7%

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

      4. associate-*r* 70.7%

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

      5. mul-1-neg 70.7%

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

   6. Simplified 70.7%

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

   7. Taylor expanded in x around inf 70.9%

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

      1. *-commutative 70.9%

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

   9. Simplified 70.9%

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

   if -4.2e6 < y5 < -9.49999999999999986e-61

   1. Initial program 52.7%

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

   3. Simplified 52.7%

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

   5. Taylor expanded in c around inf 62.9%

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

   if -9.49999999999999986e-61 < y5 < -1.70000000000000006e-109

   1. Initial program 50.0%

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

   3. Simplified 50.0%

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

   5. Taylor expanded in a around inf 99.8%

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

   if -1.70000000000000006e-109 < y5 < 2.2499999999999999e67

   1. Initial program 36.0%

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

   3. Taylor expanded in y2 around inf 50.8%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -2.05 \cdot 10^{+117}:\\ \;\;\;\;y5 \cdot \left(\left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq -4200000:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(i \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;y5 \leq -9.5 \cdot 10^{-61}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq -1.7 \cdot 10^{-109}:\\ \;\;\;\;a \cdot \left(\left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right) + b \cdot \left(x \cdot y - z \cdot t\right)\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq 2.25 \cdot 10^{+67}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(\left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 42.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot y4 - y0 \cdot y5\\ t_2 := y5 \cdot \left(\left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{if}\;y5 \leq -1.8 \cdot 10^{+117}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y5 \leq -2200000000:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot t\_1 + x \cdot \left(i \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;y5 \leq -2 \cdot 10^{-86}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 2.4 \cdot 10^{+67}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot t\_1 + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y1 y4) (* y0 y5)))
        (t_2
         (*
          y5
          (+
           (+ (* i (- (* y k) (* t j))) (* y0 (- (* j y3) (* k y2))))
           (* a (- (* t y2) (* y y3)))))))
   (if (<= y5 -1.8e+117)
     t_2
     (if (<= y5 -2200000000.0)
       (+ (* (- (* k y2) (* j y3)) t_1) (* x (* i (- (* j y1) (* y c)))))
       (if (<= y5 -2e-86)
         (*
          c
          (+
           (+ (* i (- (* z t) (* x y))) (* y0 (- (* x y2) (* z y3))))
           (* y4 (- (* y y3) (* t y2)))))
         (if (<= y5 2.4e+67)
           (*
            y2
            (+
             (+ (* k t_1) (* x (- (* c y0) (* a y1))))
             (* t (- (* a y5) (* c y4)))))
           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 = (y1 * y4) - (y0 * y5);
	double t_2 = y5 * (((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))) + (a * ((t * y2) - (y * y3))));
	double tmp;
	if (y5 <= -1.8e+117) {
		tmp = t_2;
	} else if (y5 <= -2200000000.0) {
		tmp = (((k * y2) - (j * y3)) * t_1) + (x * (i * ((j * y1) - (y * c))));
	} else if (y5 <= -2e-86) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (y5 <= 2.4e+67) {
		tmp = y2 * (((k * t_1) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} 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 = (y1 * y4) - (y0 * y5)
    t_2 = y5 * (((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))) + (a * ((t * y2) - (y * y3))))
    if (y5 <= (-1.8d+117)) then
        tmp = t_2
    else if (y5 <= (-2200000000.0d0)) then
        tmp = (((k * y2) - (j * y3)) * t_1) + (x * (i * ((j * y1) - (y * c))))
    else if (y5 <= (-2d-86)) then
        tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))))
    else if (y5 <= 2.4d+67) then
        tmp = y2 * (((k * t_1) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
    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 = (y1 * y4) - (y0 * y5);
	double t_2 = y5 * (((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))) + (a * ((t * y2) - (y * y3))));
	double tmp;
	if (y5 <= -1.8e+117) {
		tmp = t_2;
	} else if (y5 <= -2200000000.0) {
		tmp = (((k * y2) - (j * y3)) * t_1) + (x * (i * ((j * y1) - (y * c))));
	} else if (y5 <= -2e-86) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (y5 <= 2.4e+67) {
		tmp = y2 * (((k * t_1) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} 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 = (y1 * y4) - (y0 * y5)
	t_2 = y5 * (((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))) + (a * ((t * y2) - (y * y3))))
	tmp = 0
	if y5 <= -1.8e+117:
		tmp = t_2
	elif y5 <= -2200000000.0:
		tmp = (((k * y2) - (j * y3)) * t_1) + (x * (i * ((j * y1) - (y * c))))
	elif y5 <= -2e-86:
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))))
	elif y5 <= 2.4e+67:
		tmp = y2 * (((k * t_1) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
	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(y1 * y4) - Float64(y0 * y5))
	t_2 = Float64(y5 * Float64(Float64(Float64(i * Float64(Float64(y * k) - Float64(t * j))) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2)))) + Float64(a * Float64(Float64(t * y2) - Float64(y * y3)))))
	tmp = 0.0
	if (y5 <= -1.8e+117)
		tmp = t_2;
	elseif (y5 <= -2200000000.0)
		tmp = Float64(Float64(Float64(Float64(k * y2) - Float64(j * y3)) * t_1) + Float64(x * Float64(i * Float64(Float64(j * y1) - Float64(y * c)))));
	elseif (y5 <= -2e-86)
		tmp = Float64(c * Float64(Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3)))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (y5 <= 2.4e+67)
		tmp = Float64(y2 * Float64(Float64(Float64(k * t_1) + Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	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 = (y1 * y4) - (y0 * y5);
	t_2 = y5 * (((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))) + (a * ((t * y2) - (y * y3))));
	tmp = 0.0;
	if (y5 <= -1.8e+117)
		tmp = t_2;
	elseif (y5 <= -2200000000.0)
		tmp = (((k * y2) - (j * y3)) * t_1) + (x * (i * ((j * y1) - (y * c))));
	elseif (y5 <= -2e-86)
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	elseif (y5 <= 2.4e+67)
		tmp = y2 * (((k * t_1) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	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[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y5 * N[(N[(N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -1.8e+117], t$95$2, If[LessEqual[y5, -2200000000.0], N[(N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision] + N[(x * N[(i * N[(N[(j * y1), $MachinePrecision] - N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -2e-86], N[(c * N[(N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 2.4e+67], N[(y2 * N[(N[(N[(k * t$95$1), $MachinePrecision] + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if y5 < -1.80000000000000006e117 or 2.40000000000000002e67 < y5

   1. Initial program 29.6%

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

   3. Taylor expanded in y5 around -inf 68.4%

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

   if -1.80000000000000006e117 < y5 < -2.2e9

   1. Initial program 40.9%

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

   3. Taylor expanded in i around -inf 63.6%

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

   4. Taylor expanded in x around inf 67.0%

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

      1. fma-define 67.0%

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

      2. associate-/l* 70.7%

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

      3. fma-define 70.7%

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

      4. associate-*r* 70.7%

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

      5. mul-1-neg 70.7%

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

   6. Simplified 70.7%

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

   7. Taylor expanded in x around inf 70.9%

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

      1. *-commutative 70.9%

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

   9. Simplified 70.9%

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

   if -2.2e9 < y5 < -2.00000000000000017e-86

   1. Initial program 54.1%

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

   3. Simplified 54.1%

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

   5. Taylor expanded in c around inf 58.9%

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

   if -2.00000000000000017e-86 < y5 < 2.40000000000000002e67

   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 y2 around inf 50.3%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -1.8 \cdot 10^{+117}:\\ \;\;\;\;y5 \cdot \left(\left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq -2200000000:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(i \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;y5 \leq -2 \cdot 10^{-86}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 2.4 \cdot 10^{+67}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(\left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 42.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot y4 - y0 \cdot y5\\ t_2 := y5 \cdot \left(\left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{if}\;y5 \leq -2.5 \cdot 10^{+125}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y5 \leq -48000:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot t\_1 + x \cdot \left(i \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;y5 \leq -2.35 \cdot 10^{-123}:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 2.2 \cdot 10^{+67}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot t\_1 + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y1 y4) (* y0 y5)))
        (t_2
         (*
          y5
          (+
           (+ (* i (- (* y k) (* t j))) (* y0 (- (* j y3) (* k y2))))
           (* a (- (* t y2) (* y y3)))))))
   (if (<= y5 -2.5e+125)
     t_2
     (if (<= y5 -48000.0)
       (+ (* (- (* k y2) (* j y3)) t_1) (* x (* i (- (* j y1) (* y c)))))
       (if (<= y5 -2.35e-123)
         (*
          j
          (+
           (+ (* y3 (- (* y0 y5) (* y1 y4))) (* t (- (* b y4) (* i y5))))
           (* x (- (* i y1) (* b y0)))))
         (if (<= y5 2.2e+67)
           (*
            y2
            (+
             (+ (* k t_1) (* x (- (* c y0) (* a y1))))
             (* t (- (* a y5) (* c y4)))))
           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 = (y1 * y4) - (y0 * y5);
	double t_2 = y5 * (((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))) + (a * ((t * y2) - (y * y3))));
	double tmp;
	if (y5 <= -2.5e+125) {
		tmp = t_2;
	} else if (y5 <= -48000.0) {
		tmp = (((k * y2) - (j * y3)) * t_1) + (x * (i * ((j * y1) - (y * c))));
	} else if (y5 <= -2.35e-123) {
		tmp = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))));
	} else if (y5 <= 2.2e+67) {
		tmp = y2 * (((k * t_1) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} 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 = (y1 * y4) - (y0 * y5)
    t_2 = y5 * (((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))) + (a * ((t * y2) - (y * y3))))
    if (y5 <= (-2.5d+125)) then
        tmp = t_2
    else if (y5 <= (-48000.0d0)) then
        tmp = (((k * y2) - (j * y3)) * t_1) + (x * (i * ((j * y1) - (y * c))))
    else if (y5 <= (-2.35d-123)) then
        tmp = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))))
    else if (y5 <= 2.2d+67) then
        tmp = y2 * (((k * t_1) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
    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 = (y1 * y4) - (y0 * y5);
	double t_2 = y5 * (((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))) + (a * ((t * y2) - (y * y3))));
	double tmp;
	if (y5 <= -2.5e+125) {
		tmp = t_2;
	} else if (y5 <= -48000.0) {
		tmp = (((k * y2) - (j * y3)) * t_1) + (x * (i * ((j * y1) - (y * c))));
	} else if (y5 <= -2.35e-123) {
		tmp = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))));
	} else if (y5 <= 2.2e+67) {
		tmp = y2 * (((k * t_1) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} 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 = (y1 * y4) - (y0 * y5)
	t_2 = y5 * (((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))) + (a * ((t * y2) - (y * y3))))
	tmp = 0
	if y5 <= -2.5e+125:
		tmp = t_2
	elif y5 <= -48000.0:
		tmp = (((k * y2) - (j * y3)) * t_1) + (x * (i * ((j * y1) - (y * c))))
	elif y5 <= -2.35e-123:
		tmp = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))))
	elif y5 <= 2.2e+67:
		tmp = y2 * (((k * t_1) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
	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(y1 * y4) - Float64(y0 * y5))
	t_2 = Float64(y5 * Float64(Float64(Float64(i * Float64(Float64(y * k) - Float64(t * j))) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2)))) + Float64(a * Float64(Float64(t * y2) - Float64(y * y3)))))
	tmp = 0.0
	if (y5 <= -2.5e+125)
		tmp = t_2;
	elseif (y5 <= -48000.0)
		tmp = Float64(Float64(Float64(Float64(k * y2) - Float64(j * y3)) * t_1) + Float64(x * Float64(i * Float64(Float64(j * y1) - Float64(y * c)))));
	elseif (y5 <= -2.35e-123)
		tmp = Float64(j * Float64(Float64(Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(t * Float64(Float64(b * y4) - Float64(i * y5)))) + Float64(x * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (y5 <= 2.2e+67)
		tmp = Float64(y2 * Float64(Float64(Float64(k * t_1) + Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	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 = (y1 * y4) - (y0 * y5);
	t_2 = y5 * (((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))) + (a * ((t * y2) - (y * y3))));
	tmp = 0.0;
	if (y5 <= -2.5e+125)
		tmp = t_2;
	elseif (y5 <= -48000.0)
		tmp = (((k * y2) - (j * y3)) * t_1) + (x * (i * ((j * y1) - (y * c))));
	elseif (y5 <= -2.35e-123)
		tmp = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))));
	elseif (y5 <= 2.2e+67)
		tmp = y2 * (((k * t_1) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	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[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y5 * N[(N[(N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -2.5e+125], t$95$2, If[LessEqual[y5, -48000.0], N[(N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision] + N[(x * N[(i * N[(N[(j * y1), $MachinePrecision] - N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -2.35e-123], N[(j * N[(N[(N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 2.2e+67], N[(y2 * N[(N[(N[(k * t$95$1), $MachinePrecision] + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if y5 < -2.49999999999999981e125 or 2.2e67 < y5

   1. Initial program 29.6%

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

   3. Taylor expanded in y5 around -inf 68.4%

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

   if -2.49999999999999981e125 < y5 < -48000

   1. Initial program 40.9%

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

   3. Taylor expanded in i around -inf 63.6%

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

   4. Taylor expanded in x around inf 67.0%

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

      1. fma-define 67.0%

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

      2. associate-/l* 70.7%

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

      3. fma-define 70.7%

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

      4. associate-*r* 70.7%

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

      5. mul-1-neg 70.7%

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

   6. Simplified 70.7%

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

   7. Taylor expanded in x around inf 70.9%

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

      1. *-commutative 70.9%

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

   9. Simplified 70.9%

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

   if -48000 < y5 < -2.3500000000000001e-123

   1. Initial program 48.6%

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

   3. Taylor expanded in j around inf 52.5%

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

   if -2.3500000000000001e-123 < y5 < 2.2e67

   1. Initial program 36.6%

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

   3. Taylor expanded in y2 around inf 50.8%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -2.5 \cdot 10^{+125}:\\ \;\;\;\;y5 \cdot \left(\left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq -48000:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(i \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;y5 \leq -2.35 \cdot 10^{-123}:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 2.2 \cdot 10^{+67}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(\left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 42.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot y4 - y0 \cdot y5\\ t_2 := y5 \cdot \left(\left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{if}\;y5 \leq -1.7 \cdot 10^{+129}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y5 \leq -7 \cdot 10^{-35}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot t\_1 + x \cdot \left(i \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;y5 \leq -7.5 \cdot 10^{-88}:\\ \;\;\;\;j \cdot \left(i \cdot \left(\left(x \cdot y1 - t \cdot y5\right) - y3 \cdot \frac{t\_1}{i}\right)\right)\\ \mathbf{elif}\;y5 \leq 5.3 \cdot 10^{+67}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot t\_1 + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y1 y4) (* y0 y5)))
        (t_2
         (*
          y5
          (+
           (+ (* i (- (* y k) (* t j))) (* y0 (- (* j y3) (* k y2))))
           (* a (- (* t y2) (* y y3)))))))
   (if (<= y5 -1.7e+129)
     t_2
     (if (<= y5 -7e-35)
       (+ (* (- (* k y2) (* j y3)) t_1) (* x (* i (- (* j y1) (* y c)))))
       (if (<= y5 -7.5e-88)
         (* j (* i (- (- (* x y1) (* t y5)) (* y3 (/ t_1 i)))))
         (if (<= y5 5.3e+67)
           (*
            y2
            (+
             (+ (* k t_1) (* x (- (* c y0) (* a y1))))
             (* t (- (* a y5) (* c y4)))))
           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 = (y1 * y4) - (y0 * y5);
	double t_2 = y5 * (((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))) + (a * ((t * y2) - (y * y3))));
	double tmp;
	if (y5 <= -1.7e+129) {
		tmp = t_2;
	} else if (y5 <= -7e-35) {
		tmp = (((k * y2) - (j * y3)) * t_1) + (x * (i * ((j * y1) - (y * c))));
	} else if (y5 <= -7.5e-88) {
		tmp = j * (i * (((x * y1) - (t * y5)) - (y3 * (t_1 / i))));
	} else if (y5 <= 5.3e+67) {
		tmp = y2 * (((k * t_1) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} 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 = (y1 * y4) - (y0 * y5)
    t_2 = y5 * (((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))) + (a * ((t * y2) - (y * y3))))
    if (y5 <= (-1.7d+129)) then
        tmp = t_2
    else if (y5 <= (-7d-35)) then
        tmp = (((k * y2) - (j * y3)) * t_1) + (x * (i * ((j * y1) - (y * c))))
    else if (y5 <= (-7.5d-88)) then
        tmp = j * (i * (((x * y1) - (t * y5)) - (y3 * (t_1 / i))))
    else if (y5 <= 5.3d+67) then
        tmp = y2 * (((k * t_1) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
    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 = (y1 * y4) - (y0 * y5);
	double t_2 = y5 * (((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))) + (a * ((t * y2) - (y * y3))));
	double tmp;
	if (y5 <= -1.7e+129) {
		tmp = t_2;
	} else if (y5 <= -7e-35) {
		tmp = (((k * y2) - (j * y3)) * t_1) + (x * (i * ((j * y1) - (y * c))));
	} else if (y5 <= -7.5e-88) {
		tmp = j * (i * (((x * y1) - (t * y5)) - (y3 * (t_1 / i))));
	} else if (y5 <= 5.3e+67) {
		tmp = y2 * (((k * t_1) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} 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 = (y1 * y4) - (y0 * y5)
	t_2 = y5 * (((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))) + (a * ((t * y2) - (y * y3))))
	tmp = 0
	if y5 <= -1.7e+129:
		tmp = t_2
	elif y5 <= -7e-35:
		tmp = (((k * y2) - (j * y3)) * t_1) + (x * (i * ((j * y1) - (y * c))))
	elif y5 <= -7.5e-88:
		tmp = j * (i * (((x * y1) - (t * y5)) - (y3 * (t_1 / i))))
	elif y5 <= 5.3e+67:
		tmp = y2 * (((k * t_1) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
	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(y1 * y4) - Float64(y0 * y5))
	t_2 = Float64(y5 * Float64(Float64(Float64(i * Float64(Float64(y * k) - Float64(t * j))) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2)))) + Float64(a * Float64(Float64(t * y2) - Float64(y * y3)))))
	tmp = 0.0
	if (y5 <= -1.7e+129)
		tmp = t_2;
	elseif (y5 <= -7e-35)
		tmp = Float64(Float64(Float64(Float64(k * y2) - Float64(j * y3)) * t_1) + Float64(x * Float64(i * Float64(Float64(j * y1) - Float64(y * c)))));
	elseif (y5 <= -7.5e-88)
		tmp = Float64(j * Float64(i * Float64(Float64(Float64(x * y1) - Float64(t * y5)) - Float64(y3 * Float64(t_1 / i)))));
	elseif (y5 <= 5.3e+67)
		tmp = Float64(y2 * Float64(Float64(Float64(k * t_1) + Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	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 = (y1 * y4) - (y0 * y5);
	t_2 = y5 * (((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))) + (a * ((t * y2) - (y * y3))));
	tmp = 0.0;
	if (y5 <= -1.7e+129)
		tmp = t_2;
	elseif (y5 <= -7e-35)
		tmp = (((k * y2) - (j * y3)) * t_1) + (x * (i * ((j * y1) - (y * c))));
	elseif (y5 <= -7.5e-88)
		tmp = j * (i * (((x * y1) - (t * y5)) - (y3 * (t_1 / i))));
	elseif (y5 <= 5.3e+67)
		tmp = y2 * (((k * t_1) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	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[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y5 * N[(N[(N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -1.7e+129], t$95$2, If[LessEqual[y5, -7e-35], N[(N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision] + N[(x * N[(i * N[(N[(j * y1), $MachinePrecision] - N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -7.5e-88], N[(j * N[(i * N[(N[(N[(x * y1), $MachinePrecision] - N[(t * y5), $MachinePrecision]), $MachinePrecision] - N[(y3 * N[(t$95$1 / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 5.3e+67], N[(y2 * N[(N[(N[(k * t$95$1), $MachinePrecision] + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if y5 < -1.70000000000000009e129 or 5.3e67 < y5

   1. Initial program 29.6%

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

   3. Taylor expanded in y5 around -inf 68.4%

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

   if -1.70000000000000009e129 < y5 < -6.99999999999999992e-35

   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 i around -inf 62.6%

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

   4. Taylor expanded in x around inf 57.5%

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

      1. fma-define 57.5%

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

      2. associate-/l* 60.2%

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

      3. fma-define 60.2%

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

      4. associate-*r* 62.9%

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

      5. mul-1-neg 62.9%

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

   6. Simplified 62.9%

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

   7. Taylor expanded in x around inf 60.3%

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

      1. *-commutative 60.3%

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

   9. Simplified 60.3%

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

   if -6.99999999999999992e-35 < y5 < -7.50000000000000041e-88

   1. Initial program 49.9%

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

   3. Taylor expanded in i around -inf 56.4%

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

   4. Taylor expanded in j around inf 57.2%

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

   5. Taylor expanded in i around inf 63.3%

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

      1. fma-define 63.3%

         \[\leadsto j \cdot \left(i \cdot \color{blue}{\mathsf{fma}\left(-1, t \cdot y5 - x \cdot y1, -1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{i}\right)}\right) \]

      2. mul-1-neg 63.3%

         \[\leadsto j \cdot \left(i \cdot \mathsf{fma}\left(-1, t \cdot y5 - x \cdot y1, \color{blue}{-\frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{i}}\right)\right) \]

      3. fmm-undef 63.3%

         \[\leadsto j \cdot \left(i \cdot \color{blue}{\left(-1 \cdot \left(t \cdot y5 - x \cdot y1\right) - \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{i}\right)}\right) \]

      4. mul-1-neg 63.3%

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

      5. *-commutative 63.3%

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

      6. associate-/l* 63.3%

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

      7. *-commutative 63.3%

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

   7. Simplified 63.3%

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

   if -7.50000000000000041e-88 < y5 < 5.3e67

   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 y2 around inf 50.3%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -1.7 \cdot 10^{+129}:\\ \;\;\;\;y5 \cdot \left(\left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq -7 \cdot 10^{-35}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(i \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;y5 \leq -7.5 \cdot 10^{-88}:\\ \;\;\;\;j \cdot \left(i \cdot \left(\left(x \cdot y1 - t \cdot y5\right) - y3 \cdot \frac{y1 \cdot y4 - y0 \cdot y5}{i}\right)\right)\\ \mathbf{elif}\;y5 \leq 5.3 \cdot 10^{+67}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(\left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 40.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot y4 - y0 \cdot y5\\ \mathbf{if}\;y5 \leq -8.2 \cdot 10^{+128}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq -4.8 \cdot 10^{-35}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot t\_1 + x \cdot \left(i \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;y5 \leq -2.35 \cdot 10^{-86}:\\ \;\;\;\;j \cdot \left(i \cdot \left(\left(x \cdot y1 - t \cdot y5\right) - y3 \cdot \frac{t\_1}{i}\right)\right)\\ \mathbf{elif}\;y5 \leq 2.5 \cdot 10^{+68}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot t\_1 + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k\right) - k \cdot \left(y0 \cdot y2\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y1 y4) (* y0 y5))))
   (if (<= y5 -8.2e+128)
     (* i (* y5 (- (* y k) (* t j))))
     (if (<= y5 -4.8e-35)
       (+ (* (- (* k y2) (* j y3)) t_1) (* x (* i (- (* j y1) (* y c)))))
       (if (<= y5 -2.35e-86)
         (* j (* i (- (- (* x y1) (* t y5)) (* y3 (/ t_1 i)))))
         (if (<= y5 2.5e+68)
           (*
            y2
            (+
             (+ (* k t_1) (* x (- (* c y0) (* a y1))))
             (* t (- (* a y5) (* c y4)))))
           (*
            y5
            (+
             (* a (- (* t y2) (* y y3)))
             (- (* i (* y k)) (* k (* y0 y2)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y1 * y4) - (y0 * y5);
	double tmp;
	if (y5 <= -8.2e+128) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (y5 <= -4.8e-35) {
		tmp = (((k * y2) - (j * y3)) * t_1) + (x * (i * ((j * y1) - (y * c))));
	} else if (y5 <= -2.35e-86) {
		tmp = j * (i * (((x * y1) - (t * y5)) - (y3 * (t_1 / i))));
	} else if (y5 <= 2.5e+68) {
		tmp = y2 * (((k * t_1) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * (y * k)) - (k * (y0 * y2))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y1 * y4) - (y0 * y5)
    if (y5 <= (-8.2d+128)) then
        tmp = i * (y5 * ((y * k) - (t * j)))
    else if (y5 <= (-4.8d-35)) then
        tmp = (((k * y2) - (j * y3)) * t_1) + (x * (i * ((j * y1) - (y * c))))
    else if (y5 <= (-2.35d-86)) then
        tmp = j * (i * (((x * y1) - (t * y5)) - (y3 * (t_1 / i))))
    else if (y5 <= 2.5d+68) then
        tmp = y2 * (((k * t_1) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
    else
        tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * (y * k)) - (k * (y0 * y2))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y1 * y4) - (y0 * y5);
	double tmp;
	if (y5 <= -8.2e+128) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (y5 <= -4.8e-35) {
		tmp = (((k * y2) - (j * y3)) * t_1) + (x * (i * ((j * y1) - (y * c))));
	} else if (y5 <= -2.35e-86) {
		tmp = j * (i * (((x * y1) - (t * y5)) - (y3 * (t_1 / i))));
	} else if (y5 <= 2.5e+68) {
		tmp = y2 * (((k * t_1) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * (y * k)) - (k * (y0 * y2))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y1 * y4) - (y0 * y5)
	tmp = 0
	if y5 <= -8.2e+128:
		tmp = i * (y5 * ((y * k) - (t * j)))
	elif y5 <= -4.8e-35:
		tmp = (((k * y2) - (j * y3)) * t_1) + (x * (i * ((j * y1) - (y * c))))
	elif y5 <= -2.35e-86:
		tmp = j * (i * (((x * y1) - (t * y5)) - (y3 * (t_1 / i))))
	elif y5 <= 2.5e+68:
		tmp = y2 * (((k * t_1) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
	else:
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * (y * k)) - (k * (y0 * y2))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	tmp = 0.0
	if (y5 <= -8.2e+128)
		tmp = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))));
	elseif (y5 <= -4.8e-35)
		tmp = Float64(Float64(Float64(Float64(k * y2) - Float64(j * y3)) * t_1) + Float64(x * Float64(i * Float64(Float64(j * y1) - Float64(y * c)))));
	elseif (y5 <= -2.35e-86)
		tmp = Float64(j * Float64(i * Float64(Float64(Float64(x * y1) - Float64(t * y5)) - Float64(y3 * Float64(t_1 / i)))));
	elseif (y5 <= 2.5e+68)
		tmp = Float64(y2 * Float64(Float64(Float64(k * t_1) + Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	else
		tmp = Float64(y5 * Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(Float64(i * Float64(y * k)) - Float64(k * Float64(y0 * y2)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y1 * y4) - (y0 * y5);
	tmp = 0.0;
	if (y5 <= -8.2e+128)
		tmp = i * (y5 * ((y * k) - (t * j)));
	elseif (y5 <= -4.8e-35)
		tmp = (((k * y2) - (j * y3)) * t_1) + (x * (i * ((j * y1) - (y * c))));
	elseif (y5 <= -2.35e-86)
		tmp = j * (i * (((x * y1) - (t * y5)) - (y3 * (t_1 / i))));
	elseif (y5 <= 2.5e+68)
		tmp = y2 * (((k * t_1) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	else
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * (y * k)) - (k * (y0 * y2))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -8.2e+128], N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -4.8e-35], N[(N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision] + N[(x * N[(i * N[(N[(j * y1), $MachinePrecision] - N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -2.35e-86], N[(j * N[(i * N[(N[(N[(x * y1), $MachinePrecision] - N[(t * y5), $MachinePrecision]), $MachinePrecision] - N[(y3 * N[(t$95$1 / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 2.5e+68], N[(y2 * N[(N[(N[(k * t$95$1), $MachinePrecision] + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y5 * N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(i * N[(y * k), $MachinePrecision]), $MachinePrecision] - N[(k * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y5 < -8.20000000000000023e128

   1. Initial program 39.6%

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

   3. Taylor expanded in y5 around -inf 75.9%

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

   4. Taylor expanded in i around inf 70.1%

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

   if -8.20000000000000023e128 < y5 < -4.8000000000000003e-35

   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 i around -inf 62.6%

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

   4. Taylor expanded in x around inf 57.5%

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

      1. fma-define 57.5%

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

      2. associate-/l* 60.2%

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

      3. fma-define 60.2%

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

      4. associate-*r* 62.9%

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

      5. mul-1-neg 62.9%

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

   6. Simplified 62.9%

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

   7. Taylor expanded in x around inf 60.3%

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

      1. *-commutative 60.3%

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

   9. Simplified 60.3%

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

   if -4.8000000000000003e-35 < y5 < -2.35e-86

   1. Initial program 49.9%

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

   3. Taylor expanded in i around -inf 56.4%

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

   4. Taylor expanded in j around inf 57.2%

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

   5. Taylor expanded in i around inf 63.3%

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

      1. fma-define 63.3%

         \[\leadsto j \cdot \left(i \cdot \color{blue}{\mathsf{fma}\left(-1, t \cdot y5 - x \cdot y1, -1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{i}\right)}\right) \]

      2. mul-1-neg 63.3%

         \[\leadsto j \cdot \left(i \cdot \mathsf{fma}\left(-1, t \cdot y5 - x \cdot y1, \color{blue}{-\frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{i}}\right)\right) \]

      3. fmm-undef 63.3%

         \[\leadsto j \cdot \left(i \cdot \color{blue}{\left(-1 \cdot \left(t \cdot y5 - x \cdot y1\right) - \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{i}\right)}\right) \]

      4. mul-1-neg 63.3%

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

      5. *-commutative 63.3%

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

      6. associate-/l* 63.3%

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

      7. *-commutative 63.3%

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

   7. Simplified 63.3%

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

   if -2.35e-86 < y5 < 2.5000000000000002e68

   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 y2 around inf 50.3%

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

   if 2.5000000000000002e68 < y5

   1. Initial program 23.6%

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

   3. Taylor expanded in y5 around -inf 63.9%

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

   4. Taylor expanded in j around 0 56.8%

      \[\leadsto -1 \cdot \color{blue}{\left(y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(k \cdot y\right)\right) + k \cdot \left(y0 \cdot y2\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -8.2 \cdot 10^{+128}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq -4.8 \cdot 10^{-35}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(i \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;y5 \leq -2.35 \cdot 10^{-86}:\\ \;\;\;\;j \cdot \left(i \cdot \left(\left(x \cdot y1 - t \cdot y5\right) - y3 \cdot \frac{y1 \cdot y4 - y0 \cdot y5}{i}\right)\right)\\ \mathbf{elif}\;y5 \leq 2.5 \cdot 10^{+68}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k\right) - k \cdot \left(y0 \cdot y2\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 43.2% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y3 \leq -3.1 \cdot 10^{+29} \lor \neg \left(y3 \leq 175000000000\right):\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= y3 -3.1e+29) (not (<= y3 175000000000.0)))
   (*
    y3
    (+
     (* y (- (* c y4) (* a y5)))
     (+ (* j (- (* y0 y5) (* y1 y4))) (* z (- (* a y1) (* c y0))))))
   (*
    y2
    (+
     (+ (* k (- (* y1 y4) (* y0 y5))) (* x (- (* c y0) (* a y1))))
     (* t (- (* a y5) (* c y4)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y3 <= -3.1e+29) || !(y3 <= 175000000000.0)) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	} else {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((y3 <= (-3.1d+29)) .or. (.not. (y3 <= 175000000000.0d0))) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))))
    else
        tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y3 <= -3.1e+29) || !(y3 <= 175000000000.0)) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	} else {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (y3 <= -3.1e+29) or not (y3 <= 175000000000.0):
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))))
	else:
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((y3 <= -3.1e+29) || !(y3 <= 175000000000.0))
		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 = Float64(y2 * Float64(Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((y3 <= -3.1e+29) || ~((y3 <= 175000000000.0)))
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	else
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[y3, -3.1e+29], N[Not[LessEqual[y3, 175000000000.0]], $MachinePrecision]], 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], N[(y2 * N[(N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y3 < -3.0999999999999999e29 or 1.75e11 < y3

   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 y3 around -inf 56.0%

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

   if -3.0999999999999999e29 < y3 < 1.75e11

   1. Initial program 39.3%

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

   3. Taylor expanded in y2 around inf 51.2%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -3.1 \cdot 10^{+29} \lor \neg \left(y3 \leq 175000000000\right):\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 31.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -2.05 \cdot 10^{+264}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq -2.6 \cdot 10^{+112}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq -2.1 \cdot 10^{-14}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y1 \leq -3.5 \cdot 10^{-275}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 3.1 \cdot 10^{-60}:\\ \;\;\;\;j \cdot \left(i \cdot \left(y0 \cdot \left(y3 \cdot \frac{y5}{i}\right) - t \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y1 -2.05e+264)
   (* y1 (+ (* i (- (* x j) (* z k))) (* y4 (- (* k y2) (* j y3)))))
   (if (<= y1 -2.6e+112)
     (* a (* y3 (- (* z y1) (* y y5))))
     (if (<= y1 -2.1e-14)
       (* a (* b (- (* x y) (* z t))))
       (if (<= y1 -3.5e-275)
         (* i (* y5 (- (* y k) (* t j))))
         (if (<= y1 3.1e-60)
           (* j (* i (- (* y0 (* y3 (/ y5 i))) (* t y5))))
           (* k (* y2 (- (* y1 y4) (* y0 y5))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y1 <= -2.05e+264) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + (y4 * ((k * y2) - (j * y3))));
	} else if (y1 <= -2.6e+112) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (y1 <= -2.1e-14) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y1 <= -3.5e-275) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (y1 <= 3.1e-60) {
		tmp = j * (i * ((y0 * (y3 * (y5 / i))) - (t * y5)));
	} else {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y1 <= (-2.05d+264)) then
        tmp = y1 * ((i * ((x * j) - (z * k))) + (y4 * ((k * y2) - (j * y3))))
    else if (y1 <= (-2.6d+112)) then
        tmp = a * (y3 * ((z * y1) - (y * y5)))
    else if (y1 <= (-2.1d-14)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (y1 <= (-3.5d-275)) then
        tmp = i * (y5 * ((y * k) - (t * j)))
    else if (y1 <= 3.1d-60) then
        tmp = j * (i * ((y0 * (y3 * (y5 / i))) - (t * y5)))
    else
        tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y1 <= -2.05e+264) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + (y4 * ((k * y2) - (j * y3))));
	} else if (y1 <= -2.6e+112) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (y1 <= -2.1e-14) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y1 <= -3.5e-275) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (y1 <= 3.1e-60) {
		tmp = j * (i * ((y0 * (y3 * (y5 / i))) - (t * y5)));
	} else {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y1 <= -2.05e+264:
		tmp = y1 * ((i * ((x * j) - (z * k))) + (y4 * ((k * y2) - (j * y3))))
	elif y1 <= -2.6e+112:
		tmp = a * (y3 * ((z * y1) - (y * y5)))
	elif y1 <= -2.1e-14:
		tmp = a * (b * ((x * y) - (z * t)))
	elif y1 <= -3.5e-275:
		tmp = i * (y5 * ((y * k) - (t * j)))
	elif y1 <= 3.1e-60:
		tmp = j * (i * ((y0 * (y3 * (y5 / i))) - (t * y5)))
	else:
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y1 <= -2.05e+264)
		tmp = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) + Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3)))));
	elseif (y1 <= -2.6e+112)
		tmp = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))));
	elseif (y1 <= -2.1e-14)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y1 <= -3.5e-275)
		tmp = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))));
	elseif (y1 <= 3.1e-60)
		tmp = Float64(j * Float64(i * Float64(Float64(y0 * Float64(y3 * Float64(y5 / i))) - Float64(t * y5))));
	else
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y1 <= -2.05e+264)
		tmp = y1 * ((i * ((x * j) - (z * k))) + (y4 * ((k * y2) - (j * y3))));
	elseif (y1 <= -2.6e+112)
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	elseif (y1 <= -2.1e-14)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (y1 <= -3.5e-275)
		tmp = i * (y5 * ((y * k) - (t * j)));
	elseif (y1 <= 3.1e-60)
		tmp = j * (i * ((y0 * (y3 * (y5 / i))) - (t * y5)));
	else
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y1, -2.05e+264], N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -2.6e+112], N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -2.1e-14], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -3.5e-275], N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 3.1e-60], N[(j * N[(i * N[(N[(y0 * N[(y3 * N[(y5 / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y1 < -2.05e264

   1. Initial program 51.9%

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

   3. Taylor expanded in i around -inf 60.0%

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

   4. Taylor expanded in y1 around inf 71.2%

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

   if -2.05e264 < y1 < -2.6000000000000001e112

   1. Initial program 13.0%

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

   3. Simplified 13.0%

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

   5. Taylor expanded in a around inf 48.3%

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

   6. Taylor expanded in y3 around inf 57.2%

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

   if -2.6000000000000001e112 < y1 < -2.0999999999999999e-14

   1. Initial program 35.0%

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

   3. Simplified 35.0%

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

   5. Taylor expanded in a around inf 55.7%

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

   6. Taylor expanded in b around inf 65.5%

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

      1. neg-mul-1 65.5%

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

      2. +-commutative 65.5%

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

      3. sub-neg 65.5%

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

   8. Simplified 65.5%

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

   if -2.0999999999999999e-14 < y1 < -3.49999999999999969e-275

   1. Initial program 46.8%

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

   3. Taylor expanded in y5 around -inf 41.5%

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

   4. Taylor expanded in i around inf 43.4%

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

   if -3.49999999999999969e-275 < y1 < 3.09999999999999988e-60

   1. Initial program 36.0%

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

   3. Taylor expanded in i around -inf 31.8%

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

   4. Taylor expanded in j around inf 44.8%

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

   5. Taylor expanded in i around inf 47.8%

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

      1. fma-define 47.8%

         \[\leadsto j \cdot \left(i \cdot \color{blue}{\mathsf{fma}\left(-1, t \cdot y5 - x \cdot y1, -1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{i}\right)}\right) \]

      2. mul-1-neg 47.8%

         \[\leadsto j \cdot \left(i \cdot \mathsf{fma}\left(-1, t \cdot y5 - x \cdot y1, \color{blue}{-\frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{i}}\right)\right) \]

      3. fmm-undef 47.8%

         \[\leadsto j \cdot \left(i \cdot \color{blue}{\left(-1 \cdot \left(t \cdot y5 - x \cdot y1\right) - \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{i}\right)}\right) \]

      4. mul-1-neg 47.8%

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

      5. *-commutative 47.8%

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

      6. associate-/l* 47.8%

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

      7. *-commutative 47.8%

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

   7. Simplified 47.8%

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

   8. Taylor expanded in y1 around 0 43.4%

      \[\leadsto j \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(-1 \cdot \frac{y0 \cdot \left(y3 \cdot y5\right)}{i} + t \cdot y5\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 43.4%

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

      2. *-commutative 43.4%

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

      3. distribute-rgt-neg-in 43.4%

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

      4. +-commutative 43.4%

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

      5. mul-1-neg 43.4%

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

      6. unsub-neg 43.4%

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

      7. associate-/l* 44.9%

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

      8. associate-/l* 44.9%

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

   10. Simplified 44.9%

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

   if 3.09999999999999988e-60 < y1

   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 y2 around inf 56.2%

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

   4. Taylor expanded in k around inf 50.0%

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

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -2.05 \cdot 10^{+264}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq -2.6 \cdot 10^{+112}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq -2.1 \cdot 10^{-14}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y1 \leq -3.5 \cdot 10^{-275}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 3.1 \cdot 10^{-60}:\\ \;\;\;\;j \cdot \left(i \cdot \left(y0 \cdot \left(y3 \cdot \frac{y5}{i}\right) - t \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 21.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(\left(t \cdot i\right) \cdot \left(-y5\right)\right)\\ \mathbf{if}\;y1 \leq -1.28 \cdot 10^{+123}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq -5.1 \cdot 10^{-39}:\\ \;\;\;\;a \cdot \left(b \cdot \left(z \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -3 \cdot 10^{-82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq 6.8 \cdot 10^{-260}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(t \cdot \left(-c\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 3.9 \cdot 10^{-190}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y0\right) \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y1 \leq 2.3 \cdot 10^{-60}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* (* t i) (- y5)))))
   (if (<= y1 -1.28e+123)
     (* a (* y3 (* z y1)))
     (if (<= y1 -5.1e-39)
       (* a (* b (* z (- t))))
       (if (<= y1 -3e-82)
         t_1
         (if (<= y1 6.8e-260)
           (* y2 (* y4 (* t (- c))))
           (if (<= y1 3.9e-190)
             (* b (* (* x y0) (- j)))
             (if (<= y1 2.3e-60) t_1 (* k (* y4 (* 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 = j * ((t * i) * -y5);
	double tmp;
	if (y1 <= -1.28e+123) {
		tmp = a * (y3 * (z * y1));
	} else if (y1 <= -5.1e-39) {
		tmp = a * (b * (z * -t));
	} else if (y1 <= -3e-82) {
		tmp = t_1;
	} else if (y1 <= 6.8e-260) {
		tmp = y2 * (y4 * (t * -c));
	} else if (y1 <= 3.9e-190) {
		tmp = b * ((x * y0) * -j);
	} else if (y1 <= 2.3e-60) {
		tmp = t_1;
	} else {
		tmp = k * (y4 * (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 = j * ((t * i) * -y5)
    if (y1 <= (-1.28d+123)) then
        tmp = a * (y3 * (z * y1))
    else if (y1 <= (-5.1d-39)) then
        tmp = a * (b * (z * -t))
    else if (y1 <= (-3d-82)) then
        tmp = t_1
    else if (y1 <= 6.8d-260) then
        tmp = y2 * (y4 * (t * -c))
    else if (y1 <= 3.9d-190) then
        tmp = b * ((x * y0) * -j)
    else if (y1 <= 2.3d-60) then
        tmp = t_1
    else
        tmp = k * (y4 * (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 = j * ((t * i) * -y5);
	double tmp;
	if (y1 <= -1.28e+123) {
		tmp = a * (y3 * (z * y1));
	} else if (y1 <= -5.1e-39) {
		tmp = a * (b * (z * -t));
	} else if (y1 <= -3e-82) {
		tmp = t_1;
	} else if (y1 <= 6.8e-260) {
		tmp = y2 * (y4 * (t * -c));
	} else if (y1 <= 3.9e-190) {
		tmp = b * ((x * y0) * -j);
	} else if (y1 <= 2.3e-60) {
		tmp = t_1;
	} else {
		tmp = k * (y4 * (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 = j * ((t * i) * -y5)
	tmp = 0
	if y1 <= -1.28e+123:
		tmp = a * (y3 * (z * y1))
	elif y1 <= -5.1e-39:
		tmp = a * (b * (z * -t))
	elif y1 <= -3e-82:
		tmp = t_1
	elif y1 <= 6.8e-260:
		tmp = y2 * (y4 * (t * -c))
	elif y1 <= 3.9e-190:
		tmp = b * ((x * y0) * -j)
	elif y1 <= 2.3e-60:
		tmp = t_1
	else:
		tmp = k * (y4 * (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(j * Float64(Float64(t * i) * Float64(-y5)))
	tmp = 0.0
	if (y1 <= -1.28e+123)
		tmp = Float64(a * Float64(y3 * Float64(z * y1)));
	elseif (y1 <= -5.1e-39)
		tmp = Float64(a * Float64(b * Float64(z * Float64(-t))));
	elseif (y1 <= -3e-82)
		tmp = t_1;
	elseif (y1 <= 6.8e-260)
		tmp = Float64(y2 * Float64(y4 * Float64(t * Float64(-c))));
	elseif (y1 <= 3.9e-190)
		tmp = Float64(b * Float64(Float64(x * y0) * Float64(-j)));
	elseif (y1 <= 2.3e-60)
		tmp = t_1;
	else
		tmp = Float64(k * Float64(y4 * Float64(y1 * 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 = j * ((t * i) * -y5);
	tmp = 0.0;
	if (y1 <= -1.28e+123)
		tmp = a * (y3 * (z * y1));
	elseif (y1 <= -5.1e-39)
		tmp = a * (b * (z * -t));
	elseif (y1 <= -3e-82)
		tmp = t_1;
	elseif (y1 <= 6.8e-260)
		tmp = y2 * (y4 * (t * -c));
	elseif (y1 <= 3.9e-190)
		tmp = b * ((x * y0) * -j);
	elseif (y1 <= 2.3e-60)
		tmp = t_1;
	else
		tmp = k * (y4 * (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[(j * N[(N[(t * i), $MachinePrecision] * (-y5)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -1.28e+123], N[(a * N[(y3 * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -5.1e-39], N[(a * N[(b * N[(z * (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -3e-82], t$95$1, If[LessEqual[y1, 6.8e-260], N[(y2 * N[(y4 * N[(t * (-c)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 3.9e-190], N[(b * N[(N[(x * y0), $MachinePrecision] * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 2.3e-60], t$95$1, N[(k * N[(y4 * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y1 < -1.28000000000000005e123

   1. Initial program 26.4%

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

   3. Simplified 26.4%

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

   5. Taylor expanded in a around inf 45.6%

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

   6. Taylor expanded in y1 around inf 42.9%

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

      1. associate-*r* 42.9%

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

      2. neg-mul-1 42.9%

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

   8. Simplified 42.9%

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

   9. Taylor expanded in x around 0 30.5%

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

       1. *-commutative 30.5%

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

   11. Simplified 30.5%

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

   12. Taylor expanded in a around 0 30.5%

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

       1. *-commutative 30.5%

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

       2. associate-*l* 36.6%

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

       3. *-commutative 36.6%

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

   14. Simplified 36.6%

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

   if -1.28000000000000005e123 < y1 < -5.09999999999999988e-39

   1. Initial program 34.6%

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

   3. Simplified 34.6%

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

   5. Taylor expanded in a around inf 42.9%

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

   6. Taylor expanded in b around inf 54.8%

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

      1. neg-mul-1 54.8%

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

      2. +-commutative 54.8%

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

      3. sub-neg 54.8%

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

   8. Simplified 54.8%

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

   9. Taylor expanded in x around 0 35.9%

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

       1. associate-*r* 35.9%

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

       2. neg-mul-1 35.9%

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

   11. Simplified 35.9%

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

   if -5.09999999999999988e-39 < y1 < -2.9999999999999999e-82 or 3.89999999999999995e-190 < y1 < 2.3000000000000001e-60

   1. Initial program 43.8%

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

   3. Taylor expanded in i around -inf 42.0%

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

   4. Taylor expanded in j around inf 49.0%

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

   5. Taylor expanded in i around inf 49.0%

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

      1. fma-define 49.0%

         \[\leadsto j \cdot \left(i \cdot \color{blue}{\mathsf{fma}\left(-1, t \cdot y5 - x \cdot y1, -1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{i}\right)}\right) \]

      2. mul-1-neg 49.0%

         \[\leadsto j \cdot \left(i \cdot \mathsf{fma}\left(-1, t \cdot y5 - x \cdot y1, \color{blue}{-\frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{i}}\right)\right) \]

      3. fmm-undef 49.0%

         \[\leadsto j \cdot \left(i \cdot \color{blue}{\left(-1 \cdot \left(t \cdot y5 - x \cdot y1\right) - \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{i}\right)}\right) \]

      4. mul-1-neg 49.0%

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

      5. *-commutative 49.0%

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

      6. associate-/l* 49.0%

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

      7. *-commutative 49.0%

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

   7. Simplified 49.0%

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

   8. Taylor expanded in t around inf 42.7%

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

      1. mul-1-neg 42.7%

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

      2. associate-*r* 42.6%

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

   10. Simplified 42.6%

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

   if -2.9999999999999999e-82 < y1 < 6.7999999999999997e-260

   1. Initial program 42.4%

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

   3. Taylor expanded in y2 around inf 40.4%

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

   4. Taylor expanded in y4 around inf 33.7%

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

   5. Taylor expanded in k around 0 27.3%

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

      1. mul-1-neg 27.3%

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

      2. associate-*r* 32.1%

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

      3. *-commutative 32.1%

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

      4. distribute-lft-neg-in 32.1%

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

      5. distribute-rgt-neg-in 32.1%

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

   7. Simplified 32.1%

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

   if 6.7999999999999997e-260 < y1 < 3.89999999999999995e-190

   1. Initial program 26.7%

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

   3. Taylor expanded in y0 around inf 80.1%

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

   4. Taylor expanded in j around inf 67.1%

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

   5. Taylor expanded in y3 around 0 60.4%

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

      1. associate-*r* 60.4%

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

      2. neg-mul-1 60.4%

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

   7. Simplified 60.4%

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

   if 2.3000000000000001e-60 < y1

   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 y2 around inf 56.2%

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

   4. Taylor expanded in y4 around inf 43.8%

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

   5. Taylor expanded in k around inf 36.1%

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

      1. associate-*r* 37.4%

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

   7. Simplified 37.4%

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

4. Final simplification 38.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -1.28 \cdot 10^{+123}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq -5.1 \cdot 10^{-39}:\\ \;\;\;\;a \cdot \left(b \cdot \left(z \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -3 \cdot 10^{-82}:\\ \;\;\;\;j \cdot \left(\left(t \cdot i\right) \cdot \left(-y5\right)\right)\\ \mathbf{elif}\;y1 \leq 6.8 \cdot 10^{-260}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(t \cdot \left(-c\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 3.9 \cdot 10^{-190}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y0\right) \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y1 \leq 2.3 \cdot 10^{-60}:\\ \;\;\;\;j \cdot \left(\left(t \cdot i\right) \cdot \left(-y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 21.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(\left(t \cdot i\right) \cdot \left(-y5\right)\right)\\ \mathbf{if}\;y1 \leq -9.2 \cdot 10^{+123}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq -8.5 \cdot 10^{-40}:\\ \;\;\;\;a \cdot \left(b \cdot \left(z \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -5.6 \cdot 10^{-82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq 7.6 \cdot 10^{-266}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(t \cdot \left(-c\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 4.5 \cdot 10^{-190}:\\ \;\;\;\;j \cdot \left(b \cdot \left(x \cdot \left(-y0\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 2.4 \cdot 10^{-60}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* (* t i) (- y5)))))
   (if (<= y1 -9.2e+123)
     (* a (* y3 (* z y1)))
     (if (<= y1 -8.5e-40)
       (* a (* b (* z (- t))))
       (if (<= y1 -5.6e-82)
         t_1
         (if (<= y1 7.6e-266)
           (* y2 (* y4 (* t (- c))))
           (if (<= y1 4.5e-190)
             (* j (* b (* x (- y0))))
             (if (<= y1 2.4e-60) t_1 (* k (* y4 (* 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 = j * ((t * i) * -y5);
	double tmp;
	if (y1 <= -9.2e+123) {
		tmp = a * (y3 * (z * y1));
	} else if (y1 <= -8.5e-40) {
		tmp = a * (b * (z * -t));
	} else if (y1 <= -5.6e-82) {
		tmp = t_1;
	} else if (y1 <= 7.6e-266) {
		tmp = y2 * (y4 * (t * -c));
	} else if (y1 <= 4.5e-190) {
		tmp = j * (b * (x * -y0));
	} else if (y1 <= 2.4e-60) {
		tmp = t_1;
	} else {
		tmp = k * (y4 * (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 = j * ((t * i) * -y5)
    if (y1 <= (-9.2d+123)) then
        tmp = a * (y3 * (z * y1))
    else if (y1 <= (-8.5d-40)) then
        tmp = a * (b * (z * -t))
    else if (y1 <= (-5.6d-82)) then
        tmp = t_1
    else if (y1 <= 7.6d-266) then
        tmp = y2 * (y4 * (t * -c))
    else if (y1 <= 4.5d-190) then
        tmp = j * (b * (x * -y0))
    else if (y1 <= 2.4d-60) then
        tmp = t_1
    else
        tmp = k * (y4 * (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 = j * ((t * i) * -y5);
	double tmp;
	if (y1 <= -9.2e+123) {
		tmp = a * (y3 * (z * y1));
	} else if (y1 <= -8.5e-40) {
		tmp = a * (b * (z * -t));
	} else if (y1 <= -5.6e-82) {
		tmp = t_1;
	} else if (y1 <= 7.6e-266) {
		tmp = y2 * (y4 * (t * -c));
	} else if (y1 <= 4.5e-190) {
		tmp = j * (b * (x * -y0));
	} else if (y1 <= 2.4e-60) {
		tmp = t_1;
	} else {
		tmp = k * (y4 * (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 = j * ((t * i) * -y5)
	tmp = 0
	if y1 <= -9.2e+123:
		tmp = a * (y3 * (z * y1))
	elif y1 <= -8.5e-40:
		tmp = a * (b * (z * -t))
	elif y1 <= -5.6e-82:
		tmp = t_1
	elif y1 <= 7.6e-266:
		tmp = y2 * (y4 * (t * -c))
	elif y1 <= 4.5e-190:
		tmp = j * (b * (x * -y0))
	elif y1 <= 2.4e-60:
		tmp = t_1
	else:
		tmp = k * (y4 * (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(j * Float64(Float64(t * i) * Float64(-y5)))
	tmp = 0.0
	if (y1 <= -9.2e+123)
		tmp = Float64(a * Float64(y3 * Float64(z * y1)));
	elseif (y1 <= -8.5e-40)
		tmp = Float64(a * Float64(b * Float64(z * Float64(-t))));
	elseif (y1 <= -5.6e-82)
		tmp = t_1;
	elseif (y1 <= 7.6e-266)
		tmp = Float64(y2 * Float64(y4 * Float64(t * Float64(-c))));
	elseif (y1 <= 4.5e-190)
		tmp = Float64(j * Float64(b * Float64(x * Float64(-y0))));
	elseif (y1 <= 2.4e-60)
		tmp = t_1;
	else
		tmp = Float64(k * Float64(y4 * Float64(y1 * 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 = j * ((t * i) * -y5);
	tmp = 0.0;
	if (y1 <= -9.2e+123)
		tmp = a * (y3 * (z * y1));
	elseif (y1 <= -8.5e-40)
		tmp = a * (b * (z * -t));
	elseif (y1 <= -5.6e-82)
		tmp = t_1;
	elseif (y1 <= 7.6e-266)
		tmp = y2 * (y4 * (t * -c));
	elseif (y1 <= 4.5e-190)
		tmp = j * (b * (x * -y0));
	elseif (y1 <= 2.4e-60)
		tmp = t_1;
	else
		tmp = k * (y4 * (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[(j * N[(N[(t * i), $MachinePrecision] * (-y5)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -9.2e+123], N[(a * N[(y3 * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -8.5e-40], N[(a * N[(b * N[(z * (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -5.6e-82], t$95$1, If[LessEqual[y1, 7.6e-266], N[(y2 * N[(y4 * N[(t * (-c)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 4.5e-190], N[(j * N[(b * N[(x * (-y0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 2.4e-60], t$95$1, N[(k * N[(y4 * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y1 < -9.19999999999999962e123

   1. Initial program 26.4%

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

   3. Simplified 26.4%

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

   5. Taylor expanded in a around inf 45.6%

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

   6. Taylor expanded in y1 around inf 42.9%

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

      1. associate-*r* 42.9%

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

      2. neg-mul-1 42.9%

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

   8. Simplified 42.9%

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

   9. Taylor expanded in x around 0 30.5%

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

       1. *-commutative 30.5%

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

   11. Simplified 30.5%

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

   12. Taylor expanded in a around 0 30.5%

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

       1. *-commutative 30.5%

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

       2. associate-*l* 36.6%

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

       3. *-commutative 36.6%

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

   14. Simplified 36.6%

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

   if -9.19999999999999962e123 < y1 < -8.4999999999999998e-40

   1. Initial program 34.6%

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

   3. Simplified 34.6%

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

   5. Taylor expanded in a around inf 42.9%

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

   6. Taylor expanded in b around inf 54.8%

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

      1. neg-mul-1 54.8%

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

      2. +-commutative 54.8%

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

      3. sub-neg 54.8%

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

   8. Simplified 54.8%

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

   9. Taylor expanded in x around 0 35.9%

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

       1. associate-*r* 35.9%

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

       2. neg-mul-1 35.9%

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

   11. Simplified 35.9%

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

   if -8.4999999999999998e-40 < y1 < -5.60000000000000049e-82 or 4.50000000000000021e-190 < y1 < 2.40000000000000009e-60

   1. Initial program 43.8%

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

   3. Taylor expanded in i around -inf 42.0%

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

   4. Taylor expanded in j around inf 49.0%

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

   5. Taylor expanded in i around inf 49.0%

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

      1. fma-define 49.0%

         \[\leadsto j \cdot \left(i \cdot \color{blue}{\mathsf{fma}\left(-1, t \cdot y5 - x \cdot y1, -1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{i}\right)}\right) \]

      2. mul-1-neg 49.0%

         \[\leadsto j \cdot \left(i \cdot \mathsf{fma}\left(-1, t \cdot y5 - x \cdot y1, \color{blue}{-\frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{i}}\right)\right) \]

      3. fmm-undef 49.0%

         \[\leadsto j \cdot \left(i \cdot \color{blue}{\left(-1 \cdot \left(t \cdot y5 - x \cdot y1\right) - \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{i}\right)}\right) \]

      4. mul-1-neg 49.0%

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

      5. *-commutative 49.0%

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

      6. associate-/l* 49.0%

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

      7. *-commutative 49.0%

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

   7. Simplified 49.0%

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

   8. Taylor expanded in t around inf 42.7%

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

      1. mul-1-neg 42.7%

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

      2. associate-*r* 42.6%

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

   10. Simplified 42.6%

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

   if -5.60000000000000049e-82 < y1 < 7.59999999999999988e-266

   1. Initial program 43.2%

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

   3. Taylor expanded in y2 around inf 39.4%

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

   4. Taylor expanded in y4 around inf 34.3%

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

   5. Taylor expanded in k around 0 27.7%

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

      1. mul-1-neg 27.7%

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

      2. associate-*r* 32.6%

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

      3. *-commutative 32.6%

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

      4. distribute-lft-neg-in 32.6%

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

      5. distribute-rgt-neg-in 32.6%

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

   7. Simplified 32.6%

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

   if 7.59999999999999988e-266 < y1 < 4.50000000000000021e-190

   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 y0 around inf 75.1%

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

   4. Taylor expanded in j around inf 62.9%

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

   5. Taylor expanded in y3 around 0 50.9%

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

      1. associate-*r* 50.9%

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

      2. neg-mul-1 50.9%

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

   7. Simplified 50.9%

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

   if 2.40000000000000009e-60 < y1

   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 y2 around inf 56.2%

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

   4. Taylor expanded in y4 around inf 43.8%

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

   5. Taylor expanded in k around inf 36.1%

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

      1. associate-*r* 37.4%

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

   7. Simplified 37.4%

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

4. Final simplification 37.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -9.2 \cdot 10^{+123}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq -8.5 \cdot 10^{-40}:\\ \;\;\;\;a \cdot \left(b \cdot \left(z \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -5.6 \cdot 10^{-82}:\\ \;\;\;\;j \cdot \left(\left(t \cdot i\right) \cdot \left(-y5\right)\right)\\ \mathbf{elif}\;y1 \leq 7.6 \cdot 10^{-266}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(t \cdot \left(-c\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 4.5 \cdot 10^{-190}:\\ \;\;\;\;j \cdot \left(b \cdot \left(x \cdot \left(-y0\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 2.4 \cdot 10^{-60}:\\ \;\;\;\;j \cdot \left(\left(t \cdot i\right) \cdot \left(-y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 38.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot y4 - y0 \cdot y5\\ \mathbf{if}\;y \leq -1.95 \cdot 10^{+175}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-112}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot t\_1 + x \cdot \left(i \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+77}:\\ \;\;\;\;j \cdot \left(i \cdot \left(\left(x \cdot y1 - t \cdot y5\right) - y3 \cdot \frac{t\_1}{i}\right)\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+256}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y1 y4) (* y0 y5))))
   (if (<= y -1.95e+175)
     (* a (* y3 (- (* z y1) (* y y5))))
     (if (<= y -6e-112)
       (+ (* (- (* k y2) (* j y3)) t_1) (* x (* i (- (* j y1) (* y c)))))
       (if (<= y 3.3e+77)
         (* j (* i (- (- (* x y1) (* t y5)) (* y3 (/ t_1 i)))))
         (if (<= y 4.6e+256)
           (* i (* y5 (- (* y k) (* t j))))
           (* a (* y (- (* x b) (* y3 y5))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y1 * y4) - (y0 * y5);
	double tmp;
	if (y <= -1.95e+175) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (y <= -6e-112) {
		tmp = (((k * y2) - (j * y3)) * t_1) + (x * (i * ((j * y1) - (y * c))));
	} else if (y <= 3.3e+77) {
		tmp = j * (i * (((x * y1) - (t * y5)) - (y3 * (t_1 / i))));
	} else if (y <= 4.6e+256) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y1 * y4) - (y0 * y5)
    if (y <= (-1.95d+175)) then
        tmp = a * (y3 * ((z * y1) - (y * y5)))
    else if (y <= (-6d-112)) then
        tmp = (((k * y2) - (j * y3)) * t_1) + (x * (i * ((j * y1) - (y * c))))
    else if (y <= 3.3d+77) then
        tmp = j * (i * (((x * y1) - (t * y5)) - (y3 * (t_1 / i))))
    else if (y <= 4.6d+256) then
        tmp = i * (y5 * ((y * k) - (t * j)))
    else
        tmp = a * (y * ((x * b) - (y3 * y5)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y1 * y4) - (y0 * y5);
	double tmp;
	if (y <= -1.95e+175) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (y <= -6e-112) {
		tmp = (((k * y2) - (j * y3)) * t_1) + (x * (i * ((j * y1) - (y * c))));
	} else if (y <= 3.3e+77) {
		tmp = j * (i * (((x * y1) - (t * y5)) - (y3 * (t_1 / i))));
	} else if (y <= 4.6e+256) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y1 * y4) - (y0 * y5)
	tmp = 0
	if y <= -1.95e+175:
		tmp = a * (y3 * ((z * y1) - (y * y5)))
	elif y <= -6e-112:
		tmp = (((k * y2) - (j * y3)) * t_1) + (x * (i * ((j * y1) - (y * c))))
	elif y <= 3.3e+77:
		tmp = j * (i * (((x * y1) - (t * y5)) - (y3 * (t_1 / i))))
	elif y <= 4.6e+256:
		tmp = i * (y5 * ((y * k) - (t * j)))
	else:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	tmp = 0.0
	if (y <= -1.95e+175)
		tmp = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))));
	elseif (y <= -6e-112)
		tmp = Float64(Float64(Float64(Float64(k * y2) - Float64(j * y3)) * t_1) + Float64(x * Float64(i * Float64(Float64(j * y1) - Float64(y * c)))));
	elseif (y <= 3.3e+77)
		tmp = Float64(j * Float64(i * Float64(Float64(Float64(x * y1) - Float64(t * y5)) - Float64(y3 * Float64(t_1 / i)))));
	elseif (y <= 4.6e+256)
		tmp = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))));
	else
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y1 * y4) - (y0 * y5);
	tmp = 0.0;
	if (y <= -1.95e+175)
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	elseif (y <= -6e-112)
		tmp = (((k * y2) - (j * y3)) * t_1) + (x * (i * ((j * y1) - (y * c))));
	elseif (y <= 3.3e+77)
		tmp = j * (i * (((x * y1) - (t * y5)) - (y3 * (t_1 / i))));
	elseif (y <= 4.6e+256)
		tmp = i * (y5 * ((y * k) - (t * j)));
	else
		tmp = a * (y * ((x * b) - (y3 * y5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.95e+175], N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6e-112], N[(N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision] + N[(x * N[(i * N[(N[(j * y1), $MachinePrecision] - N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.3e+77], N[(j * N[(i * N[(N[(N[(x * y1), $MachinePrecision] - N[(t * y5), $MachinePrecision]), $MachinePrecision] - N[(y3 * N[(t$95$1 / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.6e+256], N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.94999999999999986e175

   1. Initial program 28.0%

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

   3. Simplified 28.0%

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

   5. Taylor expanded in a around inf 52.2%

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

   6. Taylor expanded in y3 around inf 68.1%

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

   if -1.94999999999999986e175 < y < -6.0000000000000002e-112

   1. Initial program 40.6%

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

   3. Taylor expanded in i around -inf 43.9%

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

   4. Taylor expanded in x around inf 45.3%

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

      1. fma-define 46.6%

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

      2. associate-/l* 45.3%

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

      3. fma-define 45.3%

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

      4. associate-*r* 43.9%

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

      5. mul-1-neg 43.9%

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

   6. Simplified 43.9%

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

   7. Taylor expanded in x around inf 48.2%

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

      1. *-commutative 48.2%

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

   9. Simplified 48.2%

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

   if -6.0000000000000002e-112 < y < 3.2999999999999998e77

   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 i around -inf 35.9%

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

   4. Taylor expanded in j around inf 46.5%

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

   5. Taylor expanded in i around inf 48.4%

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

      1. fma-define 48.4%

         \[\leadsto j \cdot \left(i \cdot \color{blue}{\mathsf{fma}\left(-1, t \cdot y5 - x \cdot y1, -1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{i}\right)}\right) \]

      2. mul-1-neg 48.4%

         \[\leadsto j \cdot \left(i \cdot \mathsf{fma}\left(-1, t \cdot y5 - x \cdot y1, \color{blue}{-\frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{i}}\right)\right) \]

      3. fmm-undef 48.4%

         \[\leadsto j \cdot \left(i \cdot \color{blue}{\left(-1 \cdot \left(t \cdot y5 - x \cdot y1\right) - \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{i}\right)}\right) \]

      4. mul-1-neg 48.4%

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

      5. *-commutative 48.4%

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

      6. associate-/l* 49.5%

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

      7. *-commutative 49.5%

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

   7. Simplified 49.5%

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

   if 3.2999999999999998e77 < y < 4.5999999999999997e256

   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 y5 around -inf 39.6%

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

   4. Taylor expanded in i around inf 56.9%

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

   if 4.5999999999999997e256 < y

   1. Initial program 9.1%

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

   3. Simplified 9.1%

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

   5. Taylor expanded in a around inf 63.8%

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

   6. Taylor expanded in y around inf 73.2%

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

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+175}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-112}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(i \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+77}:\\ \;\;\;\;j \cdot \left(i \cdot \left(\left(x \cdot y1 - t \cdot y5\right) - y3 \cdot \frac{y1 \cdot y4 - y0 \cdot y5}{i}\right)\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+256}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 30.3% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -3.6 \cdot 10^{+113}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq -2.9 \cdot 10^{-18}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y1 \leq -3.5 \cdot 10^{-278}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 3.1 \cdot 10^{-60}:\\ \;\;\;\;j \cdot \left(i \cdot \left(y0 \cdot \left(y3 \cdot \frac{y5}{i}\right) - t \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y1 -3.6e+113)
   (* a (* y3 (- (* z y1) (* y y5))))
   (if (<= y1 -2.9e-18)
     (* a (* b (- (* x y) (* z t))))
     (if (<= y1 -3.5e-278)
       (* i (* y5 (- (* y k) (* t j))))
       (if (<= y1 3.1e-60)
         (* j (* i (- (* y0 (* y3 (/ y5 i))) (* t y5))))
         (* k (* y2 (- (* y1 y4) (* y0 y5)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y1 <= -3.6e+113) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (y1 <= -2.9e-18) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y1 <= -3.5e-278) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (y1 <= 3.1e-60) {
		tmp = j * (i * ((y0 * (y3 * (y5 / i))) - (t * y5)));
	} else {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y1 <= (-3.6d+113)) then
        tmp = a * (y3 * ((z * y1) - (y * y5)))
    else if (y1 <= (-2.9d-18)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (y1 <= (-3.5d-278)) then
        tmp = i * (y5 * ((y * k) - (t * j)))
    else if (y1 <= 3.1d-60) then
        tmp = j * (i * ((y0 * (y3 * (y5 / i))) - (t * y5)))
    else
        tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y1 <= -3.6e+113) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (y1 <= -2.9e-18) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y1 <= -3.5e-278) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (y1 <= 3.1e-60) {
		tmp = j * (i * ((y0 * (y3 * (y5 / i))) - (t * y5)));
	} else {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y1 <= -3.6e+113:
		tmp = a * (y3 * ((z * y1) - (y * y5)))
	elif y1 <= -2.9e-18:
		tmp = a * (b * ((x * y) - (z * t)))
	elif y1 <= -3.5e-278:
		tmp = i * (y5 * ((y * k) - (t * j)))
	elif y1 <= 3.1e-60:
		tmp = j * (i * ((y0 * (y3 * (y5 / i))) - (t * y5)))
	else:
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y1 <= -3.6e+113)
		tmp = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))));
	elseif (y1 <= -2.9e-18)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y1 <= -3.5e-278)
		tmp = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))));
	elseif (y1 <= 3.1e-60)
		tmp = Float64(j * Float64(i * Float64(Float64(y0 * Float64(y3 * Float64(y5 / i))) - Float64(t * y5))));
	else
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y1 <= -3.6e+113)
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	elseif (y1 <= -2.9e-18)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (y1 <= -3.5e-278)
		tmp = i * (y5 * ((y * k) - (t * j)));
	elseif (y1 <= 3.1e-60)
		tmp = j * (i * ((y0 * (y3 * (y5 / i))) - (t * y5)));
	else
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y1, -3.6e+113], N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -2.9e-18], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -3.5e-278], N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 3.1e-60], N[(j * N[(i * N[(N[(y0 * N[(y3 * N[(y5 / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y1 < -3.59999999999999992e113

   1. Initial program 24.8%

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

   3. Simplified 24.8%

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

   5. Taylor expanded in a around inf 42.8%

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

   6. Taylor expanded in y3 around inf 49.1%

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

   if -3.59999999999999992e113 < y1 < -2.9e-18

   1. Initial program 35.0%

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

   3. Simplified 35.0%

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

   5. Taylor expanded in a around inf 55.7%

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

   6. Taylor expanded in b around inf 65.5%

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

      1. neg-mul-1 65.5%

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

      2. +-commutative 65.5%

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

      3. sub-neg 65.5%

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

   8. Simplified 65.5%

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

   if -2.9e-18 < y1 < -3.4999999999999997e-278

   1. Initial program 45.3%

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

   3. Taylor expanded in y5 around -inf 41.7%

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

   4. Taylor expanded in i around inf 43.7%

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

   if -3.4999999999999997e-278 < y1 < 3.09999999999999988e-60

   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 i around -inf 31.2%

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

   4. Taylor expanded in j around inf 46.2%

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

   5. Taylor expanded in i around inf 49.3%

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

      1. fma-define 49.3%

         \[\leadsto j \cdot \left(i \cdot \color{blue}{\mathsf{fma}\left(-1, t \cdot y5 - x \cdot y1, -1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{i}\right)}\right) \]

      2. mul-1-neg 49.3%

         \[\leadsto j \cdot \left(i \cdot \mathsf{fma}\left(-1, t \cdot y5 - x \cdot y1, \color{blue}{-\frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{i}}\right)\right) \]

      3. fmm-undef 49.3%

         \[\leadsto j \cdot \left(i \cdot \color{blue}{\left(-1 \cdot \left(t \cdot y5 - x \cdot y1\right) - \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{i}\right)}\right) \]

      4. mul-1-neg 49.3%

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

      5. *-commutative 49.3%

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

      6. associate-/l* 49.3%

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

      7. *-commutative 49.3%

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

   7. Simplified 49.3%

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

   8. Taylor expanded in y1 around 0 43.1%

      \[\leadsto j \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(-1 \cdot \frac{y0 \cdot \left(y3 \cdot y5\right)}{i} + t \cdot y5\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 43.1%

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

      2. *-commutative 43.1%

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

      3. distribute-rgt-neg-in 43.1%

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

      4. +-commutative 43.1%

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

      5. mul-1-neg 43.1%

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

      6. unsub-neg 43.1%

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

      7. associate-/l* 44.7%

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

      8. associate-/l* 44.7%

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

   10. Simplified 44.7%

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

   if 3.09999999999999988e-60 < y1

   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 y2 around inf 56.2%

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

   4. Taylor expanded in k around inf 50.0%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -3.6 \cdot 10^{+113}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq -2.9 \cdot 10^{-18}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y1 \leq -3.5 \cdot 10^{-278}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 3.1 \cdot 10^{-60}:\\ \;\;\;\;j \cdot \left(i \cdot \left(y0 \cdot \left(y3 \cdot \frac{y5}{i}\right) - t \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 30.1% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -6.6 \cdot 10^{+112}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq -6.5 \cdot 10^{-21}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y1 \leq 3 \cdot 10^{-251}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 1.5 \cdot 10^{-94}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y5 \cdot \left(y3 - \frac{x \cdot b}{y5}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y1 -6.6e+112)
   (* a (* y3 (- (* z y1) (* y y5))))
   (if (<= y1 -6.5e-21)
     (* a (* b (- (* x y) (* z t))))
     (if (<= y1 3e-251)
       (* i (* y5 (- (* y k) (* t j))))
       (if (<= y1 1.5e-94)
         (* j (* y0 (* y5 (- y3 (/ (* x b) y5)))))
         (* k (* y2 (- (* y1 y4) (* y0 y5)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y1 <= -6.6e+112) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (y1 <= -6.5e-21) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y1 <= 3e-251) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (y1 <= 1.5e-94) {
		tmp = j * (y0 * (y5 * (y3 - ((x * b) / y5))));
	} else {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y1 <= (-6.6d+112)) then
        tmp = a * (y3 * ((z * y1) - (y * y5)))
    else if (y1 <= (-6.5d-21)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (y1 <= 3d-251) then
        tmp = i * (y5 * ((y * k) - (t * j)))
    else if (y1 <= 1.5d-94) then
        tmp = j * (y0 * (y5 * (y3 - ((x * b) / y5))))
    else
        tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y1 <= -6.6e+112) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (y1 <= -6.5e-21) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y1 <= 3e-251) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (y1 <= 1.5e-94) {
		tmp = j * (y0 * (y5 * (y3 - ((x * b) / y5))));
	} else {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y1 <= -6.6e+112:
		tmp = a * (y3 * ((z * y1) - (y * y5)))
	elif y1 <= -6.5e-21:
		tmp = a * (b * ((x * y) - (z * t)))
	elif y1 <= 3e-251:
		tmp = i * (y5 * ((y * k) - (t * j)))
	elif y1 <= 1.5e-94:
		tmp = j * (y0 * (y5 * (y3 - ((x * b) / y5))))
	else:
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y1 <= -6.6e+112)
		tmp = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))));
	elseif (y1 <= -6.5e-21)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y1 <= 3e-251)
		tmp = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))));
	elseif (y1 <= 1.5e-94)
		tmp = Float64(j * Float64(y0 * Float64(y5 * Float64(y3 - Float64(Float64(x * b) / y5)))));
	else
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y1 <= -6.6e+112)
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	elseif (y1 <= -6.5e-21)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (y1 <= 3e-251)
		tmp = i * (y5 * ((y * k) - (t * j)));
	elseif (y1 <= 1.5e-94)
		tmp = j * (y0 * (y5 * (y3 - ((x * b) / y5))));
	else
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y1, -6.6e+112], N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -6.5e-21], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 3e-251], N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.5e-94], N[(j * N[(y0 * N[(y5 * N[(y3 - N[(N[(x * b), $MachinePrecision] / y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y1 < -6.5999999999999998e112

   1. Initial program 24.8%

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

   3. Simplified 24.8%

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

   5. Taylor expanded in a around inf 42.8%

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

   6. Taylor expanded in y3 around inf 49.1%

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

   if -6.5999999999999998e112 < y1 < -6.49999999999999987e-21

   1. Initial program 35.0%

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

   3. Simplified 35.0%

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

   5. Taylor expanded in a around inf 55.7%

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

   6. Taylor expanded in b around inf 65.5%

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

      1. neg-mul-1 65.5%

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

      2. +-commutative 65.5%

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

      3. sub-neg 65.5%

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

   8. Simplified 65.5%

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

   if -6.49999999999999987e-21 < y1 < 2.9999999999999999e-251

   1. Initial program 42.3%

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

   3. Taylor expanded in y5 around -inf 42.0%

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

   4. Taylor expanded in i around inf 41.2%

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

   if 2.9999999999999999e-251 < y1 < 1.5000000000000001e-94

   1. Initial program 39.7%

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

   3. Taylor expanded in y0 around inf 47.2%

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

   4. Taylor expanded in j around inf 45.4%

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

   5. Taylor expanded in y5 around inf 47.7%

      \[\leadsto j \cdot \left(y0 \cdot \color{blue}{\left(y5 \cdot \left(y3 + -1 \cdot \frac{b \cdot x}{y5}\right)\right)}\right) \]
   6. Step-by-step derivation

      1. associate-*r/ 47.7%

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

      2. mul-1-neg 47.7%

         \[\leadsto j \cdot \left(y0 \cdot \left(y5 \cdot \left(y3 + \frac{\color{blue}{-b \cdot x}}{y5}\right)\right)\right) \]

      3. distribute-lft-neg-out 47.7%

         \[\leadsto j \cdot \left(y0 \cdot \left(y5 \cdot \left(y3 + \frac{\color{blue}{\left(-b\right) \cdot x}}{y5}\right)\right)\right) \]

      4. *-commutative 47.7%

         \[\leadsto j \cdot \left(y0 \cdot \left(y5 \cdot \left(y3 + \frac{\color{blue}{x \cdot \left(-b\right)}}{y5}\right)\right)\right) \]

   7. Simplified 47.7%

      \[\leadsto j \cdot \left(y0 \cdot \color{blue}{\left(y5 \cdot \left(y3 + \frac{x \cdot \left(-b\right)}{y5}\right)\right)}\right) \]

   if 1.5000000000000001e-94 < y1

   1. Initial program 33.1%

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

   3. Taylor expanded in y2 around inf 54.1%

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

   4. Taylor expanded in k around inf 49.5%

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

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -6.6 \cdot 10^{+112}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq -6.5 \cdot 10^{-21}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y1 \leq 3 \cdot 10^{-251}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 1.5 \cdot 10^{-94}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y5 \cdot \left(y3 - \frac{x \cdot b}{y5}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 40.3% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y1 - t \cdot y5\\ \mathbf{if}\;j \leq -1.3 \cdot 10^{-28}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + i \cdot t\_1\right)\\ \mathbf{elif}\;j \leq 7 \cdot 10^{+93}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k\right) - k \cdot \left(y0 \cdot y2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(i \cdot \left(t\_1 - y3 \cdot \frac{y1 \cdot y4 - y0 \cdot y5}{i}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* x y1) (* t y5))))
   (if (<= j -1.3e-28)
     (* j (+ (* y3 (- (* y0 y5) (* y1 y4))) (* i t_1)))
     (if (<= j 7e+93)
       (* y5 (+ (* a (- (* t y2) (* y y3))) (- (* i (* y k)) (* k (* y0 y2)))))
       (* j (* i (- t_1 (* y3 (/ (- (* y1 y4) (* y0 y5)) i)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (x * y1) - (t * y5);
	double tmp;
	if (j <= -1.3e-28) {
		tmp = j * ((y3 * ((y0 * y5) - (y1 * y4))) + (i * t_1));
	} else if (j <= 7e+93) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * (y * k)) - (k * (y0 * y2))));
	} else {
		tmp = j * (i * (t_1 - (y3 * (((y1 * y4) - (y0 * y5)) / i))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y1) - (t * y5)
    if (j <= (-1.3d-28)) then
        tmp = j * ((y3 * ((y0 * y5) - (y1 * y4))) + (i * t_1))
    else if (j <= 7d+93) then
        tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * (y * k)) - (k * (y0 * y2))))
    else
        tmp = j * (i * (t_1 - (y3 * (((y1 * y4) - (y0 * y5)) / i))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (x * y1) - (t * y5);
	double tmp;
	if (j <= -1.3e-28) {
		tmp = j * ((y3 * ((y0 * y5) - (y1 * y4))) + (i * t_1));
	} else if (j <= 7e+93) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * (y * k)) - (k * (y0 * y2))));
	} else {
		tmp = j * (i * (t_1 - (y3 * (((y1 * y4) - (y0 * y5)) / i))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (x * y1) - (t * y5)
	tmp = 0
	if j <= -1.3e-28:
		tmp = j * ((y3 * ((y0 * y5) - (y1 * y4))) + (i * t_1))
	elif j <= 7e+93:
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * (y * k)) - (k * (y0 * y2))))
	else:
		tmp = j * (i * (t_1 - (y3 * (((y1 * y4) - (y0 * y5)) / i))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(x * y1) - Float64(t * y5))
	tmp = 0.0
	if (j <= -1.3e-28)
		tmp = Float64(j * Float64(Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(i * t_1)));
	elseif (j <= 7e+93)
		tmp = Float64(y5 * Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(Float64(i * Float64(y * k)) - Float64(k * Float64(y0 * y2)))));
	else
		tmp = Float64(j * Float64(i * Float64(t_1 - Float64(y3 * Float64(Float64(Float64(y1 * y4) - Float64(y0 * y5)) / i)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (x * y1) - (t * y5);
	tmp = 0.0;
	if (j <= -1.3e-28)
		tmp = j * ((y3 * ((y0 * y5) - (y1 * y4))) + (i * t_1));
	elseif (j <= 7e+93)
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * (y * k)) - (k * (y0 * y2))));
	else
		tmp = j * (i * (t_1 - (y3 * (((y1 * y4) - (y0 * y5)) / i))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(x * y1), $MachinePrecision] - N[(t * y5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.3e-28], N[(j * N[(N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7e+93], N[(y5 * N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(i * N[(y * k), $MachinePrecision]), $MachinePrecision] - N[(k * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(i * N[(t$95$1 - N[(y3 * N[(N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.3e-28

   1. Initial program 30.3%

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

   3. Taylor expanded in i around -inf 40.8%

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

   4. Taylor expanded in j around inf 56.1%

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

   if -1.3e-28 < j < 6.99999999999999996e93

   1. Initial program 39.0%

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

   3. Taylor expanded in y5 around -inf 45.3%

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

   4. Taylor expanded in j around 0 45.8%

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

   if 6.99999999999999996e93 < j

   1. Initial program 32.2%

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

   3. Taylor expanded in i around -inf 27.0%

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

   4. Taylor expanded in j around inf 50.9%

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

   5. Taylor expanded in i around inf 53.6%

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

      1. fma-define 53.6%

         \[\leadsto j \cdot \left(i \cdot \color{blue}{\mathsf{fma}\left(-1, t \cdot y5 - x \cdot y1, -1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{i}\right)}\right) \]

      2. mul-1-neg 53.6%

         \[\leadsto j \cdot \left(i \cdot \mathsf{fma}\left(-1, t \cdot y5 - x \cdot y1, \color{blue}{-\frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{i}}\right)\right) \]

      3. fmm-undef 53.6%

         \[\leadsto j \cdot \left(i \cdot \color{blue}{\left(-1 \cdot \left(t \cdot y5 - x \cdot y1\right) - \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{i}\right)}\right) \]

      4. mul-1-neg 53.6%

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

      5. *-commutative 53.6%

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

      6. associate-/l* 56.0%

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

      7. *-commutative 56.0%

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

   7. Simplified 56.0%

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

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.3 \cdot 10^{-28}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + i \cdot \left(x \cdot y1 - t \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 7 \cdot 10^{+93}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k\right) - k \cdot \left(y0 \cdot y2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(i \cdot \left(\left(x \cdot y1 - t \cdot y5\right) - y3 \cdot \frac{y1 \cdot y4 - y0 \cdot y5}{i}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 38.2% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+95}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+77}:\\ \;\;\;\;j \cdot \left(i \cdot \left(\left(x \cdot y1 - t \cdot y5\right) - y3 \cdot \frac{y1 \cdot y4 - y0 \cdot y5}{i}\right)\right)\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+257}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y -2.7e+95)
   (* a (* y3 (- (* z y1) (* y y5))))
   (if (<= y 2.8e+77)
     (* j (* i (- (- (* x y1) (* t y5)) (* y3 (/ (- (* y1 y4) (* y0 y5)) i)))))
     (if (<= y 4.7e+257)
       (* i (* y5 (- (* y k) (* t j))))
       (* a (* y (- (* x b) (* y3 y5))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -2.7e+95) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (y <= 2.8e+77) {
		tmp = j * (i * (((x * y1) - (t * y5)) - (y3 * (((y1 * y4) - (y0 * y5)) / i))));
	} else if (y <= 4.7e+257) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y <= (-2.7d+95)) then
        tmp = a * (y3 * ((z * y1) - (y * y5)))
    else if (y <= 2.8d+77) then
        tmp = j * (i * (((x * y1) - (t * y5)) - (y3 * (((y1 * y4) - (y0 * y5)) / i))))
    else if (y <= 4.7d+257) then
        tmp = i * (y5 * ((y * k) - (t * j)))
    else
        tmp = a * (y * ((x * b) - (y3 * y5)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -2.7e+95) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (y <= 2.8e+77) {
		tmp = j * (i * (((x * y1) - (t * y5)) - (y3 * (((y1 * y4) - (y0 * y5)) / i))));
	} else if (y <= 4.7e+257) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y <= -2.7e+95:
		tmp = a * (y3 * ((z * y1) - (y * y5)))
	elif y <= 2.8e+77:
		tmp = j * (i * (((x * y1) - (t * y5)) - (y3 * (((y1 * y4) - (y0 * y5)) / i))))
	elif y <= 4.7e+257:
		tmp = i * (y5 * ((y * k) - (t * j)))
	else:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y <= -2.7e+95)
		tmp = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))));
	elseif (y <= 2.8e+77)
		tmp = Float64(j * Float64(i * Float64(Float64(Float64(x * y1) - Float64(t * y5)) - Float64(y3 * Float64(Float64(Float64(y1 * y4) - Float64(y0 * y5)) / i)))));
	elseif (y <= 4.7e+257)
		tmp = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))));
	else
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y <= -2.7e+95)
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	elseif (y <= 2.8e+77)
		tmp = j * (i * (((x * y1) - (t * y5)) - (y3 * (((y1 * y4) - (y0 * y5)) / i))));
	elseif (y <= 4.7e+257)
		tmp = i * (y5 * ((y * k) - (t * j)));
	else
		tmp = a * (y * ((x * b) - (y3 * y5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y, -2.7e+95], N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e+77], N[(j * N[(i * N[(N[(N[(x * y1), $MachinePrecision] - N[(t * y5), $MachinePrecision]), $MachinePrecision] - N[(y3 * N[(N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.7e+257], N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.7e95

   1. Initial program 28.9%

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

   3. Simplified 31.1%

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

   5. Taylor expanded in a around inf 42.6%

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

   6. Taylor expanded in y3 around inf 49.7%

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

   if -2.7e95 < y < 2.8e77

   1. Initial program 41.8%

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

   3. Taylor expanded in i around -inf 38.3%

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

   4. Taylor expanded in j around inf 44.9%

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

   5. Taylor expanded in i around inf 46.8%

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

      1. fma-define 46.8%

         \[\leadsto j \cdot \left(i \cdot \color{blue}{\mathsf{fma}\left(-1, t \cdot y5 - x \cdot y1, -1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{i}\right)}\right) \]

      2. mul-1-neg 46.8%

         \[\leadsto j \cdot \left(i \cdot \mathsf{fma}\left(-1, t \cdot y5 - x \cdot y1, \color{blue}{-\frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{i}}\right)\right) \]

      3. fmm-undef 46.8%

         \[\leadsto j \cdot \left(i \cdot \color{blue}{\left(-1 \cdot \left(t \cdot y5 - x \cdot y1\right) - \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{i}\right)}\right) \]

      4. mul-1-neg 46.8%

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

      5. *-commutative 46.8%

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

      6. associate-/l* 47.5%

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

      7. *-commutative 47.5%

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

   7. Simplified 47.5%

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

   if 2.8e77 < y < 4.7e257

   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 y5 around -inf 39.6%

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

   4. Taylor expanded in i around inf 56.9%

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

   if 4.7e257 < y

   1. Initial program 9.1%

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

   3. Simplified 9.1%

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

   5. Taylor expanded in a around inf 63.8%

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

   6. Taylor expanded in y around inf 73.2%

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

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+95}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+77}:\\ \;\;\;\;j \cdot \left(i \cdot \left(\left(x \cdot y1 - t \cdot y5\right) - y3 \cdot \frac{y1 \cdot y4 - y0 \cdot y5}{i}\right)\right)\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+257}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 30.2% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{if}\;y1 \leq -4.6 \cdot 10^{+111}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq -1.02 \cdot 10^{-20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq -3.05 \cdot 10^{-276}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 6.2 \cdot 10^{-96}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* b (- (* x y) (* z t))))))
   (if (<= y1 -4.6e+111)
     (* a (* y3 (- (* z y1) (* y y5))))
     (if (<= y1 -1.02e-20)
       t_1
       (if (<= y1 -3.05e-276)
         (* i (* y5 (- (* y k) (* t j))))
         (if (<= y1 6.2e-96) t_1 (* k (* y2 (- (* y1 y4) (* y0 y5))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (b * ((x * y) - (z * t)));
	double tmp;
	if (y1 <= -4.6e+111) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (y1 <= -1.02e-20) {
		tmp = t_1;
	} else if (y1 <= -3.05e-276) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (y1 <= 6.2e-96) {
		tmp = t_1;
	} else {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (b * ((x * y) - (z * t)))
    if (y1 <= (-4.6d+111)) then
        tmp = a * (y3 * ((z * y1) - (y * y5)))
    else if (y1 <= (-1.02d-20)) then
        tmp = t_1
    else if (y1 <= (-3.05d-276)) then
        tmp = i * (y5 * ((y * k) - (t * j)))
    else if (y1 <= 6.2d-96) then
        tmp = t_1
    else
        tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (b * ((x * y) - (z * t)));
	double tmp;
	if (y1 <= -4.6e+111) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (y1 <= -1.02e-20) {
		tmp = t_1;
	} else if (y1 <= -3.05e-276) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (y1 <= 6.2e-96) {
		tmp = t_1;
	} else {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (b * ((x * y) - (z * t)))
	tmp = 0
	if y1 <= -4.6e+111:
		tmp = a * (y3 * ((z * y1) - (y * y5)))
	elif y1 <= -1.02e-20:
		tmp = t_1
	elif y1 <= -3.05e-276:
		tmp = i * (y5 * ((y * k) - (t * j)))
	elif y1 <= 6.2e-96:
		tmp = t_1
	else:
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))))
	tmp = 0.0
	if (y1 <= -4.6e+111)
		tmp = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))));
	elseif (y1 <= -1.02e-20)
		tmp = t_1;
	elseif (y1 <= -3.05e-276)
		tmp = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))));
	elseif (y1 <= 6.2e-96)
		tmp = t_1;
	else
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (b * ((x * y) - (z * t)));
	tmp = 0.0;
	if (y1 <= -4.6e+111)
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	elseif (y1 <= -1.02e-20)
		tmp = t_1;
	elseif (y1 <= -3.05e-276)
		tmp = i * (y5 * ((y * k) - (t * j)));
	elseif (y1 <= 6.2e-96)
		tmp = t_1;
	else
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -4.6e+111], N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -1.02e-20], t$95$1, If[LessEqual[y1, -3.05e-276], N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 6.2e-96], t$95$1, N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y1 < -4.60000000000000004e111

   1. Initial program 24.8%

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

   3. Simplified 24.8%

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

   5. Taylor expanded in a around inf 42.8%

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

   6. Taylor expanded in y3 around inf 49.1%

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

   if -4.60000000000000004e111 < y1 < -1.02000000000000001e-20 or -3.04999999999999989e-276 < y1 < 6.1999999999999998e-96

   1. Initial program 36.0%

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

   3. Simplified 36.0%

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

   5. Taylor expanded in a around inf 54.2%

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

   6. Taylor expanded in b around inf 48.2%

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

      1. neg-mul-1 48.2%

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

      2. +-commutative 48.2%

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

      3. sub-neg 48.2%

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

   8. Simplified 48.2%

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

   if -1.02000000000000001e-20 < y1 < -3.04999999999999989e-276

   1. Initial program 46.1%

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

   3. Taylor expanded in y5 around -inf 40.8%

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

   4. Taylor expanded in i around inf 44.3%

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

   if 6.1999999999999998e-96 < y1

   1. Initial program 33.1%

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

   3. Taylor expanded in y2 around inf 54.1%

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

   4. Taylor expanded in k around inf 49.5%

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

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -4.6 \cdot 10^{+111}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq -1.02 \cdot 10^{-20}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y1 \leq -3.05 \cdot 10^{-276}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 6.2 \cdot 10^{-96}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 26.0% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(\left(t \cdot i\right) \cdot \left(-y5\right)\right)\\ \mathbf{if}\;i \leq -9 \cdot 10^{+180}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -9 \cdot 10^{-17}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{+68}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;i \leq 1.42 \cdot 10^{+196}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y0\right) \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* (* t i) (- y5)))))
   (if (<= i -9e+180)
     t_1
     (if (<= i -9e-17)
       (* j (* y0 (* y3 y5)))
       (if (<= i 4.8e+68)
         (* a (* b (- (* x y) (* z t))))
         (if (<= i 1.42e+196) (* b (* (* x y0) (- j))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * ((t * i) * -y5);
	double tmp;
	if (i <= -9e+180) {
		tmp = t_1;
	} else if (i <= -9e-17) {
		tmp = j * (y0 * (y3 * y5));
	} else if (i <= 4.8e+68) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (i <= 1.42e+196) {
		tmp = b * ((x * y0) * -j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((t * i) * -y5)
    if (i <= (-9d+180)) then
        tmp = t_1
    else if (i <= (-9d-17)) then
        tmp = j * (y0 * (y3 * y5))
    else if (i <= 4.8d+68) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (i <= 1.42d+196) then
        tmp = b * ((x * y0) * -j)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * ((t * i) * -y5);
	double tmp;
	if (i <= -9e+180) {
		tmp = t_1;
	} else if (i <= -9e-17) {
		tmp = j * (y0 * (y3 * y5));
	} else if (i <= 4.8e+68) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (i <= 1.42e+196) {
		tmp = b * ((x * y0) * -j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = j * ((t * i) * -y5)
	tmp = 0
	if i <= -9e+180:
		tmp = t_1
	elif i <= -9e-17:
		tmp = j * (y0 * (y3 * y5))
	elif i <= 4.8e+68:
		tmp = a * (b * ((x * y) - (z * t)))
	elif i <= 1.42e+196:
		tmp = b * ((x * y0) * -j)
	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(j * Float64(Float64(t * i) * Float64(-y5)))
	tmp = 0.0
	if (i <= -9e+180)
		tmp = t_1;
	elseif (i <= -9e-17)
		tmp = Float64(j * Float64(y0 * Float64(y3 * y5)));
	elseif (i <= 4.8e+68)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (i <= 1.42e+196)
		tmp = Float64(b * Float64(Float64(x * y0) * Float64(-j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = j * ((t * i) * -y5);
	tmp = 0.0;
	if (i <= -9e+180)
		tmp = t_1;
	elseif (i <= -9e-17)
		tmp = j * (y0 * (y3 * y5));
	elseif (i <= 4.8e+68)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (i <= 1.42e+196)
		tmp = b * ((x * y0) * -j);
	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[(j * N[(N[(t * i), $MachinePrecision] * (-y5)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -9e+180], t$95$1, If[LessEqual[i, -9e-17], N[(j * N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.8e+68], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.42e+196], N[(b * N[(N[(x * y0), $MachinePrecision] * (-j)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -8.99999999999999962e180 or 1.42000000000000002e196 < i

   1. Initial program 20.7%

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

   3. Taylor expanded in i around -inf 47.0%

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

   4. Taylor expanded in j around inf 59.6%

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

   5. Taylor expanded in i around inf 59.6%

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

      1. fma-define 59.6%

         \[\leadsto j \cdot \left(i \cdot \color{blue}{\mathsf{fma}\left(-1, t \cdot y5 - x \cdot y1, -1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{i}\right)}\right) \]

      2. mul-1-neg 59.6%

         \[\leadsto j \cdot \left(i \cdot \mathsf{fma}\left(-1, t \cdot y5 - x \cdot y1, \color{blue}{-\frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{i}}\right)\right) \]

      3. fmm-undef 59.6%

         \[\leadsto j \cdot \left(i \cdot \color{blue}{\left(-1 \cdot \left(t \cdot y5 - x \cdot y1\right) - \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{i}\right)}\right) \]

      4. mul-1-neg 59.6%

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

      5. *-commutative 59.6%

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

      6. associate-/l* 59.6%

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

      7. *-commutative 59.6%

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

   7. Simplified 59.6%

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

   8. Taylor expanded in t around inf 52.1%

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

      1. mul-1-neg 52.1%

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

      2. associate-*r* 55.8%

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

   10. Simplified 55.8%

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

   if -8.99999999999999962e180 < i < -8.99999999999999957e-17

   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 y0 around inf 37.3%

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

   4. Taylor expanded in j around inf 35.9%

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

   5. Taylor expanded in y3 around inf 33.9%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 33.9%

         \[\leadsto j \cdot \left(y0 \cdot \color{blue}{\left(y5 \cdot y3\right)}\right) \]

   7. Simplified 33.9%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y5 \cdot y3\right)\right)} \]

   if -8.99999999999999957e-17 < i < 4.80000000000000016e68

   1. Initial program 41.6%

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

   3. Simplified 41.6%

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

   5. Taylor expanded in a around inf 43.5%

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

   6. Taylor expanded in b around inf 36.1%

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

      1. neg-mul-1 36.1%

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

      2. +-commutative 36.1%

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

      3. sub-neg 36.1%

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

   8. Simplified 36.1%

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

   if 4.80000000000000016e68 < i < 1.42000000000000002e196

   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 y0 around inf 54.5%

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

   4. Taylor expanded in j around inf 50.7%

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

   5. Taylor expanded in y3 around 0 43.2%

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

      1. associate-*r* 43.2%

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

      2. neg-mul-1 43.2%

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

   7. Simplified 43.2%

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

4. Final simplification 40.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -9 \cdot 10^{+180}:\\ \;\;\;\;j \cdot \left(\left(t \cdot i\right) \cdot \left(-y5\right)\right)\\ \mathbf{elif}\;i \leq -9 \cdot 10^{-17}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{+68}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;i \leq 1.42 \cdot 10^{+196}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y0\right) \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(\left(t \cdot i\right) \cdot \left(-y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 31.3% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -1.46 \cdot 10^{+98}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 5.6 \cdot 10^{-273}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y2 \leq 510000:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -1.46e+98)
   (* c (* y2 (- (* x y0) (* t y4))))
   (if (<= y2 5.6e-273)
     (* a (* b (- (* x y) (* z t))))
     (if (<= y2 510000.0)
       (* a (* y (- (* x b) (* y3 y5))))
       (* c (* y0 (- (* x y2) (* z y3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -1.46e+98) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (y2 <= 5.6e-273) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y2 <= 510000.0) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y2 <= (-1.46d+98)) then
        tmp = c * (y2 * ((x * y0) - (t * y4)))
    else if (y2 <= 5.6d-273) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (y2 <= 510000.0d0) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -1.46e+98) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (y2 <= 5.6e-273) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y2 <= 510000.0) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y2 <= -1.46e+98:
		tmp = c * (y2 * ((x * y0) - (t * y4)))
	elif y2 <= 5.6e-273:
		tmp = a * (b * ((x * y) - (z * t)))
	elif y2 <= 510000.0:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	else:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y2 <= -1.46e+98)
		tmp = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))));
	elseif (y2 <= 5.6e-273)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y2 <= 510000.0)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	else
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y2 <= -1.46e+98)
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	elseif (y2 <= 5.6e-273)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (y2 <= 510000.0)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	else
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y2, -1.46e+98], N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 5.6e-273], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 510000.0], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y2 < -1.4599999999999999e98

   1. Initial program 33.3%

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

   3. Taylor expanded in y2 around inf 54.7%

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

   4. Taylor expanded in c around inf 52.2%

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

   if -1.4599999999999999e98 < y2 < 5.59999999999999971e-273

   1. Initial program 37.0%

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

   3. Simplified 38.1%

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

   5. Taylor expanded in a around inf 41.5%

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

   6. Taylor expanded in b around inf 38.8%

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

      1. neg-mul-1 38.8%

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

      2. +-commutative 38.8%

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

      3. sub-neg 38.8%

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

   8. Simplified 38.8%

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

   if 5.59999999999999971e-273 < y2 < 5.1e5

   1. Initial program 35.1%

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

   3. Simplified 35.1%

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

   5. Taylor expanded in a around inf 48.5%

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

   6. Taylor expanded in y around inf 41.7%

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

   if 5.1e5 < y2

   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 y0 around inf 43.3%

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

   4. Taylor expanded in c around inf 45.1%

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

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.46 \cdot 10^{+98}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 5.6 \cdot 10^{-273}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y2 \leq 510000:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 31.2% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{-66}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -3.7 \cdot 10^{-233}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+120}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= b -4.2e-66)
   (* b (* y0 (- (* z k) (* x j))))
   (if (<= b -3.7e-233)
     (* c (* y0 (- (* x y2) (* z y3))))
     (if (<= b 1.4e+120)
       (* a (* y5 (- (* t y2) (* y y3))))
       (* 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 (b <= -4.2e-66) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (b <= -3.7e-233) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (b <= 1.4e+120) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} 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 (b <= (-4.2d-66)) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (b <= (-3.7d-233)) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else if (b <= 1.4d+120) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    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 (b <= -4.2e-66) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (b <= -3.7e-233) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (b <= 1.4e+120) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} 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 b <= -4.2e-66:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif b <= -3.7e-233:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	elif b <= 1.4e+120:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	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 (b <= -4.2e-66)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (b <= -3.7e-233)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (b <= 1.4e+120)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	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 (b <= -4.2e-66)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (b <= -3.7e-233)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	elseif (b <= 1.4e+120)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	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[b, -4.2e-66], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.7e-233], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.4e+120], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $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 4 regimes

2. if b < -4.2000000000000001e-66

   1. Initial program 36.4%

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

   3. Taylor expanded in y0 around inf 29.9%

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

   4. Taylor expanded in b around inf 41.3%

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

   if -4.2000000000000001e-66 < b < -3.6999999999999998e-233

   1. Initial program 53.5%

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

   3. Taylor expanded in y0 around inf 29.7%

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

   4. Taylor expanded in c around inf 45.0%

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

   if -3.6999999999999998e-233 < b < 1.4e120

   1. Initial program 33.7%

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

   3. Simplified 34.6%

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

   5. Taylor expanded in a around inf 44.7%

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

   6. Taylor expanded in y5 around inf 39.1%

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

   if 1.4e120 < b

   1. Initial program 28.2%

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

   3. Simplified 28.2%

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

   5. Taylor expanded in a around inf 43.8%

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

   6. Taylor expanded in b around inf 56.8%

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

      1. neg-mul-1 56.8%

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

      2. +-commutative 56.8%

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

      3. sub-neg 56.8%

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

   8. Simplified 56.8%

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

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{-66}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -3.7 \cdot 10^{-233}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+120}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 32.8% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{if}\;b \leq -720000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -6.6 \cdot 10^{-303}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+122}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* b (- (* x y) (* z t))))))
   (if (<= b -720000000.0)
     t_1
     (if (<= b -6.6e-303)
       (* a (* y3 (- (* z y1) (* y y5))))
       (if (<= b 2e+122) (* a (* y5 (- (* t y2) (* y y3)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (b * ((x * y) - (z * t)));
	double tmp;
	if (b <= -720000000.0) {
		tmp = t_1;
	} else if (b <= -6.6e-303) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (b <= 2e+122) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (b * ((x * y) - (z * t)))
    if (b <= (-720000000.0d0)) then
        tmp = t_1
    else if (b <= (-6.6d-303)) then
        tmp = a * (y3 * ((z * y1) - (y * y5)))
    else if (b <= 2d+122) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (b * ((x * y) - (z * t)));
	double tmp;
	if (b <= -720000000.0) {
		tmp = t_1;
	} else if (b <= -6.6e-303) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (b <= 2e+122) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (b * ((x * y) - (z * t)))
	tmp = 0
	if b <= -720000000.0:
		tmp = t_1
	elif b <= -6.6e-303:
		tmp = a * (y3 * ((z * y1) - (y * y5)))
	elif b <= 2e+122:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))))
	tmp = 0.0
	if (b <= -720000000.0)
		tmp = t_1;
	elseif (b <= -6.6e-303)
		tmp = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))));
	elseif (b <= 2e+122)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (b * ((x * y) - (z * t)));
	tmp = 0.0;
	if (b <= -720000000.0)
		tmp = t_1;
	elseif (b <= -6.6e-303)
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	elseif (b <= 2e+122)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -720000000.0], t$95$1, If[LessEqual[b, -6.6e-303], N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2e+122], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.2e8 or 2.00000000000000003e122 < b

   1. Initial program 33.9%

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

   3. Simplified 33.9%

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

   5. Taylor expanded in a around inf 44.6%

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

   6. Taylor expanded in b around inf 51.2%

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

      1. neg-mul-1 51.2%

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

      2. +-commutative 51.2%

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

      3. sub-neg 51.2%

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

   8. Simplified 51.2%

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

   if -7.2e8 < b < -6.5999999999999994e-303

   1. Initial program 46.2%

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

   3. Simplified 46.2%

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

   5. Taylor expanded in a around inf 38.3%

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

   6. Taylor expanded in y3 around inf 37.1%

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

   if -6.5999999999999994e-303 < b < 2.00000000000000003e122

   1. Initial program 32.1%

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

   3. Simplified 33.1%

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

   5. Taylor expanded in a around inf 44.5%

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

   6. Taylor expanded in y5 around inf 39.1%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -720000000:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq -6.6 \cdot 10^{-303}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+122}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 21.2% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-42}:\\ \;\;\;\;a \cdot \left(b \cdot \left(z \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;z \leq 7.1 \cdot 10^{-127}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+254}:\\ \;\;\;\;j \cdot \left(\left(t \cdot i\right) \cdot \left(-y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= z -3.9e-42)
   (* a (* b (* z (- t))))
   (if (<= z 7.1e-127)
     (* a (* (* x y) b))
     (if (<= z 1.45e+254) (* j (* (* t i) (- y5))) (* a (* y3 (* z y1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (z <= -3.9e-42) {
		tmp = a * (b * (z * -t));
	} else if (z <= 7.1e-127) {
		tmp = a * ((x * y) * b);
	} else if (z <= 1.45e+254) {
		tmp = j * ((t * i) * -y5);
	} else {
		tmp = a * (y3 * (z * y1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (z <= (-3.9d-42)) then
        tmp = a * (b * (z * -t))
    else if (z <= 7.1d-127) then
        tmp = a * ((x * y) * b)
    else if (z <= 1.45d+254) then
        tmp = j * ((t * i) * -y5)
    else
        tmp = a * (y3 * (z * y1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (z <= -3.9e-42) {
		tmp = a * (b * (z * -t));
	} else if (z <= 7.1e-127) {
		tmp = a * ((x * y) * b);
	} else if (z <= 1.45e+254) {
		tmp = j * ((t * i) * -y5);
	} else {
		tmp = a * (y3 * (z * y1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if z <= -3.9e-42:
		tmp = a * (b * (z * -t))
	elif z <= 7.1e-127:
		tmp = a * ((x * y) * b)
	elif z <= 1.45e+254:
		tmp = j * ((t * i) * -y5)
	else:
		tmp = a * (y3 * (z * y1))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (z <= -3.9e-42)
		tmp = Float64(a * Float64(b * Float64(z * Float64(-t))));
	elseif (z <= 7.1e-127)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	elseif (z <= 1.45e+254)
		tmp = Float64(j * Float64(Float64(t * i) * Float64(-y5)));
	else
		tmp = Float64(a * Float64(y3 * Float64(z * y1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (z <= -3.9e-42)
		tmp = a * (b * (z * -t));
	elseif (z <= 7.1e-127)
		tmp = a * ((x * y) * b);
	elseif (z <= 1.45e+254)
		tmp = j * ((t * i) * -y5);
	else
		tmp = a * (y3 * (z * y1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[z, -3.9e-42], N[(a * N[(b * N[(z * (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.1e-127], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e+254], N[(j * N[(N[(t * i), $MachinePrecision] * (-y5)), $MachinePrecision]), $MachinePrecision], N[(a * N[(y3 * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.9000000000000002e-42

   1. Initial program 34.4%

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

   3. Simplified 34.4%

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

   5. Taylor expanded in a around inf 42.4%

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

   6. Taylor expanded in b around inf 31.6%

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

      1. neg-mul-1 31.6%

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

      2. +-commutative 31.6%

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

      3. sub-neg 31.6%

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

   8. Simplified 31.6%

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

   9. Taylor expanded in x around 0 30.3%

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

       1. associate-*r* 30.3%

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

       2. neg-mul-1 30.3%

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

   11. Simplified 30.3%

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

   if -3.9000000000000002e-42 < z < 7.1000000000000002e-127

   1. Initial program 39.8%

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

   3. Simplified 40.9%

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

   5. Taylor expanded in a around inf 45.9%

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

   6. Taylor expanded in b around inf 29.7%

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

      1. neg-mul-1 29.7%

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

      2. +-commutative 29.7%

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

      3. sub-neg 29.7%

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

   8. Simplified 29.7%

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

   9. Taylor expanded in x around inf 29.8%

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

       1. *-commutative 29.8%

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

       2. *-commutative 29.8%

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

   11. Simplified 29.8%

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

   if 7.1000000000000002e-127 < z < 1.45e254

   1. Initial program 37.8%

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

   3. Taylor expanded in i around -inf 36.8%

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

   4. Taylor expanded in j around inf 51.4%

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

   5. Taylor expanded in i around inf 51.4%

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

      1. fma-define 51.4%

         \[\leadsto j \cdot \left(i \cdot \color{blue}{\mathsf{fma}\left(-1, t \cdot y5 - x \cdot y1, -1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{i}\right)}\right) \]

      2. mul-1-neg 51.4%

         \[\leadsto j \cdot \left(i \cdot \mathsf{fma}\left(-1, t \cdot y5 - x \cdot y1, \color{blue}{-\frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{i}}\right)\right) \]

      3. fmm-undef 51.4%

         \[\leadsto j \cdot \left(i \cdot \color{blue}{\left(-1 \cdot \left(t \cdot y5 - x \cdot y1\right) - \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{i}\right)}\right) \]

      4. mul-1-neg 51.4%

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

      5. *-commutative 51.4%

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

      6. associate-/l* 51.4%

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

      7. *-commutative 51.4%

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

   7. Simplified 51.4%

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

   8. Taylor expanded in t around inf 33.6%

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

      1. mul-1-neg 33.6%

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

      2. associate-*r* 33.6%

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

   10. Simplified 33.6%

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

   if 1.45e254 < z

   1. Initial program 8.3%

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

   3. Simplified 8.3%

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

   5. Taylor expanded in a around inf 58.3%

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

   6. Taylor expanded in y1 around inf 59.4%

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

      1. associate-*r* 59.4%

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

      2. neg-mul-1 59.4%

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

   8. Simplified 59.4%

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

   9. Taylor expanded in x around 0 59.4%

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

       1. *-commutative 59.4%

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

   11. Simplified 59.4%

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

   12. Taylor expanded in a around 0 59.4%

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

       1. *-commutative 59.4%

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

       2. associate-*l* 66.7%

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

       3. *-commutative 66.7%

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

   14. Simplified 66.7%

       \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 32.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-42}:\\ \;\;\;\;a \cdot \left(b \cdot \left(z \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;z \leq 7.1 \cdot 10^{-127}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+254}:\\ \;\;\;\;j \cdot \left(\left(t \cdot i\right) \cdot \left(-y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 22.1% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{if}\;x \leq -1.05 \cdot 10^{+113}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -8.2 \cdot 10^{-226}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+151}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* (* x y) b))))
   (if (<= x -1.05e+113)
     t_1
     (if (<= x -8.2e-226)
       (* j (* y0 (* y3 y5)))
       (if (<= x 6.5e+151) (* k (* y1 (* y2 y4))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * ((x * y) * b);
	double tmp;
	if (x <= -1.05e+113) {
		tmp = t_1;
	} else if (x <= -8.2e-226) {
		tmp = j * (y0 * (y3 * y5));
	} else if (x <= 6.5e+151) {
		tmp = k * (y1 * (y2 * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((x * y) * b)
    if (x <= (-1.05d+113)) then
        tmp = t_1
    else if (x <= (-8.2d-226)) then
        tmp = j * (y0 * (y3 * y5))
    else if (x <= 6.5d+151) then
        tmp = k * (y1 * (y2 * y4))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * ((x * y) * b);
	double tmp;
	if (x <= -1.05e+113) {
		tmp = t_1;
	} else if (x <= -8.2e-226) {
		tmp = j * (y0 * (y3 * y5));
	} else if (x <= 6.5e+151) {
		tmp = k * (y1 * (y2 * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * ((x * y) * b)
	tmp = 0
	if x <= -1.05e+113:
		tmp = t_1
	elif x <= -8.2e-226:
		tmp = j * (y0 * (y3 * y5))
	elif x <= 6.5e+151:
		tmp = k * (y1 * (y2 * y4))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(Float64(x * y) * b))
	tmp = 0.0
	if (x <= -1.05e+113)
		tmp = t_1;
	elseif (x <= -8.2e-226)
		tmp = Float64(j * Float64(y0 * Float64(y3 * y5)));
	elseif (x <= 6.5e+151)
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * ((x * y) * b);
	tmp = 0.0;
	if (x <= -1.05e+113)
		tmp = t_1;
	elseif (x <= -8.2e-226)
		tmp = j * (y0 * (y3 * y5));
	elseif (x <= 6.5e+151)
		tmp = k * (y1 * (y2 * y4));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.05e+113], t$95$1, If[LessEqual[x, -8.2e-226], N[(j * N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.5e+151], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.0499999999999999e113 or 6.5000000000000002e151 < x

   1. Initial program 28.3%

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

   3. Simplified 28.3%

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

   5. Taylor expanded in a around inf 45.0%

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

   6. Taylor expanded in b around inf 46.8%

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

      1. neg-mul-1 46.8%

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

      2. +-commutative 46.8%

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

      3. sub-neg 46.8%

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

   8. Simplified 46.8%

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

   9. Taylor expanded in x around inf 44.5%

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

       1. *-commutative 44.5%

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

       2. *-commutative 44.5%

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

   11. Simplified 44.5%

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

   if -1.0499999999999999e113 < x < -8.20000000000000074e-226

   1. Initial program 37.5%

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

   3. Taylor expanded in y0 around inf 35.6%

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

   4. Taylor expanded in j around inf 34.4%

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

   5. Taylor expanded in y3 around inf 30.4%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 30.4%

         \[\leadsto j \cdot \left(y0 \cdot \color{blue}{\left(y5 \cdot y3\right)}\right) \]

   7. Simplified 30.4%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y5 \cdot y3\right)\right)} \]

   if -8.20000000000000074e-226 < x < 6.5000000000000002e151

   1. Initial program 40.9%

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

   3. Taylor expanded in y2 around inf 37.5%

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

   4. Taylor expanded in y4 around inf 24.7%

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

   5. Taylor expanded in k around inf 23.0%

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

4. Final simplification 31.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+113}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;x \leq -8.2 \cdot 10^{-226}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+151}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 32.6% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5500000 \lor \neg \left(b \leq 4.8 \cdot 10^{+147}\right):\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= b -5500000.0) (not (<= b 4.8e+147)))
   (* a (* b (- (* x y) (* z t))))
   (* a (* y3 (- (* z y1) (* y y5))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((b <= -5500000.0) || !(b <= 4.8e+147)) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((b <= (-5500000.0d0)) .or. (.not. (b <= 4.8d+147))) then
        tmp = a * (b * ((x * y) - (z * t)))
    else
        tmp = a * (y3 * ((z * y1) - (y * y5)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((b <= -5500000.0) || !(b <= 4.8e+147)) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (b <= -5500000.0) or not (b <= 4.8e+147):
		tmp = a * (b * ((x * y) - (z * t)))
	else:
		tmp = a * (y3 * ((z * y1) - (y * y5)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((b <= -5500000.0) || !(b <= 4.8e+147))
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	else
		tmp = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((b <= -5500000.0) || ~((b <= 4.8e+147)))
		tmp = a * (b * ((x * y) - (z * t)));
	else
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[b, -5500000.0], N[Not[LessEqual[b, 4.8e+147]], $MachinePrecision]], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.5e6 or 4.80000000000000004e147 < b

   1. Initial program 35.0%

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

   3. Simplified 35.0%

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

   5. Taylor expanded in a around inf 45.3%

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

   6. Taylor expanded in b around inf 52.4%

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

      1. neg-mul-1 52.4%

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

      2. +-commutative 52.4%

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

      3. sub-neg 52.4%

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

   8. Simplified 52.4%

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

   if -5.5e6 < b < 4.80000000000000004e147

   1. Initial program 36.7%

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

   3. Simplified 37.3%

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

   5. Taylor expanded in a around inf 41.9%

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

   6. Taylor expanded in y3 around inf 34.5%

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5500000 \lor \neg \left(b \leq 4.8 \cdot 10^{+147}\right):\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 31.0% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y3 \leq -1 \cdot 10^{+68} \lor \neg \left(y3 \leq 2.95 \cdot 10^{+119}\right):\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= y3 -1e+68) (not (<= y3 2.95e+119)))
   (* a (* y (- (* x b) (* y3 y5))))
   (* 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 ((y3 <= -1e+68) || !(y3 <= 2.95e+119)) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} 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 ((y3 <= (-1d+68)) .or. (.not. (y3 <= 2.95d+119))) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    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 ((y3 <= -1e+68) || !(y3 <= 2.95e+119)) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} 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 (y3 <= -1e+68) or not (y3 <= 2.95e+119):
		tmp = a * (y * ((x * b) - (y3 * y5)))
	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 ((y3 <= -1e+68) || !(y3 <= 2.95e+119))
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	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 ((y3 <= -1e+68) || ~((y3 <= 2.95e+119)))
		tmp = a * (y * ((x * b) - (y3 * y5)));
	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[Or[LessEqual[y3, -1e+68], N[Not[LessEqual[y3, 2.95e+119]], $MachinePrecision]], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $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 2 regimes

2. if y3 < -9.99999999999999953e67 or 2.95e119 < y3

   1. Initial program 31.9%

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

   3. Simplified 31.9%

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

   5. Taylor expanded in a around inf 39.5%

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

   6. Taylor expanded in y around inf 49.6%

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

   if -9.99999999999999953e67 < y3 < 2.95e119

   1. Initial program 38.5%

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

   3. Simplified 39.2%

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

   5. Taylor expanded in a around inf 45.1%

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

   6. Taylor expanded in b around inf 33.2%

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

      1. neg-mul-1 33.2%

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

      2. +-commutative 33.2%

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

      3. sub-neg 33.2%

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

   8. Simplified 33.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 39.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -1 \cdot 10^{+68} \lor \neg \left(y3 \leq 2.95 \cdot 10^{+119}\right):\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 30.0% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -6.8 \cdot 10^{+112}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq 1.95 \cdot 10^{-94}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y1 -6.8e+112)
   (* a (* y3 (- (* z y1) (* y y5))))
   (if (<= y1 1.95e-94)
     (* a (* b (- (* x y) (* z t))))
     (* k (* y2 (- (* y1 y4) (* y0 y5)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y1 <= -6.8e+112) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (y1 <= 1.95e-94) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y1 <= (-6.8d+112)) then
        tmp = a * (y3 * ((z * y1) - (y * y5)))
    else if (y1 <= 1.95d-94) then
        tmp = a * (b * ((x * y) - (z * t)))
    else
        tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y1 <= -6.8e+112) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (y1 <= 1.95e-94) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y1 <= -6.8e+112:
		tmp = a * (y3 * ((z * y1) - (y * y5)))
	elif y1 <= 1.95e-94:
		tmp = a * (b * ((x * y) - (z * t)))
	else:
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y1 <= -6.8e+112)
		tmp = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))));
	elseif (y1 <= 1.95e-94)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	else
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y1 <= -6.8e+112)
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	elseif (y1 <= 1.95e-94)
		tmp = a * (b * ((x * y) - (z * t)));
	else
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y1, -6.8e+112], N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.95e-94], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y1 < -6.79999999999999987e112

   1. Initial program 24.8%

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

   3. Simplified 24.8%

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

   5. Taylor expanded in a around inf 42.8%

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

   6. Taylor expanded in y3 around inf 49.1%

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

   if -6.79999999999999987e112 < y1 < 1.9500000000000001e-94

   1. Initial program 40.5%

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

   3. Simplified 40.5%

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

   5. Taylor expanded in a around inf 43.0%

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

   6. Taylor expanded in b around inf 37.9%

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

      1. neg-mul-1 37.9%

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

      2. +-commutative 37.9%

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

      3. sub-neg 37.9%

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

   8. Simplified 37.9%

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

   if 1.9500000000000001e-94 < y1

   1. Initial program 33.1%

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

   3. Taylor expanded in y2 around inf 54.1%

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

   4. Taylor expanded in k around inf 49.5%

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

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -6.8 \cdot 10^{+112}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq 1.95 \cdot 10^{-94}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 31.7% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{+28}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+122}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= b -9e+28)
   (* b (* y0 (- (* z k) (* x j))))
   (if (<= b 1.4e+122)
     (* a (* y5 (- (* t y2) (* y y3))))
     (* 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 (b <= -9e+28) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (b <= 1.4e+122) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} 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 (b <= (-9d+28)) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (b <= 1.4d+122) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    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 (b <= -9e+28) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (b <= 1.4e+122) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} 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 b <= -9e+28:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif b <= 1.4e+122:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	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 (b <= -9e+28)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (b <= 1.4e+122)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	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 (b <= -9e+28)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (b <= 1.4e+122)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	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[b, -9e+28], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.4e+122], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $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 3 regimes

2. if b < -8.9999999999999994e28

   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 y0 around inf 37.2%

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

   4. Taylor expanded in b around inf 49.8%

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

   if -8.9999999999999994e28 < b < 1.4e122

   1. Initial program 36.6%

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

   3. Simplified 37.2%

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

   5. Taylor expanded in a around inf 41.6%

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

   6. Taylor expanded in y5 around inf 35.7%

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

   if 1.4e122 < b

   1. Initial program 28.2%

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

   3. Simplified 28.2%

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

   5. Taylor expanded in a around inf 43.8%

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

   6. Taylor expanded in b around inf 56.8%

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

      1. neg-mul-1 56.8%

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

      2. +-commutative 56.8%

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

      3. sub-neg 56.8%

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

   8. Simplified 56.8%

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

4. Final simplification 41.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{+28}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+122}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 22.0% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+113} \lor \neg \left(x \leq 3.75 \cdot 10^{+87}\right):\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= x -1.45e+113) (not (<= x 3.75e+87)))
   (* a (* (* x y) b))
   (* j (* y0 (* y3 y5)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((x <= -1.45e+113) || !(x <= 3.75e+87)) {
		tmp = a * ((x * y) * b);
	} else {
		tmp = j * (y0 * (y3 * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((x <= (-1.45d+113)) .or. (.not. (x <= 3.75d+87))) then
        tmp = a * ((x * y) * b)
    else
        tmp = j * (y0 * (y3 * y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((x <= -1.45e+113) || !(x <= 3.75e+87)) {
		tmp = a * ((x * y) * b);
	} else {
		tmp = j * (y0 * (y3 * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (x <= -1.45e+113) or not (x <= 3.75e+87):
		tmp = a * ((x * y) * b)
	else:
		tmp = j * (y0 * (y3 * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((x <= -1.45e+113) || !(x <= 3.75e+87))
		tmp = Float64(a * Float64(Float64(x * y) * b));
	else
		tmp = Float64(j * Float64(y0 * Float64(y3 * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((x <= -1.45e+113) || ~((x <= 3.75e+87)))
		tmp = a * ((x * y) * b);
	else
		tmp = j * (y0 * (y3 * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[x, -1.45e+113], N[Not[LessEqual[x, 3.75e+87]], $MachinePrecision]], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(j * N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.44999999999999992e113 or 3.75000000000000007e87 < x

   1. Initial program 27.6%

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

   3. Simplified 27.6%

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

   5. Taylor expanded in a around inf 45.2%

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

   6. Taylor expanded in b around inf 45.7%

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

      1. neg-mul-1 45.7%

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

      2. +-commutative 45.7%

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

      3. sub-neg 45.7%

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

   8. Simplified 45.7%

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

   9. Taylor expanded in x around inf 41.5%

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

       1. *-commutative 41.5%

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

       2. *-commutative 41.5%

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

   11. Simplified 41.5%

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

   if -1.44999999999999992e113 < x < 3.75000000000000007e87

   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 y0 around inf 33.1%

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

   4. Taylor expanded in j around inf 25.1%

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

   5. Taylor expanded in y3 around inf 21.5%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 21.5%

         \[\leadsto j \cdot \left(y0 \cdot \color{blue}{\left(y5 \cdot y3\right)}\right) \]

   7. Simplified 21.5%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y5 \cdot y3\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 28.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+113} \lor \neg \left(x \leq 3.75 \cdot 10^{+87}\right):\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 22.2% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-99} \lor \neg \left(x \leq 5.8 \cdot 10^{+107}\right):\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= x -4.5e-99) (not (<= x 5.8e+107)))
   (* a (* (* x y) b))
   (* a (* y3 (* z y1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((x <= -4.5e-99) || !(x <= 5.8e+107)) {
		tmp = a * ((x * y) * b);
	} else {
		tmp = a * (y3 * (z * y1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((x <= (-4.5d-99)) .or. (.not. (x <= 5.8d+107))) then
        tmp = a * ((x * y) * b)
    else
        tmp = a * (y3 * (z * y1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((x <= -4.5e-99) || !(x <= 5.8e+107)) {
		tmp = a * ((x * y) * b);
	} else {
		tmp = a * (y3 * (z * y1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (x <= -4.5e-99) or not (x <= 5.8e+107):
		tmp = a * ((x * y) * b)
	else:
		tmp = a * (y3 * (z * y1))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((x <= -4.5e-99) || !(x <= 5.8e+107))
		tmp = Float64(a * Float64(Float64(x * y) * b));
	else
		tmp = Float64(a * Float64(y3 * Float64(z * y1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((x <= -4.5e-99) || ~((x <= 5.8e+107)))
		tmp = a * ((x * y) * b);
	else
		tmp = a * (y3 * (z * y1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[x, -4.5e-99], N[Not[LessEqual[x, 5.8e+107]], $MachinePrecision]], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(a * N[(y3 * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.5000000000000003e-99 or 5.79999999999999975e107 < x

   1. Initial program 32.1%

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

   3. Simplified 32.1%

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

   5. Taylor expanded in a around inf 41.7%

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

   6. Taylor expanded in b around inf 38.5%

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

      1. neg-mul-1 38.5%

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

      2. +-commutative 38.5%

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

      3. sub-neg 38.5%

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

   8. Simplified 38.5%

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

   9. Taylor expanded in x around inf 34.0%

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

       1. *-commutative 34.0%

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

       2. *-commutative 34.0%

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

   11. Simplified 34.0%

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

   if -4.5000000000000003e-99 < x < 5.79999999999999975e107

   1. Initial program 40.1%

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

   3. Simplified 40.9%

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

   5. Taylor expanded in a around inf 44.4%

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

   6. Taylor expanded in y1 around inf 19.4%

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

      1. associate-*r* 19.4%

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

      2. neg-mul-1 19.4%

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

   8. Simplified 19.4%

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

   9. Taylor expanded in x around 0 17.2%

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

       1. *-commutative 17.2%

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

   11. Simplified 17.2%

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

   12. Taylor expanded in a around 0 17.2%

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

       1. *-commutative 17.2%

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

       2. associate-*l* 19.4%

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

       3. *-commutative 19.4%

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

   14. Simplified 19.4%

       \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 26.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-99} \lor \neg \left(x \leq 5.8 \cdot 10^{+107}\right):\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 31: 17.6% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* y3 (* z 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) {
	return a * (y3 * (z * y1));
}

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 * (y3 * (z * y1))
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 * (y3 * (z * y1));
}

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(y3 * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 36.1%

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

3. Simplified 36.5%

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

5. Taylor expanded in a around inf 43.1%

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

6. Taylor expanded in y1 around inf 23.6%

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

   1. associate-*r* 23.6%

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

   2. neg-mul-1 23.6%

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

8. Simplified 23.6%

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

9. Taylor expanded in x around 0 14.8%

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

    1. *-commutative 14.8%

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

11. Simplified 14.8%

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

12. Taylor expanded in a around 0 14.8%

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

    1. *-commutative 14.8%

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

    2. associate-*l* 15.1%

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

    3. *-commutative 15.1%

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

14. Simplified 15.1%

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

15. Final simplification 15.1%

    \[\leadsto a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right) \]
16. Add Preprocessing

Alternative 32: 17.4% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right) \end{array} \]

FPCore

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

C

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

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 * (y1 * (z * y3))
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 * (y1 * (z * y3));
}

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(y1 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 36.1%

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

3. Simplified 36.5%

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

5. Taylor expanded in a around inf 43.1%

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

6. Taylor expanded in y1 around inf 23.6%

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

   1. associate-*r* 23.6%

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

   2. neg-mul-1 23.6%

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

8. Simplified 23.6%

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

9. Taylor expanded in x around 0 14.8%

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

    1. *-commutative 14.8%

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

11. Simplified 14.8%

    \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)} \]
12. Add Preprocessing

Developer Target 1: 28.6% 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 2024170 
(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)))))