Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 30.0% → 41.3%

Time: 1.5min

Alternatives: 33

Speedup: 4.9×

• 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: 30.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 41.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot y5 - c \cdot y4\\ t_2 := x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ t_3 := c \cdot y4 - a \cdot y5\\ t_4 := y3 \cdot \left(y \cdot t_3 + \left(z \cdot \left(a \cdot y1 - c \cdot y0\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\right)\\ t_5 := k \cdot y2 - j \cdot y3\\ t_6 := b \cdot y4 - i \cdot y5\\ t_7 := y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot t_5\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;y3 \leq -3 \cdot 10^{+33}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y3 \leq -9.5 \cdot 10^{-197}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;y3 \leq -9.2 \cdot 10^{-280}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y3 \leq 1.25 \cdot 10^{-264}:\\ \;\;\;\;t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot t_6\right) + y2 \cdot t_1\right)\\ \mathbf{elif}\;y3 \leq 8.5 \cdot 10^{-197}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y3 \leq 1.9 \cdot 10^{-125}:\\ \;\;\;\;\left(y1 \cdot y4 - y0 \cdot y5\right) \cdot t_5 + \left(c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \left(t \cdot y2 - y \cdot y3\right) \cdot t_1\right)\\ \mathbf{elif}\;y3 \leq 2 \cdot 10^{+89}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;y3 \leq 6 \cdot 10^{+151}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y3 \leq 3.2 \cdot 10^{+161}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 1.5 \cdot 10^{+169}:\\ \;\;\;\;y \cdot \left(y3 \cdot t_3\right)\\ \mathbf{elif}\;y3 \leq 1.05 \cdot 10^{+190}:\\ \;\;\;\;\left(t \cdot j\right) \cdot t_6\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* a y5) (* c y4)))
        (t_2
         (*
          x
          (+
           (+ (* y (- (* a b) (* c i))) (* y2 (- (* c y0) (* a y1))))
           (* j (- (* i y1) (* b y0))))))
        (t_3 (- (* c y4) (* a y5)))
        (t_4
         (*
          y3
          (+
           (* y t_3)
           (+ (* z (- (* a y1) (* c y0))) (* j (- (* y0 y5) (* y1 y4)))))))
        (t_5 (- (* k y2) (* j y3)))
        (t_6 (- (* b y4) (* i y5)))
        (t_7
         (*
          y4
          (+
           (+ (* b (- (* t j) (* y k))) (* y1 t_5))
           (* c (- (* y y3) (* t y2)))))))
   (if (<= y3 -3e+33)
     t_4
     (if (<= y3 -9.5e-197)
       t_7
       (if (<= y3 -9.2e-280)
         t_2
         (if (<= y3 1.25e-264)
           (* t (+ (+ (* z (- (* c i) (* a b))) (* j t_6)) (* y2 t_1)))
           (if (<= y3 8.5e-197)
             t_2
             (if (<= y3 1.9e-125)
               (+
                (* (- (* y1 y4) (* y0 y5)) t_5)
                (+
                 (*
                  c
                  (+ (* i (- (* z t) (* x y))) (* y0 (- (* x y2) (* z y3)))))
                 (* (- (* t y2) (* y y3)) t_1)))
               (if (<= y3 2e+89)
                 t_7
                 (if (<= y3 6e+151)
                   (* y (* a (- (* x b) (* y3 y5))))
                   (if (<= y3 3.2e+161)
                     (* k (* y4 (* y1 y2)))
                     (if (<= y3 1.5e+169)
                       (* y (* y3 t_3))
                       (if (<= y3 1.05e+190) (* (* t j) t_6) t_4)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (a * y5) - (c * y4);
	double t_2 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	double t_3 = (c * y4) - (a * y5);
	double t_4 = y3 * ((y * t_3) + ((z * ((a * y1) - (c * y0))) + (j * ((y0 * y5) - (y1 * y4)))));
	double t_5 = (k * y2) - (j * y3);
	double t_6 = (b * y4) - (i * y5);
	double t_7 = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_5)) + (c * ((y * y3) - (t * y2))));
	double tmp;
	if (y3 <= -3e+33) {
		tmp = t_4;
	} else if (y3 <= -9.5e-197) {
		tmp = t_7;
	} else if (y3 <= -9.2e-280) {
		tmp = t_2;
	} else if (y3 <= 1.25e-264) {
		tmp = t * (((z * ((c * i) - (a * b))) + (j * t_6)) + (y2 * t_1));
	} else if (y3 <= 8.5e-197) {
		tmp = t_2;
	} else if (y3 <= 1.9e-125) {
		tmp = (((y1 * y4) - (y0 * y5)) * t_5) + ((c * ((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3))))) + (((t * y2) - (y * y3)) * t_1));
	} else if (y3 <= 2e+89) {
		tmp = t_7;
	} else if (y3 <= 6e+151) {
		tmp = y * (a * ((x * b) - (y3 * y5)));
	} else if (y3 <= 3.2e+161) {
		tmp = k * (y4 * (y1 * y2));
	} else if (y3 <= 1.5e+169) {
		tmp = y * (y3 * t_3);
	} else if (y3 <= 1.05e+190) {
		tmp = (t * j) * t_6;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_1 = (a * y5) - (c * y4)
    t_2 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
    t_3 = (c * y4) - (a * y5)
    t_4 = y3 * ((y * t_3) + ((z * ((a * y1) - (c * y0))) + (j * ((y0 * y5) - (y1 * y4)))))
    t_5 = (k * y2) - (j * y3)
    t_6 = (b * y4) - (i * y5)
    t_7 = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_5)) + (c * ((y * y3) - (t * y2))))
    if (y3 <= (-3d+33)) then
        tmp = t_4
    else if (y3 <= (-9.5d-197)) then
        tmp = t_7
    else if (y3 <= (-9.2d-280)) then
        tmp = t_2
    else if (y3 <= 1.25d-264) then
        tmp = t * (((z * ((c * i) - (a * b))) + (j * t_6)) + (y2 * t_1))
    else if (y3 <= 8.5d-197) then
        tmp = t_2
    else if (y3 <= 1.9d-125) then
        tmp = (((y1 * y4) - (y0 * y5)) * t_5) + ((c * ((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3))))) + (((t * y2) - (y * y3)) * t_1))
    else if (y3 <= 2d+89) then
        tmp = t_7
    else if (y3 <= 6d+151) then
        tmp = y * (a * ((x * b) - (y3 * y5)))
    else if (y3 <= 3.2d+161) then
        tmp = k * (y4 * (y1 * y2))
    else if (y3 <= 1.5d+169) then
        tmp = y * (y3 * t_3)
    else if (y3 <= 1.05d+190) then
        tmp = (t * j) * t_6
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (a * y5) - (c * y4);
	double t_2 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	double t_3 = (c * y4) - (a * y5);
	double t_4 = y3 * ((y * t_3) + ((z * ((a * y1) - (c * y0))) + (j * ((y0 * y5) - (y1 * y4)))));
	double t_5 = (k * y2) - (j * y3);
	double t_6 = (b * y4) - (i * y5);
	double t_7 = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_5)) + (c * ((y * y3) - (t * y2))));
	double tmp;
	if (y3 <= -3e+33) {
		tmp = t_4;
	} else if (y3 <= -9.5e-197) {
		tmp = t_7;
	} else if (y3 <= -9.2e-280) {
		tmp = t_2;
	} else if (y3 <= 1.25e-264) {
		tmp = t * (((z * ((c * i) - (a * b))) + (j * t_6)) + (y2 * t_1));
	} else if (y3 <= 8.5e-197) {
		tmp = t_2;
	} else if (y3 <= 1.9e-125) {
		tmp = (((y1 * y4) - (y0 * y5)) * t_5) + ((c * ((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3))))) + (((t * y2) - (y * y3)) * t_1));
	} else if (y3 <= 2e+89) {
		tmp = t_7;
	} else if (y3 <= 6e+151) {
		tmp = y * (a * ((x * b) - (y3 * y5)));
	} else if (y3 <= 3.2e+161) {
		tmp = k * (y4 * (y1 * y2));
	} else if (y3 <= 1.5e+169) {
		tmp = y * (y3 * t_3);
	} else if (y3 <= 1.05e+190) {
		tmp = (t * j) * t_6;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (a * y5) - (c * y4)
	t_2 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
	t_3 = (c * y4) - (a * y5)
	t_4 = y3 * ((y * t_3) + ((z * ((a * y1) - (c * y0))) + (j * ((y0 * y5) - (y1 * y4)))))
	t_5 = (k * y2) - (j * y3)
	t_6 = (b * y4) - (i * y5)
	t_7 = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_5)) + (c * ((y * y3) - (t * y2))))
	tmp = 0
	if y3 <= -3e+33:
		tmp = t_4
	elif y3 <= -9.5e-197:
		tmp = t_7
	elif y3 <= -9.2e-280:
		tmp = t_2
	elif y3 <= 1.25e-264:
		tmp = t * (((z * ((c * i) - (a * b))) + (j * t_6)) + (y2 * t_1))
	elif y3 <= 8.5e-197:
		tmp = t_2
	elif y3 <= 1.9e-125:
		tmp = (((y1 * y4) - (y0 * y5)) * t_5) + ((c * ((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3))))) + (((t * y2) - (y * y3)) * t_1))
	elif y3 <= 2e+89:
		tmp = t_7
	elif y3 <= 6e+151:
		tmp = y * (a * ((x * b) - (y3 * y5)))
	elif y3 <= 3.2e+161:
		tmp = k * (y4 * (y1 * y2))
	elif y3 <= 1.5e+169:
		tmp = y * (y3 * t_3)
	elif y3 <= 1.05e+190:
		tmp = (t * j) * t_6
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(a * y5) - Float64(c * y4))
	t_2 = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))))
	t_3 = Float64(Float64(c * y4) - Float64(a * y5))
	t_4 = Float64(y3 * Float64(Float64(y * t_3) + Float64(Float64(z * Float64(Float64(a * y1) - Float64(c * y0))) + Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4))))))
	t_5 = Float64(Float64(k * y2) - Float64(j * y3))
	t_6 = Float64(Float64(b * y4) - Float64(i * y5))
	t_7 = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * t_5)) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))))
	tmp = 0.0
	if (y3 <= -3e+33)
		tmp = t_4;
	elseif (y3 <= -9.5e-197)
		tmp = t_7;
	elseif (y3 <= -9.2e-280)
		tmp = t_2;
	elseif (y3 <= 1.25e-264)
		tmp = Float64(t * Float64(Float64(Float64(z * Float64(Float64(c * i) - Float64(a * b))) + Float64(j * t_6)) + Float64(y2 * t_1)));
	elseif (y3 <= 8.5e-197)
		tmp = t_2;
	elseif (y3 <= 1.9e-125)
		tmp = Float64(Float64(Float64(Float64(y1 * y4) - Float64(y0 * y5)) * t_5) + Float64(Float64(c * Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))))) + Float64(Float64(Float64(t * y2) - Float64(y * y3)) * t_1)));
	elseif (y3 <= 2e+89)
		tmp = t_7;
	elseif (y3 <= 6e+151)
		tmp = Float64(y * Float64(a * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (y3 <= 3.2e+161)
		tmp = Float64(k * Float64(y4 * Float64(y1 * y2)));
	elseif (y3 <= 1.5e+169)
		tmp = Float64(y * Float64(y3 * t_3));
	elseif (y3 <= 1.05e+190)
		tmp = Float64(Float64(t * j) * t_6);
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (a * y5) - (c * y4);
	t_2 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	t_3 = (c * y4) - (a * y5);
	t_4 = y3 * ((y * t_3) + ((z * ((a * y1) - (c * y0))) + (j * ((y0 * y5) - (y1 * y4)))));
	t_5 = (k * y2) - (j * y3);
	t_6 = (b * y4) - (i * y5);
	t_7 = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_5)) + (c * ((y * y3) - (t * y2))));
	tmp = 0.0;
	if (y3 <= -3e+33)
		tmp = t_4;
	elseif (y3 <= -9.5e-197)
		tmp = t_7;
	elseif (y3 <= -9.2e-280)
		tmp = t_2;
	elseif (y3 <= 1.25e-264)
		tmp = t * (((z * ((c * i) - (a * b))) + (j * t_6)) + (y2 * t_1));
	elseif (y3 <= 8.5e-197)
		tmp = t_2;
	elseif (y3 <= 1.9e-125)
		tmp = (((y1 * y4) - (y0 * y5)) * t_5) + ((c * ((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3))))) + (((t * y2) - (y * y3)) * t_1));
	elseif (y3 <= 2e+89)
		tmp = t_7;
	elseif (y3 <= 6e+151)
		tmp = y * (a * ((x * b) - (y3 * y5)));
	elseif (y3 <= 3.2e+161)
		tmp = k * (y4 * (y1 * y2));
	elseif (y3 <= 1.5e+169)
		tmp = y * (y3 * t_3);
	elseif (y3 <= 1.05e+190)
		tmp = (t * j) * t_6;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y3 * N[(N[(y * t$95$3), $MachinePrecision] + N[(N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * t$95$5), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -3e+33], t$95$4, If[LessEqual[y3, -9.5e-197], t$95$7, If[LessEqual[y3, -9.2e-280], t$95$2, If[LessEqual[y3, 1.25e-264], N[(t * N[(N[(N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$6), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 8.5e-197], t$95$2, If[LessEqual[y3, 1.9e-125], N[(N[(N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision] * t$95$5), $MachinePrecision] + N[(N[(c * 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]), $MachinePrecision] + N[(N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 2e+89], t$95$7, If[LessEqual[y3, 6e+151], N[(y * N[(a * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 3.2e+161], N[(k * N[(y4 * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.5e+169], N[(y * N[(y3 * t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.05e+190], N[(N[(t * j), $MachinePrecision] * t$95$6), $MachinePrecision], t$95$4]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y3 < -2.99999999999999984e33 or 1.05e190 < y3

   1. Initial program 26.5%

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

   2. Taylor expanded in y3 around -inf 65.2%

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

   if -2.99999999999999984e33 < y3 < -9.5000000000000003e-197 or 1.9000000000000001e-125 < y3 < 1.99999999999999999e89

   1. Initial program 28.6%

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

   2. Taylor expanded in y4 around inf 61.5%

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

   if -9.5000000000000003e-197 < y3 < -9.1999999999999998e-280 or 1.25e-264 < y3 < 8.5e-197

   1. Initial program 33.5%

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

   2. Taylor expanded in x around inf 73.8%

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

   if -9.1999999999999998e-280 < y3 < 1.25e-264

   1. Initial program 37.2%

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

   3. Simplified 37.2%

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

   4. Taylor expanded in t around inf 53.7%

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

   if 8.5e-197 < y3 < 1.9000000000000001e-125

   1. Initial program 55.5%

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

   2. Taylor expanded in c around inf 65.1%

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

   if 1.99999999999999999e89 < y3 < 5.9999999999999998e151

   1. Initial program 44.4%

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

   2. Taylor expanded in y around inf 44.7%

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

   3. Taylor expanded in a around inf 77.8%

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

   if 5.9999999999999998e151 < y3 < 3.20000000000000002e161

   1. Initial program 0.0%

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

   2. Taylor expanded in y4 around inf 75.0%

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

   3. Taylor expanded in y2 around inf 100.0%

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

   4. Taylor expanded in k around inf 100.0%

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

   if 3.20000000000000002e161 < y3 < 1.5e169

   1. Initial program 25.0%

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

   2. Taylor expanded in y0 around inf 50.0%

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

      1. *-commutative 50.0%

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

      2. *-commutative 50.0%

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

      3. *-commutative 50.0%

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

   4. Simplified 50.0%

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

   5. Taylor expanded in y around inf 100.0%

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

   if 1.5e169 < y3 < 1.05e190

   1. Initial program 14.3%

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

   3. Simplified 28.6%

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

   4. Taylor expanded in t around inf 42.9%

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

   5. Taylor expanded in j around inf 73.6%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 73.6%

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

      2. *-commutative 73.6%

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

      3. *-commutative 73.6%

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

   7. Simplified 73.6%

      \[\leadsto \color{blue}{\left(j \cdot t\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -3 \cdot 10^{+33}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(z \cdot \left(a \cdot y1 - c \cdot y0\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\right)\\ \mathbf{elif}\;y3 \leq -9.5 \cdot 10^{-197}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq -9.2 \cdot 10^{-280}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq 1.25 \cdot 10^{-264}:\\ \;\;\;\;t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 8.5 \cdot 10^{-197}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq 1.9 \cdot 10^{-125}:\\ \;\;\;\;\left(y1 \cdot y4 - y0 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \left(t \cdot y2 - y \cdot y3\right) \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 2 \cdot 10^{+89}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 6 \cdot 10^{+151}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y3 \leq 3.2 \cdot 10^{+161}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 1.5 \cdot 10^{+169}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;y3 \leq 1.05 \cdot 10^{+190}:\\ \;\;\;\;\left(t \cdot j\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\\ \mathbf{else}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(z \cdot \left(a \cdot y1 - c \cdot y0\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\right)\\ \end{array} \]

Alternative 2: 52.5% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 92.3%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in y3 around -inf 42.0%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - y1 \cdot a\right) \cdot z + j \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y3\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 58.7%

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

Alternative 3: 37.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot y5 - c \cdot y4\right)\\ t_2 := y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ t_3 := c \cdot y0 - a \cdot y1\\ t_4 := k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ t_5 := y2 \cdot \left(\left(t_4 + x \cdot t_3\right) + t_1\right)\\ t_6 := t \cdot y2 - y \cdot y3\\ t_7 := y5 \cdot \left(a \cdot t_6 + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{if}\;y \leq -6.8 \cdot 10^{+21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-237}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-122}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-54}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) - y4 \cdot t_6\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-35}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot \left(c \cdot i - a \cdot b\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;y \leq 1.66:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq 63000:\\ \;\;\;\;z \cdot \left(y1 \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+123}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+147}:\\ \;\;\;\;y2 \cdot \left(\left(t_4 + c \cdot \left(x \cdot y0\right)\right) + t_1\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+179}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+206}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+230}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot t_3\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* t (- (* a y5) (* c y4))))
        (t_2 (* y4 (* y (- (* c y3) (* b k)))))
        (t_3 (- (* c y0) (* a y1)))
        (t_4 (* k (- (* y1 y4) (* y0 y5))))
        (t_5 (* y2 (+ (+ t_4 (* x t_3)) t_1)))
        (t_6 (- (* t y2) (* y y3)))
        (t_7
         (*
          y5
          (+
           (* a t_6)
           (+ (* i (- (* y k) (* t j))) (* y0 (- (* j y3) (* k y2))))))))
   (if (<= y -6.8e+21)
     t_2
     (if (<= y -5e-237)
       t_5
       (if (<= y 2.2e-122)
         (*
          y4
          (+
           (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
           (* c (- (* y y3) (* t y2)))))
         (if (<= y 8.2e-54)
           (* c (- (* y0 (- (* x y2) (* z y3))) (* y4 t_6)))
           (if (<= y 1.85e-35)
             (*
              z
              (+
               (* k (- (* b y0) (* i y1)))
               (+ (* t (- (* c i) (* a b))) (* y3 (- (* a y1) (* c y0))))))
             (if (<= y 1.66)
               t_5
               (if (<= y 63000.0)
                 (* z (* y1 (- (* a y3) (* i k))))
                 (if (<= y 8.5e+123)
                   t_7
                   (if (<= y 4.6e+147)
                     (* y2 (+ (+ t_4 (* c (* x y0))) t_1))
                     (if (<= y 2.3e+179)
                       t_7
                       (if (<= y 2.8e+206)
                         (* k (* y4 (* y (- b))))
                         (if (<= y 1.95e+230)
                           (*
                            x
                            (+
                             (+ (* y (- (* a b) (* c i))) (* y2 t_3))
                             (* j (- (* i y1) (* b y0)))))
                           t_2))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * ((a * y5) - (c * y4));
	double t_2 = y4 * (y * ((c * y3) - (b * k)));
	double t_3 = (c * y0) - (a * y1);
	double t_4 = k * ((y1 * y4) - (y0 * y5));
	double t_5 = y2 * ((t_4 + (x * t_3)) + t_1);
	double t_6 = (t * y2) - (y * y3);
	double t_7 = y5 * ((a * t_6) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	double tmp;
	if (y <= -6.8e+21) {
		tmp = t_2;
	} else if (y <= -5e-237) {
		tmp = t_5;
	} else if (y <= 2.2e-122) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (y <= 8.2e-54) {
		tmp = c * ((y0 * ((x * y2) - (z * y3))) - (y4 * t_6));
	} else if (y <= 1.85e-35) {
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	} else if (y <= 1.66) {
		tmp = t_5;
	} else if (y <= 63000.0) {
		tmp = z * (y1 * ((a * y3) - (i * k)));
	} else if (y <= 8.5e+123) {
		tmp = t_7;
	} else if (y <= 4.6e+147) {
		tmp = y2 * ((t_4 + (c * (x * y0))) + t_1);
	} else if (y <= 2.3e+179) {
		tmp = t_7;
	} else if (y <= 2.8e+206) {
		tmp = k * (y4 * (y * -b));
	} else if (y <= 1.95e+230) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_3)) + (j * ((i * y1) - (b * y0))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_1 = t * ((a * y5) - (c * y4))
    t_2 = y4 * (y * ((c * y3) - (b * k)))
    t_3 = (c * y0) - (a * y1)
    t_4 = k * ((y1 * y4) - (y0 * y5))
    t_5 = y2 * ((t_4 + (x * t_3)) + t_1)
    t_6 = (t * y2) - (y * y3)
    t_7 = y5 * ((a * t_6) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))))
    if (y <= (-6.8d+21)) then
        tmp = t_2
    else if (y <= (-5d-237)) then
        tmp = t_5
    else if (y <= 2.2d-122) then
        tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    else if (y <= 8.2d-54) then
        tmp = c * ((y0 * ((x * y2) - (z * y3))) - (y4 * t_6))
    else if (y <= 1.85d-35) then
        tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))))
    else if (y <= 1.66d0) then
        tmp = t_5
    else if (y <= 63000.0d0) then
        tmp = z * (y1 * ((a * y3) - (i * k)))
    else if (y <= 8.5d+123) then
        tmp = t_7
    else if (y <= 4.6d+147) then
        tmp = y2 * ((t_4 + (c * (x * y0))) + t_1)
    else if (y <= 2.3d+179) then
        tmp = t_7
    else if (y <= 2.8d+206) then
        tmp = k * (y4 * (y * -b))
    else if (y <= 1.95d+230) then
        tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_3)) + (j * ((i * y1) - (b * y0))))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * ((a * y5) - (c * y4));
	double t_2 = y4 * (y * ((c * y3) - (b * k)));
	double t_3 = (c * y0) - (a * y1);
	double t_4 = k * ((y1 * y4) - (y0 * y5));
	double t_5 = y2 * ((t_4 + (x * t_3)) + t_1);
	double t_6 = (t * y2) - (y * y3);
	double t_7 = y5 * ((a * t_6) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	double tmp;
	if (y <= -6.8e+21) {
		tmp = t_2;
	} else if (y <= -5e-237) {
		tmp = t_5;
	} else if (y <= 2.2e-122) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (y <= 8.2e-54) {
		tmp = c * ((y0 * ((x * y2) - (z * y3))) - (y4 * t_6));
	} else if (y <= 1.85e-35) {
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	} else if (y <= 1.66) {
		tmp = t_5;
	} else if (y <= 63000.0) {
		tmp = z * (y1 * ((a * y3) - (i * k)));
	} else if (y <= 8.5e+123) {
		tmp = t_7;
	} else if (y <= 4.6e+147) {
		tmp = y2 * ((t_4 + (c * (x * y0))) + t_1);
	} else if (y <= 2.3e+179) {
		tmp = t_7;
	} else if (y <= 2.8e+206) {
		tmp = k * (y4 * (y * -b));
	} else if (y <= 1.95e+230) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_3)) + (j * ((i * y1) - (b * y0))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = t * ((a * y5) - (c * y4))
	t_2 = y4 * (y * ((c * y3) - (b * k)))
	t_3 = (c * y0) - (a * y1)
	t_4 = k * ((y1 * y4) - (y0 * y5))
	t_5 = y2 * ((t_4 + (x * t_3)) + t_1)
	t_6 = (t * y2) - (y * y3)
	t_7 = y5 * ((a * t_6) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))))
	tmp = 0
	if y <= -6.8e+21:
		tmp = t_2
	elif y <= -5e-237:
		tmp = t_5
	elif y <= 2.2e-122:
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	elif y <= 8.2e-54:
		tmp = c * ((y0 * ((x * y2) - (z * y3))) - (y4 * t_6))
	elif y <= 1.85e-35:
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))))
	elif y <= 1.66:
		tmp = t_5
	elif y <= 63000.0:
		tmp = z * (y1 * ((a * y3) - (i * k)))
	elif y <= 8.5e+123:
		tmp = t_7
	elif y <= 4.6e+147:
		tmp = y2 * ((t_4 + (c * (x * y0))) + t_1)
	elif y <= 2.3e+179:
		tmp = t_7
	elif y <= 2.8e+206:
		tmp = k * (y4 * (y * -b))
	elif y <= 1.95e+230:
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_3)) + (j * ((i * y1) - (b * y0))))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))
	t_2 = Float64(y4 * Float64(y * Float64(Float64(c * y3) - Float64(b * k))))
	t_3 = Float64(Float64(c * y0) - Float64(a * y1))
	t_4 = Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))
	t_5 = Float64(y2 * Float64(Float64(t_4 + Float64(x * t_3)) + t_1))
	t_6 = Float64(Float64(t * y2) - Float64(y * y3))
	t_7 = Float64(y5 * Float64(Float64(a * t_6) + Float64(Float64(i * Float64(Float64(y * k) - Float64(t * j))) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))))))
	tmp = 0.0
	if (y <= -6.8e+21)
		tmp = t_2;
	elseif (y <= -5e-237)
		tmp = t_5;
	elseif (y <= 2.2e-122)
		tmp = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (y <= 8.2e-54)
		tmp = Float64(c * Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) - Float64(y4 * t_6)));
	elseif (y <= 1.85e-35)
		tmp = Float64(z * Float64(Float64(k * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(Float64(t * Float64(Float64(c * i) - Float64(a * b))) + Float64(y3 * Float64(Float64(a * y1) - Float64(c * y0))))));
	elseif (y <= 1.66)
		tmp = t_5;
	elseif (y <= 63000.0)
		tmp = Float64(z * Float64(y1 * Float64(Float64(a * y3) - Float64(i * k))));
	elseif (y <= 8.5e+123)
		tmp = t_7;
	elseif (y <= 4.6e+147)
		tmp = Float64(y2 * Float64(Float64(t_4 + Float64(c * Float64(x * y0))) + t_1));
	elseif (y <= 2.3e+179)
		tmp = t_7;
	elseif (y <= 2.8e+206)
		tmp = Float64(k * Float64(y4 * Float64(y * Float64(-b))));
	elseif (y <= 1.95e+230)
		tmp = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * t_3)) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	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 = t * ((a * y5) - (c * y4));
	t_2 = y4 * (y * ((c * y3) - (b * k)));
	t_3 = (c * y0) - (a * y1);
	t_4 = k * ((y1 * y4) - (y0 * y5));
	t_5 = y2 * ((t_4 + (x * t_3)) + t_1);
	t_6 = (t * y2) - (y * y3);
	t_7 = y5 * ((a * t_6) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	tmp = 0.0;
	if (y <= -6.8e+21)
		tmp = t_2;
	elseif (y <= -5e-237)
		tmp = t_5;
	elseif (y <= 2.2e-122)
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	elseif (y <= 8.2e-54)
		tmp = c * ((y0 * ((x * y2) - (z * y3))) - (y4 * t_6));
	elseif (y <= 1.85e-35)
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	elseif (y <= 1.66)
		tmp = t_5;
	elseif (y <= 63000.0)
		tmp = z * (y1 * ((a * y3) - (i * k)));
	elseif (y <= 8.5e+123)
		tmp = t_7;
	elseif (y <= 4.6e+147)
		tmp = y2 * ((t_4 + (c * (x * y0))) + t_1);
	elseif (y <= 2.3e+179)
		tmp = t_7;
	elseif (y <= 2.8e+206)
		tmp = k * (y4 * (y * -b));
	elseif (y <= 1.95e+230)
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_3)) + (j * ((i * y1) - (b * y0))));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y4 * N[(y * N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y2 * N[(N[(t$95$4 + N[(x * t$95$3), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(y5 * N[(N[(a * t$95$6), $MachinePrecision] + 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]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.8e+21], t$95$2, If[LessEqual[y, -5e-237], t$95$5, If[LessEqual[y, 2.2e-122], N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.2e-54], N[(c * N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y4 * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.85e-35], N[(z * N[(N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.66], t$95$5, If[LessEqual[y, 63000.0], N[(z * N[(y1 * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.5e+123], t$95$7, If[LessEqual[y, 4.6e+147], N[(y2 * N[(N[(t$95$4 + N[(c * N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e+179], t$95$7, If[LessEqual[y, 2.8e+206], N[(k * N[(y4 * N[(y * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.95e+230], N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if y < -6.8e21 or 1.9499999999999999e230 < y

   1. Initial program 24.6%

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

   2. Taylor expanded in y around inf 54.3%

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

      1. add-cube-cbrt 54.2%

         \[\leadsto y \cdot \color{blue}{\left(\left(\sqrt[3]{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \cdot \sqrt[3]{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \cdot \sqrt[3]{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)} \]

   4. Applied egg-rr 54.2%

      \[\leadsto y \cdot \color{blue}{\left(\left(\sqrt[3]{\mathsf{fma}\left(-1, k \cdot \left(y4 \cdot b - i \cdot y5\right), \mathsf{fma}\left(a, b, -i \cdot c\right) \cdot x\right) + y3 \cdot \left(y4 \cdot c - y5 \cdot a\right)} \cdot \sqrt[3]{\mathsf{fma}\left(-1, k \cdot \left(y4 \cdot b - i \cdot y5\right), \mathsf{fma}\left(a, b, -i \cdot c\right) \cdot x\right) + y3 \cdot \left(y4 \cdot c - y5 \cdot a\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(-1, k \cdot \left(y4 \cdot b - i \cdot y5\right), \mathsf{fma}\left(a, b, -i \cdot c\right) \cdot x\right) + y3 \cdot \left(y4 \cdot c - y5 \cdot a\right)}\right)} \]

   5. Taylor expanded in y4 around inf 53.6%

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

      1. *-commutative 53.6%

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

      2. mul-1-neg 53.6%

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

      3. unsub-neg 53.6%

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

      4. *-commutative 53.6%

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

   7. Simplified 53.6%

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

   if -6.8e21 < y < -5.0000000000000002e-237 or 1.8499999999999999e-35 < y < 1.65999999999999992

   1. Initial program 42.5%

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

   2. Taylor expanded in y2 around inf 57.7%

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

   if -5.0000000000000002e-237 < y < 2.2e-122

   1. Initial program 37.3%

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

   2. Taylor expanded in y4 around inf 59.7%

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

   if 2.2e-122 < y < 8.2000000000000001e-54

   1. Initial program 15.0%

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

   2. Taylor expanded in y0 around inf 45.0%

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

      1. *-commutative 45.0%

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

      2. *-commutative 45.0%

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

      3. *-commutative 45.0%

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

   4. Simplified 45.0%

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

   5. Taylor expanded in c around inf 80.0%

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

      1. *-commutative 80.0%

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

      2. *-commutative 80.0%

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

   7. Simplified 80.0%

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

   if 8.2000000000000001e-54 < y < 1.8499999999999999e-35

   1. Initial program 83.3%

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

   2. Taylor expanded in z around -inf 84.5%

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

   if 1.65999999999999992 < y < 63000

   1. Initial program 0.0%

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

   2. Taylor expanded in z around -inf 66.7%

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

   3. Taylor expanded in y1 around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

   5. Simplified 100.0%

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

   if 63000 < y < 8.5e123 or 4.5999999999999998e147 < y < 2.29999999999999994e179

   1. Initial program 32.5%

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

   3. Simplified 32.5%

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

   4. Taylor expanded in y5 around -inf 65.3%

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

   if 8.5e123 < y < 4.5999999999999998e147

   1. Initial program 12.5%

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

   2. Taylor expanded in y0 around inf 12.6%

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

      1. *-commutative 12.6%

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

      2. *-commutative 12.6%

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

      3. *-commutative 12.6%

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

   4. Simplified 12.6%

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

   5. Taylor expanded in y2 around inf 77.2%

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

   if 2.29999999999999994e179 < y < 2.7999999999999998e206

   1. Initial program 15.6%

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

   2. Taylor expanded in y4 around inf 44.2%

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

   3. Taylor expanded in y around -inf 58.0%

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

      1. mul-1-neg 58.0%

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

      2. associate-*r* 58.0%

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

      3. *-commutative 58.0%

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

   5. Simplified 58.0%

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

   6. Taylor expanded in k around inf 71.7%

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

   if 2.7999999999999998e206 < y < 1.9499999999999999e230

   1. Initial program 16.4%

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

   2. Taylor expanded in x around inf 83.3%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - y1 \cdot a\right) \cdot y2\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot j\right) \cdot x} \]
3. Recombined 10 regimes into one program.

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+21}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-237}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-122}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-54}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-35}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot \left(c \cdot i - a \cdot b\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;y \leq 1.66:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 63000:\\ \;\;\;\;z \cdot \left(y1 \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+123}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+147}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + c \cdot \left(x \cdot y0\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+179}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+206}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+230}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \end{array} \]

Alternative 4: 38.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot y5 - c \cdot y4\right)\\ t_2 := k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ t_3 := y2 \cdot \left(\left(t_2 + c \cdot \left(x \cdot y0\right)\right) + t_1\right)\\ t_4 := c \cdot y0 - a \cdot y1\\ t_5 := y2 \cdot \left(\left(t_2 + x \cdot t_4\right) + t_1\right)\\ t_6 := y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ t_7 := x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot t_4\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{+21}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y \leq -8.6 \cdot 10^{-237}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-122}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-57}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 1.9:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+62}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+112}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+150}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+160}:\\ \;\;\;\;\left(k \cdot y5 - x \cdot c\right) \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+181}:\\ \;\;\;\;\left(t \cdot j\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+225}:\\ \;\;\;\;t_7\\ \mathbf{else}:\\ \;\;\;\;t_6\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* t (- (* a y5) (* c y4))))
        (t_2 (* k (- (* y1 y4) (* y0 y5))))
        (t_3 (* y2 (+ (+ t_2 (* c (* x y0))) t_1)))
        (t_4 (- (* c y0) (* a y1)))
        (t_5 (* y2 (+ (+ t_2 (* x t_4)) t_1)))
        (t_6 (* y4 (* y (- (* c y3) (* b k)))))
        (t_7
         (*
          x
          (+
           (+ (* y (- (* a b) (* c i))) (* y2 t_4))
           (* j (- (* i y1) (* b y0)))))))
   (if (<= y -3.1e+21)
     t_6
     (if (<= y -8.6e-237)
       t_5
       (if (<= y 2.2e-122)
         (*
          y4
          (+
           (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
           (* c (- (* y y3) (* t y2)))))
         (if (<= y 6e-57)
           (* c (- (* y0 (- (* x y2) (* z y3))) (* y4 (- (* t y2) (* y y3)))))
           (if (<= y 1.9)
             t_5
             (if (<= y 4.9e+62)
               t_3
               (if (<= y 1.85e+112)
                 t_7
                 (if (<= y 3.2e+150)
                   t_3
                   (if (<= y 3.4e+160)
                     (* (- (* k y5) (* x c)) (* y i))
                     (if (<= y 1.26e+181)
                       (* (* t j) (- (* b y4) (* i y5)))
                       (if (<= y 3.9e+225) t_7 t_6)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * ((a * y5) - (c * y4));
	double t_2 = k * ((y1 * y4) - (y0 * y5));
	double t_3 = y2 * ((t_2 + (c * (x * y0))) + t_1);
	double t_4 = (c * y0) - (a * y1);
	double t_5 = y2 * ((t_2 + (x * t_4)) + t_1);
	double t_6 = y4 * (y * ((c * y3) - (b * k)));
	double t_7 = x * (((y * ((a * b) - (c * i))) + (y2 * t_4)) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (y <= -3.1e+21) {
		tmp = t_6;
	} else if (y <= -8.6e-237) {
		tmp = t_5;
	} else if (y <= 2.2e-122) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (y <= 6e-57) {
		tmp = c * ((y0 * ((x * y2) - (z * y3))) - (y4 * ((t * y2) - (y * y3))));
	} else if (y <= 1.9) {
		tmp = t_5;
	} else if (y <= 4.9e+62) {
		tmp = t_3;
	} else if (y <= 1.85e+112) {
		tmp = t_7;
	} else if (y <= 3.2e+150) {
		tmp = t_3;
	} else if (y <= 3.4e+160) {
		tmp = ((k * y5) - (x * c)) * (y * i);
	} else if (y <= 1.26e+181) {
		tmp = (t * j) * ((b * y4) - (i * y5));
	} else if (y <= 3.9e+225) {
		tmp = t_7;
	} else {
		tmp = t_6;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_1 = t * ((a * y5) - (c * y4))
    t_2 = k * ((y1 * y4) - (y0 * y5))
    t_3 = y2 * ((t_2 + (c * (x * y0))) + t_1)
    t_4 = (c * y0) - (a * y1)
    t_5 = y2 * ((t_2 + (x * t_4)) + t_1)
    t_6 = y4 * (y * ((c * y3) - (b * k)))
    t_7 = x * (((y * ((a * b) - (c * i))) + (y2 * t_4)) + (j * ((i * y1) - (b * y0))))
    if (y <= (-3.1d+21)) then
        tmp = t_6
    else if (y <= (-8.6d-237)) then
        tmp = t_5
    else if (y <= 2.2d-122) then
        tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    else if (y <= 6d-57) then
        tmp = c * ((y0 * ((x * y2) - (z * y3))) - (y4 * ((t * y2) - (y * y3))))
    else if (y <= 1.9d0) then
        tmp = t_5
    else if (y <= 4.9d+62) then
        tmp = t_3
    else if (y <= 1.85d+112) then
        tmp = t_7
    else if (y <= 3.2d+150) then
        tmp = t_3
    else if (y <= 3.4d+160) then
        tmp = ((k * y5) - (x * c)) * (y * i)
    else if (y <= 1.26d+181) then
        tmp = (t * j) * ((b * y4) - (i * y5))
    else if (y <= 3.9d+225) then
        tmp = t_7
    else
        tmp = t_6
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * ((a * y5) - (c * y4));
	double t_2 = k * ((y1 * y4) - (y0 * y5));
	double t_3 = y2 * ((t_2 + (c * (x * y0))) + t_1);
	double t_4 = (c * y0) - (a * y1);
	double t_5 = y2 * ((t_2 + (x * t_4)) + t_1);
	double t_6 = y4 * (y * ((c * y3) - (b * k)));
	double t_7 = x * (((y * ((a * b) - (c * i))) + (y2 * t_4)) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (y <= -3.1e+21) {
		tmp = t_6;
	} else if (y <= -8.6e-237) {
		tmp = t_5;
	} else if (y <= 2.2e-122) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (y <= 6e-57) {
		tmp = c * ((y0 * ((x * y2) - (z * y3))) - (y4 * ((t * y2) - (y * y3))));
	} else if (y <= 1.9) {
		tmp = t_5;
	} else if (y <= 4.9e+62) {
		tmp = t_3;
	} else if (y <= 1.85e+112) {
		tmp = t_7;
	} else if (y <= 3.2e+150) {
		tmp = t_3;
	} else if (y <= 3.4e+160) {
		tmp = ((k * y5) - (x * c)) * (y * i);
	} else if (y <= 1.26e+181) {
		tmp = (t * j) * ((b * y4) - (i * y5));
	} else if (y <= 3.9e+225) {
		tmp = t_7;
	} else {
		tmp = t_6;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = t * ((a * y5) - (c * y4))
	t_2 = k * ((y1 * y4) - (y0 * y5))
	t_3 = y2 * ((t_2 + (c * (x * y0))) + t_1)
	t_4 = (c * y0) - (a * y1)
	t_5 = y2 * ((t_2 + (x * t_4)) + t_1)
	t_6 = y4 * (y * ((c * y3) - (b * k)))
	t_7 = x * (((y * ((a * b) - (c * i))) + (y2 * t_4)) + (j * ((i * y1) - (b * y0))))
	tmp = 0
	if y <= -3.1e+21:
		tmp = t_6
	elif y <= -8.6e-237:
		tmp = t_5
	elif y <= 2.2e-122:
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	elif y <= 6e-57:
		tmp = c * ((y0 * ((x * y2) - (z * y3))) - (y4 * ((t * y2) - (y * y3))))
	elif y <= 1.9:
		tmp = t_5
	elif y <= 4.9e+62:
		tmp = t_3
	elif y <= 1.85e+112:
		tmp = t_7
	elif y <= 3.2e+150:
		tmp = t_3
	elif y <= 3.4e+160:
		tmp = ((k * y5) - (x * c)) * (y * i)
	elif y <= 1.26e+181:
		tmp = (t * j) * ((b * y4) - (i * y5))
	elif y <= 3.9e+225:
		tmp = t_7
	else:
		tmp = t_6
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))
	t_2 = Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))
	t_3 = Float64(y2 * Float64(Float64(t_2 + Float64(c * Float64(x * y0))) + t_1))
	t_4 = Float64(Float64(c * y0) - Float64(a * y1))
	t_5 = Float64(y2 * Float64(Float64(t_2 + Float64(x * t_4)) + t_1))
	t_6 = Float64(y4 * Float64(y * Float64(Float64(c * y3) - Float64(b * k))))
	t_7 = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * t_4)) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))))
	tmp = 0.0
	if (y <= -3.1e+21)
		tmp = t_6;
	elseif (y <= -8.6e-237)
		tmp = t_5;
	elseif (y <= 2.2e-122)
		tmp = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (y <= 6e-57)
		tmp = Float64(c * Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) - Float64(y4 * Float64(Float64(t * y2) - Float64(y * y3)))));
	elseif (y <= 1.9)
		tmp = t_5;
	elseif (y <= 4.9e+62)
		tmp = t_3;
	elseif (y <= 1.85e+112)
		tmp = t_7;
	elseif (y <= 3.2e+150)
		tmp = t_3;
	elseif (y <= 3.4e+160)
		tmp = Float64(Float64(Float64(k * y5) - Float64(x * c)) * Float64(y * i));
	elseif (y <= 1.26e+181)
		tmp = Float64(Float64(t * j) * Float64(Float64(b * y4) - Float64(i * y5)));
	elseif (y <= 3.9e+225)
		tmp = t_7;
	else
		tmp = t_6;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = t * ((a * y5) - (c * y4));
	t_2 = k * ((y1 * y4) - (y0 * y5));
	t_3 = y2 * ((t_2 + (c * (x * y0))) + t_1);
	t_4 = (c * y0) - (a * y1);
	t_5 = y2 * ((t_2 + (x * t_4)) + t_1);
	t_6 = y4 * (y * ((c * y3) - (b * k)));
	t_7 = x * (((y * ((a * b) - (c * i))) + (y2 * t_4)) + (j * ((i * y1) - (b * y0))));
	tmp = 0.0;
	if (y <= -3.1e+21)
		tmp = t_6;
	elseif (y <= -8.6e-237)
		tmp = t_5;
	elseif (y <= 2.2e-122)
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	elseif (y <= 6e-57)
		tmp = c * ((y0 * ((x * y2) - (z * y3))) - (y4 * ((t * y2) - (y * y3))));
	elseif (y <= 1.9)
		tmp = t_5;
	elseif (y <= 4.9e+62)
		tmp = t_3;
	elseif (y <= 1.85e+112)
		tmp = t_7;
	elseif (y <= 3.2e+150)
		tmp = t_3;
	elseif (y <= 3.4e+160)
		tmp = ((k * y5) - (x * c)) * (y * i);
	elseif (y <= 1.26e+181)
		tmp = (t * j) * ((b * y4) - (i * y5));
	elseif (y <= 3.9e+225)
		tmp = t_7;
	else
		tmp = t_6;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y2 * N[(N[(t$95$2 + N[(c * N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y2 * N[(N[(t$95$2 + N[(x * t$95$4), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(y4 * N[(y * N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$4), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.1e+21], t$95$6, If[LessEqual[y, -8.6e-237], t$95$5, If[LessEqual[y, 2.2e-122], N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e-57], N[(c * N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y4 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9], t$95$5, If[LessEqual[y, 4.9e+62], t$95$3, If[LessEqual[y, 1.85e+112], t$95$7, If[LessEqual[y, 3.2e+150], t$95$3, If[LessEqual[y, 3.4e+160], N[(N[(N[(k * y5), $MachinePrecision] - N[(x * c), $MachinePrecision]), $MachinePrecision] * N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.26e+181], N[(N[(t * j), $MachinePrecision] * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.9e+225], t$95$7, t$95$6]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y < -3.1e21 or 3.90000000000000023e225 < y

   1. Initial program 24.3%

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

   2. Taylor expanded in y around inf 54.8%

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

      1. add-cube-cbrt 54.7%

         \[\leadsto y \cdot \color{blue}{\left(\left(\sqrt[3]{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \cdot \sqrt[3]{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \cdot \sqrt[3]{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)} \]

   4. Applied egg-rr 54.7%

      \[\leadsto y \cdot \color{blue}{\left(\left(\sqrt[3]{\mathsf{fma}\left(-1, k \cdot \left(y4 \cdot b - i \cdot y5\right), \mathsf{fma}\left(a, b, -i \cdot c\right) \cdot x\right) + y3 \cdot \left(y4 \cdot c - y5 \cdot a\right)} \cdot \sqrt[3]{\mathsf{fma}\left(-1, k \cdot \left(y4 \cdot b - i \cdot y5\right), \mathsf{fma}\left(a, b, -i \cdot c\right) \cdot x\right) + y3 \cdot \left(y4 \cdot c - y5 \cdot a\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(-1, k \cdot \left(y4 \cdot b - i \cdot y5\right), \mathsf{fma}\left(a, b, -i \cdot c\right) \cdot x\right) + y3 \cdot \left(y4 \cdot c - y5 \cdot a\right)}\right)} \]

   5. Taylor expanded in y4 around inf 54.1%

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

      1. *-commutative 54.1%

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

      2. mul-1-neg 54.1%

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

      3. unsub-neg 54.1%

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

      4. *-commutative 54.1%

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

   7. Simplified 54.1%

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

   if -3.1e21 < y < -8.59999999999999965e-237 or 6.00000000000000001e-57 < y < 1.8999999999999999

   1. Initial program 47.2%

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

   2. Taylor expanded in y2 around inf 58.4%

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

   if -8.59999999999999965e-237 < y < 2.2e-122

   1. Initial program 37.3%

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

   2. Taylor expanded in y4 around inf 59.7%

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

   if 2.2e-122 < y < 6.00000000000000001e-57

   1. Initial program 10.5%

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

   2. Taylor expanded in y0 around inf 42.1%

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

      1. *-commutative 42.1%

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

      2. *-commutative 42.1%

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

      3. *-commutative 42.1%

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

   4. Simplified 42.1%

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

   5. Taylor expanded in c around inf 78.9%

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

      1. *-commutative 78.9%

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

      2. *-commutative 78.9%

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

   7. Simplified 78.9%

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

   if 1.8999999999999999 < y < 4.8999999999999997e62 or 1.85000000000000002e112 < y < 3.20000000000000016e150

   1. Initial program 20.2%

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

   2. Taylor expanded in y0 around inf 36.3%

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

      1. *-commutative 36.3%

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

      2. *-commutative 36.3%

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

      3. *-commutative 36.3%

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

   4. Simplified 36.3%

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

   5. Taylor expanded in y2 around inf 61.1%

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

   if 4.8999999999999997e62 < y < 1.85000000000000002e112 or 1.26e181 < y < 3.90000000000000023e225

   1. Initial program 22.6%

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

   2. Taylor expanded in x around inf 67.2%

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

   if 3.20000000000000016e150 < y < 3.4000000000000003e160

   1. Initial program 75.0%

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

   2. Taylor expanded in y around inf 52.2%

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

   3. Taylor expanded in i around inf 77.2%

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

      1. associate-*r* 77.2%

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

      2. *-commutative 77.2%

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

      3. mul-1-neg 77.2%

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

      4. unsub-neg 77.2%

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

      5. *-commutative 77.2%

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

   5. Simplified 77.2%

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

   if 3.4000000000000003e160 < y < 1.26e181

   1. Initial program 16.7%

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

   3. Simplified 16.7%

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

   4. Taylor expanded in t around inf 34.4%

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

   5. Taylor expanded in j around inf 51.3%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 67.0%

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

      2. *-commutative 67.0%

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

      3. *-commutative 67.0%

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

   7. Simplified 67.0%

      \[\leadsto \color{blue}{\left(j \cdot t\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+21}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;y \leq -8.6 \cdot 10^{-237}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-122}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-57}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 1.9:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+62}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + c \cdot \left(x \cdot y0\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+150}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + c \cdot \left(x \cdot y0\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+160}:\\ \;\;\;\;\left(k \cdot y5 - x \cdot c\right) \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+181}:\\ \;\;\;\;\left(t \cdot j\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+225}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \end{array} \]

Alternative 5: 42.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot y1 - c \cdot y0\\ t_2 := y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(z \cdot t_1 + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\right)\\ t_3 := t \cdot y2 - y \cdot y3\\ t_4 := y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\\ t_5 := y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + t_4\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ t_6 := c \cdot y0 - a \cdot y1\\ \mathbf{if}\;y3 \leq -5.6 \cdot 10^{+32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y3 \leq -1.02 \cdot 10^{-196}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y3 \leq 9.5 \cdot 10^{-179}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot t_6\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq 1.9 \cdot 10^{-141}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot t_6\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 1.5 \cdot 10^{-127}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y3 \leq 2.6 \cdot 10^{-78}:\\ \;\;\;\;y5 \cdot \left(a \cdot t_3 + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y3 \leq 1.2 \cdot 10^{-26}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot \left(c \cdot i - a \cdot b\right) + y3 \cdot t_1\right)\right)\\ \mathbf{elif}\;y3 \leq 1.35 \cdot 10^{+55}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y3 \leq 2.5 \cdot 10^{+89}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) - y4 \cdot t_3\right)\\ \mathbf{elif}\;y3 \leq 3.2 \cdot 10^{+151}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y3 \leq 2.4 \cdot 10^{+164}:\\ \;\;\;\;y4 \cdot t_4\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* a y1) (* c y0)))
        (t_2
         (*
          y3
          (+
           (* y (- (* c y4) (* a y5)))
           (+ (* z t_1) (* j (- (* y0 y5) (* y1 y4)))))))
        (t_3 (- (* t y2) (* y y3)))
        (t_4 (* y1 (- (* k y2) (* j y3))))
        (t_5
         (*
          y4
          (+ (+ (* b (- (* t j) (* y k))) t_4) (* c (- (* y y3) (* t y2))))))
        (t_6 (- (* c y0) (* a y1))))
   (if (<= y3 -5.6e+32)
     t_2
     (if (<= y3 -1.02e-196)
       t_5
       (if (<= y3 9.5e-179)
         (*
          x
          (+
           (+ (* y (- (* a b) (* c i))) (* y2 t_6))
           (* j (- (* i y1) (* b y0)))))
         (if (<= y3 1.9e-141)
           (*
            y2
            (+
             (+ (* k (- (* y1 y4) (* y0 y5))) (* x t_6))
             (* t (- (* a y5) (* c y4)))))
           (if (<= y3 1.5e-127)
             t_2
             (if (<= y3 2.6e-78)
               (*
                y5
                (+
                 (* a t_3)
                 (+ (* i (- (* y k) (* t j))) (* y0 (- (* j y3) (* k y2))))))
               (if (<= y3 1.2e-26)
                 (*
                  z
                  (+
                   (* k (- (* b y0) (* i y1)))
                   (+ (* t (- (* c i) (* a b))) (* y3 t_1))))
                 (if (<= y3 1.35e+55)
                   t_5
                   (if (<= y3 2.5e+89)
                     (* c (- (* y0 (- (* x y2) (* z y3))) (* y4 t_3)))
                     (if (<= y3 3.2e+151)
                       (* y (* a (- (* x b) (* y3 y5))))
                       (if (<= y3 2.4e+164) (* y4 t_4) t_2)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (a * y1) - (c * y0);
	double t_2 = y3 * ((y * ((c * y4) - (a * y5))) + ((z * t_1) + (j * ((y0 * y5) - (y1 * y4)))));
	double t_3 = (t * y2) - (y * y3);
	double t_4 = y1 * ((k * y2) - (j * y3));
	double t_5 = y4 * (((b * ((t * j) - (y * k))) + t_4) + (c * ((y * y3) - (t * y2))));
	double t_6 = (c * y0) - (a * y1);
	double tmp;
	if (y3 <= -5.6e+32) {
		tmp = t_2;
	} else if (y3 <= -1.02e-196) {
		tmp = t_5;
	} else if (y3 <= 9.5e-179) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_6)) + (j * ((i * y1) - (b * y0))));
	} else if (y3 <= 1.9e-141) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_6)) + (t * ((a * y5) - (c * y4))));
	} else if (y3 <= 1.5e-127) {
		tmp = t_2;
	} else if (y3 <= 2.6e-78) {
		tmp = y5 * ((a * t_3) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	} else if (y3 <= 1.2e-26) {
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * t_1)));
	} else if (y3 <= 1.35e+55) {
		tmp = t_5;
	} else if (y3 <= 2.5e+89) {
		tmp = c * ((y0 * ((x * y2) - (z * y3))) - (y4 * t_3));
	} else if (y3 <= 3.2e+151) {
		tmp = y * (a * ((x * b) - (y3 * y5)));
	} else if (y3 <= 2.4e+164) {
		tmp = y4 * t_4;
	} 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 = (a * y1) - (c * y0)
    t_2 = y3 * ((y * ((c * y4) - (a * y5))) + ((z * t_1) + (j * ((y0 * y5) - (y1 * y4)))))
    t_3 = (t * y2) - (y * y3)
    t_4 = y1 * ((k * y2) - (j * y3))
    t_5 = y4 * (((b * ((t * j) - (y * k))) + t_4) + (c * ((y * y3) - (t * y2))))
    t_6 = (c * y0) - (a * y1)
    if (y3 <= (-5.6d+32)) then
        tmp = t_2
    else if (y3 <= (-1.02d-196)) then
        tmp = t_5
    else if (y3 <= 9.5d-179) then
        tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_6)) + (j * ((i * y1) - (b * y0))))
    else if (y3 <= 1.9d-141) then
        tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_6)) + (t * ((a * y5) - (c * y4))))
    else if (y3 <= 1.5d-127) then
        tmp = t_2
    else if (y3 <= 2.6d-78) then
        tmp = y5 * ((a * t_3) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))))
    else if (y3 <= 1.2d-26) then
        tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * t_1)))
    else if (y3 <= 1.35d+55) then
        tmp = t_5
    else if (y3 <= 2.5d+89) then
        tmp = c * ((y0 * ((x * y2) - (z * y3))) - (y4 * t_3))
    else if (y3 <= 3.2d+151) then
        tmp = y * (a * ((x * b) - (y3 * y5)))
    else if (y3 <= 2.4d+164) then
        tmp = y4 * t_4
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (a * y1) - (c * y0);
	double t_2 = y3 * ((y * ((c * y4) - (a * y5))) + ((z * t_1) + (j * ((y0 * y5) - (y1 * y4)))));
	double t_3 = (t * y2) - (y * y3);
	double t_4 = y1 * ((k * y2) - (j * y3));
	double t_5 = y4 * (((b * ((t * j) - (y * k))) + t_4) + (c * ((y * y3) - (t * y2))));
	double t_6 = (c * y0) - (a * y1);
	double tmp;
	if (y3 <= -5.6e+32) {
		tmp = t_2;
	} else if (y3 <= -1.02e-196) {
		tmp = t_5;
	} else if (y3 <= 9.5e-179) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_6)) + (j * ((i * y1) - (b * y0))));
	} else if (y3 <= 1.9e-141) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_6)) + (t * ((a * y5) - (c * y4))));
	} else if (y3 <= 1.5e-127) {
		tmp = t_2;
	} else if (y3 <= 2.6e-78) {
		tmp = y5 * ((a * t_3) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	} else if (y3 <= 1.2e-26) {
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * t_1)));
	} else if (y3 <= 1.35e+55) {
		tmp = t_5;
	} else if (y3 <= 2.5e+89) {
		tmp = c * ((y0 * ((x * y2) - (z * y3))) - (y4 * t_3));
	} else if (y3 <= 3.2e+151) {
		tmp = y * (a * ((x * b) - (y3 * y5)));
	} else if (y3 <= 2.4e+164) {
		tmp = y4 * t_4;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (a * y1) - (c * y0)
	t_2 = y3 * ((y * ((c * y4) - (a * y5))) + ((z * t_1) + (j * ((y0 * y5) - (y1 * y4)))))
	t_3 = (t * y2) - (y * y3)
	t_4 = y1 * ((k * y2) - (j * y3))
	t_5 = y4 * (((b * ((t * j) - (y * k))) + t_4) + (c * ((y * y3) - (t * y2))))
	t_6 = (c * y0) - (a * y1)
	tmp = 0
	if y3 <= -5.6e+32:
		tmp = t_2
	elif y3 <= -1.02e-196:
		tmp = t_5
	elif y3 <= 9.5e-179:
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_6)) + (j * ((i * y1) - (b * y0))))
	elif y3 <= 1.9e-141:
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_6)) + (t * ((a * y5) - (c * y4))))
	elif y3 <= 1.5e-127:
		tmp = t_2
	elif y3 <= 2.6e-78:
		tmp = y5 * ((a * t_3) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))))
	elif y3 <= 1.2e-26:
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * t_1)))
	elif y3 <= 1.35e+55:
		tmp = t_5
	elif y3 <= 2.5e+89:
		tmp = c * ((y0 * ((x * y2) - (z * y3))) - (y4 * t_3))
	elif y3 <= 3.2e+151:
		tmp = y * (a * ((x * b) - (y3 * y5)))
	elif y3 <= 2.4e+164:
		tmp = y4 * t_4
	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(a * y1) - Float64(c * y0))
	t_2 = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(z * t_1) + Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4))))))
	t_3 = Float64(Float64(t * y2) - Float64(y * y3))
	t_4 = Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))
	t_5 = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + t_4) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))))
	t_6 = Float64(Float64(c * y0) - Float64(a * y1))
	tmp = 0.0
	if (y3 <= -5.6e+32)
		tmp = t_2;
	elseif (y3 <= -1.02e-196)
		tmp = t_5;
	elseif (y3 <= 9.5e-179)
		tmp = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * t_6)) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (y3 <= 1.9e-141)
		tmp = Float64(y2 * Float64(Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(x * t_6)) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y3 <= 1.5e-127)
		tmp = t_2;
	elseif (y3 <= 2.6e-78)
		tmp = Float64(y5 * Float64(Float64(a * t_3) + Float64(Float64(i * Float64(Float64(y * k) - Float64(t * j))) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))))));
	elseif (y3 <= 1.2e-26)
		tmp = Float64(z * Float64(Float64(k * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(Float64(t * Float64(Float64(c * i) - Float64(a * b))) + Float64(y3 * t_1))));
	elseif (y3 <= 1.35e+55)
		tmp = t_5;
	elseif (y3 <= 2.5e+89)
		tmp = Float64(c * Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) - Float64(y4 * t_3)));
	elseif (y3 <= 3.2e+151)
		tmp = Float64(y * Float64(a * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (y3 <= 2.4e+164)
		tmp = Float64(y4 * t_4);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (a * y1) - (c * y0);
	t_2 = y3 * ((y * ((c * y4) - (a * y5))) + ((z * t_1) + (j * ((y0 * y5) - (y1 * y4)))));
	t_3 = (t * y2) - (y * y3);
	t_4 = y1 * ((k * y2) - (j * y3));
	t_5 = y4 * (((b * ((t * j) - (y * k))) + t_4) + (c * ((y * y3) - (t * y2))));
	t_6 = (c * y0) - (a * y1);
	tmp = 0.0;
	if (y3 <= -5.6e+32)
		tmp = t_2;
	elseif (y3 <= -1.02e-196)
		tmp = t_5;
	elseif (y3 <= 9.5e-179)
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_6)) + (j * ((i * y1) - (b * y0))));
	elseif (y3 <= 1.9e-141)
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_6)) + (t * ((a * y5) - (c * y4))));
	elseif (y3 <= 1.5e-127)
		tmp = t_2;
	elseif (y3 <= 2.6e-78)
		tmp = y5 * ((a * t_3) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	elseif (y3 <= 1.2e-26)
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * t_1)));
	elseif (y3 <= 1.35e+55)
		tmp = t_5;
	elseif (y3 <= 2.5e+89)
		tmp = c * ((y0 * ((x * y2) - (z * y3))) - (y4 * t_3));
	elseif (y3 <= 3.2e+151)
		tmp = y * (a * ((x * b) - (y3 * y5)));
	elseif (y3 <= 2.4e+164)
		tmp = y4 * t_4;
	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[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z * t$95$1), $MachinePrecision] + N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -5.6e+32], t$95$2, If[LessEqual[y3, -1.02e-196], t$95$5, If[LessEqual[y3, 9.5e-179], N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$6), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.9e-141], N[(y2 * N[(N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$6), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.5e-127], t$95$2, If[LessEqual[y3, 2.6e-78], N[(y5 * N[(N[(a * t$95$3), $MachinePrecision] + 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]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.2e-26], N[(z * N[(N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.35e+55], t$95$5, If[LessEqual[y3, 2.5e+89], N[(c * N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y4 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 3.2e+151], N[(y * N[(a * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 2.4e+164], N[(y4 * t$95$4), $MachinePrecision], t$95$2]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y3 < -5.6e32 or 1.89999999999999993e-141 < y3 < 1.50000000000000004e-127 or 2.40000000000000011e164 < y3

   1. Initial program 25.6%

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

   2. Taylor expanded in y3 around -inf 63.6%

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

   if -5.6e32 < y3 < -1.0200000000000001e-196 or 1.2e-26 < y3 < 1.34999999999999988e55

   1. Initial program 30.1%

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

   2. Taylor expanded in y4 around inf 62.3%

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

   if -1.0200000000000001e-196 < y3 < 9.50000000000000037e-179

   1. Initial program 37.9%

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

   2. Taylor expanded in x around inf 58.9%

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

   if 9.50000000000000037e-179 < y3 < 1.89999999999999993e-141

   1. Initial program 71.2%

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

   2. Taylor expanded in y2 around inf 80.8%

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

   if 1.50000000000000004e-127 < y3 < 2.6000000000000001e-78

   1. Initial program 60.0%

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

   3. Simplified 60.0%

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

   4. Taylor expanded in y5 around -inf 100.0%

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

   if 2.6000000000000001e-78 < y3 < 1.2e-26

   1. Initial program 14.3%

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

   2. Taylor expanded in z around -inf 57.8%

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

   if 1.34999999999999988e55 < y3 < 2.49999999999999992e89

   1. Initial program 16.7%

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

   2. Taylor expanded in y0 around inf 33.3%

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

      1. *-commutative 33.3%

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

      2. *-commutative 33.3%

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

      3. *-commutative 33.3%

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

   4. Simplified 33.3%

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

   5. Taylor expanded in c around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   if 2.49999999999999992e89 < y3 < 3.19999999999999994e151

   1. Initial program 44.4%

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

   2. Taylor expanded in y around inf 44.7%

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

   3. Taylor expanded in a around inf 77.8%

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

   if 3.19999999999999994e151 < y3 < 2.40000000000000011e164

   1. Initial program 0.0%

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

   2. Taylor expanded in y4 around inf 50.0%

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

   3. Taylor expanded in y1 around inf 84.8%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -5.6 \cdot 10^{+32}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(z \cdot \left(a \cdot y1 - c \cdot y0\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\right)\\ \mathbf{elif}\;y3 \leq -1.02 \cdot 10^{-196}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 9.5 \cdot 10^{-179}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq 1.9 \cdot 10^{-141}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 1.5 \cdot 10^{-127}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(z \cdot \left(a \cdot y1 - c \cdot y0\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\right)\\ \mathbf{elif}\;y3 \leq 2.6 \cdot 10^{-78}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y3 \leq 1.2 \cdot 10^{-26}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot \left(c \cdot i - a \cdot b\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;y3 \leq 1.35 \cdot 10^{+55}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 2.5 \cdot 10^{+89}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y3 \leq 3.2 \cdot 10^{+151}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y3 \leq 2.4 \cdot 10^{+164}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(z \cdot \left(a \cdot y1 - c \cdot y0\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\right)\\ \end{array} \]

Alternative 6: 37.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot y5 - c \cdot y4\right)\\ t_2 := y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ t_3 := c \cdot y0 - a \cdot y1\\ t_4 := k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ t_5 := t \cdot y2 - y \cdot y3\\ t_6 := y5 \cdot \left(a \cdot t_5 + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{if}\;y \leq -8.6 \cdot 10^{+20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-238}:\\ \;\;\;\;y2 \cdot \left(\left(t_4 + x \cdot t_3\right) + t_1\right)\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-122}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-55}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) - y4 \cdot t_5\right)\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+112}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+147}:\\ \;\;\;\;y2 \cdot \left(\left(t_4 + c \cdot \left(x \cdot y0\right)\right) + t_1\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+179}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+205}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+232}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot t_3\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* t (- (* a y5) (* c y4))))
        (t_2 (* y4 (* y (- (* c y3) (* b k)))))
        (t_3 (- (* c y0) (* a y1)))
        (t_4 (* k (- (* y1 y4) (* y0 y5))))
        (t_5 (- (* t y2) (* y y3)))
        (t_6
         (*
          y5
          (+
           (* a t_5)
           (+ (* i (- (* y k) (* t j))) (* y0 (- (* j y3) (* k y2))))))))
   (if (<= y -8.6e+20)
     t_2
     (if (<= y -1.35e-238)
       (* y2 (+ (+ t_4 (* x t_3)) t_1))
       (if (<= y 2.05e-122)
         (*
          y4
          (+
           (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
           (* c (- (* y y3) (* t y2)))))
         (if (<= y 2e-55)
           (* c (- (* y0 (- (* x y2) (* z y3))) (* y4 t_5)))
           (if (<= y 6.8e+112)
             t_6
             (if (<= y 3.9e+147)
               (* y2 (+ (+ t_4 (* c (* x y0))) t_1))
               (if (<= y 2.3e+179)
                 t_6
                 (if (<= y 7e+205)
                   (* k (* y4 (* y (- b))))
                   (if (<= y 6.5e+232)
                     (*
                      x
                      (+
                       (+ (* y (- (* a b) (* c i))) (* y2 t_3))
                       (* j (- (* i y1) (* b y0)))))
                     t_2)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * ((a * y5) - (c * y4));
	double t_2 = y4 * (y * ((c * y3) - (b * k)));
	double t_3 = (c * y0) - (a * y1);
	double t_4 = k * ((y1 * y4) - (y0 * y5));
	double t_5 = (t * y2) - (y * y3);
	double t_6 = y5 * ((a * t_5) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	double tmp;
	if (y <= -8.6e+20) {
		tmp = t_2;
	} else if (y <= -1.35e-238) {
		tmp = y2 * ((t_4 + (x * t_3)) + t_1);
	} else if (y <= 2.05e-122) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (y <= 2e-55) {
		tmp = c * ((y0 * ((x * y2) - (z * y3))) - (y4 * t_5));
	} else if (y <= 6.8e+112) {
		tmp = t_6;
	} else if (y <= 3.9e+147) {
		tmp = y2 * ((t_4 + (c * (x * y0))) + t_1);
	} else if (y <= 2.3e+179) {
		tmp = t_6;
	} else if (y <= 7e+205) {
		tmp = k * (y4 * (y * -b));
	} else if (y <= 6.5e+232) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_3)) + (j * ((i * y1) - (b * y0))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = t * ((a * y5) - (c * y4))
    t_2 = y4 * (y * ((c * y3) - (b * k)))
    t_3 = (c * y0) - (a * y1)
    t_4 = k * ((y1 * y4) - (y0 * y5))
    t_5 = (t * y2) - (y * y3)
    t_6 = y5 * ((a * t_5) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))))
    if (y <= (-8.6d+20)) then
        tmp = t_2
    else if (y <= (-1.35d-238)) then
        tmp = y2 * ((t_4 + (x * t_3)) + t_1)
    else if (y <= 2.05d-122) then
        tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    else if (y <= 2d-55) then
        tmp = c * ((y0 * ((x * y2) - (z * y3))) - (y4 * t_5))
    else if (y <= 6.8d+112) then
        tmp = t_6
    else if (y <= 3.9d+147) then
        tmp = y2 * ((t_4 + (c * (x * y0))) + t_1)
    else if (y <= 2.3d+179) then
        tmp = t_6
    else if (y <= 7d+205) then
        tmp = k * (y4 * (y * -b))
    else if (y <= 6.5d+232) then
        tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_3)) + (j * ((i * y1) - (b * y0))))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * ((a * y5) - (c * y4));
	double t_2 = y4 * (y * ((c * y3) - (b * k)));
	double t_3 = (c * y0) - (a * y1);
	double t_4 = k * ((y1 * y4) - (y0 * y5));
	double t_5 = (t * y2) - (y * y3);
	double t_6 = y5 * ((a * t_5) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	double tmp;
	if (y <= -8.6e+20) {
		tmp = t_2;
	} else if (y <= -1.35e-238) {
		tmp = y2 * ((t_4 + (x * t_3)) + t_1);
	} else if (y <= 2.05e-122) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (y <= 2e-55) {
		tmp = c * ((y0 * ((x * y2) - (z * y3))) - (y4 * t_5));
	} else if (y <= 6.8e+112) {
		tmp = t_6;
	} else if (y <= 3.9e+147) {
		tmp = y2 * ((t_4 + (c * (x * y0))) + t_1);
	} else if (y <= 2.3e+179) {
		tmp = t_6;
	} else if (y <= 7e+205) {
		tmp = k * (y4 * (y * -b));
	} else if (y <= 6.5e+232) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_3)) + (j * ((i * y1) - (b * y0))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = t * ((a * y5) - (c * y4))
	t_2 = y4 * (y * ((c * y3) - (b * k)))
	t_3 = (c * y0) - (a * y1)
	t_4 = k * ((y1 * y4) - (y0 * y5))
	t_5 = (t * y2) - (y * y3)
	t_6 = y5 * ((a * t_5) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))))
	tmp = 0
	if y <= -8.6e+20:
		tmp = t_2
	elif y <= -1.35e-238:
		tmp = y2 * ((t_4 + (x * t_3)) + t_1)
	elif y <= 2.05e-122:
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	elif y <= 2e-55:
		tmp = c * ((y0 * ((x * y2) - (z * y3))) - (y4 * t_5))
	elif y <= 6.8e+112:
		tmp = t_6
	elif y <= 3.9e+147:
		tmp = y2 * ((t_4 + (c * (x * y0))) + t_1)
	elif y <= 2.3e+179:
		tmp = t_6
	elif y <= 7e+205:
		tmp = k * (y4 * (y * -b))
	elif y <= 6.5e+232:
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_3)) + (j * ((i * y1) - (b * y0))))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))
	t_2 = Float64(y4 * Float64(y * Float64(Float64(c * y3) - Float64(b * k))))
	t_3 = Float64(Float64(c * y0) - Float64(a * y1))
	t_4 = Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))
	t_5 = Float64(Float64(t * y2) - Float64(y * y3))
	t_6 = Float64(y5 * Float64(Float64(a * t_5) + Float64(Float64(i * Float64(Float64(y * k) - Float64(t * j))) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))))))
	tmp = 0.0
	if (y <= -8.6e+20)
		tmp = t_2;
	elseif (y <= -1.35e-238)
		tmp = Float64(y2 * Float64(Float64(t_4 + Float64(x * t_3)) + t_1));
	elseif (y <= 2.05e-122)
		tmp = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (y <= 2e-55)
		tmp = Float64(c * Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) - Float64(y4 * t_5)));
	elseif (y <= 6.8e+112)
		tmp = t_6;
	elseif (y <= 3.9e+147)
		tmp = Float64(y2 * Float64(Float64(t_4 + Float64(c * Float64(x * y0))) + t_1));
	elseif (y <= 2.3e+179)
		tmp = t_6;
	elseif (y <= 7e+205)
		tmp = Float64(k * Float64(y4 * Float64(y * Float64(-b))));
	elseif (y <= 6.5e+232)
		tmp = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * t_3)) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	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 = t * ((a * y5) - (c * y4));
	t_2 = y4 * (y * ((c * y3) - (b * k)));
	t_3 = (c * y0) - (a * y1);
	t_4 = k * ((y1 * y4) - (y0 * y5));
	t_5 = (t * y2) - (y * y3);
	t_6 = y5 * ((a * t_5) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	tmp = 0.0;
	if (y <= -8.6e+20)
		tmp = t_2;
	elseif (y <= -1.35e-238)
		tmp = y2 * ((t_4 + (x * t_3)) + t_1);
	elseif (y <= 2.05e-122)
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	elseif (y <= 2e-55)
		tmp = c * ((y0 * ((x * y2) - (z * y3))) - (y4 * t_5));
	elseif (y <= 6.8e+112)
		tmp = t_6;
	elseif (y <= 3.9e+147)
		tmp = y2 * ((t_4 + (c * (x * y0))) + t_1);
	elseif (y <= 2.3e+179)
		tmp = t_6;
	elseif (y <= 7e+205)
		tmp = k * (y4 * (y * -b));
	elseif (y <= 6.5e+232)
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_3)) + (j * ((i * y1) - (b * y0))));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y4 * N[(y * N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(y5 * N[(N[(a * t$95$5), $MachinePrecision] + 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]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.6e+20], t$95$2, If[LessEqual[y, -1.35e-238], N[(y2 * N[(N[(t$95$4 + N[(x * t$95$3), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.05e-122], N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e-55], N[(c * N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y4 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.8e+112], t$95$6, If[LessEqual[y, 3.9e+147], N[(y2 * N[(N[(t$95$4 + N[(c * N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e+179], t$95$6, If[LessEqual[y, 7e+205], N[(k * N[(y4 * N[(y * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e+232], N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y < -8.6e20 or 6.50000000000000016e232 < y

   1. Initial program 24.6%

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

   2. Taylor expanded in y around inf 54.3%

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

      1. add-cube-cbrt 54.2%

         \[\leadsto y \cdot \color{blue}{\left(\left(\sqrt[3]{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \cdot \sqrt[3]{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \cdot \sqrt[3]{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)} \]

   4. Applied egg-rr 54.2%

      \[\leadsto y \cdot \color{blue}{\left(\left(\sqrt[3]{\mathsf{fma}\left(-1, k \cdot \left(y4 \cdot b - i \cdot y5\right), \mathsf{fma}\left(a, b, -i \cdot c\right) \cdot x\right) + y3 \cdot \left(y4 \cdot c - y5 \cdot a\right)} \cdot \sqrt[3]{\mathsf{fma}\left(-1, k \cdot \left(y4 \cdot b - i \cdot y5\right), \mathsf{fma}\left(a, b, -i \cdot c\right) \cdot x\right) + y3 \cdot \left(y4 \cdot c - y5 \cdot a\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(-1, k \cdot \left(y4 \cdot b - i \cdot y5\right), \mathsf{fma}\left(a, b, -i \cdot c\right) \cdot x\right) + y3 \cdot \left(y4 \cdot c - y5 \cdot a\right)}\right)} \]

   5. Taylor expanded in y4 around inf 53.6%

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

      1. *-commutative 53.6%

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

      2. mul-1-neg 53.6%

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

      3. unsub-neg 53.6%

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

      4. *-commutative 53.6%

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

   7. Simplified 53.6%

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

   if -8.6e20 < y < -1.34999999999999995e-238

   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. Taylor expanded in y2 around inf 55.1%

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

   if -1.34999999999999995e-238 < y < 2.05e-122

   1. Initial program 37.3%

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

   2. Taylor expanded in y4 around inf 59.7%

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

   if 2.05e-122 < y < 1.99999999999999999e-55

   1. Initial program 15.0%

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

   2. Taylor expanded in y0 around inf 45.0%

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

      1. *-commutative 45.0%

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

      2. *-commutative 45.0%

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

      3. *-commutative 45.0%

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

   4. Simplified 45.0%

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

   5. Taylor expanded in c around inf 80.0%

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

      1. *-commutative 80.0%

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

      2. *-commutative 80.0%

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

   7. Simplified 80.0%

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

   if 1.99999999999999999e-55 < y < 6.79999999999999987e112 or 3.90000000000000016e147 < y < 2.29999999999999994e179

   1. Initial program 37.9%

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

   3. Simplified 40.1%

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

   4. Taylor expanded in y5 around -inf 62.8%

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

   if 6.79999999999999987e112 < y < 3.90000000000000016e147

   1. Initial program 12.5%

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

   2. Taylor expanded in y0 around inf 12.6%

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

      1. *-commutative 12.6%

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

      2. *-commutative 12.6%

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

      3. *-commutative 12.6%

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

   4. Simplified 12.6%

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

   5. Taylor expanded in y2 around inf 77.2%

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

   if 2.29999999999999994e179 < y < 6.9999999999999996e205

   1. Initial program 15.6%

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

   2. Taylor expanded in y4 around inf 44.2%

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

   3. Taylor expanded in y around -inf 58.0%

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

      1. mul-1-neg 58.0%

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

      2. associate-*r* 58.0%

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

      3. *-commutative 58.0%

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

   5. Simplified 58.0%

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

   6. Taylor expanded in k around inf 71.7%

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

   if 6.9999999999999996e205 < y < 6.50000000000000016e232

   1. Initial program 16.4%

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

   2. Taylor expanded in x around inf 83.3%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - y1 \cdot a\right) \cdot y2\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot j\right) \cdot x} \]
3. Recombined 8 regimes into one program.

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{+20}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-238}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-122}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-55}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+112}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+147}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + c \cdot \left(x \cdot y0\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+179}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+205}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+232}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \end{array} \]

Alternative 7: 42.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot y5 - c \cdot y4\\ t_2 := c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ t_3 := y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(z \cdot \left(a \cdot y1 - c \cdot y0\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\right)\\ t_4 := y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ t_5 := c \cdot y0 - a \cdot y1\\ t_6 := x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot t_5\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{if}\;y3 \leq -3.2 \cdot 10^{+30}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y3 \leq -5.2 \cdot 10^{-196}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y3 \leq -1.35 \cdot 10^{-279}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y3 \leq 5.2 \cdot 10^{-266}:\\ \;\;\;\;t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot t_1\right)\\ \mathbf{elif}\;y3 \leq 1.2 \cdot 10^{-181}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y3 \leq 1.02 \cdot 10^{-140}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot t_5\right) + t \cdot t_1\right)\\ \mathbf{elif}\;y3 \leq 5.6 \cdot 10^{-130}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y3 \leq 210000000000:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y3 \leq 1.3 \cdot 10^{+87}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* a y5) (* c y4)))
        (t_2
         (* c (- (* y0 (- (* x y2) (* z y3))) (* y4 (- (* t y2) (* y y3))))))
        (t_3
         (*
          y3
          (+
           (* y (- (* c y4) (* a y5)))
           (+ (* z (- (* a y1) (* c y0))) (* j (- (* y0 y5) (* y1 y4)))))))
        (t_4
         (*
          y4
          (+
           (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
           (* c (- (* y y3) (* t y2))))))
        (t_5 (- (* c y0) (* a y1)))
        (t_6
         (*
          x
          (+
           (+ (* y (- (* a b) (* c i))) (* y2 t_5))
           (* j (- (* i y1) (* b y0)))))))
   (if (<= y3 -3.2e+30)
     t_3
     (if (<= y3 -5.2e-196)
       t_4
       (if (<= y3 -1.35e-279)
         t_6
         (if (<= y3 5.2e-266)
           (*
            t
            (+
             (+ (* z (- (* c i) (* a b))) (* j (- (* b y4) (* i y5))))
             (* y2 t_1)))
           (if (<= y3 1.2e-181)
             t_6
             (if (<= y3 1.02e-140)
               (* y2 (+ (+ (* k (- (* y1 y4) (* y0 y5))) (* x t_5)) (* t t_1)))
               (if (<= y3 5.6e-130)
                 t_2
                 (if (<= y3 210000000000.0)
                   t_4
                   (if (<= y3 1.3e+87) t_2 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 = (a * y5) - (c * y4);
	double t_2 = c * ((y0 * ((x * y2) - (z * y3))) - (y4 * ((t * y2) - (y * y3))));
	double t_3 = y3 * ((y * ((c * y4) - (a * y5))) + ((z * ((a * y1) - (c * y0))) + (j * ((y0 * y5) - (y1 * y4)))));
	double t_4 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double t_5 = (c * y0) - (a * y1);
	double t_6 = x * (((y * ((a * b) - (c * i))) + (y2 * t_5)) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (y3 <= -3.2e+30) {
		tmp = t_3;
	} else if (y3 <= -5.2e-196) {
		tmp = t_4;
	} else if (y3 <= -1.35e-279) {
		tmp = t_6;
	} else if (y3 <= 5.2e-266) {
		tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * t_1));
	} else if (y3 <= 1.2e-181) {
		tmp = t_6;
	} else if (y3 <= 1.02e-140) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_5)) + (t * t_1));
	} else if (y3 <= 5.6e-130) {
		tmp = t_2;
	} else if (y3 <= 210000000000.0) {
		tmp = t_4;
	} else if (y3 <= 1.3e+87) {
		tmp = t_2;
	} 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) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = (a * y5) - (c * y4)
    t_2 = c * ((y0 * ((x * y2) - (z * y3))) - (y4 * ((t * y2) - (y * y3))))
    t_3 = y3 * ((y * ((c * y4) - (a * y5))) + ((z * ((a * y1) - (c * y0))) + (j * ((y0 * y5) - (y1 * y4)))))
    t_4 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    t_5 = (c * y0) - (a * y1)
    t_6 = x * (((y * ((a * b) - (c * i))) + (y2 * t_5)) + (j * ((i * y1) - (b * y0))))
    if (y3 <= (-3.2d+30)) then
        tmp = t_3
    else if (y3 <= (-5.2d-196)) then
        tmp = t_4
    else if (y3 <= (-1.35d-279)) then
        tmp = t_6
    else if (y3 <= 5.2d-266) then
        tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * t_1))
    else if (y3 <= 1.2d-181) then
        tmp = t_6
    else if (y3 <= 1.02d-140) then
        tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_5)) + (t * t_1))
    else if (y3 <= 5.6d-130) then
        tmp = t_2
    else if (y3 <= 210000000000.0d0) then
        tmp = t_4
    else if (y3 <= 1.3d+87) then
        tmp = t_2
    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 = (a * y5) - (c * y4);
	double t_2 = c * ((y0 * ((x * y2) - (z * y3))) - (y4 * ((t * y2) - (y * y3))));
	double t_3 = y3 * ((y * ((c * y4) - (a * y5))) + ((z * ((a * y1) - (c * y0))) + (j * ((y0 * y5) - (y1 * y4)))));
	double t_4 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double t_5 = (c * y0) - (a * y1);
	double t_6 = x * (((y * ((a * b) - (c * i))) + (y2 * t_5)) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (y3 <= -3.2e+30) {
		tmp = t_3;
	} else if (y3 <= -5.2e-196) {
		tmp = t_4;
	} else if (y3 <= -1.35e-279) {
		tmp = t_6;
	} else if (y3 <= 5.2e-266) {
		tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * t_1));
	} else if (y3 <= 1.2e-181) {
		tmp = t_6;
	} else if (y3 <= 1.02e-140) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_5)) + (t * t_1));
	} else if (y3 <= 5.6e-130) {
		tmp = t_2;
	} else if (y3 <= 210000000000.0) {
		tmp = t_4;
	} else if (y3 <= 1.3e+87) {
		tmp = t_2;
	} 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 = (a * y5) - (c * y4)
	t_2 = c * ((y0 * ((x * y2) - (z * y3))) - (y4 * ((t * y2) - (y * y3))))
	t_3 = y3 * ((y * ((c * y4) - (a * y5))) + ((z * ((a * y1) - (c * y0))) + (j * ((y0 * y5) - (y1 * y4)))))
	t_4 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	t_5 = (c * y0) - (a * y1)
	t_6 = x * (((y * ((a * b) - (c * i))) + (y2 * t_5)) + (j * ((i * y1) - (b * y0))))
	tmp = 0
	if y3 <= -3.2e+30:
		tmp = t_3
	elif y3 <= -5.2e-196:
		tmp = t_4
	elif y3 <= -1.35e-279:
		tmp = t_6
	elif y3 <= 5.2e-266:
		tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * t_1))
	elif y3 <= 1.2e-181:
		tmp = t_6
	elif y3 <= 1.02e-140:
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_5)) + (t * t_1))
	elif y3 <= 5.6e-130:
		tmp = t_2
	elif y3 <= 210000000000.0:
		tmp = t_4
	elif y3 <= 1.3e+87:
		tmp = t_2
	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(a * y5) - Float64(c * y4))
	t_2 = Float64(c * Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) - Float64(y4 * Float64(Float64(t * y2) - Float64(y * y3)))))
	t_3 = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(z * Float64(Float64(a * y1) - Float64(c * y0))) + Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4))))))
	t_4 = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))))
	t_5 = Float64(Float64(c * y0) - Float64(a * y1))
	t_6 = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * t_5)) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))))
	tmp = 0.0
	if (y3 <= -3.2e+30)
		tmp = t_3;
	elseif (y3 <= -5.2e-196)
		tmp = t_4;
	elseif (y3 <= -1.35e-279)
		tmp = t_6;
	elseif (y3 <= 5.2e-266)
		tmp = Float64(t * Float64(Float64(Float64(z * Float64(Float64(c * i) - Float64(a * b))) + Float64(j * Float64(Float64(b * y4) - Float64(i * y5)))) + Float64(y2 * t_1)));
	elseif (y3 <= 1.2e-181)
		tmp = t_6;
	elseif (y3 <= 1.02e-140)
		tmp = Float64(y2 * Float64(Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(x * t_5)) + Float64(t * t_1)));
	elseif (y3 <= 5.6e-130)
		tmp = t_2;
	elseif (y3 <= 210000000000.0)
		tmp = t_4;
	elseif (y3 <= 1.3e+87)
		tmp = t_2;
	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 = (a * y5) - (c * y4);
	t_2 = c * ((y0 * ((x * y2) - (z * y3))) - (y4 * ((t * y2) - (y * y3))));
	t_3 = y3 * ((y * ((c * y4) - (a * y5))) + ((z * ((a * y1) - (c * y0))) + (j * ((y0 * y5) - (y1 * y4)))));
	t_4 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	t_5 = (c * y0) - (a * y1);
	t_6 = x * (((y * ((a * b) - (c * i))) + (y2 * t_5)) + (j * ((i * y1) - (b * y0))));
	tmp = 0.0;
	if (y3 <= -3.2e+30)
		tmp = t_3;
	elseif (y3 <= -5.2e-196)
		tmp = t_4;
	elseif (y3 <= -1.35e-279)
		tmp = t_6;
	elseif (y3 <= 5.2e-266)
		tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * t_1));
	elseif (y3 <= 1.2e-181)
		tmp = t_6;
	elseif (y3 <= 1.02e-140)
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_5)) + (t * t_1));
	elseif (y3 <= 5.6e-130)
		tmp = t_2;
	elseif (y3 <= 210000000000.0)
		tmp = t_4;
	elseif (y3 <= 1.3e+87)
		tmp = t_2;
	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[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y4 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$5), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -3.2e+30], t$95$3, If[LessEqual[y3, -5.2e-196], t$95$4, If[LessEqual[y3, -1.35e-279], t$95$6, If[LessEqual[y3, 5.2e-266], N[(t * N[(N[(N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.2e-181], t$95$6, If[LessEqual[y3, 1.02e-140], N[(y2 * N[(N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$5), $MachinePrecision]), $MachinePrecision] + N[(t * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 5.6e-130], t$95$2, If[LessEqual[y3, 210000000000.0], t$95$4, If[LessEqual[y3, 1.3e+87], t$95$2, t$95$3]]]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y3 < -3.19999999999999973e30 or 1.29999999999999999e87 < y3

   1. Initial program 26.8%

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

   2. Taylor expanded in y3 around -inf 63.3%

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

   if -3.19999999999999973e30 < y3 < -5.1999999999999996e-196 or 5.60000000000000032e-130 < y3 < 2.1e11

   1. Initial program 31.6%

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

   2. Taylor expanded in y4 around inf 61.9%

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

   if -5.1999999999999996e-196 < y3 < -1.3500000000000001e-279 or 5.1999999999999999e-266 < y3 < 1.2000000000000001e-181

   1. Initial program 38.4%

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

   2. Taylor expanded in x around inf 74.0%

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

   if -1.3500000000000001e-279 < y3 < 5.1999999999999999e-266

   1. Initial program 37.2%

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

   3. Simplified 37.2%

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

   4. Taylor expanded in t around inf 53.7%

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

   if 1.2000000000000001e-181 < y3 < 1.01999999999999995e-140

   1. Initial program 71.2%

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

   2. Taylor expanded in y2 around inf 80.8%

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

   if 1.01999999999999995e-140 < y3 < 5.60000000000000032e-130 or 2.1e11 < y3 < 1.29999999999999999e87

   1. Initial program 7.7%

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

   2. Taylor expanded in y0 around inf 23.1%

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

      1. *-commutative 23.1%

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

      2. *-commutative 23.1%

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

      3. *-commutative 23.1%

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

   4. Simplified 23.1%

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

   5. Taylor expanded in c around inf 71.8%

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

      1. *-commutative 71.8%

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

      2. *-commutative 71.8%

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

   7. Simplified 71.8%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(y2 \cdot t - y \cdot y3\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -3.2 \cdot 10^{+30}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(z \cdot \left(a \cdot y1 - c \cdot y0\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\right)\\ \mathbf{elif}\;y3 \leq -5.2 \cdot 10^{-196}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq -1.35 \cdot 10^{-279}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq 5.2 \cdot 10^{-266}:\\ \;\;\;\;t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 1.2 \cdot 10^{-181}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq 1.02 \cdot 10^{-140}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 5.6 \cdot 10^{-130}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y3 \leq 210000000000:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 1.3 \cdot 10^{+87}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(z \cdot \left(a \cdot y1 - c \cdot y0\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\right)\\ \end{array} \]

Alternative 8: 35.9% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + c \cdot \left(x \cdot y0\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ t_2 := y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{if}\;y \leq -7 \cdot 10^{+20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-231}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-294}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-267}:\\ \;\;\;\;z \cdot \left(y1 \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-207}:\\ \;\;\;\;y3 \cdot \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-126}:\\ \;\;\;\;y3 \cdot \left(z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-57}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+179}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          y2
          (+
           (+ (* k (- (* y1 y4) (* y0 y5))) (* c (* x y0)))
           (* t (- (* a y5) (* c y4))))))
        (t_2 (* y4 (* y (- (* c y3) (* b k))))))
   (if (<= y -7e+20)
     t_2
     (if (<= y -2.9e-231)
       t_1
       (if (<= y -3.2e-294)
         (* y4 (* y1 (- (* k y2) (* j y3))))
         (if (<= y 7.6e-267)
           (* z (* y1 (- (* a y3) (* i k))))
           (if (<= y 6.8e-207)
             (* y3 (* j (- (* y0 y5) (* y1 y4))))
             (if (<= y 3.2e-126)
               (* y3 (* z (- (* a y1) (* c y0))))
               (if (<= y 1.3e-57)
                 (*
                  c
                  (-
                   (* y0 (- (* x y2) (* z y3)))
                   (* y4 (- (* t y2) (* y y3)))))
                 (if (<= y 8.5e+179) t_1 t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (c * (x * y0))) + (t * ((a * y5) - (c * y4))));
	double t_2 = y4 * (y * ((c * y3) - (b * k)));
	double tmp;
	if (y <= -7e+20) {
		tmp = t_2;
	} else if (y <= -2.9e-231) {
		tmp = t_1;
	} else if (y <= -3.2e-294) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (y <= 7.6e-267) {
		tmp = z * (y1 * ((a * y3) - (i * k)));
	} else if (y <= 6.8e-207) {
		tmp = y3 * (j * ((y0 * y5) - (y1 * y4)));
	} else if (y <= 3.2e-126) {
		tmp = y3 * (z * ((a * y1) - (c * y0)));
	} else if (y <= 1.3e-57) {
		tmp = c * ((y0 * ((x * y2) - (z * y3))) - (y4 * ((t * y2) - (y * y3))));
	} else if (y <= 8.5e+179) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (c * (x * y0))) + (t * ((a * y5) - (c * y4))))
    t_2 = y4 * (y * ((c * y3) - (b * k)))
    if (y <= (-7d+20)) then
        tmp = t_2
    else if (y <= (-2.9d-231)) then
        tmp = t_1
    else if (y <= (-3.2d-294)) then
        tmp = y4 * (y1 * ((k * y2) - (j * y3)))
    else if (y <= 7.6d-267) then
        tmp = z * (y1 * ((a * y3) - (i * k)))
    else if (y <= 6.8d-207) then
        tmp = y3 * (j * ((y0 * y5) - (y1 * y4)))
    else if (y <= 3.2d-126) then
        tmp = y3 * (z * ((a * y1) - (c * y0)))
    else if (y <= 1.3d-57) then
        tmp = c * ((y0 * ((x * y2) - (z * y3))) - (y4 * ((t * y2) - (y * y3))))
    else if (y <= 8.5d+179) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (c * (x * y0))) + (t * ((a * y5) - (c * y4))));
	double t_2 = y4 * (y * ((c * y3) - (b * k)));
	double tmp;
	if (y <= -7e+20) {
		tmp = t_2;
	} else if (y <= -2.9e-231) {
		tmp = t_1;
	} else if (y <= -3.2e-294) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (y <= 7.6e-267) {
		tmp = z * (y1 * ((a * y3) - (i * k)));
	} else if (y <= 6.8e-207) {
		tmp = y3 * (j * ((y0 * y5) - (y1 * y4)));
	} else if (y <= 3.2e-126) {
		tmp = y3 * (z * ((a * y1) - (c * y0)));
	} else if (y <= 1.3e-57) {
		tmp = c * ((y0 * ((x * y2) - (z * y3))) - (y4 * ((t * y2) - (y * y3))));
	} else if (y <= 8.5e+179) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (c * (x * y0))) + (t * ((a * y5) - (c * y4))))
	t_2 = y4 * (y * ((c * y3) - (b * k)))
	tmp = 0
	if y <= -7e+20:
		tmp = t_2
	elif y <= -2.9e-231:
		tmp = t_1
	elif y <= -3.2e-294:
		tmp = y4 * (y1 * ((k * y2) - (j * y3)))
	elif y <= 7.6e-267:
		tmp = z * (y1 * ((a * y3) - (i * k)))
	elif y <= 6.8e-207:
		tmp = y3 * (j * ((y0 * y5) - (y1 * y4)))
	elif y <= 3.2e-126:
		tmp = y3 * (z * ((a * y1) - (c * y0)))
	elif y <= 1.3e-57:
		tmp = c * ((y0 * ((x * y2) - (z * y3))) - (y4 * ((t * y2) - (y * y3))))
	elif y <= 8.5e+179:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y2 * Float64(Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(c * Float64(x * y0))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))))
	t_2 = Float64(y4 * Float64(y * Float64(Float64(c * y3) - Float64(b * k))))
	tmp = 0.0
	if (y <= -7e+20)
		tmp = t_2;
	elseif (y <= -2.9e-231)
		tmp = t_1;
	elseif (y <= -3.2e-294)
		tmp = Float64(y4 * Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif (y <= 7.6e-267)
		tmp = Float64(z * Float64(y1 * Float64(Float64(a * y3) - Float64(i * k))));
	elseif (y <= 6.8e-207)
		tmp = Float64(y3 * Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4))));
	elseif (y <= 3.2e-126)
		tmp = Float64(y3 * Float64(z * Float64(Float64(a * y1) - Float64(c * y0))));
	elseif (y <= 1.3e-57)
		tmp = Float64(c * Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) - Float64(y4 * Float64(Float64(t * y2) - Float64(y * y3)))));
	elseif (y <= 8.5e+179)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (c * (x * y0))) + (t * ((a * y5) - (c * y4))));
	t_2 = y4 * (y * ((c * y3) - (b * k)));
	tmp = 0.0;
	if (y <= -7e+20)
		tmp = t_2;
	elseif (y <= -2.9e-231)
		tmp = t_1;
	elseif (y <= -3.2e-294)
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	elseif (y <= 7.6e-267)
		tmp = z * (y1 * ((a * y3) - (i * k)));
	elseif (y <= 6.8e-207)
		tmp = y3 * (j * ((y0 * y5) - (y1 * y4)));
	elseif (y <= 3.2e-126)
		tmp = y3 * (z * ((a * y1) - (c * y0)));
	elseif (y <= 1.3e-57)
		tmp = c * ((y0 * ((x * y2) - (z * y3))) - (y4 * ((t * y2) - (y * y3))));
	elseif (y <= 8.5e+179)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y2 * N[(N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y4 * N[(y * N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7e+20], t$95$2, If[LessEqual[y, -2.9e-231], t$95$1, If[LessEqual[y, -3.2e-294], N[(y4 * N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.6e-267], N[(z * N[(y1 * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.8e-207], N[(y3 * N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e-126], N[(y3 * N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e-57], N[(c * N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y4 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.5e+179], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -7e20 or 8.49999999999999962e179 < y

   1. Initial program 23.7%

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

   2. Taylor expanded in y around inf 54.8%

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

      1. add-cube-cbrt 54.7%

         \[\leadsto y \cdot \color{blue}{\left(\left(\sqrt[3]{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \cdot \sqrt[3]{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \cdot \sqrt[3]{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)} \]

   4. Applied egg-rr 54.7%

      \[\leadsto y \cdot \color{blue}{\left(\left(\sqrt[3]{\mathsf{fma}\left(-1, k \cdot \left(y4 \cdot b - i \cdot y5\right), \mathsf{fma}\left(a, b, -i \cdot c\right) \cdot x\right) + y3 \cdot \left(y4 \cdot c - y5 \cdot a\right)} \cdot \sqrt[3]{\mathsf{fma}\left(-1, k \cdot \left(y4 \cdot b - i \cdot y5\right), \mathsf{fma}\left(a, b, -i \cdot c\right) \cdot x\right) + y3 \cdot \left(y4 \cdot c - y5 \cdot a\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(-1, k \cdot \left(y4 \cdot b - i \cdot y5\right), \mathsf{fma}\left(a, b, -i \cdot c\right) \cdot x\right) + y3 \cdot \left(y4 \cdot c - y5 \cdot a\right)}\right)} \]

   5. Taylor expanded in y4 around inf 52.1%

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

      1. *-commutative 52.1%

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

      2. mul-1-neg 52.1%

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

      3. unsub-neg 52.1%

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

      4. *-commutative 52.1%

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

   7. Simplified 52.1%

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

   if -7e20 < y < -2.9000000000000001e-231 or 1.29999999999999993e-57 < y < 8.49999999999999962e179

   1. Initial program 37.9%

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

   2. Taylor expanded in y0 around inf 36.1%

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

      1. *-commutative 36.1%

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

      2. *-commutative 36.1%

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

      3. *-commutative 36.1%

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

   4. Simplified 36.1%

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

   5. Taylor expanded in y2 around inf 50.1%

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

   if -2.9000000000000001e-231 < y < -3.20000000000000019e-294

   1. Initial program 44.4%

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

   2. Taylor expanded in y4 around inf 66.7%

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

   3. Taylor expanded in y1 around inf 56.1%

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

   if -3.20000000000000019e-294 < y < 7.60000000000000006e-267

   1. Initial program 23.1%

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

   2. Taylor expanded in z around -inf 61.6%

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

   3. Taylor expanded in y1 around -inf 80.3%

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

      1. mul-1-neg 80.3%

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

   5. Simplified 80.3%

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

   if 7.60000000000000006e-267 < y < 6.79999999999999997e-207

   1. Initial program 58.2%

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

   2. Taylor expanded in y3 around -inf 58.8%

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

   3. Taylor expanded in j around inf 59.0%

      \[\leadsto -1 \cdot \color{blue}{\left(y3 \cdot \left(j \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 59.0%

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

   5. Simplified 59.0%

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

   if 6.79999999999999997e-207 < y < 3.2000000000000001e-126

   1. Initial program 15.5%

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

   2. Taylor expanded in y3 around -inf 39.5%

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

   3. Taylor expanded in z around inf 54.9%

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

   if 3.2000000000000001e-126 < y < 1.29999999999999993e-57

   1. Initial program 10.5%

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

   2. Taylor expanded in y0 around inf 42.1%

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

      1. *-commutative 42.1%

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

      2. *-commutative 42.1%

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

      3. *-commutative 42.1%

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

   4. Simplified 42.1%

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

   5. Taylor expanded in c around inf 78.9%

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

      1. *-commutative 78.9%

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

      2. *-commutative 78.9%

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

   7. Simplified 78.9%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(y2 \cdot t - y \cdot y3\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+20}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-231}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + c \cdot \left(x \cdot y0\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-294}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-267}:\\ \;\;\;\;z \cdot \left(y1 \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-207}:\\ \;\;\;\;y3 \cdot \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-126}:\\ \;\;\;\;y3 \cdot \left(z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-57}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+179}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + c \cdot \left(x \cdot y0\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \end{array} \]

Alternative 9: 38.0% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot y5 - c \cdot y4\right)\\ t_2 := y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ t_3 := k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ t_4 := y2 \cdot \left(\left(t_3 + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t_1\right)\\ \mathbf{if}\;y \leq -6.9 \cdot 10^{+21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-238}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-122}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-58}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 7.8:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+180}:\\ \;\;\;\;y2 \cdot \left(\left(t_3 + c \cdot \left(x \cdot y0\right)\right) + t_1\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* t (- (* a y5) (* c y4))))
        (t_2 (* y4 (* y (- (* c y3) (* b k)))))
        (t_3 (* k (- (* y1 y4) (* y0 y5))))
        (t_4 (* y2 (+ (+ t_3 (* x (- (* c y0) (* a y1)))) t_1))))
   (if (<= y -6.9e+21)
     t_2
     (if (<= y -2.15e-238)
       t_4
       (if (<= y 1.15e-122)
         (*
          y4
          (+
           (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
           (* c (- (* y y3) (* t y2)))))
         (if (<= y 9.5e-58)
           (* c (- (* y0 (- (* x y2) (* z y3))) (* y4 (- (* t y2) (* y y3)))))
           (if (<= y 7.8)
             t_4
             (if (<= y 1.45e+180)
               (* y2 (+ (+ t_3 (* c (* x y0))) t_1))
               t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * ((a * y5) - (c * y4));
	double t_2 = y4 * (y * ((c * y3) - (b * k)));
	double t_3 = k * ((y1 * y4) - (y0 * y5));
	double t_4 = y2 * ((t_3 + (x * ((c * y0) - (a * y1)))) + t_1);
	double tmp;
	if (y <= -6.9e+21) {
		tmp = t_2;
	} else if (y <= -2.15e-238) {
		tmp = t_4;
	} else if (y <= 1.15e-122) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (y <= 9.5e-58) {
		tmp = c * ((y0 * ((x * y2) - (z * y3))) - (y4 * ((t * y2) - (y * y3))));
	} else if (y <= 7.8) {
		tmp = t_4;
	} else if (y <= 1.45e+180) {
		tmp = y2 * ((t_3 + (c * (x * y0))) + t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = t * ((a * y5) - (c * y4))
    t_2 = y4 * (y * ((c * y3) - (b * k)))
    t_3 = k * ((y1 * y4) - (y0 * y5))
    t_4 = y2 * ((t_3 + (x * ((c * y0) - (a * y1)))) + t_1)
    if (y <= (-6.9d+21)) then
        tmp = t_2
    else if (y <= (-2.15d-238)) then
        tmp = t_4
    else if (y <= 1.15d-122) then
        tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    else if (y <= 9.5d-58) then
        tmp = c * ((y0 * ((x * y2) - (z * y3))) - (y4 * ((t * y2) - (y * y3))))
    else if (y <= 7.8d0) then
        tmp = t_4
    else if (y <= 1.45d+180) then
        tmp = y2 * ((t_3 + (c * (x * y0))) + t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * ((a * y5) - (c * y4));
	double t_2 = y4 * (y * ((c * y3) - (b * k)));
	double t_3 = k * ((y1 * y4) - (y0 * y5));
	double t_4 = y2 * ((t_3 + (x * ((c * y0) - (a * y1)))) + t_1);
	double tmp;
	if (y <= -6.9e+21) {
		tmp = t_2;
	} else if (y <= -2.15e-238) {
		tmp = t_4;
	} else if (y <= 1.15e-122) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (y <= 9.5e-58) {
		tmp = c * ((y0 * ((x * y2) - (z * y3))) - (y4 * ((t * y2) - (y * y3))));
	} else if (y <= 7.8) {
		tmp = t_4;
	} else if (y <= 1.45e+180) {
		tmp = y2 * ((t_3 + (c * (x * y0))) + t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = t * ((a * y5) - (c * y4))
	t_2 = y4 * (y * ((c * y3) - (b * k)))
	t_3 = k * ((y1 * y4) - (y0 * y5))
	t_4 = y2 * ((t_3 + (x * ((c * y0) - (a * y1)))) + t_1)
	tmp = 0
	if y <= -6.9e+21:
		tmp = t_2
	elif y <= -2.15e-238:
		tmp = t_4
	elif y <= 1.15e-122:
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	elif y <= 9.5e-58:
		tmp = c * ((y0 * ((x * y2) - (z * y3))) - (y4 * ((t * y2) - (y * y3))))
	elif y <= 7.8:
		tmp = t_4
	elif y <= 1.45e+180:
		tmp = y2 * ((t_3 + (c * (x * y0))) + t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))
	t_2 = Float64(y4 * Float64(y * Float64(Float64(c * y3) - Float64(b * k))))
	t_3 = Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))
	t_4 = Float64(y2 * Float64(Float64(t_3 + Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))) + t_1))
	tmp = 0.0
	if (y <= -6.9e+21)
		tmp = t_2;
	elseif (y <= -2.15e-238)
		tmp = t_4;
	elseif (y <= 1.15e-122)
		tmp = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (y <= 9.5e-58)
		tmp = Float64(c * Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) - Float64(y4 * Float64(Float64(t * y2) - Float64(y * y3)))));
	elseif (y <= 7.8)
		tmp = t_4;
	elseif (y <= 1.45e+180)
		tmp = Float64(y2 * Float64(Float64(t_3 + Float64(c * Float64(x * y0))) + t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = t * ((a * y5) - (c * y4));
	t_2 = y4 * (y * ((c * y3) - (b * k)));
	t_3 = k * ((y1 * y4) - (y0 * y5));
	t_4 = y2 * ((t_3 + (x * ((c * y0) - (a * y1)))) + t_1);
	tmp = 0.0;
	if (y <= -6.9e+21)
		tmp = t_2;
	elseif (y <= -2.15e-238)
		tmp = t_4;
	elseif (y <= 1.15e-122)
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	elseif (y <= 9.5e-58)
		tmp = c * ((y0 * ((x * y2) - (z * y3))) - (y4 * ((t * y2) - (y * y3))));
	elseif (y <= 7.8)
		tmp = t_4;
	elseif (y <= 1.45e+180)
		tmp = y2 * ((t_3 + (c * (x * y0))) + t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y4 * N[(y * N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y2 * N[(N[(t$95$3 + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.9e+21], t$95$2, If[LessEqual[y, -2.15e-238], t$95$4, If[LessEqual[y, 1.15e-122], N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5e-58], N[(c * N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y4 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.8], t$95$4, If[LessEqual[y, 1.45e+180], N[(y2 * N[(N[(t$95$3 + N[(c * N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -6.9e21 or 1.45000000000000004e180 < y

   1. Initial program 23.7%

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

   2. Taylor expanded in y around inf 54.8%

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

      1. add-cube-cbrt 54.7%

         \[\leadsto y \cdot \color{blue}{\left(\left(\sqrt[3]{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \cdot \sqrt[3]{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \cdot \sqrt[3]{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)} \]

   4. Applied egg-rr 54.7%

      \[\leadsto y \cdot \color{blue}{\left(\left(\sqrt[3]{\mathsf{fma}\left(-1, k \cdot \left(y4 \cdot b - i \cdot y5\right), \mathsf{fma}\left(a, b, -i \cdot c\right) \cdot x\right) + y3 \cdot \left(y4 \cdot c - y5 \cdot a\right)} \cdot \sqrt[3]{\mathsf{fma}\left(-1, k \cdot \left(y4 \cdot b - i \cdot y5\right), \mathsf{fma}\left(a, b, -i \cdot c\right) \cdot x\right) + y3 \cdot \left(y4 \cdot c - y5 \cdot a\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(-1, k \cdot \left(y4 \cdot b - i \cdot y5\right), \mathsf{fma}\left(a, b, -i \cdot c\right) \cdot x\right) + y3 \cdot \left(y4 \cdot c - y5 \cdot a\right)}\right)} \]

   5. Taylor expanded in y4 around inf 52.1%

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

      1. *-commutative 52.1%

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

      2. mul-1-neg 52.1%

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

      3. unsub-neg 52.1%

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

      4. *-commutative 52.1%

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

   7. Simplified 52.1%

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

   if -6.9e21 < y < -2.14999999999999984e-238 or 9.4999999999999994e-58 < y < 7.79999999999999982

   1. Initial program 47.2%

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

   2. Taylor expanded in y2 around inf 58.4%

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

   if -2.14999999999999984e-238 < y < 1.15000000000000003e-122

   1. Initial program 37.3%

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

   2. Taylor expanded in y4 around inf 59.7%

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

   if 1.15000000000000003e-122 < y < 9.4999999999999994e-58

   1. Initial program 10.5%

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

   2. Taylor expanded in y0 around inf 42.1%

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

      1. *-commutative 42.1%

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

      2. *-commutative 42.1%

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

      3. *-commutative 42.1%

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

   4. Simplified 42.1%

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

   5. Taylor expanded in c around inf 78.9%

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

      1. *-commutative 78.9%

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

      2. *-commutative 78.9%

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

   7. Simplified 78.9%

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

   if 7.79999999999999982 < y < 1.45000000000000004e180

   1. Initial program 26.3%

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

   2. Taylor expanded in y0 around inf 33.7%

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

      1. *-commutative 33.7%

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

      2. *-commutative 33.7%

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

      3. *-commutative 33.7%

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

   4. Simplified 33.7%

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

   5. Taylor expanded in y2 around inf 46.1%

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

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.9 \cdot 10^{+21}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-238}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-122}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-58}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 7.8:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+180}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + c \cdot \left(x \cdot y0\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \end{array} \]

Alternative 10: 37.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + c \cdot \left(x \cdot y0\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ t_2 := y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{if}\;y \leq -1.35 \cdot 10^{+21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-232}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-120}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 10^{+180}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          y2
          (+
           (+ (* k (- (* y1 y4) (* y0 y5))) (* c (* x y0)))
           (* t (- (* a y5) (* c y4))))))
        (t_2 (* y4 (* y (- (* c y3) (* b k))))))
   (if (<= y -1.35e+21)
     t_2
     (if (<= y -3.1e-232)
       t_1
       (if (<= y 3.1e-120)
         (*
          y4
          (+
           (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
           (* c (- (* y y3) (* t y2)))))
         (if (<= y 1e+180) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (c * (x * y0))) + (t * ((a * y5) - (c * y4))));
	double t_2 = y4 * (y * ((c * y3) - (b * k)));
	double tmp;
	if (y <= -1.35e+21) {
		tmp = t_2;
	} else if (y <= -3.1e-232) {
		tmp = t_1;
	} else if (y <= 3.1e-120) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (y <= 1e+180) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (c * (x * y0))) + (t * ((a * y5) - (c * y4))))
    t_2 = y4 * (y * ((c * y3) - (b * k)))
    if (y <= (-1.35d+21)) then
        tmp = t_2
    else if (y <= (-3.1d-232)) then
        tmp = t_1
    else if (y <= 3.1d-120) then
        tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    else if (y <= 1d+180) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (c * (x * y0))) + (t * ((a * y5) - (c * y4))));
	double t_2 = y4 * (y * ((c * y3) - (b * k)));
	double tmp;
	if (y <= -1.35e+21) {
		tmp = t_2;
	} else if (y <= -3.1e-232) {
		tmp = t_1;
	} else if (y <= 3.1e-120) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (y <= 1e+180) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (c * (x * y0))) + (t * ((a * y5) - (c * y4))))
	t_2 = y4 * (y * ((c * y3) - (b * k)))
	tmp = 0
	if y <= -1.35e+21:
		tmp = t_2
	elif y <= -3.1e-232:
		tmp = t_1
	elif y <= 3.1e-120:
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	elif y <= 1e+180:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y2 * Float64(Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(c * Float64(x * y0))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))))
	t_2 = Float64(y4 * Float64(y * Float64(Float64(c * y3) - Float64(b * k))))
	tmp = 0.0
	if (y <= -1.35e+21)
		tmp = t_2;
	elseif (y <= -3.1e-232)
		tmp = t_1;
	elseif (y <= 3.1e-120)
		tmp = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (y <= 1e+180)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (c * (x * y0))) + (t * ((a * y5) - (c * y4))));
	t_2 = y4 * (y * ((c * y3) - (b * k)));
	tmp = 0.0;
	if (y <= -1.35e+21)
		tmp = t_2;
	elseif (y <= -3.1e-232)
		tmp = t_1;
	elseif (y <= 3.1e-120)
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	elseif (y <= 1e+180)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y2 * N[(N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y4 * N[(y * N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.35e+21], t$95$2, If[LessEqual[y, -3.1e-232], t$95$1, If[LessEqual[y, 3.1e-120], N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e+180], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.35e21 or 1e180 < y

   1. Initial program 23.7%

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

   2. Taylor expanded in y around inf 54.8%

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

      1. add-cube-cbrt 54.7%

         \[\leadsto y \cdot \color{blue}{\left(\left(\sqrt[3]{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \cdot \sqrt[3]{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \cdot \sqrt[3]{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)} \]

   4. Applied egg-rr 54.7%

      \[\leadsto y \cdot \color{blue}{\left(\left(\sqrt[3]{\mathsf{fma}\left(-1, k \cdot \left(y4 \cdot b - i \cdot y5\right), \mathsf{fma}\left(a, b, -i \cdot c\right) \cdot x\right) + y3 \cdot \left(y4 \cdot c - y5 \cdot a\right)} \cdot \sqrt[3]{\mathsf{fma}\left(-1, k \cdot \left(y4 \cdot b - i \cdot y5\right), \mathsf{fma}\left(a, b, -i \cdot c\right) \cdot x\right) + y3 \cdot \left(y4 \cdot c - y5 \cdot a\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(-1, k \cdot \left(y4 \cdot b - i \cdot y5\right), \mathsf{fma}\left(a, b, -i \cdot c\right) \cdot x\right) + y3 \cdot \left(y4 \cdot c - y5 \cdot a\right)}\right)} \]

   5. Taylor expanded in y4 around inf 52.1%

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

      1. *-commutative 52.1%

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

      2. mul-1-neg 52.1%

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

      3. unsub-neg 52.1%

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

      4. *-commutative 52.1%

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

   7. Simplified 52.1%

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

   if -1.35e21 < y < -3.0999999999999999e-232 or 3.10000000000000019e-120 < y < 1e180

   1. Initial program 33.6%

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

   2. Taylor expanded in y0 around inf 37.5%

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

      1. *-commutative 37.5%

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

      2. *-commutative 37.5%

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

      3. *-commutative 37.5%

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

   4. Simplified 37.5%

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

   5. Taylor expanded in y2 around inf 51.1%

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

   if -3.0999999999999999e-232 < y < 3.10000000000000019e-120

   1. Initial program 37.1%

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

   2. Taylor expanded in y4 around inf 60.1%

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

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+21}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-232}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + c \cdot \left(x \cdot y0\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-120}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 10^{+180}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + c \cdot \left(x \cdot y0\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \end{array} \]

Alternative 11: 30.5% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ t_2 := y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ t_3 := b \cdot y4 - i \cdot y5\\ t_4 := y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{if}\;j \leq -3.3 \cdot 10^{+196}:\\ \;\;\;\;\left(t \cdot j\right) \cdot t_3\\ \mathbf{elif}\;j \leq -1.45 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.26 \cdot 10^{-10}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq -6.5 \cdot 10^{-32}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;j \leq -3.8 \cdot 10^{-122}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{-288}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 6 \cdot 10^{-113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 4.2 \cdot 10^{+20}:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 4.4 \cdot 10^{+84}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 8 \cdot 10^{+197}:\\ \;\;\;\;t \cdot \left(j \cdot t_3\right)\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y4 (* y (- (* c y3) (* b k)))))
        (t_2 (* y (* y3 (- (* c y4) (* a y5)))))
        (t_3 (- (* b y4) (* i y5)))
        (t_4 (* y4 (* y1 (- (* k y2) (* j y3))))))
   (if (<= j -3.3e+196)
     (* (* t j) t_3)
     (if (<= j -1.45e+52)
       t_1
       (if (<= j -1.26e-10)
         t_4
         (if (<= j -6.5e-32)
           (* c (* i (* z t)))
           (if (<= j -3.8e-122)
             (* c (* y4 (- (* y y3) (* t y2))))
             (if (<= j 1.15e-288)
               t_2
               (if (<= j 6e-113)
                 t_1
                 (if (<= j 4.2e+20)
                   (* y4 (* y2 (- (* k y1) (* t c))))
                   (if (<= j 4.4e+84)
                     t_2
                     (if (<= j 8e+197) (* t (* j t_3)) t_4))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * (y * ((c * y3) - (b * k)));
	double t_2 = y * (y3 * ((c * y4) - (a * y5)));
	double t_3 = (b * y4) - (i * y5);
	double t_4 = y4 * (y1 * ((k * y2) - (j * y3)));
	double tmp;
	if (j <= -3.3e+196) {
		tmp = (t * j) * t_3;
	} else if (j <= -1.45e+52) {
		tmp = t_1;
	} else if (j <= -1.26e-10) {
		tmp = t_4;
	} else if (j <= -6.5e-32) {
		tmp = c * (i * (z * t));
	} else if (j <= -3.8e-122) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (j <= 1.15e-288) {
		tmp = t_2;
	} else if (j <= 6e-113) {
		tmp = t_1;
	} else if (j <= 4.2e+20) {
		tmp = y4 * (y2 * ((k * y1) - (t * c)));
	} else if (j <= 4.4e+84) {
		tmp = t_2;
	} else if (j <= 8e+197) {
		tmp = t * (j * t_3);
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = y4 * (y * ((c * y3) - (b * k)))
    t_2 = y * (y3 * ((c * y4) - (a * y5)))
    t_3 = (b * y4) - (i * y5)
    t_4 = y4 * (y1 * ((k * y2) - (j * y3)))
    if (j <= (-3.3d+196)) then
        tmp = (t * j) * t_3
    else if (j <= (-1.45d+52)) then
        tmp = t_1
    else if (j <= (-1.26d-10)) then
        tmp = t_4
    else if (j <= (-6.5d-32)) then
        tmp = c * (i * (z * t))
    else if (j <= (-3.8d-122)) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else if (j <= 1.15d-288) then
        tmp = t_2
    else if (j <= 6d-113) then
        tmp = t_1
    else if (j <= 4.2d+20) then
        tmp = y4 * (y2 * ((k * y1) - (t * c)))
    else if (j <= 4.4d+84) then
        tmp = t_2
    else if (j <= 8d+197) then
        tmp = t * (j * t_3)
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * (y * ((c * y3) - (b * k)));
	double t_2 = y * (y3 * ((c * y4) - (a * y5)));
	double t_3 = (b * y4) - (i * y5);
	double t_4 = y4 * (y1 * ((k * y2) - (j * y3)));
	double tmp;
	if (j <= -3.3e+196) {
		tmp = (t * j) * t_3;
	} else if (j <= -1.45e+52) {
		tmp = t_1;
	} else if (j <= -1.26e-10) {
		tmp = t_4;
	} else if (j <= -6.5e-32) {
		tmp = c * (i * (z * t));
	} else if (j <= -3.8e-122) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (j <= 1.15e-288) {
		tmp = t_2;
	} else if (j <= 6e-113) {
		tmp = t_1;
	} else if (j <= 4.2e+20) {
		tmp = y4 * (y2 * ((k * y1) - (t * c)));
	} else if (j <= 4.4e+84) {
		tmp = t_2;
	} else if (j <= 8e+197) {
		tmp = t * (j * t_3);
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y4 * (y * ((c * y3) - (b * k)))
	t_2 = y * (y3 * ((c * y4) - (a * y5)))
	t_3 = (b * y4) - (i * y5)
	t_4 = y4 * (y1 * ((k * y2) - (j * y3)))
	tmp = 0
	if j <= -3.3e+196:
		tmp = (t * j) * t_3
	elif j <= -1.45e+52:
		tmp = t_1
	elif j <= -1.26e-10:
		tmp = t_4
	elif j <= -6.5e-32:
		tmp = c * (i * (z * t))
	elif j <= -3.8e-122:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	elif j <= 1.15e-288:
		tmp = t_2
	elif j <= 6e-113:
		tmp = t_1
	elif j <= 4.2e+20:
		tmp = y4 * (y2 * ((k * y1) - (t * c)))
	elif j <= 4.4e+84:
		tmp = t_2
	elif j <= 8e+197:
		tmp = t * (j * t_3)
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y4 * Float64(y * Float64(Float64(c * y3) - Float64(b * k))))
	t_2 = Float64(y * Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))))
	t_3 = Float64(Float64(b * y4) - Float64(i * y5))
	t_4 = Float64(y4 * Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))))
	tmp = 0.0
	if (j <= -3.3e+196)
		tmp = Float64(Float64(t * j) * t_3);
	elseif (j <= -1.45e+52)
		tmp = t_1;
	elseif (j <= -1.26e-10)
		tmp = t_4;
	elseif (j <= -6.5e-32)
		tmp = Float64(c * Float64(i * Float64(z * t)));
	elseif (j <= -3.8e-122)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (j <= 1.15e-288)
		tmp = t_2;
	elseif (j <= 6e-113)
		tmp = t_1;
	elseif (j <= 4.2e+20)
		tmp = Float64(y4 * Float64(y2 * Float64(Float64(k * y1) - Float64(t * c))));
	elseif (j <= 4.4e+84)
		tmp = t_2;
	elseif (j <= 8e+197)
		tmp = Float64(t * Float64(j * t_3));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y4 * (y * ((c * y3) - (b * k)));
	t_2 = y * (y3 * ((c * y4) - (a * y5)));
	t_3 = (b * y4) - (i * y5);
	t_4 = y4 * (y1 * ((k * y2) - (j * y3)));
	tmp = 0.0;
	if (j <= -3.3e+196)
		tmp = (t * j) * t_3;
	elseif (j <= -1.45e+52)
		tmp = t_1;
	elseif (j <= -1.26e-10)
		tmp = t_4;
	elseif (j <= -6.5e-32)
		tmp = c * (i * (z * t));
	elseif (j <= -3.8e-122)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	elseif (j <= 1.15e-288)
		tmp = t_2;
	elseif (j <= 6e-113)
		tmp = t_1;
	elseif (j <= 4.2e+20)
		tmp = y4 * (y2 * ((k * y1) - (t * c)));
	elseif (j <= 4.4e+84)
		tmp = t_2;
	elseif (j <= 8e+197)
		tmp = t * (j * t_3);
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y4 * N[(y * N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y4 * N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.3e+196], N[(N[(t * j), $MachinePrecision] * t$95$3), $MachinePrecision], If[LessEqual[j, -1.45e+52], t$95$1, If[LessEqual[j, -1.26e-10], t$95$4, If[LessEqual[j, -6.5e-32], N[(c * N[(i * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.8e-122], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.15e-288], t$95$2, If[LessEqual[j, 6e-113], t$95$1, If[LessEqual[j, 4.2e+20], N[(y4 * N[(y2 * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.4e+84], t$95$2, If[LessEqual[j, 8e+197], N[(t * N[(j * t$95$3), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if j < -3.3000000000000002e196

   1. Initial program 20.8%

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

   3. Simplified 24.9%

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

   4. Taylor expanded in t around inf 46.5%

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

   5. Taylor expanded in j around inf 51.2%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 58.9%

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

      2. *-commutative 58.9%

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

      3. *-commutative 58.9%

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

   7. Simplified 58.9%

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

   if -3.3000000000000002e196 < j < -1.45e52 or 1.15e-288 < j < 6.0000000000000002e-113

   1. Initial program 25.2%

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

   2. Taylor expanded in y around inf 42.1%

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

      1. add-cube-cbrt 42.0%

         \[\leadsto y \cdot \color{blue}{\left(\left(\sqrt[3]{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \cdot \sqrt[3]{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \cdot \sqrt[3]{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)} \]

   4. Applied egg-rr 42.0%

      \[\leadsto y \cdot \color{blue}{\left(\left(\sqrt[3]{\mathsf{fma}\left(-1, k \cdot \left(y4 \cdot b - i \cdot y5\right), \mathsf{fma}\left(a, b, -i \cdot c\right) \cdot x\right) + y3 \cdot \left(y4 \cdot c - y5 \cdot a\right)} \cdot \sqrt[3]{\mathsf{fma}\left(-1, k \cdot \left(y4 \cdot b - i \cdot y5\right), \mathsf{fma}\left(a, b, -i \cdot c\right) \cdot x\right) + y3 \cdot \left(y4 \cdot c - y5 \cdot a\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(-1, k \cdot \left(y4 \cdot b - i \cdot y5\right), \mathsf{fma}\left(a, b, -i \cdot c\right) \cdot x\right) + y3 \cdot \left(y4 \cdot c - y5 \cdot a\right)}\right)} \]

   5. Taylor expanded in y4 around inf 44.4%

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

      1. *-commutative 44.4%

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

      2. mul-1-neg 44.4%

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

      3. unsub-neg 44.4%

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

      4. *-commutative 44.4%

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

   7. Simplified 44.4%

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

   if -1.45e52 < j < -1.26000000000000004e-10 or 7.9999999999999996e197 < j

   1. Initial program 24.9%

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

   2. Taylor expanded in y4 around inf 52.7%

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

   3. Taylor expanded in y1 around inf 55.6%

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

   if -1.26000000000000004e-10 < j < -6.49999999999999988e-32

   1. Initial program 26.9%

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

   3. Simplified 26.9%

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

   4. Taylor expanded in t around inf 25.4%

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

   5. Taylor expanded in z around inf 50.4%

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

      1. mul-1-neg 50.4%

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

      2. associate-*r* 50.4%

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

   7. Simplified 50.4%

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

   8. Taylor expanded in a around 0 75.4%

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

      1. associate-*r* 75.4%

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

      2. neg-mul-1 75.4%

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

   10. Simplified 75.4%

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

   if -6.49999999999999988e-32 < j < -3.8000000000000001e-122

   1. Initial program 17.5%

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

   2. Taylor expanded in y4 around inf 50.6%

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

   3. Taylor expanded in c around inf 51.0%

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

   if -3.8000000000000001e-122 < j < 1.15e-288 or 4.2e20 < j < 4.3999999999999997e84

   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. Taylor expanded in y0 around inf 40.9%

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

      1. *-commutative 40.9%

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

      2. *-commutative 40.9%

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

      3. *-commutative 40.9%

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

   4. Simplified 40.9%

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

   5. Taylor expanded in y around inf 54.1%

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

   if 6.0000000000000002e-113 < j < 4.2e20

   1. Initial program 41.4%

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

   2. Taylor expanded in y4 around inf 45.2%

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

   3. Taylor expanded in y2 around inf 56.2%

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

   if 4.3999999999999997e84 < j < 7.9999999999999996e197

   1. Initial program 37.5%

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

   3. Simplified 37.5%

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

   4. Taylor expanded in t around inf 42.4%

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

   5. Taylor expanded in j around inf 46.9%

      \[\leadsto \color{blue}{\left(j \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} \cdot t \]
   6. Step-by-step derivation

      1. *-commutative 46.9%

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

   7. Simplified 46.9%

      \[\leadsto \color{blue}{\left(j \cdot \left(y4 \cdot b - y5 \cdot i\right)\right)} \cdot t \]
3. Recombined 8 regimes into one program.

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.3 \cdot 10^{+196}:\\ \;\;\;\;\left(t \cdot j\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\\ \mathbf{elif}\;j \leq -1.45 \cdot 10^{+52}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;j \leq -1.26 \cdot 10^{-10}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq -6.5 \cdot 10^{-32}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;j \leq -3.8 \cdot 10^{-122}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{-288}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 6 \cdot 10^{-113}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;j \leq 4.2 \cdot 10^{+20}:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 4.4 \cdot 10^{+84}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 8 \cdot 10^{+197}:\\ \;\;\;\;t \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \end{array} \]

Alternative 12: 30.3% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ t_2 := y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ t_3 := y3 \cdot \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{if}\;j \leq -2.3 \cdot 10^{+196}:\\ \;\;\;\;\left(t \cdot j\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\\ \mathbf{elif}\;j \leq -1.95 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -3.8 \cdot 10^{+18}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -1.2 \cdot 10^{-31}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;j \leq -1.05 \cdot 10^{-125}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 9.5 \cdot 10^{-287}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 2.45 \cdot 10^{-113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 4.2 \cdot 10^{+20}:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 6.4 \cdot 10^{+88}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 9.5 \cdot 10^{+183}:\\ \;\;\;\;\left(-i\right) \cdot \left(\left(t \cdot j\right) \cdot y5\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y4 (* y (- (* c y3) (* b k)))))
        (t_2 (* y (* y3 (- (* c y4) (* a y5)))))
        (t_3 (* y3 (* j (- (* y0 y5) (* y1 y4))))))
   (if (<= j -2.3e+196)
     (* (* t j) (- (* b y4) (* i y5)))
     (if (<= j -1.95e+55)
       t_1
       (if (<= j -3.8e+18)
         t_3
         (if (<= j -1.2e-31)
           (* c (* i (* z t)))
           (if (<= j -1.05e-125)
             (* c (* y4 (- (* y y3) (* t y2))))
             (if (<= j 9.5e-287)
               t_2
               (if (<= j 2.45e-113)
                 t_1
                 (if (<= j 4.2e+20)
                   (* y4 (* y2 (- (* k y1) (* t c))))
                   (if (<= j 6.4e+88)
                     t_2
                     (if (<= j 9.5e+183)
                       (* (- i) (* (* t j) y5))
                       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 = y4 * (y * ((c * y3) - (b * k)));
	double t_2 = y * (y3 * ((c * y4) - (a * y5)));
	double t_3 = y3 * (j * ((y0 * y5) - (y1 * y4)));
	double tmp;
	if (j <= -2.3e+196) {
		tmp = (t * j) * ((b * y4) - (i * y5));
	} else if (j <= -1.95e+55) {
		tmp = t_1;
	} else if (j <= -3.8e+18) {
		tmp = t_3;
	} else if (j <= -1.2e-31) {
		tmp = c * (i * (z * t));
	} else if (j <= -1.05e-125) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (j <= 9.5e-287) {
		tmp = t_2;
	} else if (j <= 2.45e-113) {
		tmp = t_1;
	} else if (j <= 4.2e+20) {
		tmp = y4 * (y2 * ((k * y1) - (t * c)));
	} else if (j <= 6.4e+88) {
		tmp = t_2;
	} else if (j <= 9.5e+183) {
		tmp = -i * ((t * j) * y5);
	} 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 = y4 * (y * ((c * y3) - (b * k)))
    t_2 = y * (y3 * ((c * y4) - (a * y5)))
    t_3 = y3 * (j * ((y0 * y5) - (y1 * y4)))
    if (j <= (-2.3d+196)) then
        tmp = (t * j) * ((b * y4) - (i * y5))
    else if (j <= (-1.95d+55)) then
        tmp = t_1
    else if (j <= (-3.8d+18)) then
        tmp = t_3
    else if (j <= (-1.2d-31)) then
        tmp = c * (i * (z * t))
    else if (j <= (-1.05d-125)) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else if (j <= 9.5d-287) then
        tmp = t_2
    else if (j <= 2.45d-113) then
        tmp = t_1
    else if (j <= 4.2d+20) then
        tmp = y4 * (y2 * ((k * y1) - (t * c)))
    else if (j <= 6.4d+88) then
        tmp = t_2
    else if (j <= 9.5d+183) then
        tmp = -i * ((t * j) * y5)
    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 = y4 * (y * ((c * y3) - (b * k)));
	double t_2 = y * (y3 * ((c * y4) - (a * y5)));
	double t_3 = y3 * (j * ((y0 * y5) - (y1 * y4)));
	double tmp;
	if (j <= -2.3e+196) {
		tmp = (t * j) * ((b * y4) - (i * y5));
	} else if (j <= -1.95e+55) {
		tmp = t_1;
	} else if (j <= -3.8e+18) {
		tmp = t_3;
	} else if (j <= -1.2e-31) {
		tmp = c * (i * (z * t));
	} else if (j <= -1.05e-125) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (j <= 9.5e-287) {
		tmp = t_2;
	} else if (j <= 2.45e-113) {
		tmp = t_1;
	} else if (j <= 4.2e+20) {
		tmp = y4 * (y2 * ((k * y1) - (t * c)));
	} else if (j <= 6.4e+88) {
		tmp = t_2;
	} else if (j <= 9.5e+183) {
		tmp = -i * ((t * j) * y5);
	} 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 = y4 * (y * ((c * y3) - (b * k)))
	t_2 = y * (y3 * ((c * y4) - (a * y5)))
	t_3 = y3 * (j * ((y0 * y5) - (y1 * y4)))
	tmp = 0
	if j <= -2.3e+196:
		tmp = (t * j) * ((b * y4) - (i * y5))
	elif j <= -1.95e+55:
		tmp = t_1
	elif j <= -3.8e+18:
		tmp = t_3
	elif j <= -1.2e-31:
		tmp = c * (i * (z * t))
	elif j <= -1.05e-125:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	elif j <= 9.5e-287:
		tmp = t_2
	elif j <= 2.45e-113:
		tmp = t_1
	elif j <= 4.2e+20:
		tmp = y4 * (y2 * ((k * y1) - (t * c)))
	elif j <= 6.4e+88:
		tmp = t_2
	elif j <= 9.5e+183:
		tmp = -i * ((t * j) * y5)
	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(y4 * Float64(y * Float64(Float64(c * y3) - Float64(b * k))))
	t_2 = Float64(y * Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))))
	t_3 = Float64(y3 * Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4))))
	tmp = 0.0
	if (j <= -2.3e+196)
		tmp = Float64(Float64(t * j) * Float64(Float64(b * y4) - Float64(i * y5)));
	elseif (j <= -1.95e+55)
		tmp = t_1;
	elseif (j <= -3.8e+18)
		tmp = t_3;
	elseif (j <= -1.2e-31)
		tmp = Float64(c * Float64(i * Float64(z * t)));
	elseif (j <= -1.05e-125)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (j <= 9.5e-287)
		tmp = t_2;
	elseif (j <= 2.45e-113)
		tmp = t_1;
	elseif (j <= 4.2e+20)
		tmp = Float64(y4 * Float64(y2 * Float64(Float64(k * y1) - Float64(t * c))));
	elseif (j <= 6.4e+88)
		tmp = t_2;
	elseif (j <= 9.5e+183)
		tmp = Float64(Float64(-i) * Float64(Float64(t * j) * y5));
	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 = y4 * (y * ((c * y3) - (b * k)));
	t_2 = y * (y3 * ((c * y4) - (a * y5)));
	t_3 = y3 * (j * ((y0 * y5) - (y1 * y4)));
	tmp = 0.0;
	if (j <= -2.3e+196)
		tmp = (t * j) * ((b * y4) - (i * y5));
	elseif (j <= -1.95e+55)
		tmp = t_1;
	elseif (j <= -3.8e+18)
		tmp = t_3;
	elseif (j <= -1.2e-31)
		tmp = c * (i * (z * t));
	elseif (j <= -1.05e-125)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	elseif (j <= 9.5e-287)
		tmp = t_2;
	elseif (j <= 2.45e-113)
		tmp = t_1;
	elseif (j <= 4.2e+20)
		tmp = y4 * (y2 * ((k * y1) - (t * c)));
	elseif (j <= 6.4e+88)
		tmp = t_2;
	elseif (j <= 9.5e+183)
		tmp = -i * ((t * j) * y5);
	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[(y4 * N[(y * N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y3 * N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.3e+196], N[(N[(t * j), $MachinePrecision] * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.95e+55], t$95$1, If[LessEqual[j, -3.8e+18], t$95$3, If[LessEqual[j, -1.2e-31], N[(c * N[(i * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.05e-125], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 9.5e-287], t$95$2, If[LessEqual[j, 2.45e-113], t$95$1, If[LessEqual[j, 4.2e+20], N[(y4 * N[(y2 * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6.4e+88], t$95$2, If[LessEqual[j, 9.5e+183], N[((-i) * N[(N[(t * j), $MachinePrecision] * y5), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if j < -2.2999999999999998e196

   1. Initial program 20.8%

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

   3. Simplified 24.9%

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

   4. Taylor expanded in t around inf 46.5%

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

   5. Taylor expanded in j around inf 51.2%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 58.9%

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

      2. *-commutative 58.9%

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

      3. *-commutative 58.9%

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

   7. Simplified 58.9%

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

   if -2.2999999999999998e196 < j < -1.95000000000000014e55 or 9.5000000000000004e-287 < j < 2.4500000000000001e-113

   1. Initial program 23.9%

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

   2. Taylor expanded in y around inf 42.8%

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

      1. add-cube-cbrt 42.7%

         \[\leadsto y \cdot \color{blue}{\left(\left(\sqrt[3]{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \cdot \sqrt[3]{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \cdot \sqrt[3]{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)} \]

   4. Applied egg-rr 42.7%

      \[\leadsto y \cdot \color{blue}{\left(\left(\sqrt[3]{\mathsf{fma}\left(-1, k \cdot \left(y4 \cdot b - i \cdot y5\right), \mathsf{fma}\left(a, b, -i \cdot c\right) \cdot x\right) + y3 \cdot \left(y4 \cdot c - y5 \cdot a\right)} \cdot \sqrt[3]{\mathsf{fma}\left(-1, k \cdot \left(y4 \cdot b - i \cdot y5\right), \mathsf{fma}\left(a, b, -i \cdot c\right) \cdot x\right) + y3 \cdot \left(y4 \cdot c - y5 \cdot a\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(-1, k \cdot \left(y4 \cdot b - i \cdot y5\right), \mathsf{fma}\left(a, b, -i \cdot c\right) \cdot x\right) + y3 \cdot \left(y4 \cdot c - y5 \cdot a\right)}\right)} \]

   5. Taylor expanded in y4 around inf 45.1%

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

      1. *-commutative 45.1%

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

      2. mul-1-neg 45.1%

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

      3. unsub-neg 45.1%

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

      4. *-commutative 45.1%

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

   7. Simplified 45.1%

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

   if -1.95000000000000014e55 < j < -3.8e18 or 9.5000000000000003e183 < j

   1. Initial program 26.2%

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

   2. Taylor expanded in y3 around -inf 64.8%

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

   3. Taylor expanded in j around inf 60.0%

      \[\leadsto -1 \cdot \color{blue}{\left(y3 \cdot \left(j \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 60.0%

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

   5. Simplified 60.0%

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

   if -3.8e18 < j < -1.2e-31

   1. Initial program 34.0%

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

   3. Simplified 34.0%

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

   4. Taylor expanded in t around inf 33.9%

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

   5. Taylor expanded in z around inf 46.0%

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

      1. mul-1-neg 46.0%

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

      2. associate-*r* 46.0%

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

   7. Simplified 46.0%

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

   8. Taylor expanded in a around 0 46.2%

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

      1. associate-*r* 46.2%

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

      2. neg-mul-1 46.2%

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

   10. Simplified 46.2%

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

   if -1.2e-31 < j < -1.05e-125

   1. Initial program 17.5%

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

   2. Taylor expanded in y4 around inf 50.6%

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

   3. Taylor expanded in c around inf 51.0%

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

   if -1.05e-125 < j < 9.5000000000000004e-287 or 4.2e20 < j < 6.3999999999999997e88

   1. Initial program 41.6%

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

   2. Taylor expanded in y0 around inf 40.3%

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

      1. *-commutative 40.3%

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

      2. *-commutative 40.3%

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

      3. *-commutative 40.3%

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

   4. Simplified 40.3%

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

   5. Taylor expanded in y around inf 54.9%

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

   if 2.4500000000000001e-113 < j < 4.2e20

   1. Initial program 41.4%

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

   2. Taylor expanded in y4 around inf 45.2%

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

   3. Taylor expanded in y2 around inf 56.2%

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

   if 6.3999999999999997e88 < j < 9.5000000000000003e183

   1. Initial program 35.3%

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

   3. Simplified 35.3%

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

   4. Taylor expanded in t around inf 42.2%

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

   5. Taylor expanded in j around inf 30.8%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 30.9%

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

      2. *-commutative 30.9%

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

      3. *-commutative 30.9%

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

   7. Simplified 30.9%

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

   8. Taylor expanded in y4 around 0 36.6%

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

      1. associate-*r* 36.6%

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

      2. neg-mul-1 36.6%

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

      3. associate-*r* 41.9%

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

   10. Simplified 41.9%

       \[\leadsto \color{blue}{\left(-i\right) \cdot \left(\left(t \cdot j\right) \cdot y5\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.3 \cdot 10^{+196}:\\ \;\;\;\;\left(t \cdot j\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\\ \mathbf{elif}\;j \leq -1.95 \cdot 10^{+55}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;j \leq -3.8 \cdot 10^{+18}:\\ \;\;\;\;y3 \cdot \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq -1.2 \cdot 10^{-31}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;j \leq -1.05 \cdot 10^{-125}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 9.5 \cdot 10^{-287}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 2.45 \cdot 10^{-113}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;j \leq 4.2 \cdot 10^{+20}:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 6.4 \cdot 10^{+88}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 9.5 \cdot 10^{+183}:\\ \;\;\;\;\left(-i\right) \cdot \left(\left(t \cdot j\right) \cdot y5\right)\\ \mathbf{else}:\\ \;\;\;\;y3 \cdot \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \end{array} \]

Alternative 13: 30.7% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ t_2 := y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ t_3 := y4 \cdot \left(y2 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{if}\;j \leq -3.1 \cdot 10^{+196}:\\ \;\;\;\;\left(t \cdot j\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\\ \mathbf{elif}\;j \leq -2.4 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -7.5 \cdot 10^{-122}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 5.5 \cdot 10^{-285}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 9.4 \cdot 10^{-113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 2.55 \cdot 10^{+22}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{+87}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 2.4 \cdot 10^{+201}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y4 (* y (- (* c y3) (* b k)))))
        (t_2 (* y (* y3 (- (* c y4) (* a y5)))))
        (t_3 (* y4 (* y2 (- (* k y1) (* t c))))))
   (if (<= j -3.1e+196)
     (* (* t j) (- (* b y4) (* i y5)))
     (if (<= j -2.4e+52)
       t_1
       (if (<= j -7.5e-122)
         t_3
         (if (<= j 5.5e-285)
           t_2
           (if (<= j 9.4e-113)
             t_1
             (if (<= j 2.55e+22)
               t_3
               (if (<= j 1.15e+87)
                 t_2
                 (if (<= j 2.4e+201)
                   (* y4 (* t (- (* b j) (* c y2))))
                   (* y4 (* y1 (- (* k y2) (* j y3))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * (y * ((c * y3) - (b * k)));
	double t_2 = y * (y3 * ((c * y4) - (a * y5)));
	double t_3 = y4 * (y2 * ((k * y1) - (t * c)));
	double tmp;
	if (j <= -3.1e+196) {
		tmp = (t * j) * ((b * y4) - (i * y5));
	} else if (j <= -2.4e+52) {
		tmp = t_1;
	} else if (j <= -7.5e-122) {
		tmp = t_3;
	} else if (j <= 5.5e-285) {
		tmp = t_2;
	} else if (j <= 9.4e-113) {
		tmp = t_1;
	} else if (j <= 2.55e+22) {
		tmp = t_3;
	} else if (j <= 1.15e+87) {
		tmp = t_2;
	} else if (j <= 2.4e+201) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y4 * (y * ((c * y3) - (b * k)))
    t_2 = y * (y3 * ((c * y4) - (a * y5)))
    t_3 = y4 * (y2 * ((k * y1) - (t * c)))
    if (j <= (-3.1d+196)) then
        tmp = (t * j) * ((b * y4) - (i * y5))
    else if (j <= (-2.4d+52)) then
        tmp = t_1
    else if (j <= (-7.5d-122)) then
        tmp = t_3
    else if (j <= 5.5d-285) then
        tmp = t_2
    else if (j <= 9.4d-113) then
        tmp = t_1
    else if (j <= 2.55d+22) then
        tmp = t_3
    else if (j <= 1.15d+87) then
        tmp = t_2
    else if (j <= 2.4d+201) then
        tmp = y4 * (t * ((b * j) - (c * y2)))
    else
        tmp = y4 * (y1 * ((k * y2) - (j * y3)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * (y * ((c * y3) - (b * k)));
	double t_2 = y * (y3 * ((c * y4) - (a * y5)));
	double t_3 = y4 * (y2 * ((k * y1) - (t * c)));
	double tmp;
	if (j <= -3.1e+196) {
		tmp = (t * j) * ((b * y4) - (i * y5));
	} else if (j <= -2.4e+52) {
		tmp = t_1;
	} else if (j <= -7.5e-122) {
		tmp = t_3;
	} else if (j <= 5.5e-285) {
		tmp = t_2;
	} else if (j <= 9.4e-113) {
		tmp = t_1;
	} else if (j <= 2.55e+22) {
		tmp = t_3;
	} else if (j <= 1.15e+87) {
		tmp = t_2;
	} else if (j <= 2.4e+201) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y4 * (y * ((c * y3) - (b * k)))
	t_2 = y * (y3 * ((c * y4) - (a * y5)))
	t_3 = y4 * (y2 * ((k * y1) - (t * c)))
	tmp = 0
	if j <= -3.1e+196:
		tmp = (t * j) * ((b * y4) - (i * y5))
	elif j <= -2.4e+52:
		tmp = t_1
	elif j <= -7.5e-122:
		tmp = t_3
	elif j <= 5.5e-285:
		tmp = t_2
	elif j <= 9.4e-113:
		tmp = t_1
	elif j <= 2.55e+22:
		tmp = t_3
	elif j <= 1.15e+87:
		tmp = t_2
	elif j <= 2.4e+201:
		tmp = y4 * (t * ((b * j) - (c * y2)))
	else:
		tmp = y4 * (y1 * ((k * y2) - (j * y3)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y4 * Float64(y * Float64(Float64(c * y3) - Float64(b * k))))
	t_2 = Float64(y * Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))))
	t_3 = Float64(y4 * Float64(y2 * Float64(Float64(k * y1) - Float64(t * c))))
	tmp = 0.0
	if (j <= -3.1e+196)
		tmp = Float64(Float64(t * j) * Float64(Float64(b * y4) - Float64(i * y5)));
	elseif (j <= -2.4e+52)
		tmp = t_1;
	elseif (j <= -7.5e-122)
		tmp = t_3;
	elseif (j <= 5.5e-285)
		tmp = t_2;
	elseif (j <= 9.4e-113)
		tmp = t_1;
	elseif (j <= 2.55e+22)
		tmp = t_3;
	elseif (j <= 1.15e+87)
		tmp = t_2;
	elseif (j <= 2.4e+201)
		tmp = Float64(y4 * Float64(t * Float64(Float64(b * j) - Float64(c * y2))));
	else
		tmp = Float64(y4 * Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y4 * (y * ((c * y3) - (b * k)));
	t_2 = y * (y3 * ((c * y4) - (a * y5)));
	t_3 = y4 * (y2 * ((k * y1) - (t * c)));
	tmp = 0.0;
	if (j <= -3.1e+196)
		tmp = (t * j) * ((b * y4) - (i * y5));
	elseif (j <= -2.4e+52)
		tmp = t_1;
	elseif (j <= -7.5e-122)
		tmp = t_3;
	elseif (j <= 5.5e-285)
		tmp = t_2;
	elseif (j <= 9.4e-113)
		tmp = t_1;
	elseif (j <= 2.55e+22)
		tmp = t_3;
	elseif (j <= 1.15e+87)
		tmp = t_2;
	elseif (j <= 2.4e+201)
		tmp = y4 * (t * ((b * j) - (c * y2)));
	else
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y4 * N[(y * N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y4 * N[(y2 * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.1e+196], N[(N[(t * j), $MachinePrecision] * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.4e+52], t$95$1, If[LessEqual[j, -7.5e-122], t$95$3, If[LessEqual[j, 5.5e-285], t$95$2, If[LessEqual[j, 9.4e-113], t$95$1, If[LessEqual[j, 2.55e+22], t$95$3, If[LessEqual[j, 1.15e+87], t$95$2, If[LessEqual[j, 2.4e+201], N[(y4 * N[(t * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y4 * N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -3.1000000000000001e196

   1. Initial program 20.8%

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

   3. Simplified 24.9%

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

   4. Taylor expanded in t around inf 46.5%

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

   5. Taylor expanded in j around inf 51.2%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 58.9%

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

      2. *-commutative 58.9%

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

      3. *-commutative 58.9%

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

   7. Simplified 58.9%

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

   if -3.1000000000000001e196 < j < -2.4e52 or 5.5000000000000001e-285 < j < 9.4000000000000004e-113

   1. Initial program 25.2%

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

   2. Taylor expanded in y around inf 42.1%

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

      1. add-cube-cbrt 42.0%

         \[\leadsto y \cdot \color{blue}{\left(\left(\sqrt[3]{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \cdot \sqrt[3]{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \cdot \sqrt[3]{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)} \]

   4. Applied egg-rr 42.0%

      \[\leadsto y \cdot \color{blue}{\left(\left(\sqrt[3]{\mathsf{fma}\left(-1, k \cdot \left(y4 \cdot b - i \cdot y5\right), \mathsf{fma}\left(a, b, -i \cdot c\right) \cdot x\right) + y3 \cdot \left(y4 \cdot c - y5 \cdot a\right)} \cdot \sqrt[3]{\mathsf{fma}\left(-1, k \cdot \left(y4 \cdot b - i \cdot y5\right), \mathsf{fma}\left(a, b, -i \cdot c\right) \cdot x\right) + y3 \cdot \left(y4 \cdot c - y5 \cdot a\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(-1, k \cdot \left(y4 \cdot b - i \cdot y5\right), \mathsf{fma}\left(a, b, -i \cdot c\right) \cdot x\right) + y3 \cdot \left(y4 \cdot c - y5 \cdot a\right)}\right)} \]

   5. Taylor expanded in y4 around inf 44.4%

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

      1. *-commutative 44.4%

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

      2. mul-1-neg 44.4%

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

      3. unsub-neg 44.4%

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

      4. *-commutative 44.4%

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

   7. Simplified 44.4%

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

   if -2.4e52 < j < -7.4999999999999998e-122 or 9.4000000000000004e-113 < j < 2.5500000000000001e22

   1. Initial program 30.6%

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

   2. Taylor expanded in y4 around inf 45.7%

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

   3. Taylor expanded in y2 around inf 49.1%

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

   if -7.4999999999999998e-122 < j < 5.5000000000000001e-285 or 2.5500000000000001e22 < j < 1.1500000000000001e87

   1. Initial program 41.6%

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

   2. Taylor expanded in y0 around inf 40.3%

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

      1. *-commutative 40.3%

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

      2. *-commutative 40.3%

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

      3. *-commutative 40.3%

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

   4. Simplified 40.3%

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

   5. Taylor expanded in y around inf 54.9%

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

   if 1.1500000000000001e87 < j < 2.39999999999999993e201

   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. Taylor expanded in y4 around inf 37.2%

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

   3. Taylor expanded in t around inf 45.0%

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

   if 2.39999999999999993e201 < j

   1. Initial program 22.2%

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

   2. Taylor expanded in y4 around inf 51.9%

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

   3. Taylor expanded in y1 around inf 56.0%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.1 \cdot 10^{+196}:\\ \;\;\;\;\left(t \cdot j\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\\ \mathbf{elif}\;j \leq -2.4 \cdot 10^{+52}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;j \leq -7.5 \cdot 10^{-122}:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 5.5 \cdot 10^{-285}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 9.4 \cdot 10^{-113}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;j \leq 2.55 \cdot 10^{+22}:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{+87}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 2.4 \cdot 10^{+201}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \end{array} \]

Alternative 14: 32.6% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+21}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{-166}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-57}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 58000:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+101}:\\ \;\;\;\;\left(y \cdot k\right) \cdot \left(i \cdot y5 - b \cdot y4\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+135}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y -3.5e+21)
   (* y4 (* y (- (* c y3) (* b k))))
   (if (<= y 1.18e-166)
     (* y4 (* y1 (- (* k y2) (* j y3))))
     (if (<= y 3.3e-57)
       (* c (- (* y0 (- (* x y2) (* z y3))) (* y4 (- (* t y2) (* y y3)))))
       (if (<= y 58000.0)
         (* b (* y0 (- (* z k) (* x j))))
         (if (<= y 1.02e+101)
           (* (* y k) (- (* i y5) (* b y4)))
           (if (<= y 6.5e+135)
             (* y (* a (- (* x b) (* y3 y5))))
             (* c (* y (- (* y3 y4) (* x i)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -3.5e+21) {
		tmp = y4 * (y * ((c * y3) - (b * k)));
	} else if (y <= 1.18e-166) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (y <= 3.3e-57) {
		tmp = c * ((y0 * ((x * y2) - (z * y3))) - (y4 * ((t * y2) - (y * y3))));
	} else if (y <= 58000.0) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y <= 1.02e+101) {
		tmp = (y * k) * ((i * y5) - (b * y4));
	} else if (y <= 6.5e+135) {
		tmp = y * (a * ((x * b) - (y3 * y5)));
	} else {
		tmp = c * (y * ((y3 * y4) - (x * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y <= (-3.5d+21)) then
        tmp = y4 * (y * ((c * y3) - (b * k)))
    else if (y <= 1.18d-166) then
        tmp = y4 * (y1 * ((k * y2) - (j * y3)))
    else if (y <= 3.3d-57) then
        tmp = c * ((y0 * ((x * y2) - (z * y3))) - (y4 * ((t * y2) - (y * y3))))
    else if (y <= 58000.0d0) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (y <= 1.02d+101) then
        tmp = (y * k) * ((i * y5) - (b * y4))
    else if (y <= 6.5d+135) then
        tmp = y * (a * ((x * b) - (y3 * y5)))
    else
        tmp = c * (y * ((y3 * y4) - (x * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -3.5e+21) {
		tmp = y4 * (y * ((c * y3) - (b * k)));
	} else if (y <= 1.18e-166) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (y <= 3.3e-57) {
		tmp = c * ((y0 * ((x * y2) - (z * y3))) - (y4 * ((t * y2) - (y * y3))));
	} else if (y <= 58000.0) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y <= 1.02e+101) {
		tmp = (y * k) * ((i * y5) - (b * y4));
	} else if (y <= 6.5e+135) {
		tmp = y * (a * ((x * b) - (y3 * y5)));
	} else {
		tmp = c * (y * ((y3 * y4) - (x * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y <= -3.5e+21:
		tmp = y4 * (y * ((c * y3) - (b * k)))
	elif y <= 1.18e-166:
		tmp = y4 * (y1 * ((k * y2) - (j * y3)))
	elif y <= 3.3e-57:
		tmp = c * ((y0 * ((x * y2) - (z * y3))) - (y4 * ((t * y2) - (y * y3))))
	elif y <= 58000.0:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif y <= 1.02e+101:
		tmp = (y * k) * ((i * y5) - (b * y4))
	elif y <= 6.5e+135:
		tmp = y * (a * ((x * b) - (y3 * y5)))
	else:
		tmp = c * (y * ((y3 * y4) - (x * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y <= -3.5e+21)
		tmp = Float64(y4 * Float64(y * Float64(Float64(c * y3) - Float64(b * k))));
	elseif (y <= 1.18e-166)
		tmp = Float64(y4 * Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif (y <= 3.3e-57)
		tmp = Float64(c * Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) - Float64(y4 * Float64(Float64(t * y2) - Float64(y * y3)))));
	elseif (y <= 58000.0)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (y <= 1.02e+101)
		tmp = Float64(Float64(y * k) * Float64(Float64(i * y5) - Float64(b * y4)));
	elseif (y <= 6.5e+135)
		tmp = Float64(y * Float64(a * Float64(Float64(x * b) - Float64(y3 * y5))));
	else
		tmp = Float64(c * Float64(y * Float64(Float64(y3 * y4) - Float64(x * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y <= -3.5e+21)
		tmp = y4 * (y * ((c * y3) - (b * k)));
	elseif (y <= 1.18e-166)
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	elseif (y <= 3.3e-57)
		tmp = c * ((y0 * ((x * y2) - (z * y3))) - (y4 * ((t * y2) - (y * y3))));
	elseif (y <= 58000.0)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (y <= 1.02e+101)
		tmp = (y * k) * ((i * y5) - (b * y4));
	elseif (y <= 6.5e+135)
		tmp = y * (a * ((x * b) - (y3 * y5)));
	else
		tmp = c * (y * ((y3 * y4) - (x * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y, -3.5e+21], N[(y4 * N[(y * N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.18e-166], N[(y4 * N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.3e-57], N[(c * N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y4 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 58000.0], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.02e+101], N[(N[(y * k), $MachinePrecision] * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e+135], N[(y * N[(a * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -3.5e21

   1. Initial program 24.9%

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

   2. Taylor expanded in y around inf 53.0%

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

      1. add-cube-cbrt 52.9%

         \[\leadsto y \cdot \color{blue}{\left(\left(\sqrt[3]{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \cdot \sqrt[3]{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \cdot \sqrt[3]{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)} \]

   4. Applied egg-rr 52.9%

      \[\leadsto y \cdot \color{blue}{\left(\left(\sqrt[3]{\mathsf{fma}\left(-1, k \cdot \left(y4 \cdot b - i \cdot y5\right), \mathsf{fma}\left(a, b, -i \cdot c\right) \cdot x\right) + y3 \cdot \left(y4 \cdot c - y5 \cdot a\right)} \cdot \sqrt[3]{\mathsf{fma}\left(-1, k \cdot \left(y4 \cdot b - i \cdot y5\right), \mathsf{fma}\left(a, b, -i \cdot c\right) \cdot x\right) + y3 \cdot \left(y4 \cdot c - y5 \cdot a\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(-1, k \cdot \left(y4 \cdot b - i \cdot y5\right), \mathsf{fma}\left(a, b, -i \cdot c\right) \cdot x\right) + y3 \cdot \left(y4 \cdot c - y5 \cdot a\right)}\right)} \]

   5. Taylor expanded in y4 around inf 50.4%

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

      1. *-commutative 50.4%

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

      2. mul-1-neg 50.4%

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

      3. unsub-neg 50.4%

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

      4. *-commutative 50.4%

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

   7. Simplified 50.4%

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

   if -3.5e21 < y < 1.18000000000000004e-166

   1. Initial program 41.1%

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

   2. Taylor expanded in y4 around inf 46.7%

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

   3. Taylor expanded in y1 around inf 38.5%

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

   if 1.18000000000000004e-166 < y < 3.2999999999999998e-57

   1. Initial program 12.4%

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

   2. Taylor expanded in y0 around inf 37.4%

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

      1. *-commutative 37.4%

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

      2. *-commutative 37.4%

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

      3. *-commutative 37.4%

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

   4. Simplified 37.4%

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

   5. Taylor expanded in c around inf 67.0%

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

      1. *-commutative 67.0%

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

      2. *-commutative 67.0%

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

   7. Simplified 67.0%

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

   if 3.2999999999999998e-57 < y < 58000

   1. Initial program 57.1%

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

   2. Taylor expanded in y0 around inf 42.9%

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

      1. *-commutative 42.9%

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

      2. *-commutative 42.9%

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

      3. *-commutative 42.9%

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

   4. Simplified 42.9%

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

   5. Taylor expanded in b around -inf 44.0%

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

      1. mul-1-neg 44.0%

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

      2. associate-*r* 50.6%

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

      3. *-commutative 50.6%

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

   7. Simplified 50.6%

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

   if 58000 < y < 1.02000000000000002e101

   1. Initial program 21.1%

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

   2. Taylor expanded in y around inf 42.5%

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

   3. Taylor expanded in k around inf 48.3%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y \cdot \left(y4 \cdot b - i \cdot y5\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 48.3%

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

      2. associate-*r* 48.3%

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

      3. distribute-lft-neg-in 48.3%

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

      4. *-commutative 48.3%

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

      5. *-commutative 48.3%

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

   5. Simplified 48.3%

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

   if 1.02000000000000002e101 < y < 6.5000000000000003e135

   1. Initial program 50.0%

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

   2. Taylor expanded in y around inf 66.7%

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

   3. Taylor expanded in a around inf 68.0%

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

   if 6.5000000000000003e135 < y

   1. Initial program 22.5%

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

   2. Taylor expanded in y around inf 55.7%

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

      1. add-cube-cbrt 55.7%

         \[\leadsto y \cdot \color{blue}{\left(\left(\sqrt[3]{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \cdot \sqrt[3]{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \cdot \sqrt[3]{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)} \]

   4. Applied egg-rr 55.7%

      \[\leadsto y \cdot \color{blue}{\left(\left(\sqrt[3]{\mathsf{fma}\left(-1, k \cdot \left(y4 \cdot b - i \cdot y5\right), \mathsf{fma}\left(a, b, -i \cdot c\right) \cdot x\right) + y3 \cdot \left(y4 \cdot c - y5 \cdot a\right)} \cdot \sqrt[3]{\mathsf{fma}\left(-1, k \cdot \left(y4 \cdot b - i \cdot y5\right), \mathsf{fma}\left(a, b, -i \cdot c\right) \cdot x\right) + y3 \cdot \left(y4 \cdot c - y5 \cdot a\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(-1, k \cdot \left(y4 \cdot b - i \cdot y5\right), \mathsf{fma}\left(a, b, -i \cdot c\right) \cdot x\right) + y3 \cdot \left(y4 \cdot c - y5 \cdot a\right)}\right)} \]

   5. Taylor expanded in c around inf 49.6%

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

      1. *-commutative 49.6%

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

      2. mul-1-neg 49.6%

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

      3. unsub-neg 49.6%

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

      4. *-commutative 49.6%

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

   7. Simplified 49.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(y3 \cdot y4 - i \cdot x\right) \cdot y\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+21}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{-166}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-57}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 58000:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+101}:\\ \;\;\;\;\left(y \cdot k\right) \cdot \left(i \cdot y5 - b \cdot y4\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+135}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \end{array} \]

Alternative 15: 29.1% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot \left(y2 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ t_2 := y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ t_3 := y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{if}\;j \leq -7 \cdot 10^{+52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -4.1 \cdot 10^{-128}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 6.4 \cdot 10^{-285}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 10^{-112}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 1.06 \cdot 10^{+91}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 1.36 \cdot 10^{+201}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y4 (* y2 (- (* k y1) (* t c)))))
        (t_2 (* y4 (* y (- (* c y3) (* b k)))))
        (t_3 (* y (* y3 (- (* c y4) (* a y5))))))
   (if (<= j -7e+52)
     t_2
     (if (<= j -4.1e-128)
       t_1
       (if (<= j 6.4e-285)
         t_3
         (if (<= j 1e-112)
           t_2
           (if (<= j 1.5e+22)
             t_1
             (if (<= j 1.06e+91)
               t_3
               (if (<= j 1.36e+201)
                 (* y4 (* t (- (* b j) (* c y2))))
                 (* y4 (* y1 (- (* k y2) (* j y3)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * (y2 * ((k * y1) - (t * c)));
	double t_2 = y4 * (y * ((c * y3) - (b * k)));
	double t_3 = y * (y3 * ((c * y4) - (a * y5)));
	double tmp;
	if (j <= -7e+52) {
		tmp = t_2;
	} else if (j <= -4.1e-128) {
		tmp = t_1;
	} else if (j <= 6.4e-285) {
		tmp = t_3;
	} else if (j <= 1e-112) {
		tmp = t_2;
	} else if (j <= 1.5e+22) {
		tmp = t_1;
	} else if (j <= 1.06e+91) {
		tmp = t_3;
	} else if (j <= 1.36e+201) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y4 * (y2 * ((k * y1) - (t * c)))
    t_2 = y4 * (y * ((c * y3) - (b * k)))
    t_3 = y * (y3 * ((c * y4) - (a * y5)))
    if (j <= (-7d+52)) then
        tmp = t_2
    else if (j <= (-4.1d-128)) then
        tmp = t_1
    else if (j <= 6.4d-285) then
        tmp = t_3
    else if (j <= 1d-112) then
        tmp = t_2
    else if (j <= 1.5d+22) then
        tmp = t_1
    else if (j <= 1.06d+91) then
        tmp = t_3
    else if (j <= 1.36d+201) then
        tmp = y4 * (t * ((b * j) - (c * y2)))
    else
        tmp = y4 * (y1 * ((k * y2) - (j * y3)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * (y2 * ((k * y1) - (t * c)));
	double t_2 = y4 * (y * ((c * y3) - (b * k)));
	double t_3 = y * (y3 * ((c * y4) - (a * y5)));
	double tmp;
	if (j <= -7e+52) {
		tmp = t_2;
	} else if (j <= -4.1e-128) {
		tmp = t_1;
	} else if (j <= 6.4e-285) {
		tmp = t_3;
	} else if (j <= 1e-112) {
		tmp = t_2;
	} else if (j <= 1.5e+22) {
		tmp = t_1;
	} else if (j <= 1.06e+91) {
		tmp = t_3;
	} else if (j <= 1.36e+201) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y4 * (y2 * ((k * y1) - (t * c)))
	t_2 = y4 * (y * ((c * y3) - (b * k)))
	t_3 = y * (y3 * ((c * y4) - (a * y5)))
	tmp = 0
	if j <= -7e+52:
		tmp = t_2
	elif j <= -4.1e-128:
		tmp = t_1
	elif j <= 6.4e-285:
		tmp = t_3
	elif j <= 1e-112:
		tmp = t_2
	elif j <= 1.5e+22:
		tmp = t_1
	elif j <= 1.06e+91:
		tmp = t_3
	elif j <= 1.36e+201:
		tmp = y4 * (t * ((b * j) - (c * y2)))
	else:
		tmp = y4 * (y1 * ((k * y2) - (j * y3)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y4 * Float64(y2 * Float64(Float64(k * y1) - Float64(t * c))))
	t_2 = Float64(y4 * Float64(y * Float64(Float64(c * y3) - Float64(b * k))))
	t_3 = Float64(y * Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))))
	tmp = 0.0
	if (j <= -7e+52)
		tmp = t_2;
	elseif (j <= -4.1e-128)
		tmp = t_1;
	elseif (j <= 6.4e-285)
		tmp = t_3;
	elseif (j <= 1e-112)
		tmp = t_2;
	elseif (j <= 1.5e+22)
		tmp = t_1;
	elseif (j <= 1.06e+91)
		tmp = t_3;
	elseif (j <= 1.36e+201)
		tmp = Float64(y4 * Float64(t * Float64(Float64(b * j) - Float64(c * y2))));
	else
		tmp = Float64(y4 * Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y4 * (y2 * ((k * y1) - (t * c)));
	t_2 = y4 * (y * ((c * y3) - (b * k)));
	t_3 = y * (y3 * ((c * y4) - (a * y5)));
	tmp = 0.0;
	if (j <= -7e+52)
		tmp = t_2;
	elseif (j <= -4.1e-128)
		tmp = t_1;
	elseif (j <= 6.4e-285)
		tmp = t_3;
	elseif (j <= 1e-112)
		tmp = t_2;
	elseif (j <= 1.5e+22)
		tmp = t_1;
	elseif (j <= 1.06e+91)
		tmp = t_3;
	elseif (j <= 1.36e+201)
		tmp = y4 * (t * ((b * j) - (c * y2)));
	else
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y4 * N[(y2 * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y4 * N[(y * N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -7e+52], t$95$2, If[LessEqual[j, -4.1e-128], t$95$1, If[LessEqual[j, 6.4e-285], t$95$3, If[LessEqual[j, 1e-112], t$95$2, If[LessEqual[j, 1.5e+22], t$95$1, If[LessEqual[j, 1.06e+91], t$95$3, If[LessEqual[j, 1.36e+201], N[(y4 * N[(t * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y4 * N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -7e52 or 6.40000000000000032e-285 < j < 9.9999999999999995e-113

   1. Initial program 23.9%

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

   2. Taylor expanded in y around inf 41.0%

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

      1. add-cube-cbrt 41.0%

         \[\leadsto y \cdot \color{blue}{\left(\left(\sqrt[3]{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \cdot \sqrt[3]{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \cdot \sqrt[3]{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)} \]

   4. Applied egg-rr 41.0%

      \[\leadsto y \cdot \color{blue}{\left(\left(\sqrt[3]{\mathsf{fma}\left(-1, k \cdot \left(y4 \cdot b - i \cdot y5\right), \mathsf{fma}\left(a, b, -i \cdot c\right) \cdot x\right) + y3 \cdot \left(y4 \cdot c - y5 \cdot a\right)} \cdot \sqrt[3]{\mathsf{fma}\left(-1, k \cdot \left(y4 \cdot b - i \cdot y5\right), \mathsf{fma}\left(a, b, -i \cdot c\right) \cdot x\right) + y3 \cdot \left(y4 \cdot c - y5 \cdot a\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(-1, k \cdot \left(y4 \cdot b - i \cdot y5\right), \mathsf{fma}\left(a, b, -i \cdot c\right) \cdot x\right) + y3 \cdot \left(y4 \cdot c - y5 \cdot a\right)}\right)} \]

   5. Taylor expanded in y4 around inf 42.7%

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

      1. *-commutative 42.7%

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

      2. mul-1-neg 42.7%

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

      3. unsub-neg 42.7%

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

      4. *-commutative 42.7%

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

   7. Simplified 42.7%

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

   if -7e52 < j < -4.1e-128 or 9.9999999999999995e-113 < j < 1.5e22

   1. Initial program 30.6%

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

   2. Taylor expanded in y4 around inf 45.7%

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

   3. Taylor expanded in y2 around inf 49.1%

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

   if -4.1e-128 < j < 6.40000000000000032e-285 or 1.5e22 < j < 1.05999999999999996e91

   1. Initial program 41.6%

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

   2. Taylor expanded in y0 around inf 40.3%

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

      1. *-commutative 40.3%

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

      2. *-commutative 40.3%

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

      3. *-commutative 40.3%

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

   4. Simplified 40.3%

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

   5. Taylor expanded in y around inf 54.9%

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

   if 1.05999999999999996e91 < j < 1.35999999999999988e201

   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. Taylor expanded in y4 around inf 37.2%

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

   3. Taylor expanded in t around inf 45.0%

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

   if 1.35999999999999988e201 < j

   1. Initial program 22.2%

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

   2. Taylor expanded in y4 around inf 51.9%

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

   3. Taylor expanded in y1 around inf 56.0%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 48.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -7 \cdot 10^{+52}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;j \leq -4.1 \cdot 10^{-128}:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 6.4 \cdot 10^{-285}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 10^{-112}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{+22}:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 1.06 \cdot 10^{+91}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 1.36 \cdot 10^{+201}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \end{array} \]

Alternative 16: 18.7% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y5 \cdot \left(y \cdot \left(-y3\right)\right)\right)\\ t_2 := \left(-i\right) \cdot \left(\left(t \cdot j\right) \cdot y5\right)\\ \mathbf{if}\;k \leq -1.85 \cdot 10^{+226}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq -2.4 \cdot 10^{+125}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq -4 \cdot 10^{+71}:\\ \;\;\;\;c \cdot \left(\left(t \cdot y4\right) \cdot \left(-y2\right)\right)\\ \mathbf{elif}\;k \leq -1.4 \cdot 10^{-115}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq -1.55 \cdot 10^{-280}:\\ \;\;\;\;y2 \cdot \left(a \cdot \left(t \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 5 \cdot 10^{-227}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j\right)\right)\\ \mathbf{elif}\;k \leq 2.4 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot y4\right) \cdot \left(k \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y5 (* y (- y3))))) (t_2 (* (- i) (* (* t j) y5))))
   (if (<= k -1.85e+226)
     t_1
     (if (<= k -2.4e+125)
       t_2
       (if (<= k -4e+71)
         (* c (* (* t y4) (- y2)))
         (if (<= k -1.4e-115)
           t_2
           (if (<= k -1.55e-280)
             (* y2 (* a (* t y5)))
             (if (<= k 5e-227)
               (* y4 (* b (* t j)))
               (if (<= k 2.4e-46) t_1 (* (* y y4) (* k (- b))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y5 * (y * -y3));
	double t_2 = -i * ((t * j) * y5);
	double tmp;
	if (k <= -1.85e+226) {
		tmp = t_1;
	} else if (k <= -2.4e+125) {
		tmp = t_2;
	} else if (k <= -4e+71) {
		tmp = c * ((t * y4) * -y2);
	} else if (k <= -1.4e-115) {
		tmp = t_2;
	} else if (k <= -1.55e-280) {
		tmp = y2 * (a * (t * y5));
	} else if (k <= 5e-227) {
		tmp = y4 * (b * (t * j));
	} else if (k <= 2.4e-46) {
		tmp = t_1;
	} else {
		tmp = (y * y4) * (k * -b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (y5 * (y * -y3))
    t_2 = -i * ((t * j) * y5)
    if (k <= (-1.85d+226)) then
        tmp = t_1
    else if (k <= (-2.4d+125)) then
        tmp = t_2
    else if (k <= (-4d+71)) then
        tmp = c * ((t * y4) * -y2)
    else if (k <= (-1.4d-115)) then
        tmp = t_2
    else if (k <= (-1.55d-280)) then
        tmp = y2 * (a * (t * y5))
    else if (k <= 5d-227) then
        tmp = y4 * (b * (t * j))
    else if (k <= 2.4d-46) then
        tmp = t_1
    else
        tmp = (y * y4) * (k * -b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y5 * (y * -y3));
	double t_2 = -i * ((t * j) * y5);
	double tmp;
	if (k <= -1.85e+226) {
		tmp = t_1;
	} else if (k <= -2.4e+125) {
		tmp = t_2;
	} else if (k <= -4e+71) {
		tmp = c * ((t * y4) * -y2);
	} else if (k <= -1.4e-115) {
		tmp = t_2;
	} else if (k <= -1.55e-280) {
		tmp = y2 * (a * (t * y5));
	} else if (k <= 5e-227) {
		tmp = y4 * (b * (t * j));
	} else if (k <= 2.4e-46) {
		tmp = t_1;
	} else {
		tmp = (y * y4) * (k * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y5 * (y * -y3))
	t_2 = -i * ((t * j) * y5)
	tmp = 0
	if k <= -1.85e+226:
		tmp = t_1
	elif k <= -2.4e+125:
		tmp = t_2
	elif k <= -4e+71:
		tmp = c * ((t * y4) * -y2)
	elif k <= -1.4e-115:
		tmp = t_2
	elif k <= -1.55e-280:
		tmp = y2 * (a * (t * y5))
	elif k <= 5e-227:
		tmp = y4 * (b * (t * j))
	elif k <= 2.4e-46:
		tmp = t_1
	else:
		tmp = (y * y4) * (k * -b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y5 * Float64(y * Float64(-y3))))
	t_2 = Float64(Float64(-i) * Float64(Float64(t * j) * y5))
	tmp = 0.0
	if (k <= -1.85e+226)
		tmp = t_1;
	elseif (k <= -2.4e+125)
		tmp = t_2;
	elseif (k <= -4e+71)
		tmp = Float64(c * Float64(Float64(t * y4) * Float64(-y2)));
	elseif (k <= -1.4e-115)
		tmp = t_2;
	elseif (k <= -1.55e-280)
		tmp = Float64(y2 * Float64(a * Float64(t * y5)));
	elseif (k <= 5e-227)
		tmp = Float64(y4 * Float64(b * Float64(t * j)));
	elseif (k <= 2.4e-46)
		tmp = t_1;
	else
		tmp = Float64(Float64(y * y4) * Float64(k * Float64(-b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y5 * (y * -y3));
	t_2 = -i * ((t * j) * y5);
	tmp = 0.0;
	if (k <= -1.85e+226)
		tmp = t_1;
	elseif (k <= -2.4e+125)
		tmp = t_2;
	elseif (k <= -4e+71)
		tmp = c * ((t * y4) * -y2);
	elseif (k <= -1.4e-115)
		tmp = t_2;
	elseif (k <= -1.55e-280)
		tmp = y2 * (a * (t * y5));
	elseif (k <= 5e-227)
		tmp = y4 * (b * (t * j));
	elseif (k <= 2.4e-46)
		tmp = t_1;
	else
		tmp = (y * y4) * (k * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y5 * N[(y * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[((-i) * N[(N[(t * j), $MachinePrecision] * y5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -1.85e+226], t$95$1, If[LessEqual[k, -2.4e+125], t$95$2, If[LessEqual[k, -4e+71], N[(c * N[(N[(t * y4), $MachinePrecision] * (-y2)), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -1.4e-115], t$95$2, If[LessEqual[k, -1.55e-280], N[(y2 * N[(a * N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 5e-227], N[(y4 * N[(b * N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.4e-46], t$95$1, N[(N[(y * y4), $MachinePrecision] * N[(k * (-b)), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if k < -1.84999999999999991e226 or 4.99999999999999961e-227 < k < 2.40000000000000013e-46

   1. Initial program 27.1%

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

   2. Taylor expanded in y0 around inf 32.0%

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

      1. *-commutative 32.0%

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

      2. *-commutative 32.0%

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

      3. *-commutative 32.0%

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

   4. Simplified 32.0%

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

   5. Taylor expanded in a around inf 36.9%

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

   6. Taylor expanded in t around 0 33.1%

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

      1. neg-mul-1 33.1%

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

      2. distribute-rgt-neg-in 33.1%

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

   8. Simplified 33.1%

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

   if -1.84999999999999991e226 < k < -2.4e125 or -4.0000000000000002e71 < k < -1.39999999999999994e-115

   1. Initial program 31.5%

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

   3. Simplified 31.5%

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

   4. Taylor expanded in t around inf 42.6%

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

   5. Taylor expanded in j around inf 39.5%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 37.7%

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

      2. *-commutative 37.7%

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

      3. *-commutative 37.7%

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

   7. Simplified 37.7%

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

   8. Taylor expanded in y4 around 0 38.0%

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

      1. associate-*r* 38.0%

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

      2. neg-mul-1 38.0%

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

      3. associate-*r* 36.4%

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

   10. Simplified 36.4%

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

   if -2.4e125 < k < -4.0000000000000002e71

   1. Initial program 20.0%

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

   2. Taylor expanded in y4 around inf 50.7%

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

   3. Taylor expanded in y2 around inf 61.0%

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

   4. Taylor expanded in k around 0 61.1%

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

      1. associate-*r* 61.1%

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

      2. neg-mul-1 61.1%

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

      3. associate-*r* 61.1%

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

   6. Simplified 61.1%

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

   if -1.39999999999999994e-115 < k < -1.55000000000000011e-280

   1. Initial program 50.5%

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

   2. Taylor expanded in y0 around inf 25.9%

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

      1. *-commutative 25.9%

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

      2. *-commutative 25.9%

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

      3. *-commutative 25.9%

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

   4. Simplified 25.9%

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

   5. Taylor expanded in a around inf 26.7%

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

   6. Taylor expanded in t around inf 19.7%

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

      1. associate-*r* 22.9%

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

      2. associate-*r* 29.6%

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

      3. *-commutative 29.6%

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

   8. Simplified 29.6%

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

   if -1.55000000000000011e-280 < k < 4.99999999999999961e-227

   1. Initial program 33.8%

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

   3. Simplified 33.8%

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

   4. Taylor expanded in t around inf 34.2%

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

   5. Taylor expanded in j around inf 45.6%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 45.6%

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

      2. *-commutative 45.6%

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

      3. *-commutative 45.6%

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

   7. Simplified 45.6%

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

   8. Taylor expanded in y4 around inf 40.3%

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

      1. *-commutative 40.3%

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

      2. *-commutative 40.3%

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

      3. associate-*l* 40.3%

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

      4. *-commutative 40.3%

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

   10. Simplified 40.3%

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

   if 2.40000000000000013e-46 < k

   1. Initial program 26.4%

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

   2. Taylor expanded in y4 around inf 51.6%

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

   3. Taylor expanded in y around -inf 44.8%

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

      1. mul-1-neg 44.8%

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

      2. associate-*r* 44.6%

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

      3. *-commutative 44.6%

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

   5. Simplified 44.6%

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

   6. Taylor expanded in k around inf 37.2%

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

4. Final simplification 36.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.85 \cdot 10^{+226}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(y \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;k \leq -2.4 \cdot 10^{+125}:\\ \;\;\;\;\left(-i\right) \cdot \left(\left(t \cdot j\right) \cdot y5\right)\\ \mathbf{elif}\;k \leq -4 \cdot 10^{+71}:\\ \;\;\;\;c \cdot \left(\left(t \cdot y4\right) \cdot \left(-y2\right)\right)\\ \mathbf{elif}\;k \leq -1.4 \cdot 10^{-115}:\\ \;\;\;\;\left(-i\right) \cdot \left(\left(t \cdot j\right) \cdot y5\right)\\ \mathbf{elif}\;k \leq -1.55 \cdot 10^{-280}:\\ \;\;\;\;y2 \cdot \left(a \cdot \left(t \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 5 \cdot 10^{-227}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j\right)\right)\\ \mathbf{elif}\;k \leq 2.4 \cdot 10^{-46}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(y \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot y4\right) \cdot \left(k \cdot \left(-b\right)\right)\\ \end{array} \]

Alternative 17: 21.1% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{if}\;k \leq -6.2 \cdot 10^{+70}:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(t \cdot \left(-c\right)\right)\right)\\ \mathbf{elif}\;k \leq -1.4 \cdot 10^{-155}:\\ \;\;\;\;\left(t \cdot j\right) \cdot \left(y5 \cdot \left(-i\right)\right)\\ \mathbf{elif}\;k \leq -8.5 \cdot 10^{-274}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 1.25 \cdot 10^{-225}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j\right)\right)\\ \mathbf{elif}\;k \leq 4 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot y4\right) \cdot \left(k \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y5 (- (* t y2) (* y y3))))))
   (if (<= k -6.2e+70)
     (* y4 (* y2 (* t (- c))))
     (if (<= k -1.4e-155)
       (* (* t j) (* y5 (- i)))
       (if (<= k -8.5e-274)
         t_1
         (if (<= k 1.25e-225)
           (* y4 (* b (* t j)))
           (if (<= k 4e-46) t_1 (* (* y y4) (* k (- b))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y5 * ((t * y2) - (y * y3)));
	double tmp;
	if (k <= -6.2e+70) {
		tmp = y4 * (y2 * (t * -c));
	} else if (k <= -1.4e-155) {
		tmp = (t * j) * (y5 * -i);
	} else if (k <= -8.5e-274) {
		tmp = t_1;
	} else if (k <= 1.25e-225) {
		tmp = y4 * (b * (t * j));
	} else if (k <= 4e-46) {
		tmp = t_1;
	} else {
		tmp = (y * y4) * (k * -b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (y5 * ((t * y2) - (y * y3)))
    if (k <= (-6.2d+70)) then
        tmp = y4 * (y2 * (t * -c))
    else if (k <= (-1.4d-155)) then
        tmp = (t * j) * (y5 * -i)
    else if (k <= (-8.5d-274)) then
        tmp = t_1
    else if (k <= 1.25d-225) then
        tmp = y4 * (b * (t * j))
    else if (k <= 4d-46) then
        tmp = t_1
    else
        tmp = (y * y4) * (k * -b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y5 * ((t * y2) - (y * y3)));
	double tmp;
	if (k <= -6.2e+70) {
		tmp = y4 * (y2 * (t * -c));
	} else if (k <= -1.4e-155) {
		tmp = (t * j) * (y5 * -i);
	} else if (k <= -8.5e-274) {
		tmp = t_1;
	} else if (k <= 1.25e-225) {
		tmp = y4 * (b * (t * j));
	} else if (k <= 4e-46) {
		tmp = t_1;
	} else {
		tmp = (y * y4) * (k * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y5 * ((t * y2) - (y * y3)))
	tmp = 0
	if k <= -6.2e+70:
		tmp = y4 * (y2 * (t * -c))
	elif k <= -1.4e-155:
		tmp = (t * j) * (y5 * -i)
	elif k <= -8.5e-274:
		tmp = t_1
	elif k <= 1.25e-225:
		tmp = y4 * (b * (t * j))
	elif k <= 4e-46:
		tmp = t_1
	else:
		tmp = (y * y4) * (k * -b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))
	tmp = 0.0
	if (k <= -6.2e+70)
		tmp = Float64(y4 * Float64(y2 * Float64(t * Float64(-c))));
	elseif (k <= -1.4e-155)
		tmp = Float64(Float64(t * j) * Float64(y5 * Float64(-i)));
	elseif (k <= -8.5e-274)
		tmp = t_1;
	elseif (k <= 1.25e-225)
		tmp = Float64(y4 * Float64(b * Float64(t * j)));
	elseif (k <= 4e-46)
		tmp = t_1;
	else
		tmp = Float64(Float64(y * y4) * Float64(k * Float64(-b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y5 * ((t * y2) - (y * y3)));
	tmp = 0.0;
	if (k <= -6.2e+70)
		tmp = y4 * (y2 * (t * -c));
	elseif (k <= -1.4e-155)
		tmp = (t * j) * (y5 * -i);
	elseif (k <= -8.5e-274)
		tmp = t_1;
	elseif (k <= 1.25e-225)
		tmp = y4 * (b * (t * j));
	elseif (k <= 4e-46)
		tmp = t_1;
	else
		tmp = (y * y4) * (k * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -6.2e+70], N[(y4 * N[(y2 * N[(t * (-c)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -1.4e-155], N[(N[(t * j), $MachinePrecision] * N[(y5 * (-i)), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -8.5e-274], t$95$1, If[LessEqual[k, 1.25e-225], N[(y4 * N[(b * N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 4e-46], t$95$1, N[(N[(y * y4), $MachinePrecision] * N[(k * (-b)), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if k < -6.2000000000000006e70

   1. Initial program 20.4%

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

   2. Taylor expanded in y4 around inf 26.9%

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

   3. Taylor expanded in y2 around inf 39.4%

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

   4. Taylor expanded in k around 0 29.8%

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

      1. neg-mul-1 29.8%

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

      2. distribute-rgt-neg-in 29.8%

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

   6. Simplified 29.8%

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

   if -6.2000000000000006e70 < k < -1.4e-155

   1. Initial program 38.2%

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

   3. Simplified 38.2%

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

   4. Taylor expanded in t around inf 47.9%

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

   5. Taylor expanded in j around inf 43.7%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 43.7%

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

      2. *-commutative 43.7%

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

      3. *-commutative 43.7%

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

   7. Simplified 43.7%

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

   8. Taylor expanded in y4 around 0 41.5%

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

      1. neg-mul-1 41.5%

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

      2. distribute-rgt-neg-in 41.5%

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

   10. Simplified 41.5%

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

   if -1.4e-155 < k < -8.49999999999999978e-274 or 1.25e-225 < k < 4.00000000000000009e-46

   1. Initial program 38.1%

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

   2. Taylor expanded in y0 around inf 36.7%

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

      1. *-commutative 36.7%

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

      2. *-commutative 36.7%

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

      3. *-commutative 36.7%

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

   4. Simplified 36.7%

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

   5. Taylor expanded in a around inf 34.0%

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

   if -8.49999999999999978e-274 < k < 1.25e-225

   1. Initial program 32.0%

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

   3. Simplified 32.0%

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

   4. Taylor expanded in t around inf 32.5%

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

   5. Taylor expanded in j around inf 43.2%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 43.2%

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

      2. *-commutative 43.2%

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

      3. *-commutative 43.2%

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

   7. Simplified 43.2%

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

   8. Taylor expanded in y4 around inf 38.2%

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

      1. *-commutative 38.2%

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

      2. *-commutative 38.2%

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

      3. associate-*l* 38.2%

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

      4. *-commutative 38.2%

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

   10. Simplified 38.2%

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

   if 4.00000000000000009e-46 < k

   1. Initial program 26.4%

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

   2. Taylor expanded in y4 around inf 51.6%

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

   3. Taylor expanded in y around -inf 44.8%

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

      1. mul-1-neg 44.8%

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

      2. associate-*r* 44.6%

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

      3. *-commutative 44.6%

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

   5. Simplified 44.6%

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

   6. Taylor expanded in k around inf 37.2%

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

4. Final simplification 35.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -6.2 \cdot 10^{+70}:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(t \cdot \left(-c\right)\right)\right)\\ \mathbf{elif}\;k \leq -1.4 \cdot 10^{-155}:\\ \;\;\;\;\left(t \cdot j\right) \cdot \left(y5 \cdot \left(-i\right)\right)\\ \mathbf{elif}\;k \leq -8.5 \cdot 10^{-274}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq 1.25 \cdot 10^{-225}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j\right)\right)\\ \mathbf{elif}\;k \leq 4 \cdot 10^{-46}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot y4\right) \cdot \left(k \cdot \left(-b\right)\right)\\ \end{array} \]

Alternative 18: 29.1% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{if}\;y1 \leq -4.6 \cdot 10^{+173}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -3 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y1 \leq -1.02 \cdot 10^{+43}:\\ \;\;\;\;\left(-i\right) \cdot \left(\left(t \cdot j\right) \cdot y5\right)\\ \mathbf{elif}\;y1 \leq 4.7 \cdot 10^{-128}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq 7.5 \cdot 10^{+180}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(k \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y (- (* y3 y4) (* x i))))))
   (if (<= y1 -4.6e+173)
     (* k (* y4 (* y1 y2)))
     (if (<= y1 -3e+51)
       t_1
       (if (<= y1 -1.02e+43)
         (* (- i) (* (* t j) y5))
         (if (<= y1 4.7e-128)
           (* c (* y4 (- (* y y3) (* t y2))))
           (if (<= y1 7.5e+180) t_1 (* y4 (* y2 (* k y1))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y * ((y3 * y4) - (x * i)));
	double tmp;
	if (y1 <= -4.6e+173) {
		tmp = k * (y4 * (y1 * y2));
	} else if (y1 <= -3e+51) {
		tmp = t_1;
	} else if (y1 <= -1.02e+43) {
		tmp = -i * ((t * j) * y5);
	} else if (y1 <= 4.7e-128) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (y1 <= 7.5e+180) {
		tmp = t_1;
	} else {
		tmp = y4 * (y2 * (k * y1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (y * ((y3 * y4) - (x * i)))
    if (y1 <= (-4.6d+173)) then
        tmp = k * (y4 * (y1 * y2))
    else if (y1 <= (-3d+51)) then
        tmp = t_1
    else if (y1 <= (-1.02d+43)) then
        tmp = -i * ((t * j) * y5)
    else if (y1 <= 4.7d-128) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else if (y1 <= 7.5d+180) then
        tmp = t_1
    else
        tmp = y4 * (y2 * (k * y1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y * ((y3 * y4) - (x * i)));
	double tmp;
	if (y1 <= -4.6e+173) {
		tmp = k * (y4 * (y1 * y2));
	} else if (y1 <= -3e+51) {
		tmp = t_1;
	} else if (y1 <= -1.02e+43) {
		tmp = -i * ((t * j) * y5);
	} else if (y1 <= 4.7e-128) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (y1 <= 7.5e+180) {
		tmp = t_1;
	} else {
		tmp = y4 * (y2 * (k * y1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (y * ((y3 * y4) - (x * i)))
	tmp = 0
	if y1 <= -4.6e+173:
		tmp = k * (y4 * (y1 * y2))
	elif y1 <= -3e+51:
		tmp = t_1
	elif y1 <= -1.02e+43:
		tmp = -i * ((t * j) * y5)
	elif y1 <= 4.7e-128:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	elif y1 <= 7.5e+180:
		tmp = t_1
	else:
		tmp = y4 * (y2 * (k * y1))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(y * Float64(Float64(y3 * y4) - Float64(x * i))))
	tmp = 0.0
	if (y1 <= -4.6e+173)
		tmp = Float64(k * Float64(y4 * Float64(y1 * y2)));
	elseif (y1 <= -3e+51)
		tmp = t_1;
	elseif (y1 <= -1.02e+43)
		tmp = Float64(Float64(-i) * Float64(Float64(t * j) * y5));
	elseif (y1 <= 4.7e-128)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (y1 <= 7.5e+180)
		tmp = t_1;
	else
		tmp = Float64(y4 * Float64(y2 * Float64(k * y1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (y * ((y3 * y4) - (x * i)));
	tmp = 0.0;
	if (y1 <= -4.6e+173)
		tmp = k * (y4 * (y1 * y2));
	elseif (y1 <= -3e+51)
		tmp = t_1;
	elseif (y1 <= -1.02e+43)
		tmp = -i * ((t * j) * y5);
	elseif (y1 <= 4.7e-128)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	elseif (y1 <= 7.5e+180)
		tmp = t_1;
	else
		tmp = y4 * (y2 * (k * y1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(y * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -4.6e+173], N[(k * N[(y4 * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -3e+51], t$95$1, If[LessEqual[y1, -1.02e+43], N[((-i) * N[(N[(t * j), $MachinePrecision] * y5), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 4.7e-128], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 7.5e+180], t$95$1, N[(y4 * N[(y2 * N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y1 < -4.5999999999999999e173

   1. Initial program 28.3%

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

   2. Taylor expanded in y4 around inf 47.5%

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

   3. Taylor expanded in y2 around inf 34.9%

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

   4. Taylor expanded in k around inf 41.3%

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

   if -4.5999999999999999e173 < y1 < -3e51 or 4.7000000000000004e-128 < y1 < 7.5000000000000003e180

   1. Initial program 38.2%

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

   2. Taylor expanded in y around inf 38.6%

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

      1. add-cube-cbrt 38.5%

         \[\leadsto y \cdot \color{blue}{\left(\left(\sqrt[3]{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \cdot \sqrt[3]{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \cdot \sqrt[3]{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)} \]

   4. Applied egg-rr 38.5%

      \[\leadsto y \cdot \color{blue}{\left(\left(\sqrt[3]{\mathsf{fma}\left(-1, k \cdot \left(y4 \cdot b - i \cdot y5\right), \mathsf{fma}\left(a, b, -i \cdot c\right) \cdot x\right) + y3 \cdot \left(y4 \cdot c - y5 \cdot a\right)} \cdot \sqrt[3]{\mathsf{fma}\left(-1, k \cdot \left(y4 \cdot b - i \cdot y5\right), \mathsf{fma}\left(a, b, -i \cdot c\right) \cdot x\right) + y3 \cdot \left(y4 \cdot c - y5 \cdot a\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(-1, k \cdot \left(y4 \cdot b - i \cdot y5\right), \mathsf{fma}\left(a, b, -i \cdot c\right) \cdot x\right) + y3 \cdot \left(y4 \cdot c - y5 \cdot a\right)}\right)} \]

   5. Taylor expanded in c around inf 31.0%

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

      1. *-commutative 31.0%

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

      2. mul-1-neg 31.0%

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

      3. unsub-neg 31.0%

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

      4. *-commutative 31.0%

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

   7. Simplified 31.0%

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

   if -3e51 < y1 < -1.02e43

   1. Initial program 25.0%

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

   3. Simplified 25.0%

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

   4. Taylor expanded in t around inf 50.1%

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

   5. Taylor expanded in j around inf 50.4%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 50.0%

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

      2. *-commutative 50.0%

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

      3. *-commutative 50.0%

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

   7. Simplified 50.0%

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

   8. Taylor expanded in y4 around 0 50.7%

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

      1. associate-*r* 50.7%

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

      2. neg-mul-1 50.7%

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

      3. associate-*r* 75.0%

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

   10. Simplified 75.0%

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

   if -1.02e43 < y1 < 4.7000000000000004e-128

   1. Initial program 28.4%

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

   2. Taylor expanded in y4 around inf 42.3%

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

   3. Taylor expanded in c around inf 38.6%

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

   if 7.5000000000000003e180 < y1

   1. Initial program 16.0%

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

   2. Taylor expanded in y4 around inf 56.3%

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

   3. Taylor expanded in y2 around inf 64.3%

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

   4. Taylor expanded in k around inf 64.7%

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

4. Final simplification 39.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -4.6 \cdot 10^{+173}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -3 \cdot 10^{+51}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;y1 \leq -1.02 \cdot 10^{+43}:\\ \;\;\;\;\left(-i\right) \cdot \left(\left(t \cdot j\right) \cdot y5\right)\\ \mathbf{elif}\;y1 \leq 4.7 \cdot 10^{-128}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq 7.5 \cdot 10^{+180}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(k \cdot y1\right)\right)\\ \end{array} \]

Alternative 19: 29.7% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y4 \leq -5.4 \cdot 10^{-134}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;y4 \leq 3.5 \cdot 10^{-84}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq 3.2 \cdot 10^{+145} \lor \neg \left(y4 \leq 4 \cdot 10^{+199}\right):\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y \cdot \left(-b\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y4 -5.4e-134)
   (* c (* y (- (* y3 y4) (* x i))))
   (if (<= y4 3.5e-84)
     (* y (* a (- (* x b) (* y3 y5))))
     (if (or (<= y4 3.2e+145) (not (<= y4 4e+199)))
       (* c (* y4 (- (* y y3) (* t y2))))
       (* k (* y4 (* y (- b))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -5.4e-134) {
		tmp = c * (y * ((y3 * y4) - (x * i)));
	} else if (y4 <= 3.5e-84) {
		tmp = y * (a * ((x * b) - (y3 * y5)));
	} else if ((y4 <= 3.2e+145) || !(y4 <= 4e+199)) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else {
		tmp = k * (y4 * (y * -b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y4 <= (-5.4d-134)) then
        tmp = c * (y * ((y3 * y4) - (x * i)))
    else if (y4 <= 3.5d-84) then
        tmp = y * (a * ((x * b) - (y3 * y5)))
    else if ((y4 <= 3.2d+145) .or. (.not. (y4 <= 4d+199))) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else
        tmp = k * (y4 * (y * -b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -5.4e-134) {
		tmp = c * (y * ((y3 * y4) - (x * i)));
	} else if (y4 <= 3.5e-84) {
		tmp = y * (a * ((x * b) - (y3 * y5)));
	} else if ((y4 <= 3.2e+145) || !(y4 <= 4e+199)) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else {
		tmp = k * (y4 * (y * -b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y4 <= -5.4e-134:
		tmp = c * (y * ((y3 * y4) - (x * i)))
	elif y4 <= 3.5e-84:
		tmp = y * (a * ((x * b) - (y3 * y5)))
	elif (y4 <= 3.2e+145) or not (y4 <= 4e+199):
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	else:
		tmp = k * (y4 * (y * -b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y4 <= -5.4e-134)
		tmp = Float64(c * Float64(y * Float64(Float64(y3 * y4) - Float64(x * i))));
	elseif (y4 <= 3.5e-84)
		tmp = Float64(y * Float64(a * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif ((y4 <= 3.2e+145) || !(y4 <= 4e+199))
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	else
		tmp = Float64(k * Float64(y4 * Float64(y * Float64(-b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y4 <= -5.4e-134)
		tmp = c * (y * ((y3 * y4) - (x * i)));
	elseif (y4 <= 3.5e-84)
		tmp = y * (a * ((x * b) - (y3 * y5)));
	elseif ((y4 <= 3.2e+145) || ~((y4 <= 4e+199)))
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	else
		tmp = k * (y4 * (y * -b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y4, -5.4e-134], N[(c * N[(y * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 3.5e-84], N[(y * N[(a * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y4, 3.2e+145], N[Not[LessEqual[y4, 4e+199]], $MachinePrecision]], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(y4 * N[(y * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y4 < -5.3999999999999996e-134

   1. Initial program 28.0%

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

   2. Taylor expanded in y around inf 46.0%

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

      1. add-cube-cbrt 46.0%

         \[\leadsto y \cdot \color{blue}{\left(\left(\sqrt[3]{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \cdot \sqrt[3]{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \cdot \sqrt[3]{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)} \]

   4. Applied egg-rr 46.0%

      \[\leadsto y \cdot \color{blue}{\left(\left(\sqrt[3]{\mathsf{fma}\left(-1, k \cdot \left(y4 \cdot b - i \cdot y5\right), \mathsf{fma}\left(a, b, -i \cdot c\right) \cdot x\right) + y3 \cdot \left(y4 \cdot c - y5 \cdot a\right)} \cdot \sqrt[3]{\mathsf{fma}\left(-1, k \cdot \left(y4 \cdot b - i \cdot y5\right), \mathsf{fma}\left(a, b, -i \cdot c\right) \cdot x\right) + y3 \cdot \left(y4 \cdot c - y5 \cdot a\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(-1, k \cdot \left(y4 \cdot b - i \cdot y5\right), \mathsf{fma}\left(a, b, -i \cdot c\right) \cdot x\right) + y3 \cdot \left(y4 \cdot c - y5 \cdot a\right)}\right)} \]

   5. Taylor expanded in c around inf 38.5%

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

      1. *-commutative 38.5%

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

      2. mul-1-neg 38.5%

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

      3. unsub-neg 38.5%

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

      4. *-commutative 38.5%

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

   7. Simplified 38.5%

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

   if -5.3999999999999996e-134 < y4 < 3.5000000000000001e-84

   1. Initial program 35.9%

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

   2. Taylor expanded in y around inf 39.2%

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

   3. Taylor expanded in a around inf 33.3%

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

   if 3.5000000000000001e-84 < y4 < 3.20000000000000008e145 or 4.00000000000000039e199 < y4

   1. Initial program 25.7%

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

   2. Taylor expanded in y4 around inf 48.5%

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

   3. Taylor expanded in c around inf 46.0%

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

   if 3.20000000000000008e145 < y4 < 4.00000000000000039e199

   1. Initial program 36.6%

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

   2. Taylor expanded in y4 around inf 45.7%

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

   3. Taylor expanded in y around -inf 33.1%

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

      1. mul-1-neg 33.1%

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

      2. associate-*r* 37.4%

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

      3. *-commutative 37.4%

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

   5. Simplified 37.4%

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

   6. Taylor expanded in k around inf 37.6%

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

4. Final simplification 38.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -5.4 \cdot 10^{-134}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;y4 \leq 3.5 \cdot 10^{-84}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq 3.2 \cdot 10^{+145} \lor \neg \left(y4 \leq 4 \cdot 10^{+199}\right):\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y \cdot \left(-b\right)\right)\right)\\ \end{array} \]

Alternative 20: 27.6% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{if}\;y2 \leq -3.6 \cdot 10^{+138}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 2 \cdot 10^{-305}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq 1.35 \cdot 10^{-266}:\\ \;\;\;\;k \cdot \left(y \cdot \left(b \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 6.6 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(t \cdot y4\right) \cdot \left(-y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y (* y3 (- (* c y4) (* a y5))))))
   (if (<= y2 -3.6e+138)
     (* k (* y4 (* y1 y2)))
     (if (<= y2 2e-305)
       t_1
       (if (<= y2 1.35e-266)
         (* k (* y (* b (- y4))))
         (if (<= y2 6.6e+48) t_1 (* c (* (* t y4) (- 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 = y * (y3 * ((c * y4) - (a * y5)));
	double tmp;
	if (y2 <= -3.6e+138) {
		tmp = k * (y4 * (y1 * y2));
	} else if (y2 <= 2e-305) {
		tmp = t_1;
	} else if (y2 <= 1.35e-266) {
		tmp = k * (y * (b * -y4));
	} else if (y2 <= 6.6e+48) {
		tmp = t_1;
	} else {
		tmp = c * ((t * y4) * -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 = y * (y3 * ((c * y4) - (a * y5)))
    if (y2 <= (-3.6d+138)) then
        tmp = k * (y4 * (y1 * y2))
    else if (y2 <= 2d-305) then
        tmp = t_1
    else if (y2 <= 1.35d-266) then
        tmp = k * (y * (b * -y4))
    else if (y2 <= 6.6d+48) then
        tmp = t_1
    else
        tmp = c * ((t * y4) * -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 = y * (y3 * ((c * y4) - (a * y5)));
	double tmp;
	if (y2 <= -3.6e+138) {
		tmp = k * (y4 * (y1 * y2));
	} else if (y2 <= 2e-305) {
		tmp = t_1;
	} else if (y2 <= 1.35e-266) {
		tmp = k * (y * (b * -y4));
	} else if (y2 <= 6.6e+48) {
		tmp = t_1;
	} else {
		tmp = c * ((t * y4) * -y2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y * (y3 * ((c * y4) - (a * y5)))
	tmp = 0
	if y2 <= -3.6e+138:
		tmp = k * (y4 * (y1 * y2))
	elif y2 <= 2e-305:
		tmp = t_1
	elif y2 <= 1.35e-266:
		tmp = k * (y * (b * -y4))
	elif y2 <= 6.6e+48:
		tmp = t_1
	else:
		tmp = c * ((t * y4) * -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(y * Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))))
	tmp = 0.0
	if (y2 <= -3.6e+138)
		tmp = Float64(k * Float64(y4 * Float64(y1 * y2)));
	elseif (y2 <= 2e-305)
		tmp = t_1;
	elseif (y2 <= 1.35e-266)
		tmp = Float64(k * Float64(y * Float64(b * Float64(-y4))));
	elseif (y2 <= 6.6e+48)
		tmp = t_1;
	else
		tmp = Float64(c * Float64(Float64(t * y4) * Float64(-y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y * (y3 * ((c * y4) - (a * y5)));
	tmp = 0.0;
	if (y2 <= -3.6e+138)
		tmp = k * (y4 * (y1 * y2));
	elseif (y2 <= 2e-305)
		tmp = t_1;
	elseif (y2 <= 1.35e-266)
		tmp = k * (y * (b * -y4));
	elseif (y2 <= 6.6e+48)
		tmp = t_1;
	else
		tmp = c * ((t * y4) * -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[(y * N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -3.6e+138], N[(k * N[(y4 * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2e-305], t$95$1, If[LessEqual[y2, 1.35e-266], N[(k * N[(y * N[(b * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 6.6e+48], t$95$1, N[(c * N[(N[(t * y4), $MachinePrecision] * (-y2)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y2 < -3.6000000000000001e138

   1. Initial program 24.5%

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

   2. Taylor expanded in y4 around inf 57.1%

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

   3. Taylor expanded in y2 around inf 57.6%

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

   4. Taylor expanded in k around inf 46.8%

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

   if -3.6000000000000001e138 < y2 < 1.99999999999999999e-305 or 1.34999999999999998e-266 < y2 < 6.60000000000000045e48

   1. Initial program 34.4%

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

   2. Taylor expanded in y0 around inf 36.5%

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

      1. *-commutative 36.5%

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

      2. *-commutative 36.5%

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

      3. *-commutative 36.5%

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

   4. Simplified 36.5%

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

   5. Taylor expanded in y around inf 38.9%

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

   if 1.99999999999999999e-305 < y2 < 1.34999999999999998e-266

   1. Initial program 45.1%

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

   2. Taylor expanded in y4 around inf 45.8%

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

   3. Taylor expanded in y around -inf 46.6%

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

      1. mul-1-neg 46.6%

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

      2. associate-*r* 46.6%

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

      3. *-commutative 46.6%

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

   5. Simplified 46.6%

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

   6. Taylor expanded in k around inf 55.1%

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

      1. *-commutative 55.1%

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

      2. associate-*l* 55.3%

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

   8. Simplified 55.3%

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

   if 6.60000000000000045e48 < y2

   1. Initial program 21.6%

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

   2. Taylor expanded in y4 around inf 29.2%

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

   3. Taylor expanded in y2 around inf 45.4%

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

   4. Taylor expanded in k around 0 38.7%

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

      1. associate-*r* 38.7%

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

      2. neg-mul-1 38.7%

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

      3. associate-*r* 35.3%

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

   6. Simplified 35.3%

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

4. Final simplification 40.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -3.6 \cdot 10^{+138}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 2 \cdot 10^{-305}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 1.35 \cdot 10^{-266}:\\ \;\;\;\;k \cdot \left(y \cdot \left(b \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 6.6 \cdot 10^{+48}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(t \cdot y4\right) \cdot \left(-y2\right)\right)\\ \end{array} \]

Alternative 21: 29.5% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{if}\;y2 \leq -1.25 \cdot 10^{+137}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 1.8 \cdot 10^{-305}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq 5 \cdot 10^{-267}:\\ \;\;\;\;k \cdot \left(y \cdot \left(b \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 1.4 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y (* y3 (- (* c y4) (* a y5))))))
   (if (<= y2 -1.25e+137)
     (* k (* y4 (* y1 y2)))
     (if (<= y2 1.8e-305)
       t_1
       (if (<= y2 5e-267)
         (* k (* y (* b (- y4))))
         (if (<= y2 1.4e+67) t_1 (* y4 (* t (- (* b j) (* c 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 = y * (y3 * ((c * y4) - (a * y5)));
	double tmp;
	if (y2 <= -1.25e+137) {
		tmp = k * (y4 * (y1 * y2));
	} else if (y2 <= 1.8e-305) {
		tmp = t_1;
	} else if (y2 <= 5e-267) {
		tmp = k * (y * (b * -y4));
	} else if (y2 <= 1.4e+67) {
		tmp = t_1;
	} else {
		tmp = y4 * (t * ((b * j) - (c * 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 = y * (y3 * ((c * y4) - (a * y5)))
    if (y2 <= (-1.25d+137)) then
        tmp = k * (y4 * (y1 * y2))
    else if (y2 <= 1.8d-305) then
        tmp = t_1
    else if (y2 <= 5d-267) then
        tmp = k * (y * (b * -y4))
    else if (y2 <= 1.4d+67) then
        tmp = t_1
    else
        tmp = y4 * (t * ((b * j) - (c * 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 = y * (y3 * ((c * y4) - (a * y5)));
	double tmp;
	if (y2 <= -1.25e+137) {
		tmp = k * (y4 * (y1 * y2));
	} else if (y2 <= 1.8e-305) {
		tmp = t_1;
	} else if (y2 <= 5e-267) {
		tmp = k * (y * (b * -y4));
	} else if (y2 <= 1.4e+67) {
		tmp = t_1;
	} else {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y * (y3 * ((c * y4) - (a * y5)))
	tmp = 0
	if y2 <= -1.25e+137:
		tmp = k * (y4 * (y1 * y2))
	elif y2 <= 1.8e-305:
		tmp = t_1
	elif y2 <= 5e-267:
		tmp = k * (y * (b * -y4))
	elif y2 <= 1.4e+67:
		tmp = t_1
	else:
		tmp = y4 * (t * ((b * j) - (c * 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(y * Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))))
	tmp = 0.0
	if (y2 <= -1.25e+137)
		tmp = Float64(k * Float64(y4 * Float64(y1 * y2)));
	elseif (y2 <= 1.8e-305)
		tmp = t_1;
	elseif (y2 <= 5e-267)
		tmp = Float64(k * Float64(y * Float64(b * Float64(-y4))));
	elseif (y2 <= 1.4e+67)
		tmp = t_1;
	else
		tmp = Float64(y4 * Float64(t * Float64(Float64(b * j) - Float64(c * 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 = y * (y3 * ((c * y4) - (a * y5)));
	tmp = 0.0;
	if (y2 <= -1.25e+137)
		tmp = k * (y4 * (y1 * y2));
	elseif (y2 <= 1.8e-305)
		tmp = t_1;
	elseif (y2 <= 5e-267)
		tmp = k * (y * (b * -y4));
	elseif (y2 <= 1.4e+67)
		tmp = t_1;
	else
		tmp = y4 * (t * ((b * j) - (c * 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[(y * N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -1.25e+137], N[(k * N[(y4 * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.8e-305], t$95$1, If[LessEqual[y2, 5e-267], N[(k * N[(y * N[(b * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.4e+67], t$95$1, N[(y4 * N[(t * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y2 < -1.25e137

   1. Initial program 24.5%

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

   2. Taylor expanded in y4 around inf 57.1%

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

   3. Taylor expanded in y2 around inf 57.6%

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

   4. Taylor expanded in k around inf 46.8%

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

   if -1.25e137 < y2 < 1.80000000000000002e-305 or 4.9999999999999999e-267 < y2 < 1.3999999999999999e67

   1. Initial program 35.0%

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

   2. Taylor expanded in y0 around inf 36.5%

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

      1. *-commutative 36.5%

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

      2. *-commutative 36.5%

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

      3. *-commutative 36.5%

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

   4. Simplified 36.5%

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

   5. Taylor expanded in y around inf 38.9%

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

   if 1.80000000000000002e-305 < y2 < 4.9999999999999999e-267

   1. Initial program 45.1%

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

   2. Taylor expanded in y4 around inf 45.8%

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

   3. Taylor expanded in y around -inf 46.6%

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

      1. mul-1-neg 46.6%

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

      2. associate-*r* 46.6%

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

      3. *-commutative 46.6%

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

   5. Simplified 46.6%

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

   6. Taylor expanded in k around inf 55.1%

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

      1. *-commutative 55.1%

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

      2. associate-*l* 55.3%

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

   8. Simplified 55.3%

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

   if 1.3999999999999999e67 < y2

   1. Initial program 19.0%

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

   2. Taylor expanded in y4 around inf 30.6%

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

   3. Taylor expanded in t around inf 42.7%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b - c \cdot y2\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.25 \cdot 10^{+137}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 1.8 \cdot 10^{-305}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 5 \cdot 10^{-267}:\\ \;\;\;\;k \cdot \left(y \cdot \left(b \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 1.4 \cdot 10^{+67}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \end{array} \]

Alternative 22: 33.0% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ t_2 := y4 \cdot \left(y2 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{if}\;y2 \leq -2.2 \cdot 10^{+104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y2 \leq 5.2 \cdot 10^{-306}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq 5.8 \cdot 10^{-266}:\\ \;\;\;\;k \cdot \left(y \cdot \left(b \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 9.2 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y (* y3 (- (* c y4) (* a y5)))))
        (t_2 (* y4 (* y2 (- (* k y1) (* t c))))))
   (if (<= y2 -2.2e+104)
     t_2
     (if (<= y2 5.2e-306)
       t_1
       (if (<= y2 5.8e-266)
         (* k (* y (* b (- y4))))
         (if (<= y2 9.2e+49) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y * (y3 * ((c * y4) - (a * y5)));
	double t_2 = y4 * (y2 * ((k * y1) - (t * c)));
	double tmp;
	if (y2 <= -2.2e+104) {
		tmp = t_2;
	} else if (y2 <= 5.2e-306) {
		tmp = t_1;
	} else if (y2 <= 5.8e-266) {
		tmp = k * (y * (b * -y4));
	} else if (y2 <= 9.2e+49) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (y3 * ((c * y4) - (a * y5)))
    t_2 = y4 * (y2 * ((k * y1) - (t * c)))
    if (y2 <= (-2.2d+104)) then
        tmp = t_2
    else if (y2 <= 5.2d-306) then
        tmp = t_1
    else if (y2 <= 5.8d-266) then
        tmp = k * (y * (b * -y4))
    else if (y2 <= 9.2d+49) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y * (y3 * ((c * y4) - (a * y5)));
	double t_2 = y4 * (y2 * ((k * y1) - (t * c)));
	double tmp;
	if (y2 <= -2.2e+104) {
		tmp = t_2;
	} else if (y2 <= 5.2e-306) {
		tmp = t_1;
	} else if (y2 <= 5.8e-266) {
		tmp = k * (y * (b * -y4));
	} else if (y2 <= 9.2e+49) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y * (y3 * ((c * y4) - (a * y5)))
	t_2 = y4 * (y2 * ((k * y1) - (t * c)))
	tmp = 0
	if y2 <= -2.2e+104:
		tmp = t_2
	elif y2 <= 5.2e-306:
		tmp = t_1
	elif y2 <= 5.8e-266:
		tmp = k * (y * (b * -y4))
	elif y2 <= 9.2e+49:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y * Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))))
	t_2 = Float64(y4 * Float64(y2 * Float64(Float64(k * y1) - Float64(t * c))))
	tmp = 0.0
	if (y2 <= -2.2e+104)
		tmp = t_2;
	elseif (y2 <= 5.2e-306)
		tmp = t_1;
	elseif (y2 <= 5.8e-266)
		tmp = Float64(k * Float64(y * Float64(b * Float64(-y4))));
	elseif (y2 <= 9.2e+49)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y * (y3 * ((c * y4) - (a * y5)));
	t_2 = y4 * (y2 * ((k * y1) - (t * c)));
	tmp = 0.0;
	if (y2 <= -2.2e+104)
		tmp = t_2;
	elseif (y2 <= 5.2e-306)
		tmp = t_1;
	elseif (y2 <= 5.8e-266)
		tmp = k * (y * (b * -y4));
	elseif (y2 <= 9.2e+49)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y * N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y4 * N[(y2 * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -2.2e+104], t$95$2, If[LessEqual[y2, 5.2e-306], t$95$1, If[LessEqual[y2, 5.8e-266], N[(k * N[(y * N[(b * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 9.2e+49], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y2 < -2.2e104 or 9.20000000000000008e49 < y2

   1. Initial program 22.0%

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

   2. Taylor expanded in y4 around inf 40.1%

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

   3. Taylor expanded in y2 around inf 50.8%

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

   if -2.2e104 < y2 < 5.2000000000000001e-306 or 5.79999999999999991e-266 < y2 < 9.20000000000000008e49

   1. Initial program 35.1%

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

   2. Taylor expanded in y0 around inf 36.6%

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

      1. *-commutative 36.6%

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

      2. *-commutative 36.6%

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

      3. *-commutative 36.6%

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

   4. Simplified 36.6%

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

   5. Taylor expanded in y around inf 39.0%

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

   if 5.2000000000000001e-306 < y2 < 5.79999999999999991e-266

   1. Initial program 45.1%

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

   2. Taylor expanded in y4 around inf 45.8%

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

   3. Taylor expanded in y around -inf 46.6%

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

      1. mul-1-neg 46.6%

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

      2. associate-*r* 46.6%

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

      3. *-commutative 46.6%

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

   5. Simplified 46.6%

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

   6. Taylor expanded in k around inf 55.1%

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

      1. *-commutative 55.1%

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

      2. associate-*l* 55.3%

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

   8. Simplified 55.3%

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

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -2.2 \cdot 10^{+104}:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;y2 \leq 5.2 \cdot 10^{-306}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 5.8 \cdot 10^{-266}:\\ \;\;\;\;k \cdot \left(y \cdot \left(b \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 9.2 \cdot 10^{+49}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \end{array} \]

Alternative 23: 22.3% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ t_2 := k \cdot \left(y \cdot \left(b \cdot \left(-y4\right)\right)\right)\\ \mathbf{if}\;y2 \leq -1.22 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq -4.2 \cdot 10^{-214}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq 1.45 \cdot 10^{-270}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y2 \leq 3.55 \cdot 10^{-91}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq 1.25 \cdot 10^{+151}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (* y4 (* y1 y2)))) (t_2 (* k (* y (* b (- y4))))))
   (if (<= y2 -1.22e+36)
     t_1
     (if (<= y2 -4.2e-214)
       (* y4 (* b (* t j)))
       (if (<= y2 1.45e-270)
         t_2
         (if (<= y2 3.55e-91)
           (* y4 (* t (* b j)))
           (if (<= y2 1.25e+151) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (y4 * (y1 * y2));
	double t_2 = k * (y * (b * -y4));
	double tmp;
	if (y2 <= -1.22e+36) {
		tmp = t_1;
	} else if (y2 <= -4.2e-214) {
		tmp = y4 * (b * (t * j));
	} else if (y2 <= 1.45e-270) {
		tmp = t_2;
	} else if (y2 <= 3.55e-91) {
		tmp = y4 * (t * (b * j));
	} else if (y2 <= 1.25e+151) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = k * (y4 * (y1 * y2))
    t_2 = k * (y * (b * -y4))
    if (y2 <= (-1.22d+36)) then
        tmp = t_1
    else if (y2 <= (-4.2d-214)) then
        tmp = y4 * (b * (t * j))
    else if (y2 <= 1.45d-270) then
        tmp = t_2
    else if (y2 <= 3.55d-91) then
        tmp = y4 * (t * (b * j))
    else if (y2 <= 1.25d+151) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (y4 * (y1 * y2));
	double t_2 = k * (y * (b * -y4));
	double tmp;
	if (y2 <= -1.22e+36) {
		tmp = t_1;
	} else if (y2 <= -4.2e-214) {
		tmp = y4 * (b * (t * j));
	} else if (y2 <= 1.45e-270) {
		tmp = t_2;
	} else if (y2 <= 3.55e-91) {
		tmp = y4 * (t * (b * j));
	} else if (y2 <= 1.25e+151) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = k * (y4 * (y1 * y2))
	t_2 = k * (y * (b * -y4))
	tmp = 0
	if y2 <= -1.22e+36:
		tmp = t_1
	elif y2 <= -4.2e-214:
		tmp = y4 * (b * (t * j))
	elif y2 <= 1.45e-270:
		tmp = t_2
	elif y2 <= 3.55e-91:
		tmp = y4 * (t * (b * j))
	elif y2 <= 1.25e+151:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(k * Float64(y4 * Float64(y1 * y2)))
	t_2 = Float64(k * Float64(y * Float64(b * Float64(-y4))))
	tmp = 0.0
	if (y2 <= -1.22e+36)
		tmp = t_1;
	elseif (y2 <= -4.2e-214)
		tmp = Float64(y4 * Float64(b * Float64(t * j)));
	elseif (y2 <= 1.45e-270)
		tmp = t_2;
	elseif (y2 <= 3.55e-91)
		tmp = Float64(y4 * Float64(t * Float64(b * j)));
	elseif (y2 <= 1.25e+151)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = k * (y4 * (y1 * y2));
	t_2 = k * (y * (b * -y4));
	tmp = 0.0;
	if (y2 <= -1.22e+36)
		tmp = t_1;
	elseif (y2 <= -4.2e-214)
		tmp = y4 * (b * (t * j));
	elseif (y2 <= 1.45e-270)
		tmp = t_2;
	elseif (y2 <= 3.55e-91)
		tmp = y4 * (t * (b * j));
	elseif (y2 <= 1.25e+151)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(k * N[(y4 * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(y * N[(b * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -1.22e+36], t$95$1, If[LessEqual[y2, -4.2e-214], N[(y4 * N[(b * N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.45e-270], t$95$2, If[LessEqual[y2, 3.55e-91], N[(y4 * N[(t * N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.25e+151], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y2 < -1.21999999999999995e36 or 1.2500000000000001e151 < y2

   1. Initial program 25.3%

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

   2. Taylor expanded in y4 around inf 45.0%

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

   3. Taylor expanded in y2 around inf 51.4%

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

   4. Taylor expanded in k around inf 39.6%

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

   if -1.21999999999999995e36 < y2 < -4.19999999999999984e-214

   1. Initial program 30.8%

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

   3. Simplified 30.8%

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

   4. Taylor expanded in t around inf 26.0%

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

   5. Taylor expanded in j around inf 27.9%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 29.8%

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

      2. *-commutative 29.8%

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

      3. *-commutative 29.8%

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

   7. Simplified 29.8%

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

   8. Taylor expanded in y4 around inf 17.8%

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

      1. *-commutative 17.8%

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

      2. *-commutative 17.8%

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

      3. associate-*l* 21.7%

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

      4. *-commutative 21.7%

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

   10. Simplified 21.7%

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

   if -4.19999999999999984e-214 < y2 < 1.44999999999999991e-270 or 3.54999999999999995e-91 < y2 < 1.2500000000000001e151

   1. Initial program 34.0%

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

   2. Taylor expanded in y4 around inf 28.3%

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

   3. Taylor expanded in y around -inf 37.4%

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

      1. mul-1-neg 37.4%

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

      2. associate-*r* 35.3%

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

      3. *-commutative 35.3%

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

   5. Simplified 35.3%

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

   6. Taylor expanded in k around inf 31.1%

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

      1. *-commutative 31.1%

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

      2. associate-*l* 32.4%

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

   8. Simplified 32.4%

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

   if 1.44999999999999991e-270 < y2 < 3.54999999999999995e-91

   1. Initial program 34.3%

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

   3. Simplified 34.3%

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

   4. Taylor expanded in t around inf 37.3%

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

   5. Taylor expanded in j around inf 37.4%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 31.2%

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

      2. *-commutative 31.2%

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

      3. *-commutative 31.2%

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

   7. Simplified 31.2%

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

   8. Taylor expanded in y4 around inf 22.9%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 30.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.22 \cdot 10^{+36}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -4.2 \cdot 10^{-214}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq 1.45 \cdot 10^{-270}:\\ \;\;\;\;k \cdot \left(y \cdot \left(b \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 3.55 \cdot 10^{-91}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq 1.25 \cdot 10^{+151}:\\ \;\;\;\;k \cdot \left(y \cdot \left(b \cdot \left(-y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \end{array} \]

Alternative 24: 18.2% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq -1.76 \cdot 10^{+68}:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(t \cdot \left(-c\right)\right)\right)\\ \mathbf{elif}\;k \leq -2.1 \cdot 10^{-155}:\\ \;\;\;\;\left(t \cdot j\right) \cdot \left(y5 \cdot \left(-i\right)\right)\\ \mathbf{elif}\;k \leq -1.65 \cdot 10^{-280}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 2.1 \cdot 10^{-225}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j\right)\right)\\ \mathbf{elif}\;k \leq 2.2 \cdot 10^{-46}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(y \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot y4\right) \cdot \left(k \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= k -1.76e+68)
   (* y4 (* y2 (* t (- c))))
   (if (<= k -2.1e-155)
     (* (* t j) (* y5 (- i)))
     (if (<= k -1.65e-280)
       (* k (* y4 (* y1 y2)))
       (if (<= k 2.1e-225)
         (* y4 (* b (* t j)))
         (if (<= k 2.2e-46)
           (* a (* y5 (* y (- y3))))
           (* (* y y4) (* k (- b)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (k <= -1.76e+68) {
		tmp = y4 * (y2 * (t * -c));
	} else if (k <= -2.1e-155) {
		tmp = (t * j) * (y5 * -i);
	} else if (k <= -1.65e-280) {
		tmp = k * (y4 * (y1 * y2));
	} else if (k <= 2.1e-225) {
		tmp = y4 * (b * (t * j));
	} else if (k <= 2.2e-46) {
		tmp = a * (y5 * (y * -y3));
	} else {
		tmp = (y * y4) * (k * -b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (k <= (-1.76d+68)) then
        tmp = y4 * (y2 * (t * -c))
    else if (k <= (-2.1d-155)) then
        tmp = (t * j) * (y5 * -i)
    else if (k <= (-1.65d-280)) then
        tmp = k * (y4 * (y1 * y2))
    else if (k <= 2.1d-225) then
        tmp = y4 * (b * (t * j))
    else if (k <= 2.2d-46) then
        tmp = a * (y5 * (y * -y3))
    else
        tmp = (y * y4) * (k * -b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (k <= -1.76e+68) {
		tmp = y4 * (y2 * (t * -c));
	} else if (k <= -2.1e-155) {
		tmp = (t * j) * (y5 * -i);
	} else if (k <= -1.65e-280) {
		tmp = k * (y4 * (y1 * y2));
	} else if (k <= 2.1e-225) {
		tmp = y4 * (b * (t * j));
	} else if (k <= 2.2e-46) {
		tmp = a * (y5 * (y * -y3));
	} else {
		tmp = (y * y4) * (k * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if k <= -1.76e+68:
		tmp = y4 * (y2 * (t * -c))
	elif k <= -2.1e-155:
		tmp = (t * j) * (y5 * -i)
	elif k <= -1.65e-280:
		tmp = k * (y4 * (y1 * y2))
	elif k <= 2.1e-225:
		tmp = y4 * (b * (t * j))
	elif k <= 2.2e-46:
		tmp = a * (y5 * (y * -y3))
	else:
		tmp = (y * y4) * (k * -b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (k <= -1.76e+68)
		tmp = Float64(y4 * Float64(y2 * Float64(t * Float64(-c))));
	elseif (k <= -2.1e-155)
		tmp = Float64(Float64(t * j) * Float64(y5 * Float64(-i)));
	elseif (k <= -1.65e-280)
		tmp = Float64(k * Float64(y4 * Float64(y1 * y2)));
	elseif (k <= 2.1e-225)
		tmp = Float64(y4 * Float64(b * Float64(t * j)));
	elseif (k <= 2.2e-46)
		tmp = Float64(a * Float64(y5 * Float64(y * Float64(-y3))));
	else
		tmp = Float64(Float64(y * y4) * Float64(k * Float64(-b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (k <= -1.76e+68)
		tmp = y4 * (y2 * (t * -c));
	elseif (k <= -2.1e-155)
		tmp = (t * j) * (y5 * -i);
	elseif (k <= -1.65e-280)
		tmp = k * (y4 * (y1 * y2));
	elseif (k <= 2.1e-225)
		tmp = y4 * (b * (t * j));
	elseif (k <= 2.2e-46)
		tmp = a * (y5 * (y * -y3));
	else
		tmp = (y * y4) * (k * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[k, -1.76e+68], N[(y4 * N[(y2 * N[(t * (-c)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -2.1e-155], N[(N[(t * j), $MachinePrecision] * N[(y5 * (-i)), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -1.65e-280], N[(k * N[(y4 * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.1e-225], N[(y4 * N[(b * N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.2e-46], N[(a * N[(y5 * N[(y * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * y4), $MachinePrecision] * N[(k * (-b)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if k < -1.76e68

   1. Initial program 20.4%

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

   2. Taylor expanded in y4 around inf 26.9%

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

   3. Taylor expanded in y2 around inf 39.4%

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

   4. Taylor expanded in k around 0 29.8%

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

      1. neg-mul-1 29.8%

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

      2. distribute-rgt-neg-in 29.8%

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

   6. Simplified 29.8%

      \[\leadsto y4 \cdot \left(y2 \cdot \color{blue}{\left(c \cdot \left(-t\right)\right)}\right) \]

   if -1.76e68 < k < -2.1000000000000002e-155

   1. Initial program 38.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 38.2%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, -\mathsf{fma}\left(x, j, k \cdot \left(-z\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \mathsf{fma}\left(t, j, -y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \mathsf{fma}\left(y1, y4, y0 \cdot \left(-y5\right)\right)\right)} \]

   4. Taylor expanded in t around inf 47.9%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot t} \]

   5. Taylor expanded in j around inf 43.7%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 43.7%

         \[\leadsto \color{blue}{\left(t \cdot j\right) \cdot \left(y4 \cdot b - i \cdot y5\right)} \]

      2. *-commutative 43.7%

         \[\leadsto \color{blue}{\left(j \cdot t\right)} \cdot \left(y4 \cdot b - i \cdot y5\right) \]

      3. *-commutative 43.7%

         \[\leadsto \left(j \cdot t\right) \cdot \left(y4 \cdot b - \color{blue}{y5 \cdot i}\right) \]

   7. Simplified 43.7%

      \[\leadsto \color{blue}{\left(j \cdot t\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)} \]

   8. Taylor expanded in y4 around 0 41.5%

      \[\leadsto \left(j \cdot t\right) \cdot \color{blue}{\left(-1 \cdot \left(i \cdot y5\right)\right)} \]
   9. Step-by-step derivation

      1. neg-mul-1 41.5%

         \[\leadsto \left(j \cdot t\right) \cdot \color{blue}{\left(-i \cdot y5\right)} \]

      2. distribute-rgt-neg-in 41.5%

         \[\leadsto \left(j \cdot t\right) \cdot \color{blue}{\left(i \cdot \left(-y5\right)\right)} \]

   10. Simplified 41.5%

       \[\leadsto \left(j \cdot t\right) \cdot \color{blue}{\left(i \cdot \left(-y5\right)\right)} \]

   if -2.1000000000000002e-155 < k < -1.64999999999999995e-280

   1. Initial program 47.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf 20.8%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   3. Taylor expanded in y2 around inf 15.8%

      \[\leadsto \color{blue}{y4 \cdot \left(y2 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]

   4. Taylor expanded in k around inf 25.3%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]

   if -1.64999999999999995e-280 < k < 2.1e-225

   1. Initial program 33.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 33.8%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, -\mathsf{fma}\left(x, j, k \cdot \left(-z\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \mathsf{fma}\left(t, j, -y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \mathsf{fma}\left(y1, y4, y0 \cdot \left(-y5\right)\right)\right)} \]

   4. Taylor expanded in t around inf 34.2%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot t} \]

   5. Taylor expanded in j around inf 45.6%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 45.6%

         \[\leadsto \color{blue}{\left(t \cdot j\right) \cdot \left(y4 \cdot b - i \cdot y5\right)} \]

      2. *-commutative 45.6%

         \[\leadsto \color{blue}{\left(j \cdot t\right)} \cdot \left(y4 \cdot b - i \cdot y5\right) \]

      3. *-commutative 45.6%

         \[\leadsto \left(j \cdot t\right) \cdot \left(y4 \cdot b - \color{blue}{y5 \cdot i}\right) \]

   7. Simplified 45.6%

      \[\leadsto \color{blue}{\left(j \cdot t\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)} \]

   8. Taylor expanded in y4 around inf 40.3%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 40.3%

         \[\leadsto y4 \cdot \left(t \cdot \color{blue}{\left(b \cdot j\right)}\right) \]

      2. *-commutative 40.3%

         \[\leadsto y4 \cdot \color{blue}{\left(\left(b \cdot j\right) \cdot t\right)} \]

      3. associate-*l* 40.3%

         \[\leadsto y4 \cdot \color{blue}{\left(b \cdot \left(j \cdot t\right)\right)} \]

      4. *-commutative 40.3%

         \[\leadsto y4 \cdot \left(b \cdot \color{blue}{\left(t \cdot j\right)}\right) \]

   10. Simplified 40.3%

       \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(t \cdot j\right)\right)} \]

   if 2.1e-225 < k < 2.2000000000000001e-46

   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. Taylor expanded in y0 around inf 39.4%

      \[\leadsto \left(\color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. *-commutative 39.4%

         \[\leadsto \left(y0 \cdot \left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. *-commutative 39.4%

         \[\leadsto \left(y0 \cdot \left(c \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 39.4%

         \[\leadsto \left(y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - \color{blue}{b \cdot \left(j \cdot x - k \cdot z\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 39.4%

      \[\leadsto \left(\color{blue}{y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 37.1%

      \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)} \]

   6. Taylor expanded in t around 0 31.7%

      \[\leadsto a \cdot \left(\color{blue}{\left(-1 \cdot \left(y \cdot y3\right)\right)} \cdot y5\right) \]
   7. Step-by-step derivation

      1. neg-mul-1 31.7%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y \cdot y3\right)} \cdot y5\right) \]

      2. distribute-rgt-neg-in 31.7%

         \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot \left(-y3\right)\right)} \cdot y5\right) \]

   8. Simplified 31.7%

      \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot \left(-y3\right)\right)} \cdot y5\right) \]

   if 2.2000000000000001e-46 < k

   1. Initial program 26.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf 51.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   3. Taylor expanded in y around -inf 44.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y4 \cdot \left(y \cdot \left(k \cdot b - c \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 44.8%

         \[\leadsto \color{blue}{-y4 \cdot \left(y \cdot \left(k \cdot b - c \cdot y3\right)\right)} \]

      2. associate-*r* 44.6%

         \[\leadsto -\color{blue}{\left(y4 \cdot y\right) \cdot \left(k \cdot b - c \cdot y3\right)} \]

      3. *-commutative 44.6%

         \[\leadsto -\left(y4 \cdot y\right) \cdot \left(k \cdot b - \color{blue}{y3 \cdot c}\right) \]

   5. Simplified 44.6%

      \[\leadsto \color{blue}{-\left(y4 \cdot y\right) \cdot \left(k \cdot b - y3 \cdot c\right)} \]

   6. Taylor expanded in k around inf 37.2%

      \[\leadsto -\left(y4 \cdot y\right) \cdot \color{blue}{\left(k \cdot b\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 34.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.76 \cdot 10^{+68}:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(t \cdot \left(-c\right)\right)\right)\\ \mathbf{elif}\;k \leq -2.1 \cdot 10^{-155}:\\ \;\;\;\;\left(t \cdot j\right) \cdot \left(y5 \cdot \left(-i\right)\right)\\ \mathbf{elif}\;k \leq -1.65 \cdot 10^{-280}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 2.1 \cdot 10^{-225}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j\right)\right)\\ \mathbf{elif}\;k \leq 2.2 \cdot 10^{-46}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(y \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot y4\right) \cdot \left(k \cdot \left(-b\right)\right)\\ \end{array} \]

Alternative 25: 28.8% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -1.9 \cdot 10^{+173}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq 2.9 \cdot 10^{-84}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq 5.2 \cdot 10^{+143}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq 7.9 \cdot 10^{+180}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(k \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y1 -1.9e+173)
   (* k (* y4 (* y1 y2)))
   (if (<= y1 2.9e-84)
     (* c (* y4 (- (* y y3) (* t y2))))
     (if (<= y1 5.2e+143)
       (* a (* y5 (- (* t y2) (* y y3))))
       (if (<= y1 7.9e+180) (* c (* i (* z t))) (* y4 (* y2 (* k 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 (y1 <= -1.9e+173) {
		tmp = k * (y4 * (y1 * y2));
	} else if (y1 <= 2.9e-84) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (y1 <= 5.2e+143) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (y1 <= 7.9e+180) {
		tmp = c * (i * (z * t));
	} else {
		tmp = y4 * (y2 * (k * 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 (y1 <= (-1.9d+173)) then
        tmp = k * (y4 * (y1 * y2))
    else if (y1 <= 2.9d-84) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else if (y1 <= 5.2d+143) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else if (y1 <= 7.9d+180) then
        tmp = c * (i * (z * t))
    else
        tmp = y4 * (y2 * (k * 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 (y1 <= -1.9e+173) {
		tmp = k * (y4 * (y1 * y2));
	} else if (y1 <= 2.9e-84) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (y1 <= 5.2e+143) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (y1 <= 7.9e+180) {
		tmp = c * (i * (z * t));
	} else {
		tmp = y4 * (y2 * (k * 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 y1 <= -1.9e+173:
		tmp = k * (y4 * (y1 * y2))
	elif y1 <= 2.9e-84:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	elif y1 <= 5.2e+143:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	elif y1 <= 7.9e+180:
		tmp = c * (i * (z * t))
	else:
		tmp = y4 * (y2 * (k * 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 (y1 <= -1.9e+173)
		tmp = Float64(k * Float64(y4 * Float64(y1 * y2)));
	elseif (y1 <= 2.9e-84)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (y1 <= 5.2e+143)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (y1 <= 7.9e+180)
		tmp = Float64(c * Float64(i * Float64(z * t)));
	else
		tmp = Float64(y4 * Float64(y2 * Float64(k * 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 (y1 <= -1.9e+173)
		tmp = k * (y4 * (y1 * y2));
	elseif (y1 <= 2.9e-84)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	elseif (y1 <= 5.2e+143)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	elseif (y1 <= 7.9e+180)
		tmp = c * (i * (z * t));
	else
		tmp = y4 * (y2 * (k * 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[y1, -1.9e+173], N[(k * N[(y4 * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 2.9e-84], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 5.2e+143], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 7.9e+180], N[(c * N[(i * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y4 * N[(y2 * N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y1 < -1.90000000000000005e173

   1. Initial program 28.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf 47.5%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   3. Taylor expanded in y2 around inf 34.9%

      \[\leadsto \color{blue}{y4 \cdot \left(y2 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]

   4. Taylor expanded in k around inf 41.3%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]

   if -1.90000000000000005e173 < y1 < 2.90000000000000019e-84

   1. Initial program 31.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf 42.2%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   3. Taylor expanded in c around inf 32.6%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   if 2.90000000000000019e-84 < y1 < 5.1999999999999998e143

   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. Taylor expanded in y0 around inf 30.8%

      \[\leadsto \left(\color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. *-commutative 30.8%

         \[\leadsto \left(y0 \cdot \left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. *-commutative 30.8%

         \[\leadsto \left(y0 \cdot \left(c \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 30.8%

         \[\leadsto \left(y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - \color{blue}{b \cdot \left(j \cdot x - k \cdot z\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 30.8%

      \[\leadsto \left(\color{blue}{y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 33.8%

      \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)} \]

   if 5.1999999999999998e143 < y1 < 7.90000000000000012e180

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.0%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, -\mathsf{fma}\left(x, j, k \cdot \left(-z\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \mathsf{fma}\left(t, j, -y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \mathsf{fma}\left(y1, y4, y0 \cdot \left(-y5\right)\right)\right)} \]

   4. Taylor expanded in t around inf 51.5%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot t} \]

   5. Taylor expanded in z around inf 27.1%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 27.1%

         \[\leadsto \color{blue}{-t \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

      2. associate-*r* 38.1%

         \[\leadsto -\color{blue}{\left(t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right)} \]

   7. Simplified 38.1%

      \[\leadsto \color{blue}{-\left(t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right)} \]

   8. Taylor expanded in a around 0 38.7%

      \[\leadsto -\color{blue}{-1 \cdot \left(c \cdot \left(i \cdot \left(t \cdot z\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 38.7%

         \[\leadsto -\color{blue}{\left(-1 \cdot c\right) \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]

      2. neg-mul-1 38.7%

         \[\leadsto -\color{blue}{\left(-c\right)} \cdot \left(i \cdot \left(t \cdot z\right)\right) \]

   10. Simplified 38.7%

       \[\leadsto -\color{blue}{\left(-c\right) \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]

   if 7.90000000000000012e180 < y1

   1. Initial program 16.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf 56.3%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   3. Taylor expanded in y2 around inf 64.3%

      \[\leadsto \color{blue}{y4 \cdot \left(y2 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]

   4. Taylor expanded in k around inf 64.7%

      \[\leadsto y4 \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y1\right)}\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 37.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -1.9 \cdot 10^{+173}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq 2.9 \cdot 10^{-84}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq 5.2 \cdot 10^{+143}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq 7.9 \cdot 10^{+180}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(k \cdot y1\right)\right)\\ \end{array} \]

Alternative 26: 22.3% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(y4 \cdot \left(y \cdot \left(-b\right)\right)\right)\\ \mathbf{if}\;y \leq -7.8 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-181}:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(k \cdot y1\right)\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-236}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j\right)\right)\\ \mathbf{elif}\;y \leq 11:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (* y4 (* y (- b))))))
   (if (<= y -7.8e+21)
     t_1
     (if (<= y -1.3e-181)
       (* y4 (* y2 (* k y1)))
       (if (<= y 2.1e-236)
         (* y4 (* b (* t j)))
         (if (<= y 11.0) (* k (* y4 (* y1 y2))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (y4 * (y * -b));
	double tmp;
	if (y <= -7.8e+21) {
		tmp = t_1;
	} else if (y <= -1.3e-181) {
		tmp = y4 * (y2 * (k * y1));
	} else if (y <= 2.1e-236) {
		tmp = y4 * (b * (t * j));
	} else if (y <= 11.0) {
		tmp = k * (y4 * (y1 * y2));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = k * (y4 * (y * -b))
    if (y <= (-7.8d+21)) then
        tmp = t_1
    else if (y <= (-1.3d-181)) then
        tmp = y4 * (y2 * (k * y1))
    else if (y <= 2.1d-236) then
        tmp = y4 * (b * (t * j))
    else if (y <= 11.0d0) then
        tmp = k * (y4 * (y1 * y2))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (y4 * (y * -b));
	double tmp;
	if (y <= -7.8e+21) {
		tmp = t_1;
	} else if (y <= -1.3e-181) {
		tmp = y4 * (y2 * (k * y1));
	} else if (y <= 2.1e-236) {
		tmp = y4 * (b * (t * j));
	} else if (y <= 11.0) {
		tmp = k * (y4 * (y1 * y2));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = k * (y4 * (y * -b))
	tmp = 0
	if y <= -7.8e+21:
		tmp = t_1
	elif y <= -1.3e-181:
		tmp = y4 * (y2 * (k * y1))
	elif y <= 2.1e-236:
		tmp = y4 * (b * (t * j))
	elif y <= 11.0:
		tmp = k * (y4 * (y1 * y2))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(k * Float64(y4 * Float64(y * Float64(-b))))
	tmp = 0.0
	if (y <= -7.8e+21)
		tmp = t_1;
	elseif (y <= -1.3e-181)
		tmp = Float64(y4 * Float64(y2 * Float64(k * y1)));
	elseif (y <= 2.1e-236)
		tmp = Float64(y4 * Float64(b * Float64(t * j)));
	elseif (y <= 11.0)
		tmp = Float64(k * Float64(y4 * Float64(y1 * y2)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = k * (y4 * (y * -b));
	tmp = 0.0;
	if (y <= -7.8e+21)
		tmp = t_1;
	elseif (y <= -1.3e-181)
		tmp = y4 * (y2 * (k * y1));
	elseif (y <= 2.1e-236)
		tmp = y4 * (b * (t * j));
	elseif (y <= 11.0)
		tmp = k * (y4 * (y1 * y2));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(k * N[(y4 * N[(y * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.8e+21], t$95$1, If[LessEqual[y, -1.3e-181], N[(y4 * N[(y2 * N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e-236], N[(y4 * N[(b * N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 11.0], N[(k * N[(y4 * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.8e21 or 11 < y

   1. Initial program 24.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf 37.3%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   3. Taylor expanded in y around -inf 43.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y4 \cdot \left(y \cdot \left(k \cdot b - c \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 43.7%

         \[\leadsto \color{blue}{-y4 \cdot \left(y \cdot \left(k \cdot b - c \cdot y3\right)\right)} \]

      2. associate-*r* 41.1%

         \[\leadsto -\color{blue}{\left(y4 \cdot y\right) \cdot \left(k \cdot b - c \cdot y3\right)} \]

      3. *-commutative 41.1%

         \[\leadsto -\left(y4 \cdot y\right) \cdot \left(k \cdot b - \color{blue}{y3 \cdot c}\right) \]

   5. Simplified 41.1%

      \[\leadsto \color{blue}{-\left(y4 \cdot y\right) \cdot \left(k \cdot b - y3 \cdot c\right)} \]

   6. Taylor expanded in k around inf 31.3%

      \[\leadsto -\color{blue}{k \cdot \left(y4 \cdot \left(y \cdot b\right)\right)} \]

   if -7.8e21 < y < -1.29999999999999999e-181

   1. Initial program 42.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf 38.0%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   3. Taylor expanded in y2 around inf 35.2%

      \[\leadsto \color{blue}{y4 \cdot \left(y2 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]

   4. Taylor expanded in k around inf 30.0%

      \[\leadsto y4 \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y1\right)}\right) \]

   if -1.29999999999999999e-181 < y < 2.09999999999999979e-236

   1. Initial program 43.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 43.3%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, -\mathsf{fma}\left(x, j, k \cdot \left(-z\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \mathsf{fma}\left(t, j, -y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \mathsf{fma}\left(y1, y4, y0 \cdot \left(-y5\right)\right)\right)} \]

   4. Taylor expanded in t around inf 38.5%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot t} \]

   5. Taylor expanded in j around inf 38.7%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 36.0%

         \[\leadsto \color{blue}{\left(t \cdot j\right) \cdot \left(y4 \cdot b - i \cdot y5\right)} \]

      2. *-commutative 36.0%

         \[\leadsto \color{blue}{\left(j \cdot t\right)} \cdot \left(y4 \cdot b - i \cdot y5\right) \]

      3. *-commutative 36.0%

         \[\leadsto \left(j \cdot t\right) \cdot \left(y4 \cdot b - \color{blue}{y5 \cdot i}\right) \]

   7. Simplified 36.0%

      \[\leadsto \color{blue}{\left(j \cdot t\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)} \]

   8. Taylor expanded in y4 around inf 28.0%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 28.0%

         \[\leadsto y4 \cdot \left(t \cdot \color{blue}{\left(b \cdot j\right)}\right) \]

      2. *-commutative 28.0%

         \[\leadsto y4 \cdot \color{blue}{\left(\left(b \cdot j\right) \cdot t\right)} \]

      3. associate-*l* 30.8%

         \[\leadsto y4 \cdot \color{blue}{\left(b \cdot \left(j \cdot t\right)\right)} \]

      4. *-commutative 30.8%

         \[\leadsto y4 \cdot \left(b \cdot \color{blue}{\left(t \cdot j\right)}\right) \]

   10. Simplified 30.8%

       \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(t \cdot j\right)\right)} \]

   if 2.09999999999999979e-236 < y < 11

   1. Initial program 30.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf 40.8%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   3. Taylor expanded in y2 around inf 33.4%

      \[\leadsto \color{blue}{y4 \cdot \left(y2 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]

   4. Taylor expanded in k around inf 27.4%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 30.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+21}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-181}:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(k \cdot y1\right)\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-236}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j\right)\right)\\ \mathbf{elif}\;y \leq 11:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y \cdot \left(-b\right)\right)\right)\\ \end{array} \]

Alternative 27: 20.9% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -1.1 \cdot 10^{+172}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -3.6 \cdot 10^{-14} \lor \neg \left(y1 \leq -1 \cdot 10^{-213}\right) \land y1 \leq 2.75 \cdot 10^{+63}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(k \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y1 -1.1e+172)
   (* k (* y4 (* y1 y2)))
   (if (or (<= y1 -3.6e-14) (and (not (<= y1 -1e-213)) (<= y1 2.75e+63)))
     (* y4 (* b (* t j)))
     (* y4 (* y2 (* k 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 (y1 <= -1.1e+172) {
		tmp = k * (y4 * (y1 * y2));
	} else if ((y1 <= -3.6e-14) || (!(y1 <= -1e-213) && (y1 <= 2.75e+63))) {
		tmp = y4 * (b * (t * j));
	} else {
		tmp = y4 * (y2 * (k * 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 (y1 <= (-1.1d+172)) then
        tmp = k * (y4 * (y1 * y2))
    else if ((y1 <= (-3.6d-14)) .or. (.not. (y1 <= (-1d-213))) .and. (y1 <= 2.75d+63)) then
        tmp = y4 * (b * (t * j))
    else
        tmp = y4 * (y2 * (k * 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 (y1 <= -1.1e+172) {
		tmp = k * (y4 * (y1 * y2));
	} else if ((y1 <= -3.6e-14) || (!(y1 <= -1e-213) && (y1 <= 2.75e+63))) {
		tmp = y4 * (b * (t * j));
	} else {
		tmp = y4 * (y2 * (k * 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 y1 <= -1.1e+172:
		tmp = k * (y4 * (y1 * y2))
	elif (y1 <= -3.6e-14) or (not (y1 <= -1e-213) and (y1 <= 2.75e+63)):
		tmp = y4 * (b * (t * j))
	else:
		tmp = y4 * (y2 * (k * 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 (y1 <= -1.1e+172)
		tmp = Float64(k * Float64(y4 * Float64(y1 * y2)));
	elseif ((y1 <= -3.6e-14) || (!(y1 <= -1e-213) && (y1 <= 2.75e+63)))
		tmp = Float64(y4 * Float64(b * Float64(t * j)));
	else
		tmp = Float64(y4 * Float64(y2 * Float64(k * 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 (y1 <= -1.1e+172)
		tmp = k * (y4 * (y1 * y2));
	elseif ((y1 <= -3.6e-14) || (~((y1 <= -1e-213)) && (y1 <= 2.75e+63)))
		tmp = y4 * (b * (t * j));
	else
		tmp = y4 * (y2 * (k * 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[y1, -1.1e+172], N[(k * N[(y4 * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y1, -3.6e-14], And[N[Not[LessEqual[y1, -1e-213]], $MachinePrecision], LessEqual[y1, 2.75e+63]]], N[(y4 * N[(b * N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y4 * N[(y2 * N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y1 < -1.1000000000000001e172

   1. Initial program 27.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf 49.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   3. Taylor expanded in y2 around inf 34.0%

      \[\leadsto \color{blue}{y4 \cdot \left(y2 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]

   4. Taylor expanded in k around inf 40.1%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]

   if -1.1000000000000001e172 < y1 < -3.5999999999999998e-14 or -9.9999999999999995e-214 < y1 < 2.75000000000000002e63

   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%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, -\mathsf{fma}\left(x, j, k \cdot \left(-z\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \mathsf{fma}\left(t, j, -y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \mathsf{fma}\left(y1, y4, y0 \cdot \left(-y5\right)\right)\right)} \]

   4. Taylor expanded in t around inf 38.6%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot t} \]

   5. Taylor expanded in j around inf 30.9%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 29.4%

         \[\leadsto \color{blue}{\left(t \cdot j\right) \cdot \left(y4 \cdot b - i \cdot y5\right)} \]

      2. *-commutative 29.4%

         \[\leadsto \color{blue}{\left(j \cdot t\right)} \cdot \left(y4 \cdot b - i \cdot y5\right) \]

      3. *-commutative 29.4%

         \[\leadsto \left(j \cdot t\right) \cdot \left(y4 \cdot b - \color{blue}{y5 \cdot i}\right) \]

   7. Simplified 29.4%

      \[\leadsto \color{blue}{\left(j \cdot t\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)} \]

   8. Taylor expanded in y4 around inf 21.4%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 21.4%

         \[\leadsto y4 \cdot \left(t \cdot \color{blue}{\left(b \cdot j\right)}\right) \]

      2. *-commutative 21.4%

         \[\leadsto y4 \cdot \color{blue}{\left(\left(b \cdot j\right) \cdot t\right)} \]

      3. associate-*l* 22.8%

         \[\leadsto y4 \cdot \color{blue}{\left(b \cdot \left(j \cdot t\right)\right)} \]

      4. *-commutative 22.8%

         \[\leadsto y4 \cdot \left(b \cdot \color{blue}{\left(t \cdot j\right)}\right) \]

   10. Simplified 22.8%

       \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(t \cdot j\right)\right)} \]

   if -3.5999999999999998e-14 < y1 < -9.9999999999999995e-214 or 2.75000000000000002e63 < y1

   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. Taylor expanded in y4 around inf 41.5%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   3. Taylor expanded in y2 around inf 38.4%

      \[\leadsto \color{blue}{y4 \cdot \left(y2 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]

   4. Taylor expanded in k around inf 30.6%

      \[\leadsto y4 \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y1\right)}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 27.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -1.1 \cdot 10^{+172}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -3.6 \cdot 10^{-14} \lor \neg \left(y1 \leq -1 \cdot 10^{-213}\right) \land y1 \leq 2.75 \cdot 10^{+63}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(k \cdot y1\right)\right)\\ \end{array} \]

Alternative 28: 20.1% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)\\ \mathbf{if}\;y5 \leq -2.1 \cdot 10^{+80}:\\ \;\;\;\;y2 \cdot \left(a \cdot \left(t \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq 4.9 \cdot 10^{-119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y5 \leq 4 \cdot 10^{+16}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 1.15 \cdot 10^{+197}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(k \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y4 (* t (* b j)))))
   (if (<= y5 -2.1e+80)
     (* y2 (* a (* t y5)))
     (if (<= y5 4.9e-119)
       t_1
       (if (<= y5 4e+16)
         (* k (* y4 (* y1 y2)))
         (if (<= y5 1.15e+197) t_1 (* y4 (* y2 (* k y1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * (t * (b * j));
	double tmp;
	if (y5 <= -2.1e+80) {
		tmp = y2 * (a * (t * y5));
	} else if (y5 <= 4.9e-119) {
		tmp = t_1;
	} else if (y5 <= 4e+16) {
		tmp = k * (y4 * (y1 * y2));
	} else if (y5 <= 1.15e+197) {
		tmp = t_1;
	} else {
		tmp = y4 * (y2 * (k * y1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y4 * (t * (b * j))
    if (y5 <= (-2.1d+80)) then
        tmp = y2 * (a * (t * y5))
    else if (y5 <= 4.9d-119) then
        tmp = t_1
    else if (y5 <= 4d+16) then
        tmp = k * (y4 * (y1 * y2))
    else if (y5 <= 1.15d+197) then
        tmp = t_1
    else
        tmp = y4 * (y2 * (k * y1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * (t * (b * j));
	double tmp;
	if (y5 <= -2.1e+80) {
		tmp = y2 * (a * (t * y5));
	} else if (y5 <= 4.9e-119) {
		tmp = t_1;
	} else if (y5 <= 4e+16) {
		tmp = k * (y4 * (y1 * y2));
	} else if (y5 <= 1.15e+197) {
		tmp = t_1;
	} else {
		tmp = y4 * (y2 * (k * y1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y4 * (t * (b * j))
	tmp = 0
	if y5 <= -2.1e+80:
		tmp = y2 * (a * (t * y5))
	elif y5 <= 4.9e-119:
		tmp = t_1
	elif y5 <= 4e+16:
		tmp = k * (y4 * (y1 * y2))
	elif y5 <= 1.15e+197:
		tmp = t_1
	else:
		tmp = y4 * (y2 * (k * y1))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y4 * Float64(t * Float64(b * j)))
	tmp = 0.0
	if (y5 <= -2.1e+80)
		tmp = Float64(y2 * Float64(a * Float64(t * y5)));
	elseif (y5 <= 4.9e-119)
		tmp = t_1;
	elseif (y5 <= 4e+16)
		tmp = Float64(k * Float64(y4 * Float64(y1 * y2)));
	elseif (y5 <= 1.15e+197)
		tmp = t_1;
	else
		tmp = Float64(y4 * Float64(y2 * Float64(k * y1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y4 * (t * (b * j));
	tmp = 0.0;
	if (y5 <= -2.1e+80)
		tmp = y2 * (a * (t * y5));
	elseif (y5 <= 4.9e-119)
		tmp = t_1;
	elseif (y5 <= 4e+16)
		tmp = k * (y4 * (y1 * y2));
	elseif (y5 <= 1.15e+197)
		tmp = t_1;
	else
		tmp = y4 * (y2 * (k * y1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y4 * N[(t * N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -2.1e+80], N[(y2 * N[(a * N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 4.9e-119], t$95$1, If[LessEqual[y5, 4e+16], N[(k * N[(y4 * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.15e+197], t$95$1, N[(y4 * N[(y2 * N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y5 < -2.10000000000000001e80

   1. Initial program 32.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y0 around inf 28.5%

      \[\leadsto \left(\color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. *-commutative 28.5%

         \[\leadsto \left(y0 \cdot \left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. *-commutative 28.5%

         \[\leadsto \left(y0 \cdot \left(c \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 28.5%

         \[\leadsto \left(y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - \color{blue}{b \cdot \left(j \cdot x - k \cdot z\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 28.5%

      \[\leadsto \left(\color{blue}{y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 40.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)} \]

   6. Taylor expanded in t around inf 34.1%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 38.1%

         \[\leadsto a \cdot \color{blue}{\left(\left(t \cdot y5\right) \cdot y2\right)} \]

      2. associate-*r* 40.1%

         \[\leadsto \color{blue}{\left(a \cdot \left(t \cdot y5\right)\right) \cdot y2} \]

      3. *-commutative 40.1%

         \[\leadsto \left(a \cdot \color{blue}{\left(y5 \cdot t\right)}\right) \cdot y2 \]

   8. Simplified 40.1%

      \[\leadsto \color{blue}{\left(a \cdot \left(y5 \cdot t\right)\right) \cdot y2} \]

   if -2.10000000000000001e80 < y5 < 4.9e-119 or 4e16 < y5 < 1.15e197

   1. Initial program 30.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.7%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, -\mathsf{fma}\left(x, j, k \cdot \left(-z\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \mathsf{fma}\left(t, j, -y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \mathsf{fma}\left(y1, y4, y0 \cdot \left(-y5\right)\right)\right)} \]

   4. Taylor expanded in t around inf 32.3%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot t} \]

   5. Taylor expanded in j around inf 24.2%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 24.1%

         \[\leadsto \color{blue}{\left(t \cdot j\right) \cdot \left(y4 \cdot b - i \cdot y5\right)} \]

      2. *-commutative 24.1%

         \[\leadsto \color{blue}{\left(j \cdot t\right)} \cdot \left(y4 \cdot b - i \cdot y5\right) \]

      3. *-commutative 24.1%

         \[\leadsto \left(j \cdot t\right) \cdot \left(y4 \cdot b - \color{blue}{y5 \cdot i}\right) \]

   7. Simplified 24.1%

      \[\leadsto \color{blue}{\left(j \cdot t\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)} \]

   8. Taylor expanded in y4 around inf 20.9%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b\right)\right)} \]

   if 4.9e-119 < y5 < 4e16

   1. Initial program 38.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf 45.8%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   3. Taylor expanded in y2 around inf 36.3%

      \[\leadsto \color{blue}{y4 \cdot \left(y2 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]

   4. Taylor expanded in k around inf 39.5%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]

   if 1.15e197 < y5

   1. Initial program 20.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf 44.7%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   3. Taylor expanded in y2 around inf 37.0%

      \[\leadsto \color{blue}{y4 \cdot \left(y2 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]

   4. Taylor expanded in k around inf 41.0%

      \[\leadsto y4 \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y1\right)}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 28.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -2.1 \cdot 10^{+80}:\\ \;\;\;\;y2 \cdot \left(a \cdot \left(t \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq 4.9 \cdot 10^{-119}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq 4 \cdot 10^{+16}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 1.15 \cdot 10^{+197}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(k \cdot y1\right)\right)\\ \end{array} \]

Alternative 29: 18.7% accurate, 6.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq -5.2 \cdot 10^{+74}:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(t \cdot \left(-c\right)\right)\right)\\ \mathbf{elif}\;k \leq -2.65 \cdot 10^{-244}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;k \leq 8.2 \cdot 10^{-47}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(y \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot y4\right) \cdot \left(k \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= k -5.2e+74)
   (* y4 (* y2 (* t (- c))))
   (if (<= k -2.65e-244)
     (* (* t a) (* z (- b)))
     (if (<= k 8.2e-47) (* a (* y5 (* y (- y3)))) (* (* y y4) (* k (- b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (k <= -5.2e+74) {
		tmp = y4 * (y2 * (t * -c));
	} else if (k <= -2.65e-244) {
		tmp = (t * a) * (z * -b);
	} else if (k <= 8.2e-47) {
		tmp = a * (y5 * (y * -y3));
	} else {
		tmp = (y * y4) * (k * -b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (k <= (-5.2d+74)) then
        tmp = y4 * (y2 * (t * -c))
    else if (k <= (-2.65d-244)) then
        tmp = (t * a) * (z * -b)
    else if (k <= 8.2d-47) then
        tmp = a * (y5 * (y * -y3))
    else
        tmp = (y * y4) * (k * -b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (k <= -5.2e+74) {
		tmp = y4 * (y2 * (t * -c));
	} else if (k <= -2.65e-244) {
		tmp = (t * a) * (z * -b);
	} else if (k <= 8.2e-47) {
		tmp = a * (y5 * (y * -y3));
	} else {
		tmp = (y * y4) * (k * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if k <= -5.2e+74:
		tmp = y4 * (y2 * (t * -c))
	elif k <= -2.65e-244:
		tmp = (t * a) * (z * -b)
	elif k <= 8.2e-47:
		tmp = a * (y5 * (y * -y3))
	else:
		tmp = (y * y4) * (k * -b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (k <= -5.2e+74)
		tmp = Float64(y4 * Float64(y2 * Float64(t * Float64(-c))));
	elseif (k <= -2.65e-244)
		tmp = Float64(Float64(t * a) * Float64(z * Float64(-b)));
	elseif (k <= 8.2e-47)
		tmp = Float64(a * Float64(y5 * Float64(y * Float64(-y3))));
	else
		tmp = Float64(Float64(y * y4) * Float64(k * Float64(-b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (k <= -5.2e+74)
		tmp = y4 * (y2 * (t * -c));
	elseif (k <= -2.65e-244)
		tmp = (t * a) * (z * -b);
	elseif (k <= 8.2e-47)
		tmp = a * (y5 * (y * -y3));
	else
		tmp = (y * y4) * (k * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[k, -5.2e+74], N[(y4 * N[(y2 * N[(t * (-c)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -2.65e-244], N[(N[(t * a), $MachinePrecision] * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 8.2e-47], N[(a * N[(y5 * N[(y * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * y4), $MachinePrecision] * N[(k * (-b)), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if k < -5.2000000000000001e74

   1. Initial program 19.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf 23.8%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   3. Taylor expanded in y2 around inf 36.9%

      \[\leadsto \color{blue}{y4 \cdot \left(y2 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]

   4. Taylor expanded in k around 0 30.9%

      \[\leadsto y4 \cdot \left(y2 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot t\right)\right)}\right) \]
   5. Step-by-step derivation

      1. neg-mul-1 30.9%

         \[\leadsto y4 \cdot \left(y2 \cdot \color{blue}{\left(-c \cdot t\right)}\right) \]

      2. distribute-rgt-neg-in 30.9%

         \[\leadsto y4 \cdot \left(y2 \cdot \color{blue}{\left(c \cdot \left(-t\right)\right)}\right) \]

   6. Simplified 30.9%

      \[\leadsto y4 \cdot \left(y2 \cdot \color{blue}{\left(c \cdot \left(-t\right)\right)}\right) \]

   if -5.2000000000000001e74 < k < -2.6500000000000001e-244

   1. Initial program 42.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 42.2%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, -\mathsf{fma}\left(x, j, k \cdot \left(-z\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \mathsf{fma}\left(t, j, -y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \mathsf{fma}\left(y1, y4, y0 \cdot \left(-y5\right)\right)\right)} \]

   4. Taylor expanded in t around inf 47.4%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot t} \]

   5. Taylor expanded in z around inf 35.1%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 35.1%

         \[\leadsto \color{blue}{-t \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

      2. associate-*r* 34.9%

         \[\leadsto -\color{blue}{\left(t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right)} \]

   7. Simplified 34.9%

      \[\leadsto \color{blue}{-\left(t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right)} \]

   8. Taylor expanded in a around inf 21.8%

      \[\leadsto -\color{blue}{a \cdot \left(t \cdot \left(z \cdot b\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 28.1%

         \[\leadsto -\color{blue}{\left(a \cdot t\right) \cdot \left(z \cdot b\right)} \]

      2. *-commutative 28.1%

         \[\leadsto -\left(a \cdot t\right) \cdot \color{blue}{\left(b \cdot z\right)} \]

   10. Simplified 28.1%

       \[\leadsto -\color{blue}{\left(a \cdot t\right) \cdot \left(b \cdot z\right)} \]

   if -2.6500000000000001e-244 < k < 8.20000000000000003e-47

   1. Initial program 33.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y0 around inf 35.0%

      \[\leadsto \left(\color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. *-commutative 35.0%

         \[\leadsto \left(y0 \cdot \left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. *-commutative 35.0%

         \[\leadsto \left(y0 \cdot \left(c \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 35.0%

         \[\leadsto \left(y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - \color{blue}{b \cdot \left(j \cdot x - k \cdot z\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 35.0%

      \[\leadsto \left(\color{blue}{y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 31.1%

      \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)} \]

   6. Taylor expanded in t around 0 26.3%

      \[\leadsto a \cdot \left(\color{blue}{\left(-1 \cdot \left(y \cdot y3\right)\right)} \cdot y5\right) \]
   7. Step-by-step derivation

      1. neg-mul-1 26.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y \cdot y3\right)} \cdot y5\right) \]

      2. distribute-rgt-neg-in 26.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot \left(-y3\right)\right)} \cdot y5\right) \]

   8. Simplified 26.3%

      \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot \left(-y3\right)\right)} \cdot y5\right) \]

   if 8.20000000000000003e-47 < k

   1. Initial program 26.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf 51.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   3. Taylor expanded in y around -inf 44.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y4 \cdot \left(y \cdot \left(k \cdot b - c \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 44.8%

         \[\leadsto \color{blue}{-y4 \cdot \left(y \cdot \left(k \cdot b - c \cdot y3\right)\right)} \]

      2. associate-*r* 44.6%

         \[\leadsto -\color{blue}{\left(y4 \cdot y\right) \cdot \left(k \cdot b - c \cdot y3\right)} \]

      3. *-commutative 44.6%

         \[\leadsto -\left(y4 \cdot y\right) \cdot \left(k \cdot b - \color{blue}{y3 \cdot c}\right) \]

   5. Simplified 44.6%

      \[\leadsto \color{blue}{-\left(y4 \cdot y\right) \cdot \left(k \cdot b - y3 \cdot c\right)} \]

   6. Taylor expanded in k around inf 37.2%

      \[\leadsto -\left(y4 \cdot y\right) \cdot \color{blue}{\left(k \cdot b\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 31.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -5.2 \cdot 10^{+74}:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(t \cdot \left(-c\right)\right)\right)\\ \mathbf{elif}\;k \leq -2.65 \cdot 10^{-244}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;k \leq 8.2 \cdot 10^{-47}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(y \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot y4\right) \cdot \left(k \cdot \left(-b\right)\right)\\ \end{array} \]

Alternative 30: 22.3% accurate, 7.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y5 \leq -6.8 \cdot 10^{+78}:\\ \;\;\;\;y2 \cdot \left(a \cdot \left(t \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq 1.25 \cdot 10^{+118}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y \cdot \left(-b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y \cdot \left(y3 \cdot \left(-y5\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y5 -6.8e+78)
   (* y2 (* a (* t y5)))
   (if (<= y5 1.25e+118) (* k (* y4 (* y (- b)))) (* a (* y (* 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 (y5 <= -6.8e+78) {
		tmp = y2 * (a * (t * y5));
	} else if (y5 <= 1.25e+118) {
		tmp = k * (y4 * (y * -b));
	} else {
		tmp = a * (y * (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 (y5 <= (-6.8d+78)) then
        tmp = y2 * (a * (t * y5))
    else if (y5 <= 1.25d+118) then
        tmp = k * (y4 * (y * -b))
    else
        tmp = a * (y * (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 (y5 <= -6.8e+78) {
		tmp = y2 * (a * (t * y5));
	} else if (y5 <= 1.25e+118) {
		tmp = k * (y4 * (y * -b));
	} else {
		tmp = a * (y * (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 y5 <= -6.8e+78:
		tmp = y2 * (a * (t * y5))
	elif y5 <= 1.25e+118:
		tmp = k * (y4 * (y * -b))
	else:
		tmp = a * (y * (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 (y5 <= -6.8e+78)
		tmp = Float64(y2 * Float64(a * Float64(t * y5)));
	elseif (y5 <= 1.25e+118)
		tmp = Float64(k * Float64(y4 * Float64(y * Float64(-b))));
	else
		tmp = Float64(a * Float64(y * Float64(y3 * Float64(-y5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y5 <= -6.8e+78)
		tmp = y2 * (a * (t * y5));
	elseif (y5 <= 1.25e+118)
		tmp = k * (y4 * (y * -b));
	else
		tmp = a * (y * (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[y5, -6.8e+78], N[(y2 * N[(a * N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.25e+118], N[(k * N[(y4 * N[(y * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y * N[(y3 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y5 < -6.80000000000000014e78

   1. Initial program 32.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y0 around inf 28.5%

      \[\leadsto \left(\color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. *-commutative 28.5%

         \[\leadsto \left(y0 \cdot \left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. *-commutative 28.5%

         \[\leadsto \left(y0 \cdot \left(c \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 28.5%

         \[\leadsto \left(y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - \color{blue}{b \cdot \left(j \cdot x - k \cdot z\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 28.5%

      \[\leadsto \left(\color{blue}{y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 40.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)} \]

   6. Taylor expanded in t around inf 34.1%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 38.1%

         \[\leadsto a \cdot \color{blue}{\left(\left(t \cdot y5\right) \cdot y2\right)} \]

      2. associate-*r* 40.1%

         \[\leadsto \color{blue}{\left(a \cdot \left(t \cdot y5\right)\right) \cdot y2} \]

      3. *-commutative 40.1%

         \[\leadsto \left(a \cdot \color{blue}{\left(y5 \cdot t\right)}\right) \cdot y2 \]

   8. Simplified 40.1%

      \[\leadsto \color{blue}{\left(a \cdot \left(y5 \cdot t\right)\right) \cdot y2} \]

   if -6.80000000000000014e78 < y5 < 1.24999999999999993e118

   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. Taylor expanded in y4 around inf 39.3%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   3. Taylor expanded in y around -inf 34.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y4 \cdot \left(y \cdot \left(k \cdot b - c \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 34.8%

         \[\leadsto \color{blue}{-y4 \cdot \left(y \cdot \left(k \cdot b - c \cdot y3\right)\right)} \]

      2. associate-*r* 31.5%

         \[\leadsto -\color{blue}{\left(y4 \cdot y\right) \cdot \left(k \cdot b - c \cdot y3\right)} \]

      3. *-commutative 31.5%

         \[\leadsto -\left(y4 \cdot y\right) \cdot \left(k \cdot b - \color{blue}{y3 \cdot c}\right) \]

   5. Simplified 31.5%

      \[\leadsto \color{blue}{-\left(y4 \cdot y\right) \cdot \left(k \cdot b - y3 \cdot c\right)} \]

   6. Taylor expanded in k around inf 22.5%

      \[\leadsto -\color{blue}{k \cdot \left(y4 \cdot \left(y \cdot b\right)\right)} \]

   if 1.24999999999999993e118 < y5

   1. Initial program 27.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y0 around inf 42.9%

      \[\leadsto \left(\color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. *-commutative 42.9%

         \[\leadsto \left(y0 \cdot \left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. *-commutative 42.9%

         \[\leadsto \left(y0 \cdot \left(c \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 42.9%

         \[\leadsto \left(y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - \color{blue}{b \cdot \left(j \cdot x - k \cdot z\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 42.9%

      \[\leadsto \left(\color{blue}{y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 45.9%

      \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)} \]

   6. Taylor expanded in t around 0 41.0%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 41.0%

         \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot y\right) \cdot \left(y3 \cdot y5\right)\right)} \]

      2. neg-mul-1 41.0%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y\right)} \cdot \left(y3 \cdot y5\right)\right) \]

   8. Simplified 41.0%

      \[\leadsto a \cdot \color{blue}{\left(\left(-y\right) \cdot \left(y3 \cdot y5\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 28.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -6.8 \cdot 10^{+78}:\\ \;\;\;\;y2 \cdot \left(a \cdot \left(t \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq 1.25 \cdot 10^{+118}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y \cdot \left(-b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y \cdot \left(y3 \cdot \left(-y5\right)\right)\right)\\ \end{array} \]

Alternative 31: 22.0% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -8.5 \cdot 10^{+109} \lor \neg \left(y1 \leq 1.16 \cdot 10^{+63}\right):\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= y1 -8.5e+109) (not (<= y1 1.16e+63)))
   (* k (* y4 (* y1 y2)))
   (* a (* t (* y2 y5)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y1 <= -8.5e+109) || !(y1 <= 1.16e+63)) {
		tmp = k * (y4 * (y1 * y2));
	} else {
		tmp = a * (t * (y2 * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((y1 <= (-8.5d+109)) .or. (.not. (y1 <= 1.16d+63))) then
        tmp = k * (y4 * (y1 * y2))
    else
        tmp = a * (t * (y2 * y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y1 <= -8.5e+109) || !(y1 <= 1.16e+63)) {
		tmp = k * (y4 * (y1 * y2));
	} else {
		tmp = a * (t * (y2 * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (y1 <= -8.5e+109) or not (y1 <= 1.16e+63):
		tmp = k * (y4 * (y1 * y2))
	else:
		tmp = a * (t * (y2 * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((y1 <= -8.5e+109) || !(y1 <= 1.16e+63))
		tmp = Float64(k * Float64(y4 * Float64(y1 * y2)));
	else
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((y1 <= -8.5e+109) || ~((y1 <= 1.16e+63)))
		tmp = k * (y4 * (y1 * y2));
	else
		tmp = a * (t * (y2 * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[y1, -8.5e+109], N[Not[LessEqual[y1, 1.16e+63]], $MachinePrecision]], N[(k * N[(y4 * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y1 < -8.5000000000000004e109 or 1.15999999999999994e63 < y1

   1. Initial program 25.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf 42.3%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   3. Taylor expanded in y2 around inf 35.8%

      \[\leadsto \color{blue}{y4 \cdot \left(y2 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]

   4. Taylor expanded in k around inf 36.1%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]

   if -8.5000000000000004e109 < y1 < 1.15999999999999994e63

   1. Initial program 33.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y0 around inf 32.6%

      \[\leadsto \left(\color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. *-commutative 32.6%

         \[\leadsto \left(y0 \cdot \left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. *-commutative 32.6%

         \[\leadsto \left(y0 \cdot \left(c \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 32.6%

         \[\leadsto \left(y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - \color{blue}{b \cdot \left(j \cdot x - k \cdot z\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 32.6%

      \[\leadsto \left(\color{blue}{y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 24.6%

      \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)} \]

   6. Taylor expanded in t around inf 15.1%

      \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(y5 \cdot y2\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 22.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -8.5 \cdot 10^{+109} \lor \neg \left(y1 \leq 1.16 \cdot 10^{+63}\right):\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \]

Alternative 32: 22.2% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -1.32 \cdot 10^{+172} \lor \neg \left(y1 \leq 5.1 \cdot 10^{+63}\right):\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= y1 -1.32e+172) (not (<= y1 5.1e+63)))
   (* k (* y4 (* y1 y2)))
   (* y4 (* b (* t j)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y1 <= -1.32e+172) || !(y1 <= 5.1e+63)) {
		tmp = k * (y4 * (y1 * y2));
	} else {
		tmp = y4 * (b * (t * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((y1 <= (-1.32d+172)) .or. (.not. (y1 <= 5.1d+63))) then
        tmp = k * (y4 * (y1 * y2))
    else
        tmp = y4 * (b * (t * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y1 <= -1.32e+172) || !(y1 <= 5.1e+63)) {
		tmp = k * (y4 * (y1 * y2));
	} else {
		tmp = y4 * (b * (t * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (y1 <= -1.32e+172) or not (y1 <= 5.1e+63):
		tmp = k * (y4 * (y1 * y2))
	else:
		tmp = y4 * (b * (t * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((y1 <= -1.32e+172) || !(y1 <= 5.1e+63))
		tmp = Float64(k * Float64(y4 * Float64(y1 * y2)));
	else
		tmp = Float64(y4 * Float64(b * Float64(t * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((y1 <= -1.32e+172) || ~((y1 <= 5.1e+63)))
		tmp = k * (y4 * (y1 * y2));
	else
		tmp = y4 * (b * (t * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[y1, -1.32e+172], N[Not[LessEqual[y1, 5.1e+63]], $MachinePrecision]], N[(k * N[(y4 * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y4 * N[(b * N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y1 < -1.31999999999999996e172 or 5.0999999999999998e63 < y1

   1. Initial program 25.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf 41.0%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   3. Taylor expanded in y2 around inf 38.6%

      \[\leadsto \color{blue}{y4 \cdot \left(y2 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]

   4. Taylor expanded in k around inf 37.8%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]

   if -1.31999999999999996e172 < y1 < 5.0999999999999998e63

   1. Initial program 33.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 33.3%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, -\mathsf{fma}\left(x, j, k \cdot \left(-z\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \mathsf{fma}\left(t, j, -y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \mathsf{fma}\left(y1, y4, y0 \cdot \left(-y5\right)\right)\right)} \]

   4. Taylor expanded in t around inf 38.1%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot t} \]

   5. Taylor expanded in j around inf 26.9%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 25.7%

         \[\leadsto \color{blue}{\left(t \cdot j\right) \cdot \left(y4 \cdot b - i \cdot y5\right)} \]

      2. *-commutative 25.7%

         \[\leadsto \color{blue}{\left(j \cdot t\right)} \cdot \left(y4 \cdot b - i \cdot y5\right) \]

      3. *-commutative 25.7%

         \[\leadsto \left(j \cdot t\right) \cdot \left(y4 \cdot b - \color{blue}{y5 \cdot i}\right) \]

   7. Simplified 25.7%

      \[\leadsto \color{blue}{\left(j \cdot t\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)} \]

   8. Taylor expanded in y4 around inf 17.8%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 17.8%

         \[\leadsto y4 \cdot \left(t \cdot \color{blue}{\left(b \cdot j\right)}\right) \]

      2. *-commutative 17.8%

         \[\leadsto y4 \cdot \color{blue}{\left(\left(b \cdot j\right) \cdot t\right)} \]

      3. associate-*l* 18.9%

         \[\leadsto y4 \cdot \color{blue}{\left(b \cdot \left(j \cdot t\right)\right)} \]

      4. *-commutative 18.9%

         \[\leadsto y4 \cdot \left(b \cdot \color{blue}{\left(t \cdot j\right)}\right) \]

   10. Simplified 18.9%

       \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(t \cdot j\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 25.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -1.32 \cdot 10^{+172} \lor \neg \left(y1 \leq 5.1 \cdot 10^{+63}\right):\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j\right)\right)\\ \end{array} \]

Alternative 33: 17.0% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* t (* y2 y5))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (t * (y2 * y5));
}

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 * (t * (y2 * y5))
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 * (t * (y2 * y5));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * (t * (y2 * y5))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(t * Float64(y2 * y5)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * (t * (y2 * y5));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 30.6%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

2. Taylor expanded in y0 around inf 32.4%

   \[\leadsto \left(\color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
3. Step-by-step derivation

   1. *-commutative 32.4%

      \[\leadsto \left(y0 \cdot \left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. *-commutative 32.4%

      \[\leadsto \left(y0 \cdot \left(c \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. *-commutative 32.4%

      \[\leadsto \left(y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - \color{blue}{b \cdot \left(j \cdot x - k \cdot z\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

4. Simplified 32.4%

   \[\leadsto \left(\color{blue}{y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

5. Taylor expanded in a around inf 23.8%

   \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)} \]

6. Taylor expanded in t around inf 13.2%

   \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(y5 \cdot y2\right)\right)} \]

7. Final simplification 13.2%

   \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right) \]

Developer target: 27.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot c - y5 \cdot a\\ t_2 := x \cdot y2 - z \cdot y3\\ t_3 := y2 \cdot t - y3 \cdot y\\ t_4 := k \cdot y2 - j \cdot y3\\ t_5 := y4 \cdot b - y5 \cdot i\\ t_6 := \left(j \cdot t - k \cdot y\right) \cdot t_5\\ t_7 := b \cdot a - i \cdot c\\ t_8 := t_7 \cdot \left(y \cdot x - t \cdot z\right)\\ t_9 := j \cdot x - k \cdot z\\ t_10 := \left(b \cdot y0 - i \cdot y1\right) \cdot t_9\\ t_11 := t_9 \cdot \left(y0 \cdot b - i \cdot y1\right)\\ t_12 := y4 \cdot y1 - y5 \cdot y0\\ t_13 := t_4 \cdot t_12\\ t_14 := \left(y2 \cdot k - y3 \cdot j\right) \cdot t_12\\ t_15 := \left(\left(\left(\left(k \cdot y\right) \cdot \left(y5 \cdot i\right) - \left(y \cdot b\right) \cdot \left(y4 \cdot k\right)\right) - \left(y5 \cdot t\right) \cdot \left(i \cdot j\right)\right) - \left(t_3 \cdot t_1 - t_14\right)\right) + \left(t_8 - \left(t_11 - \left(y2 \cdot x - y3 \cdot z\right) \cdot \left(c \cdot y0 - y1 \cdot a\right)\right)\right)\\ t_16 := \left(\left(t_6 - \left(y3 \cdot y\right) \cdot \left(y5 \cdot a - y4 \cdot c\right)\right) + \left(\left(y5 \cdot a\right) \cdot \left(t \cdot y2\right) + t_13\right)\right) + \left(t_2 \cdot \left(c \cdot y0 - a \cdot y1\right) - \left(t_10 - \left(y \cdot x - z \cdot t\right) \cdot t_7\right)\right)\\ t_17 := t \cdot y2 - y \cdot y3\\ \mathbf{if}\;y4 < -7.206256231996481 \cdot 10^{+60}:\\ \;\;\;\;\left(t_8 - \left(t_11 - t_6\right)\right) - \left(\frac{t_3}{\frac{1}{t_1}} - t_14\right)\\ \mathbf{elif}\;y4 < -3.364603505246317 \cdot 10^{-66}:\\ \;\;\;\;\left(\left(\left(\left(t \cdot c\right) \cdot \left(i \cdot z\right) - \left(a \cdot t\right) \cdot \left(b \cdot z\right)\right) - \left(y \cdot c\right) \cdot \left(i \cdot x\right)\right) - t_10\right) + \left(\left(y0 \cdot c - a \cdot y1\right) \cdot t_2 - \left(t_17 \cdot \left(y4 \cdot c - a \cdot y5\right) - \left(y1 \cdot y4 - y5 \cdot y0\right) \cdot t_4\right)\right)\\ \mathbf{elif}\;y4 < -1.2000065055686116 \cdot 10^{-105}:\\ \;\;\;\;t_16\\ \mathbf{elif}\;y4 < 6.718963124057495 \cdot 10^{-279}:\\ \;\;\;\;t_15\\ \mathbf{elif}\;y4 < 4.77962681403792 \cdot 10^{-222}:\\ \;\;\;\;t_16\\ \mathbf{elif}\;y4 < 2.2852241541266835 \cdot 10^{-175}:\\ \;\;\;\;t_15\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(k \cdot \left(i \cdot \left(z \cdot y1\right)\right) - \left(j \cdot \left(i \cdot \left(x \cdot y1\right)\right) + y0 \cdot \left(k \cdot \left(z \cdot b\right)\right)\right)\right)\right) + \left(z \cdot \left(y3 \cdot \left(a \cdot y1\right)\right) - \left(y2 \cdot \left(x \cdot \left(a \cdot y1\right)\right) + y0 \cdot \left(z \cdot \left(c \cdot y3\right)\right)\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot t_5\right) - t_17 \cdot t_1\right) + t_13\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y4 c) (* y5 a)))
        (t_2 (- (* x y2) (* z y3)))
        (t_3 (- (* y2 t) (* y3 y)))
        (t_4 (- (* k y2) (* j y3)))
        (t_5 (- (* y4 b) (* y5 i)))
        (t_6 (* (- (* j t) (* k y)) t_5))
        (t_7 (- (* b a) (* i c)))
        (t_8 (* t_7 (- (* y x) (* t z))))
        (t_9 (- (* j x) (* k z)))
        (t_10 (* (- (* b y0) (* i y1)) t_9))
        (t_11 (* t_9 (- (* y0 b) (* i y1))))
        (t_12 (- (* y4 y1) (* y5 y0)))
        (t_13 (* t_4 t_12))
        (t_14 (* (- (* y2 k) (* y3 j)) t_12))
        (t_15
         (+
          (-
           (-
            (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k)))
            (* (* y5 t) (* i j)))
           (- (* t_3 t_1) t_14))
          (- t_8 (- t_11 (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))))
        (t_16
         (+
          (+
           (- t_6 (* (* y3 y) (- (* y5 a) (* y4 c))))
           (+ (* (* y5 a) (* t y2)) t_13))
          (-
           (* t_2 (- (* c y0) (* a y1)))
           (- t_10 (* (- (* y x) (* z t)) t_7)))))
        (t_17 (- (* t y2) (* y y3))))
   (if (< y4 -7.206256231996481e+60)
     (- (- t_8 (- t_11 t_6)) (- (/ t_3 (/ 1.0 t_1)) t_14))
     (if (< y4 -3.364603505246317e-66)
       (+
        (-
         (- (- (* (* t c) (* i z)) (* (* a t) (* b z))) (* (* y c) (* i x)))
         t_10)
        (-
         (* (- (* y0 c) (* a y1)) t_2)
         (- (* t_17 (- (* y4 c) (* a y5))) (* (- (* y1 y4) (* y5 y0)) t_4))))
       (if (< y4 -1.2000065055686116e-105)
         t_16
         (if (< y4 6.718963124057495e-279)
           t_15
           (if (< y4 4.77962681403792e-222)
             t_16
             (if (< y4 2.2852241541266835e-175)
               t_15
               (+
                (-
                 (+
                  (+
                   (-
                    (* (- (* x y) (* z t)) (- (* a b) (* c i)))
                    (-
                     (* k (* i (* z y1)))
                     (+ (* j (* i (* x y1))) (* y0 (* k (* z b))))))
                   (-
                    (* z (* y3 (* a y1)))
                    (+ (* y2 (* x (* a y1))) (* y0 (* z (* c y3))))))
                  (* (- (* t j) (* y k)) t_5))
                 (* t_17 t_1))
                t_13)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y4 * c) - (y5 * a);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (y2 * t) - (y3 * y);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = (y4 * b) - (y5 * i);
	double t_6 = ((j * t) - (k * y)) * t_5;
	double t_7 = (b * a) - (i * c);
	double t_8 = t_7 * ((y * x) - (t * z));
	double t_9 = (j * x) - (k * z);
	double t_10 = ((b * y0) - (i * y1)) * t_9;
	double t_11 = t_9 * ((y0 * b) - (i * y1));
	double t_12 = (y4 * y1) - (y5 * y0);
	double t_13 = t_4 * t_12;
	double t_14 = ((y2 * k) - (y3 * j)) * t_12;
	double t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	double t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	double t_17 = (t * y2) - (y * y3);
	double tmp;
	if (y4 < -7.206256231996481e+60) {
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	} else if (y4 < -3.364603505246317e-66) {
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	} else if (y4 < -1.2000065055686116e-105) {
		tmp = t_16;
	} else if (y4 < 6.718963124057495e-279) {
		tmp = t_15;
	} else if (y4 < 4.77962681403792e-222) {
		tmp = t_16;
	} else if (y4 < 2.2852241541266835e-175) {
		tmp = t_15;
	} else {
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_10
    real(8) :: t_11
    real(8) :: t_12
    real(8) :: t_13
    real(8) :: t_14
    real(8) :: t_15
    real(8) :: t_16
    real(8) :: t_17
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = (y4 * c) - (y5 * a)
    t_2 = (x * y2) - (z * y3)
    t_3 = (y2 * t) - (y3 * y)
    t_4 = (k * y2) - (j * y3)
    t_5 = (y4 * b) - (y5 * i)
    t_6 = ((j * t) - (k * y)) * t_5
    t_7 = (b * a) - (i * c)
    t_8 = t_7 * ((y * x) - (t * z))
    t_9 = (j * x) - (k * z)
    t_10 = ((b * y0) - (i * y1)) * t_9
    t_11 = t_9 * ((y0 * b) - (i * y1))
    t_12 = (y4 * y1) - (y5 * y0)
    t_13 = t_4 * t_12
    t_14 = ((y2 * k) - (y3 * j)) * t_12
    t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))))
    t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)))
    t_17 = (t * y2) - (y * y3)
    if (y4 < (-7.206256231996481d+60)) then
        tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0d0 / t_1)) - t_14)
    else if (y4 < (-3.364603505246317d-66)) then
        tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)))
    else if (y4 < (-1.2000065055686116d-105)) then
        tmp = t_16
    else if (y4 < 6.718963124057495d-279) then
        tmp = t_15
    else if (y4 < 4.77962681403792d-222) then
        tmp = t_16
    else if (y4 < 2.2852241541266835d-175) then
        tmp = t_15
    else
        tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y4 * c) - (y5 * a);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (y2 * t) - (y3 * y);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = (y4 * b) - (y5 * i);
	double t_6 = ((j * t) - (k * y)) * t_5;
	double t_7 = (b * a) - (i * c);
	double t_8 = t_7 * ((y * x) - (t * z));
	double t_9 = (j * x) - (k * z);
	double t_10 = ((b * y0) - (i * y1)) * t_9;
	double t_11 = t_9 * ((y0 * b) - (i * y1));
	double t_12 = (y4 * y1) - (y5 * y0);
	double t_13 = t_4 * t_12;
	double t_14 = ((y2 * k) - (y3 * j)) * t_12;
	double t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	double t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	double t_17 = (t * y2) - (y * y3);
	double tmp;
	if (y4 < -7.206256231996481e+60) {
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	} else if (y4 < -3.364603505246317e-66) {
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	} else if (y4 < -1.2000065055686116e-105) {
		tmp = t_16;
	} else if (y4 < 6.718963124057495e-279) {
		tmp = t_15;
	} else if (y4 < 4.77962681403792e-222) {
		tmp = t_16;
	} else if (y4 < 2.2852241541266835e-175) {
		tmp = t_15;
	} else {
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y4 * c) - (y5 * a)
	t_2 = (x * y2) - (z * y3)
	t_3 = (y2 * t) - (y3 * y)
	t_4 = (k * y2) - (j * y3)
	t_5 = (y4 * b) - (y5 * i)
	t_6 = ((j * t) - (k * y)) * t_5
	t_7 = (b * a) - (i * c)
	t_8 = t_7 * ((y * x) - (t * z))
	t_9 = (j * x) - (k * z)
	t_10 = ((b * y0) - (i * y1)) * t_9
	t_11 = t_9 * ((y0 * b) - (i * y1))
	t_12 = (y4 * y1) - (y5 * y0)
	t_13 = t_4 * t_12
	t_14 = ((y2 * k) - (y3 * j)) * t_12
	t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))))
	t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)))
	t_17 = (t * y2) - (y * y3)
	tmp = 0
	if y4 < -7.206256231996481e+60:
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14)
	elif y4 < -3.364603505246317e-66:
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)))
	elif y4 < -1.2000065055686116e-105:
		tmp = t_16
	elif y4 < 6.718963124057495e-279:
		tmp = t_15
	elif y4 < 4.77962681403792e-222:
		tmp = t_16
	elif y4 < 2.2852241541266835e-175:
		tmp = t_15
	else:
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y4 * c) - Float64(y5 * a))
	t_2 = Float64(Float64(x * y2) - Float64(z * y3))
	t_3 = Float64(Float64(y2 * t) - Float64(y3 * y))
	t_4 = Float64(Float64(k * y2) - Float64(j * y3))
	t_5 = Float64(Float64(y4 * b) - Float64(y5 * i))
	t_6 = Float64(Float64(Float64(j * t) - Float64(k * y)) * t_5)
	t_7 = Float64(Float64(b * a) - Float64(i * c))
	t_8 = Float64(t_7 * Float64(Float64(y * x) - Float64(t * z)))
	t_9 = Float64(Float64(j * x) - Float64(k * z))
	t_10 = Float64(Float64(Float64(b * y0) - Float64(i * y1)) * t_9)
	t_11 = Float64(t_9 * Float64(Float64(y0 * b) - Float64(i * y1)))
	t_12 = Float64(Float64(y4 * y1) - Float64(y5 * y0))
	t_13 = Float64(t_4 * t_12)
	t_14 = Float64(Float64(Float64(y2 * k) - Float64(y3 * j)) * t_12)
	t_15 = Float64(Float64(Float64(Float64(Float64(Float64(k * y) * Float64(y5 * i)) - Float64(Float64(y * b) * Float64(y4 * k))) - Float64(Float64(y5 * t) * Float64(i * j))) - Float64(Float64(t_3 * t_1) - t_14)) + Float64(t_8 - Float64(t_11 - Float64(Float64(Float64(y2 * x) - Float64(y3 * z)) * Float64(Float64(c * y0) - Float64(y1 * a))))))
	t_16 = Float64(Float64(Float64(t_6 - Float64(Float64(y3 * y) * Float64(Float64(y5 * a) - Float64(y4 * c)))) + Float64(Float64(Float64(y5 * a) * Float64(t * y2)) + t_13)) + Float64(Float64(t_2 * Float64(Float64(c * y0) - Float64(a * y1))) - Float64(t_10 - Float64(Float64(Float64(y * x) - Float64(z * t)) * t_7))))
	t_17 = Float64(Float64(t * y2) - Float64(y * y3))
	tmp = 0.0
	if (y4 < -7.206256231996481e+60)
		tmp = Float64(Float64(t_8 - Float64(t_11 - t_6)) - Float64(Float64(t_3 / Float64(1.0 / t_1)) - t_14));
	elseif (y4 < -3.364603505246317e-66)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(t * c) * Float64(i * z)) - Float64(Float64(a * t) * Float64(b * z))) - Float64(Float64(y * c) * Float64(i * x))) - t_10) + Float64(Float64(Float64(Float64(y0 * c) - Float64(a * y1)) * t_2) - Float64(Float64(t_17 * Float64(Float64(y4 * c) - Float64(a * y5))) - Float64(Float64(Float64(y1 * y4) - Float64(y5 * y0)) * t_4))));
	elseif (y4 < -1.2000065055686116e-105)
		tmp = t_16;
	elseif (y4 < 6.718963124057495e-279)
		tmp = t_15;
	elseif (y4 < 4.77962681403792e-222)
		tmp = t_16;
	elseif (y4 < 2.2852241541266835e-175)
		tmp = t_15;
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) - Float64(z * t)) * Float64(Float64(a * b) - Float64(c * i))) - Float64(Float64(k * Float64(i * Float64(z * y1))) - Float64(Float64(j * Float64(i * Float64(x * y1))) + Float64(y0 * Float64(k * Float64(z * b)))))) + Float64(Float64(z * Float64(y3 * Float64(a * y1))) - Float64(Float64(y2 * Float64(x * Float64(a * y1))) + Float64(y0 * Float64(z * Float64(c * y3)))))) + Float64(Float64(Float64(t * j) - Float64(y * k)) * t_5)) - Float64(t_17 * t_1)) + t_13);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y4 * c) - (y5 * a);
	t_2 = (x * y2) - (z * y3);
	t_3 = (y2 * t) - (y3 * y);
	t_4 = (k * y2) - (j * y3);
	t_5 = (y4 * b) - (y5 * i);
	t_6 = ((j * t) - (k * y)) * t_5;
	t_7 = (b * a) - (i * c);
	t_8 = t_7 * ((y * x) - (t * z));
	t_9 = (j * x) - (k * z);
	t_10 = ((b * y0) - (i * y1)) * t_9;
	t_11 = t_9 * ((y0 * b) - (i * y1));
	t_12 = (y4 * y1) - (y5 * y0);
	t_13 = t_4 * t_12;
	t_14 = ((y2 * k) - (y3 * j)) * t_12;
	t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	t_17 = (t * y2) - (y * y3);
	tmp = 0.0;
	if (y4 < -7.206256231996481e+60)
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	elseif (y4 < -3.364603505246317e-66)
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	elseif (y4 < -1.2000065055686116e-105)
		tmp = t_16;
	elseif (y4 < 6.718963124057495e-279)
		tmp = t_15;
	elseif (y4 < 4.77962681403792e-222)
		tmp = t_16;
	elseif (y4 < 2.2852241541266835e-175)
		tmp = t_15;
	else
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y4 * c), $MachinePrecision] - N[(y5 * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y2 * t), $MachinePrecision] - N[(y3 * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(y4 * b), $MachinePrecision] - N[(y5 * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision] * t$95$5), $MachinePrecision]}, Block[{t$95$7 = N[(N[(b * a), $MachinePrecision] - N[(i * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(t$95$7 * N[(N[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$10 = N[(N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision] * t$95$9), $MachinePrecision]}, Block[{t$95$11 = N[(t$95$9 * N[(N[(y0 * b), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$12 = N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$13 = N[(t$95$4 * t$95$12), $MachinePrecision]}, Block[{t$95$14 = N[(N[(N[(y2 * k), $MachinePrecision] - N[(y3 * j), $MachinePrecision]), $MachinePrecision] * t$95$12), $MachinePrecision]}, Block[{t$95$15 = N[(N[(N[(N[(N[(N[(k * y), $MachinePrecision] * N[(y5 * i), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] * N[(y4 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y5 * t), $MachinePrecision] * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$3 * t$95$1), $MachinePrecision] - t$95$14), $MachinePrecision]), $MachinePrecision] + N[(t$95$8 - N[(t$95$11 - N[(N[(N[(y2 * x), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision] * N[(N[(c * y0), $MachinePrecision] - N[(y1 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$16 = N[(N[(N[(t$95$6 - N[(N[(y3 * y), $MachinePrecision] * N[(N[(y5 * a), $MachinePrecision] - N[(y4 * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y5 * a), $MachinePrecision] * N[(t * y2), $MachinePrecision]), $MachinePrecision] + t$95$13), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$10 - N[(N[(N[(y * x), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$17 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, If[Less[y4, -7.206256231996481e+60], N[(N[(t$95$8 - N[(t$95$11 - t$95$6), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$3 / N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision] - t$95$14), $MachinePrecision]), $MachinePrecision], If[Less[y4, -3.364603505246317e-66], N[(N[(N[(N[(N[(N[(t * c), $MachinePrecision] * N[(i * z), $MachinePrecision]), $MachinePrecision] - N[(N[(a * t), $MachinePrecision] * N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * c), $MachinePrecision] * N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$10), $MachinePrecision] + N[(N[(N[(N[(y0 * c), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision] - N[(N[(t$95$17 * N[(N[(y4 * c), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(y1 * y4), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision] * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[y4, -1.2000065055686116e-105], t$95$16, If[Less[y4, 6.718963124057495e-279], t$95$15, If[Less[y4, 4.77962681403792e-222], t$95$16, If[Less[y4, 2.2852241541266835e-175], t$95$15, N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(k * N[(i * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * N[(i * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(k * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(y3 * N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y2 * N[(x * N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(z * N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * t$95$5), $MachinePrecision]), $MachinePrecision] - N[(t$95$17 * t$95$1), $MachinePrecision]), $MachinePrecision] + t$95$13), $MachinePrecision]]]]]]]]]]]]]]]]]]]]]]]]

Reproduce

herbie shell --seed 2023268 
(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :name "Linear.Matrix:det44 from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< y4 -7.206256231996481e+60) (- (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))))) (- (/ (- (* y2 t) (* y3 y)) (/ 1.0 (- (* y4 c) (* y5 a)))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (if (< y4 -3.364603505246317e-66) (+ (- (- (- (* (* t c) (* i z)) (* (* a t) (* b z))) (* (* y c) (* i x))) (* (- (* b y0) (* i y1)) (- (* j x) (* k z)))) (- (* (- (* y0 c) (* a y1)) (- (* x y2) (* z y3))) (- (* (- (* t y2) (* y y3)) (- (* y4 c) (* a y5))) (* (- (* y1 y4) (* y5 y0)) (- (* k y2) (* j y3)))))) (if (< y4 -1.2000065055686116e-105) (+ (+ (- (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))) (* (* y3 y) (- (* y5 a) (* y4 c)))) (+ (* (* y5 a) (* t y2)) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* x y2) (* z y3)) (- (* c y0) (* a y1))) (- (* (- (* b y0) (* i y1)) (- (* j x) (* k z))) (* (- (* y x) (* z t)) (- (* b a) (* i c)))))) (if (< y4 6.718963124057495e-279) (+ (- (- (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k))) (* (* y5 t) (* i j))) (- (* (- (* y2 t) (* y3 y)) (- (* y4 c) (* y5 a))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))) (if (< y4 4.77962681403792e-222) (+ (+ (- (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))) (* (* y3 y) (- (* y5 a) (* y4 c)))) (+ (* (* y5 a) (* t y2)) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* x y2) (* z y3)) (- (* c y0) (* a y1))) (- (* (- (* b y0) (* i y1)) (- (* j x) (* k z))) (* (- (* y x) (* z t)) (- (* b a) (* i c)))))) (if (< y4 2.2852241541266835e-175) (+ (- (- (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k))) (* (* y5 t) (* i j))) (- (* (- (* y2 t) (* y3 y)) (- (* y4 c) (* y5 a))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))) (+ (- (+ (+ (- (* (- (* x y) (* z t)) (- (* a b) (* c i))) (- (* k (* i (* z y1))) (+ (* j (* i (* x y1))) (* y0 (* k (* z b)))))) (- (* z (* y3 (* a y1))) (+ (* y2 (* x (* a y1))) (* y0 (* z (* c y3)))))) (* (- (* t j) (* y k)) (- (* y4 b) (* y5 i)))) (* (- (* t y2) (* y y3)) (- (* y4 c) (* y5 a)))) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))))))))

  (+ (- (+ (+ (- (* (- (* x y) (* z t)) (- (* a b) (* c i))) (* (- (* x j) (* z k)) (- (* y0 b) (* y1 i)))) (* (- (* x y2) (* z y3)) (- (* y0 c) (* y1 a)))) (* (- (* t j) (* y k)) (- (* y4 b) (* y5 i)))) (* (- (* t y2) (* y y3)) (- (* y4 c) (* y5 a)))) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0)))))