Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 30.4% → 42.8%

Time: 30.5s

Alternatives: 26

Speedup: 5.6×

• 89.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 30.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 42.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b - c \cdot i\\ t_2 := t \cdot j - y \cdot k\\ t_3 := b \cdot y4 - i \cdot y5\\ t_4 := y \cdot \mathsf{fma}\left(t\_3, -k, \mathsf{fma}\left(t\_1, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ t_5 := \mathsf{fma}\left(k, y2, j \cdot \left(-y3\right)\right)\\ t_6 := y \cdot y3 - t \cdot y2\\ \mathbf{if}\;y \leq -5.6 \cdot 10^{+135}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-271}:\\ \;\;\;\;y4 \cdot \left(\mathsf{fma}\left(b, t\_2, y1 \cdot t\_5\right) + c \cdot t\_6\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-215}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(a, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(y4, t\_5, i \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-29}:\\ \;\;\;\;\left(-y5\right) \cdot \mathsf{fma}\left(i, t\_2, \mathsf{fma}\left(y0, t\_5, a \cdot t\_6\right)\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+102}:\\ \;\;\;\;t \cdot \left(\mathsf{fma}\left(t\_1, -z, j \cdot t\_3\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+219}:\\ \;\;\;\;a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* a b) (* c i)))
        (t_2 (- (* t j) (* y k)))
        (t_3 (- (* b y4) (* i y5)))
        (t_4 (* y (fma t_3 (- k) (fma t_1 x (* y3 (- (* c y4) (* a y5)))))))
        (t_5 (fma k y2 (* j (- y3))))
        (t_6 (- (* y y3) (* t y2))))
   (if (<= y -5.6e+135)
     t_4
     (if (<= y -2.3e-271)
       (* y4 (+ (fma b t_2 (* y1 t_5)) (* c t_6)))
       (if (<= y 3.6e-215)
         (*
          y1
          (fma a (- (* z y3) (* x y2)) (fma y4 t_5 (* i (- (* x j) (* z k))))))
         (if (<= y 4.2e-29)
           (* (- y5) (fma i t_2 (fma y0 t_5 (* a t_6))))
           (if (<= y 3.8e+102)
             (* t (+ (fma t_1 (- z) (* j t_3)) (* y2 (- (* a y5) (* c y4)))))
             (if (<= y 2.2e+219)
               (* a (* y (fma (- y3) y5 (* x b))))
               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 * b) - (c * i);
	double t_2 = (t * j) - (y * k);
	double t_3 = (b * y4) - (i * y5);
	double t_4 = y * fma(t_3, -k, fma(t_1, x, (y3 * ((c * y4) - (a * y5)))));
	double t_5 = fma(k, y2, (j * -y3));
	double t_6 = (y * y3) - (t * y2);
	double tmp;
	if (y <= -5.6e+135) {
		tmp = t_4;
	} else if (y <= -2.3e-271) {
		tmp = y4 * (fma(b, t_2, (y1 * t_5)) + (c * t_6));
	} else if (y <= 3.6e-215) {
		tmp = y1 * fma(a, ((z * y3) - (x * y2)), fma(y4, t_5, (i * ((x * j) - (z * k)))));
	} else if (y <= 4.2e-29) {
		tmp = -y5 * fma(i, t_2, fma(y0, t_5, (a * t_6)));
	} else if (y <= 3.8e+102) {
		tmp = t * (fma(t_1, -z, (j * t_3)) + (y2 * ((a * y5) - (c * y4))));
	} else if (y <= 2.2e+219) {
		tmp = a * (y * fma(-y3, y5, (x * b)));
	} 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 * b) - Float64(c * i))
	t_2 = Float64(Float64(t * j) - Float64(y * k))
	t_3 = Float64(Float64(b * y4) - Float64(i * y5))
	t_4 = Float64(y * fma(t_3, Float64(-k), fma(t_1, x, Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))))))
	t_5 = fma(k, y2, Float64(j * Float64(-y3)))
	t_6 = Float64(Float64(y * y3) - Float64(t * y2))
	tmp = 0.0
	if (y <= -5.6e+135)
		tmp = t_4;
	elseif (y <= -2.3e-271)
		tmp = Float64(y4 * Float64(fma(b, t_2, Float64(y1 * t_5)) + Float64(c * t_6)));
	elseif (y <= 3.6e-215)
		tmp = Float64(y1 * fma(a, Float64(Float64(z * y3) - Float64(x * y2)), fma(y4, t_5, Float64(i * Float64(Float64(x * j) - Float64(z * k))))));
	elseif (y <= 4.2e-29)
		tmp = Float64(Float64(-y5) * fma(i, t_2, fma(y0, t_5, Float64(a * t_6))));
	elseif (y <= 3.8e+102)
		tmp = Float64(t * Float64(fma(t_1, Float64(-z), Float64(j * t_3)) + Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y <= 2.2e+219)
		tmp = Float64(a * Float64(y * fma(Float64(-y3), y5, Float64(x * b))));
	else
		tmp = t_4;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y * N[(t$95$3 * (-k) + N[(t$95$1 * x + N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(k * y2 + N[(j * (-y3)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.6e+135], t$95$4, If[LessEqual[y, -2.3e-271], N[(y4 * N[(N[(b * t$95$2 + N[(y1 * t$95$5), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e-215], N[(y1 * N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$5 + N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e-29], N[((-y5) * N[(i * t$95$2 + N[(y0 * t$95$5 + N[(a * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.8e+102], N[(t * N[(N[(t$95$1 * (-z) + N[(j * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.2e+219], N[(a * N[(y * N[((-y3) * y5 + N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -5.60000000000000004e135 or 2.2000000000000001e219 < y

   1. Initial program 10.0%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

      4. *-commutative N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. neg-mul-1 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. neg-mul-1 N/A

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

      12. lower-neg.f64 N/A

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

      13. sub-neg N/A

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

   5. Simplified 78.5%

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

   if -5.60000000000000004e135 < y < -2.30000000000000009e-271

   1. Initial program 29.1%

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

   3. Taylor expanded in y4 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   5. Simplified 49.9%

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

   if -2.30000000000000009e-271 < y < 3.5999999999999999e-215

   1. Initial program 39.0%

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

   3. Taylor expanded in y1 around inf

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

      1. lower-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. associate--l+ N/A

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

      4. mul-1-neg N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. lower-fma.f64 N/A

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

   5. Simplified 62.9%

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

   if 3.5999999999999999e-215 < y < 4.19999999999999979e-29

   1. Initial program 29.4%

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

   3. Taylor expanded in y5 around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Simplified 56.8%

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

   if 4.19999999999999979e-29 < y < 3.79999999999999979e102

   1. Initial program 21.7%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   5. Simplified 68.0%

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

   if 3.79999999999999979e102 < y < 2.2000000000000001e219

   1. Initial program 37.9%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

   5. Simplified 62.1%

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

   6. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y3\right)}, y5, b \cdot x\right)\right) \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y3\right)}, y5, b \cdot x\right)\right) \]

      7. lower-*.f64 65.7

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

   8. Simplified 65.7%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, b \cdot x\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+135}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-271}:\\ \;\;\;\;y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - y \cdot k, y1 \cdot \mathsf{fma}\left(k, y2, j \cdot \left(-y3\right)\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-215}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(a, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(y4, \mathsf{fma}\left(k, y2, j \cdot \left(-y3\right)\right), i \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-29}:\\ \;\;\;\;\left(-y5\right) \cdot \mathsf{fma}\left(i, t \cdot j - y \cdot k, \mathsf{fma}\left(y0, \mathsf{fma}\left(k, y2, j \cdot \left(-y3\right)\right), a \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+102}:\\ \;\;\;\;t \cdot \left(\mathsf{fma}\left(a \cdot b - c \cdot i, -z, j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+219}:\\ \;\;\;\;a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 55.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot y4 - a \cdot y5\\ t_2 := b \cdot y4 - i \cdot y5\\ t_3 := a \cdot b - c \cdot i\\ t_4 := \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot t\_3 + \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right) + \left(z \cdot y3 - x \cdot y2\right) \cdot \left(a \cdot y1 - c \cdot y0\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot t\_2\right) + t\_1 \cdot \left(y \cdot y3 - t \cdot y2\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y5 \cdot y0\right)\\ \mathbf{if}\;t\_4 \leq \infty:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(t\_2, -k, \mathsf{fma}\left(t\_3, x, y3 \cdot t\_1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* c y4) (* a y5)))
        (t_2 (- (* b y4) (* i y5)))
        (t_3 (- (* a b) (* c i)))
        (t_4
         (+
          (+
           (+
            (+
             (+
              (* (- (* x y) (* z t)) t_3)
              (* (- (* x j) (* z k)) (- (* i y1) (* b y0))))
             (* (- (* z y3) (* x y2)) (- (* a y1) (* c y0))))
            (* (- (* t j) (* y k)) t_2))
           (* t_1 (- (* y y3) (* t y2))))
          (* (- (* k y2) (* j y3)) (- (* y1 y4) (* y5 y0))))))
   (if (<= t_4 INFINITY) t_4 (* y (fma t_2 (- k) (fma t_3 x (* y3 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y4) - (a * y5);
	double t_2 = (b * y4) - (i * y5);
	double t_3 = (a * b) - (c * i);
	double t_4 = (((((((x * y) - (z * t)) * t_3) + (((x * j) - (z * k)) * ((i * y1) - (b * y0)))) + (((z * y3) - (x * y2)) * ((a * y1) - (c * y0)))) + (((t * j) - (y * k)) * t_2)) + (t_1 * ((y * y3) - (t * y2)))) + (((k * y2) - (j * y3)) * ((y1 * y4) - (y5 * y0)));
	double tmp;
	if (t_4 <= ((double) INFINITY)) {
		tmp = t_4;
	} else {
		tmp = y * fma(t_2, -k, fma(t_3, x, (y3 * t_1)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(c * y4) - Float64(a * y5))
	t_2 = Float64(Float64(b * y4) - Float64(i * y5))
	t_3 = Float64(Float64(a * b) - Float64(c * i))
	t_4 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) - Float64(z * t)) * t_3) + Float64(Float64(Float64(x * j) - Float64(z * k)) * Float64(Float64(i * y1) - Float64(b * y0)))) + Float64(Float64(Float64(z * y3) - Float64(x * y2)) * Float64(Float64(a * y1) - Float64(c * y0)))) + Float64(Float64(Float64(t * j) - Float64(y * k)) * t_2)) + Float64(t_1 * Float64(Float64(y * y3) - Float64(t * y2)))) + Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y1 * y4) - Float64(y5 * y0))))
	tmp = 0.0
	if (t_4 <= Inf)
		tmp = t_4;
	else
		tmp = Float64(y * fma(t_2, Float64(-k), fma(t_3, x, Float64(y3 * t_1))));
	end
	return tmp
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 84.2%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

      4. *-commutative N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. neg-mul-1 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. neg-mul-1 N/A

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

      12. lower-neg.f64 N/A

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

      13. sub-neg N/A

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

   5. Simplified 44.6%

      \[\leadsto \color{blue}{y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.6%

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

Alternative 3: 40.3% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y4 \leq -3.7 \cdot 10^{+202}:\\ \;\;\;\;y4 \cdot \left(c \cdot \mathsf{fma}\left(y, y3, t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;y4 \leq -9.2 \cdot 10^{-33}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 1.35 \cdot 10^{+113}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 6 \cdot 10^{+164}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \mathsf{fma}\left(y3, -j, k \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y4 -3.7e+202)
   (* y4 (* c (fma y y3 (* t (- y2)))))
   (if (<= y4 -9.2e-33)
     (*
      y
      (fma
       (- (* b y4) (* i y5))
       (- k)
       (fma (- (* a b) (* c i)) x (* y3 (- (* c y4) (* a y5))))))
     (if (<= y4 1.35e+113)
       (*
        a
        (fma
         y1
         (- (* z y3) (* x y2))
         (fma b (- (* x y) (* z t)) (* y5 (- (* t y2) (* y y3))))))
       (if (<= y4 6e+164)
         (* y4 (* j (- (* t b) (* y1 y3))))
         (* y4 (* y1 (fma y3 (- j) (* k y2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -3.7e+202) {
		tmp = y4 * (c * fma(y, y3, (t * -y2)));
	} else if (y4 <= -9.2e-33) {
		tmp = y * fma(((b * y4) - (i * y5)), -k, fma(((a * b) - (c * i)), x, (y3 * ((c * y4) - (a * y5)))));
	} else if (y4 <= 1.35e+113) {
		tmp = a * fma(y1, ((z * y3) - (x * y2)), fma(b, ((x * y) - (z * t)), (y5 * ((t * y2) - (y * y3)))));
	} else if (y4 <= 6e+164) {
		tmp = y4 * (j * ((t * b) - (y1 * y3)));
	} else {
		tmp = y4 * (y1 * fma(y3, -j, (k * y2)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y4 <= -3.7e+202)
		tmp = Float64(y4 * Float64(c * fma(y, y3, Float64(t * Float64(-y2)))));
	elseif (y4 <= -9.2e-33)
		tmp = Float64(y * fma(Float64(Float64(b * y4) - Float64(i * y5)), Float64(-k), fma(Float64(Float64(a * b) - Float64(c * i)), x, Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))))));
	elseif (y4 <= 1.35e+113)
		tmp = Float64(a * fma(y1, Float64(Float64(z * y3) - Float64(x * y2)), fma(b, Float64(Float64(x * y) - Float64(z * t)), Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))));
	elseif (y4 <= 6e+164)
		tmp = Float64(y4 * Float64(j * Float64(Float64(t * b) - Float64(y1 * y3))));
	else
		tmp = Float64(y4 * Float64(y1 * fma(y3, Float64(-j), Float64(k * y2))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y4, -3.7e+202], N[(y4 * N[(c * N[(y * y3 + N[(t * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -9.2e-33], N[(y * N[(N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision] * (-k) + N[(N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision] * x + N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 1.35e+113], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 6e+164], N[(y4 * N[(j * N[(N[(t * b), $MachinePrecision] - N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y4 * N[(y1 * N[(y3 * (-j) + N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y4 < -3.6999999999999999e202

   1. Initial program 23.1%

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

   3. Taylor expanded in y4 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   5. Simplified 65.4%

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

   6. Taylor expanded in c around inf

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

      1. lower-*.f64 N/A

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

      2. cancel-sign-sub-inv N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto y4 \cdot \left(c \cdot \color{blue}{\mathsf{fma}\left(y, y3, \left(\mathsf{neg}\left(t\right)\right) \cdot y2\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto y4 \cdot \left(c \cdot \mathsf{fma}\left(y, y3, \color{blue}{\left(-1 \cdot t\right)} \cdot y2\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(c \cdot \mathsf{fma}\left(y, y3, \color{blue}{\left(-1 \cdot t\right) \cdot y2}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto y4 \cdot \left(c \cdot \mathsf{fma}\left(y, y3, \color{blue}{\left(\mathsf{neg}\left(t\right)\right)} \cdot y2\right)\right) \]

      7. lower-neg.f64 69.4

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

   8. Simplified 69.4%

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

   if -3.6999999999999999e202 < y4 < -9.19999999999999942e-33

   1. Initial program 18.9%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

      4. *-commutative N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. neg-mul-1 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. neg-mul-1 N/A

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

      12. lower-neg.f64 N/A

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

      13. sub-neg N/A

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

   5. Simplified 54.4%

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

   if -9.19999999999999942e-33 < y4 < 1.35000000000000006e113

   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. Add Preprocessing

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

   5. Simplified 53.8%

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

   if 1.35000000000000006e113 < y4 < 6.00000000000000001e164

   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. Add Preprocessing

   3. Taylor expanded in y4 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   5. Simplified 61.5%

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

   6. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 78.1

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

   8. Simplified 78.1%

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

   if 6.00000000000000001e164 < y4

   1. Initial program 9.0%

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

   3. Taylor expanded in y1 around inf

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

      1. lower-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. associate--l+ N/A

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

      4. mul-1-neg N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. lower-fma.f64 N/A

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

   5. Simplified 56.8%

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

   6. Taylor expanded in y4 around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. mul-1-neg N/A

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

      7. *-commutative N/A

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

      8. distribute-rgt-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

          \[\leadsto y4 \cdot \left(y1 \cdot \color{blue}{\mathsf{fma}\left(y3, -1 \cdot j, k \cdot y2\right)}\right) \]

      11. mul-1-neg N/A

          \[\leadsto y4 \cdot \left(y1 \cdot \mathsf{fma}\left(y3, \color{blue}{\mathsf{neg}\left(j\right)}, k \cdot y2\right)\right) \]

      12. lower-neg.f64 N/A

          \[\leadsto y4 \cdot \left(y1 \cdot \mathsf{fma}\left(y3, \color{blue}{\mathsf{neg}\left(j\right)}, k \cdot y2\right)\right) \]

      13. *-commutative N/A

          \[\leadsto y4 \cdot \left(y1 \cdot \mathsf{fma}\left(y3, \mathsf{neg}\left(j\right), \color{blue}{y2 \cdot k}\right)\right) \]

      14. lower-*.f64 61.4

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

   8. Simplified 61.4%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -3.7 \cdot 10^{+202}:\\ \;\;\;\;y4 \cdot \left(c \cdot \mathsf{fma}\left(y, y3, t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;y4 \leq -9.2 \cdot 10^{-33}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 1.35 \cdot 10^{+113}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 6 \cdot 10^{+164}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \mathsf{fma}\left(y3, -j, k \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 39.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y4 \leq -3.3 \cdot 10^{+144}:\\ \;\;\;\;y4 \cdot \left(c \cdot \mathsf{fma}\left(y, y3, t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;y4 \leq -2.1 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \left(\mathsf{fma}\left(a \cdot b - c \cdot i, y, y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq 1.35 \cdot 10^{+113}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 6 \cdot 10^{+164}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \mathsf{fma}\left(y3, -j, k \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y4 -3.3e+144)
   (* y4 (* c (fma y y3 (* t (- y2)))))
   (if (<= y4 -2.1e-28)
     (*
      x
      (+
       (fma (- (* a b) (* c i)) y (* y2 (- (* c y0) (* a y1))))
       (* j (- (* i y1) (* b y0)))))
     (if (<= y4 1.35e+113)
       (*
        a
        (fma
         y1
         (- (* z y3) (* x y2))
         (fma b (- (* x y) (* z t)) (* y5 (- (* t y2) (* y y3))))))
       (if (<= y4 6e+164)
         (* y4 (* j (- (* t b) (* y1 y3))))
         (* y4 (* y1 (fma y3 (- j) (* k y2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -3.3e+144) {
		tmp = y4 * (c * fma(y, y3, (t * -y2)));
	} else if (y4 <= -2.1e-28) {
		tmp = x * (fma(((a * b) - (c * i)), y, (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	} else if (y4 <= 1.35e+113) {
		tmp = a * fma(y1, ((z * y3) - (x * y2)), fma(b, ((x * y) - (z * t)), (y5 * ((t * y2) - (y * y3)))));
	} else if (y4 <= 6e+164) {
		tmp = y4 * (j * ((t * b) - (y1 * y3)));
	} else {
		tmp = y4 * (y1 * fma(y3, -j, (k * y2)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y4 <= -3.3e+144)
		tmp = Float64(y4 * Float64(c * fma(y, y3, Float64(t * Float64(-y2)))));
	elseif (y4 <= -2.1e-28)
		tmp = Float64(x * Float64(fma(Float64(Float64(a * b) - Float64(c * i)), y, Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (y4 <= 1.35e+113)
		tmp = Float64(a * fma(y1, Float64(Float64(z * y3) - Float64(x * y2)), fma(b, Float64(Float64(x * y) - Float64(z * t)), Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))));
	elseif (y4 <= 6e+164)
		tmp = Float64(y4 * Float64(j * Float64(Float64(t * b) - Float64(y1 * y3))));
	else
		tmp = Float64(y4 * Float64(y1 * fma(y3, Float64(-j), Float64(k * y2))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y4, -3.3e+144], N[(y4 * N[(c * N[(y * y3 + N[(t * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -2.1e-28], N[(x * N[(N[(N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision] * y + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 1.35e+113], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 6e+164], N[(y4 * N[(j * N[(N[(t * b), $MachinePrecision] - N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y4 * N[(y1 * N[(y3 * (-j) + N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y4 < -3.3e144

   1. Initial program 21.9%

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

   3. Taylor expanded in y4 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   5. Simplified 68.9%

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

   6. Taylor expanded in c around inf

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

      1. lower-*.f64 N/A

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

      2. cancel-sign-sub-inv N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto y4 \cdot \left(c \cdot \color{blue}{\mathsf{fma}\left(y, y3, \left(\mathsf{neg}\left(t\right)\right) \cdot y2\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto y4 \cdot \left(c \cdot \mathsf{fma}\left(y, y3, \color{blue}{\left(-1 \cdot t\right)} \cdot y2\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(c \cdot \mathsf{fma}\left(y, y3, \color{blue}{\left(-1 \cdot t\right) \cdot y2}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto y4 \cdot \left(c \cdot \mathsf{fma}\left(y, y3, \color{blue}{\left(\mathsf{neg}\left(t\right)\right)} \cdot y2\right)\right) \]

      7. lower-neg.f64 66.2

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

   8. Simplified 66.2%

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

   if -3.3e144 < y4 < -2.10000000000000006e-28

   1. Initial program 20.7%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower--.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. lower-*.f64 52.2

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

   5. Simplified 52.2%

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

   if -2.10000000000000006e-28 < y4 < 1.35000000000000006e113

   1. Initial program 30.9%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

   5. Simplified 53.4%

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

   if 1.35000000000000006e113 < y4 < 6.00000000000000001e164

   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. Add Preprocessing

   3. Taylor expanded in y4 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   5. Simplified 61.5%

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

   6. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 78.1

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

   8. Simplified 78.1%

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

   if 6.00000000000000001e164 < y4

   1. Initial program 9.0%

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

   3. Taylor expanded in y1 around inf

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

      1. lower-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. associate--l+ N/A

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

      4. mul-1-neg N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. lower-fma.f64 N/A

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

   5. Simplified 56.8%

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

   6. Taylor expanded in y4 around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. mul-1-neg N/A

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

      7. *-commutative N/A

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

      8. distribute-rgt-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

          \[\leadsto y4 \cdot \left(y1 \cdot \color{blue}{\mathsf{fma}\left(y3, -1 \cdot j, k \cdot y2\right)}\right) \]

      11. mul-1-neg N/A

          \[\leadsto y4 \cdot \left(y1 \cdot \mathsf{fma}\left(y3, \color{blue}{\mathsf{neg}\left(j\right)}, k \cdot y2\right)\right) \]

      12. lower-neg.f64 N/A

          \[\leadsto y4 \cdot \left(y1 \cdot \mathsf{fma}\left(y3, \color{blue}{\mathsf{neg}\left(j\right)}, k \cdot y2\right)\right) \]

      13. *-commutative N/A

          \[\leadsto y4 \cdot \left(y1 \cdot \mathsf{fma}\left(y3, \mathsf{neg}\left(j\right), \color{blue}{y2 \cdot k}\right)\right) \]

      14. lower-*.f64 61.4

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

   8. Simplified 61.4%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -3.3 \cdot 10^{+144}:\\ \;\;\;\;y4 \cdot \left(c \cdot \mathsf{fma}\left(y, y3, t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;y4 \leq -2.1 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \left(\mathsf{fma}\left(a \cdot b - c \cdot i, y, y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq 1.35 \cdot 10^{+113}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 6 \cdot 10^{+164}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \mathsf{fma}\left(y3, -j, k \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 46.1% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - y \cdot k, y1 \cdot \mathsf{fma}\left(k, y2, j \cdot \left(-y3\right)\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;y4 \leq -2.5 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq 2.7 \cdot 10^{+78}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          y4
          (+
           (fma b (- (* t j) (* y k)) (* y1 (fma k y2 (* j (- y3)))))
           (* c (- (* y y3) (* t y2)))))))
   (if (<= y4 -2.5e+25)
     t_1
     (if (<= y4 2.7e+78)
       (*
        a
        (fma
         y1
         (- (* z y3) (* x y2))
         (fma b (- (* x y) (* z t)) (* y5 (- (* t y2) (* y y3))))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * (fma(b, ((t * j) - (y * k)), (y1 * fma(k, y2, (j * -y3)))) + (c * ((y * y3) - (t * y2))));
	double tmp;
	if (y4 <= -2.5e+25) {
		tmp = t_1;
	} else if (y4 <= 2.7e+78) {
		tmp = a * fma(y1, ((z * y3) - (x * y2)), fma(b, ((x * y) - (z * t)), (y5 * ((t * y2) - (y * y3)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y4 * Float64(fma(b, Float64(Float64(t * j) - Float64(y * k)), Float64(y1 * fma(k, y2, Float64(j * Float64(-y3))))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))))
	tmp = 0.0
	if (y4 <= -2.5e+25)
		tmp = t_1;
	elseif (y4 <= 2.7e+78)
		tmp = Float64(a * fma(y1, Float64(Float64(z * y3) - Float64(x * y2)), fma(b, Float64(Float64(x * y) - Float64(z * t)), Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))));
	else
		tmp = t_1;
	end
	return 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[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(k * y2 + N[(j * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -2.5e+25], t$95$1, If[LessEqual[y4, 2.7e+78], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y4 < -2.50000000000000012e25 or 2.70000000000000004e78 < y4

   1. Initial program 19.7%

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

   3. Taylor expanded in y4 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   5. Simplified 58.2%

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

   if -2.50000000000000012e25 < y4 < 2.70000000000000004e78

   1. Initial program 30.2%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

   5. Simplified 54.8%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -2.5 \cdot 10^{+25}:\\ \;\;\;\;y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - y \cdot k, y1 \cdot \mathsf{fma}\left(k, y2, j \cdot \left(-y3\right)\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq 2.7 \cdot 10^{+78}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - y \cdot k, y1 \cdot \mathsf{fma}\left(k, y2, j \cdot \left(-y3\right)\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 40.4% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y4 \leq -1.4 \cdot 10^{+131}:\\ \;\;\;\;y4 \cdot \left(c \cdot \mathsf{fma}\left(y, y3, t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 1.35 \cdot 10^{+113}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 6 \cdot 10^{+164}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \mathsf{fma}\left(y3, -j, k \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y4 -1.4e+131)
   (* y4 (* c (fma y y3 (* t (- y2)))))
   (if (<= y4 1.35e+113)
     (*
      a
      (fma
       y1
       (- (* z y3) (* x y2))
       (fma b (- (* x y) (* z t)) (* y5 (- (* t y2) (* y y3))))))
     (if (<= y4 6e+164)
       (* y4 (* j (- (* t b) (* y1 y3))))
       (* y4 (* y1 (fma y3 (- j) (* k y2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -1.4e+131) {
		tmp = y4 * (c * fma(y, y3, (t * -y2)));
	} else if (y4 <= 1.35e+113) {
		tmp = a * fma(y1, ((z * y3) - (x * y2)), fma(b, ((x * y) - (z * t)), (y5 * ((t * y2) - (y * y3)))));
	} else if (y4 <= 6e+164) {
		tmp = y4 * (j * ((t * b) - (y1 * y3)));
	} else {
		tmp = y4 * (y1 * fma(y3, -j, (k * y2)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y4 <= -1.4e+131)
		tmp = Float64(y4 * Float64(c * fma(y, y3, Float64(t * Float64(-y2)))));
	elseif (y4 <= 1.35e+113)
		tmp = Float64(a * fma(y1, Float64(Float64(z * y3) - Float64(x * y2)), fma(b, Float64(Float64(x * y) - Float64(z * t)), Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))));
	elseif (y4 <= 6e+164)
		tmp = Float64(y4 * Float64(j * Float64(Float64(t * b) - Float64(y1 * y3))));
	else
		tmp = Float64(y4 * Float64(y1 * fma(y3, Float64(-j), Float64(k * y2))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y4, -1.4e+131], N[(y4 * N[(c * N[(y * y3 + N[(t * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 1.35e+113], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 6e+164], N[(y4 * N[(j * N[(N[(t * b), $MachinePrecision] - N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y4 * N[(y1 * N[(y3 * (-j) + N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y4 < -1.4e131

   1. Initial program 23.5%

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

   3. Taylor expanded in y4 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   5. Simplified 67.8%

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

   6. Taylor expanded in c around inf

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

      1. lower-*.f64 N/A

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

      2. cancel-sign-sub-inv N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto y4 \cdot \left(c \cdot \color{blue}{\mathsf{fma}\left(y, y3, \left(\mathsf{neg}\left(t\right)\right) \cdot y2\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto y4 \cdot \left(c \cdot \mathsf{fma}\left(y, y3, \color{blue}{\left(-1 \cdot t\right)} \cdot y2\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(c \cdot \mathsf{fma}\left(y, y3, \color{blue}{\left(-1 \cdot t\right) \cdot y2}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto y4 \cdot \left(c \cdot \mathsf{fma}\left(y, y3, \color{blue}{\left(\mathsf{neg}\left(t\right)\right)} \cdot y2\right)\right) \]

      7. lower-neg.f64 65.3

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

   8. Simplified 65.3%

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

   if -1.4e131 < y4 < 1.35000000000000006e113

   1. Initial program 28.5%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

   5. Simplified 50.8%

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

   if 1.35000000000000006e113 < y4 < 6.00000000000000001e164

   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. Add Preprocessing

   3. Taylor expanded in y4 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   5. Simplified 61.5%

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

   6. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 78.1

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

   8. Simplified 78.1%

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

   if 6.00000000000000001e164 < y4

   1. Initial program 9.0%

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

   3. Taylor expanded in y1 around inf

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

      1. lower-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. associate--l+ N/A

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

      4. mul-1-neg N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. lower-fma.f64 N/A

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

   5. Simplified 56.8%

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

   6. Taylor expanded in y4 around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. mul-1-neg N/A

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

      7. *-commutative N/A

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

      8. distribute-rgt-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

          \[\leadsto y4 \cdot \left(y1 \cdot \color{blue}{\mathsf{fma}\left(y3, -1 \cdot j, k \cdot y2\right)}\right) \]

      11. mul-1-neg N/A

          \[\leadsto y4 \cdot \left(y1 \cdot \mathsf{fma}\left(y3, \color{blue}{\mathsf{neg}\left(j\right)}, k \cdot y2\right)\right) \]

      12. lower-neg.f64 N/A

          \[\leadsto y4 \cdot \left(y1 \cdot \mathsf{fma}\left(y3, \color{blue}{\mathsf{neg}\left(j\right)}, k \cdot y2\right)\right) \]

      13. *-commutative N/A

          \[\leadsto y4 \cdot \left(y1 \cdot \mathsf{fma}\left(y3, \mathsf{neg}\left(j\right), \color{blue}{y2 \cdot k}\right)\right) \]

      14. lower-*.f64 61.4

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

   8. Simplified 61.4%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \mathsf{fma}\left(y3, -j, y2 \cdot k\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -1.4 \cdot 10^{+131}:\\ \;\;\;\;y4 \cdot \left(c \cdot \mathsf{fma}\left(y, y3, t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 1.35 \cdot 10^{+113}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 6 \cdot 10^{+164}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \mathsf{fma}\left(y3, -j, k \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 29.9% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot \left(j \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{if}\;y4 \leq -4.4 \cdot 10^{+129}:\\ \;\;\;\;y4 \cdot \left(c \cdot \mathsf{fma}\left(y, y3, t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;y4 \leq -1.35 \cdot 10^{-294}:\\ \;\;\;\;a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, x \cdot b\right)\right)\\ \mathbf{elif}\;y4 \leq 6.5 \cdot 10^{-227}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq 5 \cdot 10^{-105}:\\ \;\;\;\;a \cdot \left(y3 \cdot \mathsf{fma}\left(-y, y5, z \cdot y1\right)\right)\\ \mathbf{elif}\;y4 \leq 3.8 \cdot 10^{+63}:\\ \;\;\;\;a \cdot \left(y2 \cdot \mathsf{fma}\left(-x, y1, t \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq 6 \cdot 10^{+164}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \mathsf{fma}\left(y3, -j, k \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y4 (* j (- (* t b) (* y1 y3))))))
   (if (<= y4 -4.4e+129)
     (* y4 (* c (fma y y3 (* t (- y2)))))
     (if (<= y4 -1.35e-294)
       (* a (* y (fma (- y3) y5 (* x b))))
       (if (<= y4 6.5e-227)
         t_1
         (if (<= y4 5e-105)
           (* a (* y3 (fma (- y) y5 (* z y1))))
           (if (<= y4 3.8e+63)
             (* a (* y2 (fma (- x) y1 (* t y5))))
             (if (<= y4 6e+164)
               t_1
               (* y4 (* y1 (fma y3 (- j) (* k 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 = y4 * (j * ((t * b) - (y1 * y3)));
	double tmp;
	if (y4 <= -4.4e+129) {
		tmp = y4 * (c * fma(y, y3, (t * -y2)));
	} else if (y4 <= -1.35e-294) {
		tmp = a * (y * fma(-y3, y5, (x * b)));
	} else if (y4 <= 6.5e-227) {
		tmp = t_1;
	} else if (y4 <= 5e-105) {
		tmp = a * (y3 * fma(-y, y5, (z * y1)));
	} else if (y4 <= 3.8e+63) {
		tmp = a * (y2 * fma(-x, y1, (t * y5)));
	} else if (y4 <= 6e+164) {
		tmp = t_1;
	} else {
		tmp = y4 * (y1 * fma(y3, -j, (k * 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(y4 * Float64(j * Float64(Float64(t * b) - Float64(y1 * y3))))
	tmp = 0.0
	if (y4 <= -4.4e+129)
		tmp = Float64(y4 * Float64(c * fma(y, y3, Float64(t * Float64(-y2)))));
	elseif (y4 <= -1.35e-294)
		tmp = Float64(a * Float64(y * fma(Float64(-y3), y5, Float64(x * b))));
	elseif (y4 <= 6.5e-227)
		tmp = t_1;
	elseif (y4 <= 5e-105)
		tmp = Float64(a * Float64(y3 * fma(Float64(-y), y5, Float64(z * y1))));
	elseif (y4 <= 3.8e+63)
		tmp = Float64(a * Float64(y2 * fma(Float64(-x), y1, Float64(t * y5))));
	elseif (y4 <= 6e+164)
		tmp = t_1;
	else
		tmp = Float64(y4 * Float64(y1 * fma(y3, Float64(-j), Float64(k * y2))));
	end
	return 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[(j * N[(N[(t * b), $MachinePrecision] - N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -4.4e+129], N[(y4 * N[(c * N[(y * y3 + N[(t * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -1.35e-294], N[(a * N[(y * N[((-y3) * y5 + N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 6.5e-227], t$95$1, If[LessEqual[y4, 5e-105], N[(a * N[(y3 * N[((-y) * y5 + N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 3.8e+63], N[(a * N[(y2 * N[((-x) * y1 + N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 6e+164], t$95$1, N[(y4 * N[(y1 * N[(y3 * (-j) + N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y4 < -4.3999999999999999e129

   1. Initial program 23.5%

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

   3. Taylor expanded in y4 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   5. Simplified 67.8%

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

   6. Taylor expanded in c around inf

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

      1. lower-*.f64 N/A

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

      2. cancel-sign-sub-inv N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto y4 \cdot \left(c \cdot \color{blue}{\mathsf{fma}\left(y, y3, \left(\mathsf{neg}\left(t\right)\right) \cdot y2\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto y4 \cdot \left(c \cdot \mathsf{fma}\left(y, y3, \color{blue}{\left(-1 \cdot t\right)} \cdot y2\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(c \cdot \mathsf{fma}\left(y, y3, \color{blue}{\left(-1 \cdot t\right) \cdot y2}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto y4 \cdot \left(c \cdot \mathsf{fma}\left(y, y3, \color{blue}{\left(\mathsf{neg}\left(t\right)\right)} \cdot y2\right)\right) \]

      7. lower-neg.f64 65.3

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

   8. Simplified 65.3%

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

   if -4.3999999999999999e129 < y4 < -1.35000000000000005e-294

   1. Initial program 19.6%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

   5. Simplified 51.5%

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

   6. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y3\right)}, y5, b \cdot x\right)\right) \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y3\right)}, y5, b \cdot x\right)\right) \]

      7. lower-*.f64 47.3

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

   8. Simplified 47.3%

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

   if -1.35000000000000005e-294 < y4 < 6.4999999999999996e-227 or 3.8000000000000001e63 < y4 < 6.00000000000000001e164

   1. Initial program 33.3%

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

   3. Taylor expanded in y4 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   5. Simplified 50.2%

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

   6. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 52.6

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

   8. Simplified 52.6%

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

   if 6.4999999999999996e-227 < y4 < 4.99999999999999963e-105

   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. Add Preprocessing

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

   5. Simplified 54.6%

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

   6. Taylor expanded in y3 around inf

      \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot y, y5, y1 \cdot z\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y\right)}, y5, y1 \cdot z\right)\right) \]

      5. lower-neg.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y\right)}, y5, y1 \cdot z\right)\right) \]

      6. lower-*.f64 54.3

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

   8. Simplified 54.3%

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

   if 4.99999999999999963e-105 < y4 < 3.8000000000000001e63

   1. Initial program 37.9%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

   5. Simplified 52.1%

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

   6. Taylor expanded in y2 around inf

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

      1. lower-*.f64 N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. mul-1-neg N/A

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y1, t \cdot y5\right)\right) \]

      5. lower-neg.f64 N/A

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y1, t \cdot y5\right)\right) \]

      6. lower-*.f64 46.4

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

   8. Simplified 46.4%

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

   if 6.00000000000000001e164 < y4

   1. Initial program 9.0%

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

   3. Taylor expanded in y1 around inf

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

      1. lower-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. associate--l+ N/A

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

      4. mul-1-neg N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. lower-fma.f64 N/A

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

   5. Simplified 56.8%

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

   6. Taylor expanded in y4 around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. mul-1-neg N/A

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

      7. *-commutative N/A

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

      8. distribute-rgt-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

          \[\leadsto y4 \cdot \left(y1 \cdot \color{blue}{\mathsf{fma}\left(y3, -1 \cdot j, k \cdot y2\right)}\right) \]

      11. mul-1-neg N/A

          \[\leadsto y4 \cdot \left(y1 \cdot \mathsf{fma}\left(y3, \color{blue}{\mathsf{neg}\left(j\right)}, k \cdot y2\right)\right) \]

      12. lower-neg.f64 N/A

          \[\leadsto y4 \cdot \left(y1 \cdot \mathsf{fma}\left(y3, \color{blue}{\mathsf{neg}\left(j\right)}, k \cdot y2\right)\right) \]

      13. *-commutative N/A

          \[\leadsto y4 \cdot \left(y1 \cdot \mathsf{fma}\left(y3, \mathsf{neg}\left(j\right), \color{blue}{y2 \cdot k}\right)\right) \]

      14. lower-*.f64 61.4

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

   8. Simplified 61.4%

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

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -4.4 \cdot 10^{+129}:\\ \;\;\;\;y4 \cdot \left(c \cdot \mathsf{fma}\left(y, y3, t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;y4 \leq -1.35 \cdot 10^{-294}:\\ \;\;\;\;a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, x \cdot b\right)\right)\\ \mathbf{elif}\;y4 \leq 6.5 \cdot 10^{-227}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;y4 \leq 5 \cdot 10^{-105}:\\ \;\;\;\;a \cdot \left(y3 \cdot \mathsf{fma}\left(-y, y5, z \cdot y1\right)\right)\\ \mathbf{elif}\;y4 \leq 3.8 \cdot 10^{+63}:\\ \;\;\;\;a \cdot \left(y2 \cdot \mathsf{fma}\left(-x, y1, t \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq 6 \cdot 10^{+164}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \mathsf{fma}\left(y3, -j, k \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 29.8% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot \left(j \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{if}\;y4 \leq -4.4 \cdot 10^{+129}:\\ \;\;\;\;y4 \cdot \left(c \cdot \mathsf{fma}\left(y, y3, t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;y4 \leq -1.35 \cdot 10^{-294}:\\ \;\;\;\;a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, x \cdot b\right)\right)\\ \mathbf{elif}\;y4 \leq 6.5 \cdot 10^{-227}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq 5 \cdot 10^{-105}:\\ \;\;\;\;a \cdot \left(y3 \cdot \mathsf{fma}\left(-y, y5, z \cdot y1\right)\right)\\ \mathbf{elif}\;y4 \leq 3.8 \cdot 10^{+63}:\\ \;\;\;\;a \cdot \left(y2 \cdot \mathsf{fma}\left(-x, y1, t \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y4 (* j (- (* t b) (* y1 y3))))))
   (if (<= y4 -4.4e+129)
     (* y4 (* c (fma y y3 (* t (- y2)))))
     (if (<= y4 -1.35e-294)
       (* a (* y (fma (- y3) y5 (* x b))))
       (if (<= y4 6.5e-227)
         t_1
         (if (<= y4 5e-105)
           (* a (* y3 (fma (- y) y5 (* z y1))))
           (if (<= y4 3.8e+63) (* a (* y2 (fma (- x) y1 (* t y5)))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * (j * ((t * b) - (y1 * y3)));
	double tmp;
	if (y4 <= -4.4e+129) {
		tmp = y4 * (c * fma(y, y3, (t * -y2)));
	} else if (y4 <= -1.35e-294) {
		tmp = a * (y * fma(-y3, y5, (x * b)));
	} else if (y4 <= 6.5e-227) {
		tmp = t_1;
	} else if (y4 <= 5e-105) {
		tmp = a * (y3 * fma(-y, y5, (z * y1)));
	} else if (y4 <= 3.8e+63) {
		tmp = a * (y2 * fma(-x, y1, (t * y5)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y4 * Float64(j * Float64(Float64(t * b) - Float64(y1 * y3))))
	tmp = 0.0
	if (y4 <= -4.4e+129)
		tmp = Float64(y4 * Float64(c * fma(y, y3, Float64(t * Float64(-y2)))));
	elseif (y4 <= -1.35e-294)
		tmp = Float64(a * Float64(y * fma(Float64(-y3), y5, Float64(x * b))));
	elseif (y4 <= 6.5e-227)
		tmp = t_1;
	elseif (y4 <= 5e-105)
		tmp = Float64(a * Float64(y3 * fma(Float64(-y), y5, Float64(z * y1))));
	elseif (y4 <= 3.8e+63)
		tmp = Float64(a * Float64(y2 * fma(Float64(-x), y1, Float64(t * y5))));
	else
		tmp = t_1;
	end
	return 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[(j * N[(N[(t * b), $MachinePrecision] - N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -4.4e+129], N[(y4 * N[(c * N[(y * y3 + N[(t * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -1.35e-294], N[(a * N[(y * N[((-y3) * y5 + N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 6.5e-227], t$95$1, If[LessEqual[y4, 5e-105], N[(a * N[(y3 * N[((-y) * y5 + N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 3.8e+63], N[(a * N[(y2 * N[((-x) * y1 + N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y4 < -4.3999999999999999e129

   1. Initial program 23.5%

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

   3. Taylor expanded in y4 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   5. Simplified 67.8%

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

   6. Taylor expanded in c around inf

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

      1. lower-*.f64 N/A

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

      2. cancel-sign-sub-inv N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto y4 \cdot \left(c \cdot \color{blue}{\mathsf{fma}\left(y, y3, \left(\mathsf{neg}\left(t\right)\right) \cdot y2\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto y4 \cdot \left(c \cdot \mathsf{fma}\left(y, y3, \color{blue}{\left(-1 \cdot t\right)} \cdot y2\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(c \cdot \mathsf{fma}\left(y, y3, \color{blue}{\left(-1 \cdot t\right) \cdot y2}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto y4 \cdot \left(c \cdot \mathsf{fma}\left(y, y3, \color{blue}{\left(\mathsf{neg}\left(t\right)\right)} \cdot y2\right)\right) \]

      7. lower-neg.f64 65.3

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

   8. Simplified 65.3%

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

   if -4.3999999999999999e129 < y4 < -1.35000000000000005e-294

   1. Initial program 19.6%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

   5. Simplified 51.5%

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

   6. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y3\right)}, y5, b \cdot x\right)\right) \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y3\right)}, y5, b \cdot x\right)\right) \]

      7. lower-*.f64 47.3

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

   8. Simplified 47.3%

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

   if -1.35000000000000005e-294 < y4 < 6.4999999999999996e-227 or 3.8000000000000001e63 < y4

   1. Initial program 25.4%

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

   3. Taylor expanded in y4 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   5. Simplified 55.1%

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

   6. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 49.8

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

   8. Simplified 49.8%

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

   if 6.4999999999999996e-227 < y4 < 4.99999999999999963e-105

   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. Add Preprocessing

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

   5. Simplified 54.6%

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

   6. Taylor expanded in y3 around inf

      \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot y, y5, y1 \cdot z\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y\right)}, y5, y1 \cdot z\right)\right) \]

      5. lower-neg.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y\right)}, y5, y1 \cdot z\right)\right) \]

      6. lower-*.f64 54.3

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

   8. Simplified 54.3%

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

   if 4.99999999999999963e-105 < y4 < 3.8000000000000001e63

   1. Initial program 37.9%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

   5. Simplified 52.1%

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

   6. Taylor expanded in y2 around inf

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

      1. lower-*.f64 N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. mul-1-neg N/A

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y1, t \cdot y5\right)\right) \]

      5. lower-neg.f64 N/A

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y1, t \cdot y5\right)\right) \]

      6. lower-*.f64 46.4

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

   8. Simplified 46.4%

      \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \mathsf{fma}\left(-x, y1, t \cdot y5\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -4.4 \cdot 10^{+129}:\\ \;\;\;\;y4 \cdot \left(c \cdot \mathsf{fma}\left(y, y3, t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;y4 \leq -1.35 \cdot 10^{-294}:\\ \;\;\;\;a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, x \cdot b\right)\right)\\ \mathbf{elif}\;y4 \leq 6.5 \cdot 10^{-227}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;y4 \leq 5 \cdot 10^{-105}:\\ \;\;\;\;a \cdot \left(y3 \cdot \mathsf{fma}\left(-y, y5, z \cdot y1\right)\right)\\ \mathbf{elif}\;y4 \leq 3.8 \cdot 10^{+63}:\\ \;\;\;\;a \cdot \left(y2 \cdot \mathsf{fma}\left(-x, y1, t \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 31.6% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, x \cdot b\right)\right)\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-302}:\\ \;\;\;\;\left(t \cdot y4\right) \cdot \left(b \cdot j - c \cdot y2\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-156}:\\ \;\;\;\;k \cdot \left(y1 \cdot \mathsf{fma}\left(z, -i, y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+52}:\\ \;\;\;\;\left(t \cdot y5\right) \cdot \mathsf{fma}\left(a, y2, i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y (fma (- y3) y5 (* x b))))))
   (if (<= y -8.5e+34)
     t_1
     (if (<= y 9e-302)
       (* (* t y4) (- (* b j) (* c y2)))
       (if (<= y 1.2e-156)
         (* k (* y1 (fma z (- i) (* y2 y4))))
         (if (<= y 2.8e+52) (* (* t y5) (fma a y2 (* i (- j)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y * fma(-y3, y5, (x * b)));
	double tmp;
	if (y <= -8.5e+34) {
		tmp = t_1;
	} else if (y <= 9e-302) {
		tmp = (t * y4) * ((b * j) - (c * y2));
	} else if (y <= 1.2e-156) {
		tmp = k * (y1 * fma(z, -i, (y2 * y4)));
	} else if (y <= 2.8e+52) {
		tmp = (t * y5) * fma(a, y2, (i * -j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y * fma(Float64(-y3), y5, Float64(x * b))))
	tmp = 0.0
	if (y <= -8.5e+34)
		tmp = t_1;
	elseif (y <= 9e-302)
		tmp = Float64(Float64(t * y4) * Float64(Float64(b * j) - Float64(c * y2)));
	elseif (y <= 1.2e-156)
		tmp = Float64(k * Float64(y1 * fma(z, Float64(-i), Float64(y2 * y4))));
	elseif (y <= 2.8e+52)
		tmp = Float64(Float64(t * y5) * fma(a, y2, Float64(i * Float64(-j))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y * N[((-y3) * y5 + N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.5e+34], t$95$1, If[LessEqual[y, 9e-302], N[(N[(t * y4), $MachinePrecision] * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e-156], N[(k * N[(y1 * N[(z * (-i) + N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e+52], N[(N[(t * y5), $MachinePrecision] * N[(a * y2 + N[(i * (-j)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.5000000000000003e34 or 2.8e52 < y

   1. Initial program 18.8%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

   5. Simplified 49.5%

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

   6. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y3\right)}, y5, b \cdot x\right)\right) \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y3\right)}, y5, b \cdot x\right)\right) \]

      7. lower-*.f64 54.5

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

   8. Simplified 54.5%

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

   if -8.5000000000000003e34 < y < 9.00000000000000018e-302

   1. Initial program 34.7%

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

   3. Taylor expanded in y4 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   5. Simplified 47.5%

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

   6. Taylor expanded in t around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 44.5

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

   8. Simplified 44.5%

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

   if 9.00000000000000018e-302 < y < 1.2e-156

   1. Initial program 28.8%

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

   3. Taylor expanded in y1 around inf

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

      1. lower-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. associate--l+ N/A

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

      4. mul-1-neg N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. lower-fma.f64 N/A

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

   5. Simplified 57.4%

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

   6. Taylor expanded in k around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. *-commutative N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

         \[\leadsto k \cdot \left(y1 \cdot \color{blue}{\mathsf{fma}\left(z, -1 \cdot i, y2 \cdot y4\right)}\right) \]

      8. mul-1-neg N/A

         \[\leadsto k \cdot \left(y1 \cdot \mathsf{fma}\left(z, \color{blue}{\mathsf{neg}\left(i\right)}, y2 \cdot y4\right)\right) \]

      9. lower-neg.f64 N/A

         \[\leadsto k \cdot \left(y1 \cdot \mathsf{fma}\left(z, \color{blue}{\mathsf{neg}\left(i\right)}, y2 \cdot y4\right)\right) \]

      10. lower-*.f64 51.1

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

   8. Simplified 51.1%

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

   if 1.2e-156 < y < 2.8e52

   1. Initial program 31.7%

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

   3. Taylor expanded in y5 around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Simplified 48.1%

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

   6. Taylor expanded in t around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. associate-*r* N/A

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

      7. lower-*.f64 N/A

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

      8. mul-1-neg N/A

         \[\leadsto \left(t \cdot y5\right) \cdot \mathsf{fma}\left(a, y2, \color{blue}{\left(\mathsf{neg}\left(i\right)\right)} \cdot j\right) \]

      9. lower-neg.f64 48.3

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

   8. Simplified 48.3%

      \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \mathsf{fma}\left(a, y2, \left(-i\right) \cdot j\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+34}:\\ \;\;\;\;a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, x \cdot b\right)\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-302}:\\ \;\;\;\;\left(t \cdot y4\right) \cdot \left(b \cdot j - c \cdot y2\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-156}:\\ \;\;\;\;k \cdot \left(y1 \cdot \mathsf{fma}\left(z, -i, y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+52}:\\ \;\;\;\;\left(t \cdot y5\right) \cdot \mathsf{fma}\left(a, y2, i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, x \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 32.1% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, x \cdot b\right)\right)\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-302}:\\ \;\;\;\;\left(t \cdot y4\right) \cdot \left(b \cdot j - c \cdot y2\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-10}:\\ \;\;\;\;k \cdot \left(y1 \cdot \mathsf{fma}\left(z, -i, y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+82}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y (fma (- y3) y5 (* x b))))))
   (if (<= y -8.5e+34)
     t_1
     (if (<= y 9e-302)
       (* (* t y4) (- (* b j) (* c y2)))
       (if (<= y 2.3e-10)
         (* k (* y1 (fma z (- i) (* y2 y4))))
         (if (<= y 4.1e+82) (* b (* t (- (* j y4) (* z a)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y * fma(-y3, y5, (x * b)));
	double tmp;
	if (y <= -8.5e+34) {
		tmp = t_1;
	} else if (y <= 9e-302) {
		tmp = (t * y4) * ((b * j) - (c * y2));
	} else if (y <= 2.3e-10) {
		tmp = k * (y1 * fma(z, -i, (y2 * y4)));
	} else if (y <= 4.1e+82) {
		tmp = b * (t * ((j * y4) - (z * a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y * fma(Float64(-y3), y5, Float64(x * b))))
	tmp = 0.0
	if (y <= -8.5e+34)
		tmp = t_1;
	elseif (y <= 9e-302)
		tmp = Float64(Float64(t * y4) * Float64(Float64(b * j) - Float64(c * y2)));
	elseif (y <= 2.3e-10)
		tmp = Float64(k * Float64(y1 * fma(z, Float64(-i), Float64(y2 * y4))));
	elseif (y <= 4.1e+82)
		tmp = Float64(b * Float64(t * Float64(Float64(j * y4) - Float64(z * a))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y * N[((-y3) * y5 + N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.5e+34], t$95$1, If[LessEqual[y, 9e-302], N[(N[(t * y4), $MachinePrecision] * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e-10], N[(k * N[(y1 * N[(z * (-i) + N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.1e+82], N[(b * N[(t * N[(N[(j * y4), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.5000000000000003e34 or 4.09999999999999995e82 < y

   1. Initial program 17.7%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

   5. Simplified 49.9%

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

   6. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y3\right)}, y5, b \cdot x\right)\right) \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y3\right)}, y5, b \cdot x\right)\right) \]

      7. lower-*.f64 56.9

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

   8. Simplified 56.9%

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

   if -8.5000000000000003e34 < y < 9.00000000000000018e-302

   1. Initial program 34.7%

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

   3. Taylor expanded in y4 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   5. Simplified 47.5%

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

   6. Taylor expanded in t around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 44.5

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

   8. Simplified 44.5%

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

   if 9.00000000000000018e-302 < y < 2.30000000000000007e-10

   1. Initial program 30.7%

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

   3. Taylor expanded in y1 around inf

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

      1. lower-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. associate--l+ N/A

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

      4. mul-1-neg N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. lower-fma.f64 N/A

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

   5. Simplified 46.7%

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

   6. Taylor expanded in k around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. *-commutative N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

         \[\leadsto k \cdot \left(y1 \cdot \color{blue}{\mathsf{fma}\left(z, -1 \cdot i, y2 \cdot y4\right)}\right) \]

      8. mul-1-neg N/A

         \[\leadsto k \cdot \left(y1 \cdot \mathsf{fma}\left(z, \color{blue}{\mathsf{neg}\left(i\right)}, y2 \cdot y4\right)\right) \]

      9. lower-neg.f64 N/A

         \[\leadsto k \cdot \left(y1 \cdot \mathsf{fma}\left(z, \color{blue}{\mathsf{neg}\left(i\right)}, y2 \cdot y4\right)\right) \]

      10. lower-*.f64 43.6

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

   8. Simplified 43.6%

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

   if 2.30000000000000007e-10 < y < 4.09999999999999995e82

   1. Initial program 31.3%

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

   3. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower--.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 44.6

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

   5. Simplified 44.6%

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

   6. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

         \[\leadsto b \cdot \left(t \cdot \left(j \cdot y4 + \color{blue}{\left(\mathsf{neg}\left(a \cdot z\right)\right)}\right)\right) \]

      4. unsub-neg N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 51.2

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

   8. Simplified 51.2%

      \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(j \cdot y4 - a \cdot z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+34}:\\ \;\;\;\;a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, x \cdot b\right)\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-302}:\\ \;\;\;\;\left(t \cdot y4\right) \cdot \left(b \cdot j - c \cdot y2\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-10}:\\ \;\;\;\;k \cdot \left(y1 \cdot \mathsf{fma}\left(z, -i, y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+82}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, x \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 32.0% accurate, 4.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, x \cdot b\right)\right)\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-10}:\\ \;\;\;\;k \cdot \left(y1 \cdot \mathsf{fma}\left(z, -i, y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+82}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y (fma (- y3) y5 (* x b))))))
   (if (<= y -4.5e-31)
     t_1
     (if (<= y 2.3e-10)
       (* k (* y1 (fma z (- i) (* y2 y4))))
       (if (<= y 4.1e+82) (* b (* t (- (* j y4) (* z a)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y * fma(-y3, y5, (x * b)));
	double tmp;
	if (y <= -4.5e-31) {
		tmp = t_1;
	} else if (y <= 2.3e-10) {
		tmp = k * (y1 * fma(z, -i, (y2 * y4)));
	} else if (y <= 4.1e+82) {
		tmp = b * (t * ((j * y4) - (z * a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y * fma(Float64(-y3), y5, Float64(x * b))))
	tmp = 0.0
	if (y <= -4.5e-31)
		tmp = t_1;
	elseif (y <= 2.3e-10)
		tmp = Float64(k * Float64(y1 * fma(z, Float64(-i), Float64(y2 * y4))));
	elseif (y <= 4.1e+82)
		tmp = Float64(b * Float64(t * Float64(Float64(j * y4) - Float64(z * a))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y * N[((-y3) * y5 + N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.5e-31], t$95$1, If[LessEqual[y, 2.3e-10], N[(k * N[(y1 * N[(z * (-i) + N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.1e+82], N[(b * N[(t * N[(N[(j * y4), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.5000000000000004e-31 or 4.09999999999999995e82 < y

   1. Initial program 17.8%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

   5. Simplified 49.9%

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

   6. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y3\right)}, y5, b \cdot x\right)\right) \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y3\right)}, y5, b \cdot x\right)\right) \]

      7. lower-*.f64 55.7

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

   8. Simplified 55.7%

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

   if -4.5000000000000004e-31 < y < 2.30000000000000007e-10

   1. Initial program 34.3%

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

   3. Taylor expanded in y1 around inf

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

      1. lower-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. associate--l+ N/A

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

      4. mul-1-neg N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. lower-fma.f64 N/A

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

   5. Simplified 43.1%

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

   6. Taylor expanded in k around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. *-commutative N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

         \[\leadsto k \cdot \left(y1 \cdot \color{blue}{\mathsf{fma}\left(z, -1 \cdot i, y2 \cdot y4\right)}\right) \]

      8. mul-1-neg N/A

         \[\leadsto k \cdot \left(y1 \cdot \mathsf{fma}\left(z, \color{blue}{\mathsf{neg}\left(i\right)}, y2 \cdot y4\right)\right) \]

      9. lower-neg.f64 N/A

         \[\leadsto k \cdot \left(y1 \cdot \mathsf{fma}\left(z, \color{blue}{\mathsf{neg}\left(i\right)}, y2 \cdot y4\right)\right) \]

      10. lower-*.f64 37.0

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

   8. Simplified 37.0%

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

   if 2.30000000000000007e-10 < y < 4.09999999999999995e82

   1. Initial program 31.3%

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

   3. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower--.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 44.6

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

   5. Simplified 44.6%

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

   6. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

         \[\leadsto b \cdot \left(t \cdot \left(j \cdot y4 + \color{blue}{\left(\mathsf{neg}\left(a \cdot z\right)\right)}\right)\right) \]

      4. unsub-neg N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 51.2

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

   8. Simplified 51.2%

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

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-31}:\\ \;\;\;\;a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, x \cdot b\right)\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-10}:\\ \;\;\;\;k \cdot \left(y1 \cdot \mathsf{fma}\left(z, -i, y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+82}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, x \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 31.1% accurate, 4.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, x \cdot b\right)\right)\\ \mathbf{if}\;y \leq -1.45 \cdot 10^{-190}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-42}:\\ \;\;\;\;a \cdot \left(z \cdot \mathsf{fma}\left(y1, y3, t \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+82}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y (fma (- y3) y5 (* x b))))))
   (if (<= y -1.45e-190)
     t_1
     (if (<= y 3.1e-42)
       (* a (* z (fma y1 y3 (* t (- b)))))
       (if (<= y 4.1e+82) (* b (* t (- (* j y4) (* z a)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y * fma(-y3, y5, (x * b)));
	double tmp;
	if (y <= -1.45e-190) {
		tmp = t_1;
	} else if (y <= 3.1e-42) {
		tmp = a * (z * fma(y1, y3, (t * -b)));
	} else if (y <= 4.1e+82) {
		tmp = b * (t * ((j * y4) - (z * a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y * fma(Float64(-y3), y5, Float64(x * b))))
	tmp = 0.0
	if (y <= -1.45e-190)
		tmp = t_1;
	elseif (y <= 3.1e-42)
		tmp = Float64(a * Float64(z * fma(y1, y3, Float64(t * Float64(-b)))));
	elseif (y <= 4.1e+82)
		tmp = Float64(b * Float64(t * Float64(Float64(j * y4) - Float64(z * a))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y * N[((-y3) * y5 + N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.45e-190], t$95$1, If[LessEqual[y, 3.1e-42], N[(a * N[(z * N[(y1 * y3 + N[(t * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.1e+82], N[(b * N[(t * N[(N[(j * y4), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4500000000000001e-190 or 4.09999999999999995e82 < y

   1. Initial program 21.0%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

   5. Simplified 45.1%

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

   6. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y3\right)}, y5, b \cdot x\right)\right) \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y3\right)}, y5, b \cdot x\right)\right) \]

      7. lower-*.f64 49.9

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

   8. Simplified 49.9%

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

   if -1.4500000000000001e-190 < y < 3.1000000000000003e-42

   1. Initial program 34.2%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

   5. Simplified 41.4%

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

   6. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. mul-1-neg N/A

         \[\leadsto a \cdot \left(z \cdot \mathsf{fma}\left(y1, y3, \color{blue}{\left(\mathsf{neg}\left(b\right)\right)} \cdot t\right)\right) \]

      7. lower-neg.f64 38.6

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

   8. Simplified 38.6%

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

   if 3.1000000000000003e-42 < y < 4.09999999999999995e82

   1. Initial program 30.4%

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

   3. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower--.f64 N/A

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

      15. lower-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(\color{blue}{j \cdot x} - k \cdot z\right)\right) \]

      16. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

      17. lower-*.f64 48.7

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 48.7%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 + -1 \cdot \left(a \cdot z\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto b \cdot \left(t \cdot \left(j \cdot y4 + \color{blue}{\left(\mathsf{neg}\left(a \cdot z\right)\right)}\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 - a \cdot z\right)}\right) \]

      5. lower--.f64 N/A

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 - a \cdot z\right)}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto b \cdot \left(t \cdot \left(\color{blue}{j \cdot y4} - a \cdot z\right)\right) \]

      7. lower-*.f64 44.6

         \[\leadsto b \cdot \left(t \cdot \left(j \cdot y4 - \color{blue}{a \cdot z}\right)\right) \]

   8. Simplified 44.6%

      \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(j \cdot y4 - a \cdot z\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-190}:\\ \;\;\;\;a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, x \cdot b\right)\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-42}:\\ \;\;\;\;a \cdot \left(z \cdot \mathsf{fma}\left(y1, y3, t \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+82}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, x \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 20.1% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+19}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(t \cdot b\right)\right)\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-233}:\\ \;\;\;\;\left(-a\right) \cdot \left(y5 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-230}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(y4 \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-a \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= t -2.05e+19)
   (* y4 (* j (* t b)))
   (if (<= t -1.85e-233)
     (* (- a) (* y5 (* y y3)))
     (if (<= t 4.1e-230)
       (* j (* y1 (* y4 (- y3))))
       (- (* 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 (t <= -2.05e+19) {
		tmp = y4 * (j * (t * b));
	} else if (t <= -1.85e-233) {
		tmp = -a * (y5 * (y * y3));
	} else if (t <= 4.1e-230) {
		tmp = j * (y1 * (y4 * -y3));
	} 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 (t <= (-2.05d+19)) then
        tmp = y4 * (j * (t * b))
    else if (t <= (-1.85d-233)) then
        tmp = -a * (y5 * (y * y3))
    else if (t <= 4.1d-230) then
        tmp = j * (y1 * (y4 * -y3))
    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 (t <= -2.05e+19) {
		tmp = y4 * (j * (t * b));
	} else if (t <= -1.85e-233) {
		tmp = -a * (y5 * (y * y3));
	} else if (t <= 4.1e-230) {
		tmp = j * (y1 * (y4 * -y3));
	} 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 t <= -2.05e+19:
		tmp = y4 * (j * (t * b))
	elif t <= -1.85e-233:
		tmp = -a * (y5 * (y * y3))
	elif t <= 4.1e-230:
		tmp = j * (y1 * (y4 * -y3))
	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 (t <= -2.05e+19)
		tmp = Float64(y4 * Float64(j * Float64(t * b)));
	elseif (t <= -1.85e-233)
		tmp = Float64(Float64(-a) * Float64(y5 * Float64(y * y3)));
	elseif (t <= 4.1e-230)
		tmp = Float64(j * Float64(y1 * Float64(y4 * Float64(-y3))));
	else
		tmp = Float64(-Float64(a * Float64(y * Float64(y3 * y5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (t <= -2.05e+19)
		tmp = y4 * (j * (t * b));
	elseif (t <= -1.85e-233)
		tmp = -a * (y5 * (y * y3));
	elseif (t <= 4.1e-230)
		tmp = j * (y1 * (y4 * -y3));
	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[t, -2.05e+19], N[(y4 * N[(j * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.85e-233], N[((-a) * N[(y5 * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.1e-230], N[(j * N[(y1 * N[(y4 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], (-N[(a * N[(y * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision])]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.05e19

   1. Initial program 29.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Simplified 51.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right)\right) - c \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto y4 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto y4 \cdot \left(j \cdot \left(b \cdot t + \color{blue}{\left(\mathsf{neg}\left(y1 \cdot y3\right)\right)}\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t - y1 \cdot y3\right)}\right) \]

      5. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t - y1 \cdot y3\right)}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(j \cdot \left(\color{blue}{b \cdot t} - y1 \cdot y3\right)\right) \]

      7. lower-*.f64 46.0

         \[\leadsto y4 \cdot \left(j \cdot \left(b \cdot t - \color{blue}{y1 \cdot y3}\right)\right) \]

   8. Simplified 46.0%

      \[\leadsto y4 \cdot \color{blue}{\left(j \cdot \left(b \cdot t - y1 \cdot y3\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t\right)}\right) \]
   10. Step-by-step derivation

       1. lower-*.f64 46.2

          \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t\right)}\right) \]

   11. Simplified 46.2%

       \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t\right)}\right) \]

   if -2.05e19 < t < -1.8499999999999999e-233

   1. Initial program 21.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Simplified 54.8%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto a \cdot \left(y \cdot \left(\color{blue}{\left(-1 \cdot y3\right) \cdot y5} + b \cdot x\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot y3, y5, b \cdot x\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y3\right)}, y5, b \cdot x\right)\right) \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y3\right)}, y5, b \cdot x\right)\right) \]

      7. lower-*.f64 42.2

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, \color{blue}{b \cdot x}\right)\right) \]

   8. Simplified 42.2%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, b \cdot x\right)\right)} \]

   9. Taylor expanded in y3 around inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(a \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]

       2. distribute-rgt-neg-in N/A

          \[\leadsto \color{blue}{a \cdot \left(\mathsf{neg}\left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]

       3. mul-1-neg N/A

          \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]

       4. lower-*.f64 N/A

          \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]

       5. mul-1-neg N/A

          \[\leadsto a \cdot \color{blue}{\left(\mathsf{neg}\left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]

       6. *-commutative N/A

          \[\leadsto a \cdot \left(\mathsf{neg}\left(\color{blue}{\left(y3 \cdot y5\right) \cdot y}\right)\right) \]

       7. distribute-lft-neg-in N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(\mathsf{neg}\left(y3 \cdot y5\right)\right) \cdot y\right)} \]

       8. mul-1-neg N/A

          \[\leadsto a \cdot \left(\color{blue}{\left(-1 \cdot \left(y3 \cdot y5\right)\right)} \cdot y\right) \]

       9. lower-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot y5\right)\right) \cdot y\right)} \]

       10. mul-1-neg N/A

           \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y3 \cdot y5\right)\right)} \cdot y\right) \]

       11. *-commutative N/A

           \[\leadsto a \cdot \left(\left(\mathsf{neg}\left(\color{blue}{y5 \cdot y3}\right)\right) \cdot y\right) \]

       12. distribute-rgt-neg-in N/A

           \[\leadsto a \cdot \left(\color{blue}{\left(y5 \cdot \left(\mathsf{neg}\left(y3\right)\right)\right)} \cdot y\right) \]

       13. mul-1-neg N/A

           \[\leadsto a \cdot \left(\left(y5 \cdot \color{blue}{\left(-1 \cdot y3\right)}\right) \cdot y\right) \]

       14. lower-*.f64 N/A

           \[\leadsto a \cdot \left(\color{blue}{\left(y5 \cdot \left(-1 \cdot y3\right)\right)} \cdot y\right) \]

       15. mul-1-neg N/A

           \[\leadsto a \cdot \left(\left(y5 \cdot \color{blue}{\left(\mathsf{neg}\left(y3\right)\right)}\right) \cdot y\right) \]

       16. lower-neg.f64 33.9

           \[\leadsto a \cdot \left(\left(y5 \cdot \color{blue}{\left(-y3\right)}\right) \cdot y\right) \]

   11. Simplified 33.9%

       \[\leadsto \color{blue}{a \cdot \left(\left(y5 \cdot \left(-y3\right)\right) \cdot y\right)} \]
   12. Step-by-step derivation

       1. lift-neg.f64 N/A

          \[\leadsto a \cdot \left(\left(y5 \cdot \color{blue}{\left(\mathsf{neg}\left(y3\right)\right)}\right) \cdot y\right) \]

       2. associate-*l* N/A

          \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(\left(\mathsf{neg}\left(y3\right)\right) \cdot y\right)\right)} \]

       3. *-commutative N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(\left(\mathsf{neg}\left(y3\right)\right) \cdot y\right) \cdot y5\right)} \]

       4. lower-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(\left(\mathsf{neg}\left(y3\right)\right) \cdot y\right) \cdot y5\right)} \]

       5. *-commutative N/A

          \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot \left(\mathsf{neg}\left(y3\right)\right)\right)} \cdot y5\right) \]

       6. lower-*.f64 36.0

          \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot \left(-y3\right)\right)} \cdot y5\right) \]

   13. Applied egg-rr 36.0%

       \[\leadsto a \cdot \color{blue}{\left(\left(y \cdot \left(-y3\right)\right) \cdot y5\right)} \]

   if -1.8499999999999999e-233 < t < 4.1000000000000002e-230

   1. Initial program 30.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Simplified 50.7%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right)\right) - c \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto y4 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto y4 \cdot \left(j \cdot \left(b \cdot t + \color{blue}{\left(\mathsf{neg}\left(y1 \cdot y3\right)\right)}\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t - y1 \cdot y3\right)}\right) \]

      5. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t - y1 \cdot y3\right)}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(j \cdot \left(\color{blue}{b \cdot t} - y1 \cdot y3\right)\right) \]

      7. lower-*.f64 32.1

         \[\leadsto y4 \cdot \left(j \cdot \left(b \cdot t - \color{blue}{y1 \cdot y3}\right)\right) \]

   8. Simplified 32.1%

      \[\leadsto y4 \cdot \color{blue}{\left(j \cdot \left(b \cdot t - y1 \cdot y3\right)\right)} \]

   9. Taylor expanded in b around 0

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(y1 \cdot \left(y3 \cdot y4\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(y1 \cdot \left(y3 \cdot y4\right)\right)\right)} \]

       2. lower-neg.f64 N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(y1 \cdot \left(y3 \cdot y4\right)\right)\right)} \]

       3. lower-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{j \cdot \left(y1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

       4. lower-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(j \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

       5. lower-*.f64 35.3

          \[\leadsto -j \cdot \left(y1 \cdot \color{blue}{\left(y3 \cdot y4\right)}\right) \]

   11. Simplified 35.3%

       \[\leadsto \color{blue}{-j \cdot \left(y1 \cdot \left(y3 \cdot y4\right)\right)} \]

   if 4.1000000000000002e-230 < t

   1. Initial program 22.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Simplified 48.0%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto a \cdot \left(y \cdot \left(\color{blue}{\left(-1 \cdot y3\right) \cdot y5} + b \cdot x\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot y3, y5, b \cdot x\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y3\right)}, y5, b \cdot x\right)\right) \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y3\right)}, y5, b \cdot x\right)\right) \]

      7. lower-*.f64 41.8

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, \color{blue}{b \cdot x}\right)\right) \]

   8. Simplified 41.8%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, b \cdot x\right)\right)} \]

   9. Taylor expanded in y3 around inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(a \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]

       2. distribute-rgt-neg-in N/A

          \[\leadsto \color{blue}{a \cdot \left(\mathsf{neg}\left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]

       3. mul-1-neg N/A

          \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]

       4. lower-*.f64 N/A

          \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]

       5. mul-1-neg N/A

          \[\leadsto a \cdot \color{blue}{\left(\mathsf{neg}\left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]

       6. *-commutative N/A

          \[\leadsto a \cdot \left(\mathsf{neg}\left(\color{blue}{\left(y3 \cdot y5\right) \cdot y}\right)\right) \]

       7. distribute-lft-neg-in N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(\mathsf{neg}\left(y3 \cdot y5\right)\right) \cdot y\right)} \]

       8. mul-1-neg N/A

          \[\leadsto a \cdot \left(\color{blue}{\left(-1 \cdot \left(y3 \cdot y5\right)\right)} \cdot y\right) \]

       9. lower-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot y5\right)\right) \cdot y\right)} \]

       10. mul-1-neg N/A

           \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y3 \cdot y5\right)\right)} \cdot y\right) \]

       11. *-commutative N/A

           \[\leadsto a \cdot \left(\left(\mathsf{neg}\left(\color{blue}{y5 \cdot y3}\right)\right) \cdot y\right) \]

       12. distribute-rgt-neg-in N/A

           \[\leadsto a \cdot \left(\color{blue}{\left(y5 \cdot \left(\mathsf{neg}\left(y3\right)\right)\right)} \cdot y\right) \]

       13. mul-1-neg N/A

           \[\leadsto a \cdot \left(\left(y5 \cdot \color{blue}{\left(-1 \cdot y3\right)}\right) \cdot y\right) \]

       14. lower-*.f64 N/A

           \[\leadsto a \cdot \left(\color{blue}{\left(y5 \cdot \left(-1 \cdot y3\right)\right)} \cdot y\right) \]

       15. mul-1-neg N/A

           \[\leadsto a \cdot \left(\left(y5 \cdot \color{blue}{\left(\mathsf{neg}\left(y3\right)\right)}\right) \cdot y\right) \]

       16. lower-neg.f64 29.3

           \[\leadsto a \cdot \left(\left(y5 \cdot \color{blue}{\left(-y3\right)}\right) \cdot y\right) \]

   11. Simplified 29.3%

       \[\leadsto \color{blue}{a \cdot \left(\left(y5 \cdot \left(-y3\right)\right) \cdot y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 36.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+19}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(t \cdot b\right)\right)\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-233}:\\ \;\;\;\;\left(-a\right) \cdot \left(y5 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-230}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(y4 \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-a \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 21.8% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -9600000000:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(x \cdot \left(-y1\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -4.8 \cdot 10^{-292}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a\right)\right)\\ \mathbf{elif}\;y2 \leq 2.05 \cdot 10^{+77}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(t \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot y5\right) \cdot \left(-y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -9600000000.0)
   (* a (* y2 (* x (- y1))))
   (if (<= y2 -4.8e-292)
     (* b (* x (* y a)))
     (if (<= y2 2.05e+77) (* y4 (* j (* t b))) (* k (* (* y2 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) {
	double tmp;
	if (y2 <= -9600000000.0) {
		tmp = a * (y2 * (x * -y1));
	} else if (y2 <= -4.8e-292) {
		tmp = b * (x * (y * a));
	} else if (y2 <= 2.05e+77) {
		tmp = y4 * (j * (t * b));
	} else {
		tmp = k * ((y2 * y5) * -y0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y2 <= (-9600000000.0d0)) then
        tmp = a * (y2 * (x * -y1))
    else if (y2 <= (-4.8d-292)) then
        tmp = b * (x * (y * a))
    else if (y2 <= 2.05d+77) then
        tmp = y4 * (j * (t * b))
    else
        tmp = k * ((y2 * y5) * -y0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -9600000000.0) {
		tmp = a * (y2 * (x * -y1));
	} else if (y2 <= -4.8e-292) {
		tmp = b * (x * (y * a));
	} else if (y2 <= 2.05e+77) {
		tmp = y4 * (j * (t * b));
	} else {
		tmp = k * ((y2 * y5) * -y0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y2 <= -9600000000.0:
		tmp = a * (y2 * (x * -y1))
	elif y2 <= -4.8e-292:
		tmp = b * (x * (y * a))
	elif y2 <= 2.05e+77:
		tmp = y4 * (j * (t * b))
	else:
		tmp = k * ((y2 * y5) * -y0)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y2 <= -9600000000.0)
		tmp = Float64(a * Float64(y2 * Float64(x * Float64(-y1))));
	elseif (y2 <= -4.8e-292)
		tmp = Float64(b * Float64(x * Float64(y * a)));
	elseif (y2 <= 2.05e+77)
		tmp = Float64(y4 * Float64(j * Float64(t * b)));
	else
		tmp = Float64(k * Float64(Float64(y2 * y5) * Float64(-y0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y2 <= -9600000000.0)
		tmp = a * (y2 * (x * -y1));
	elseif (y2 <= -4.8e-292)
		tmp = b * (x * (y * a));
	elseif (y2 <= 2.05e+77)
		tmp = y4 * (j * (t * b));
	else
		tmp = k * ((y2 * y5) * -y0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y2, -9600000000.0], N[(a * N[(y2 * N[(x * (-y1)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -4.8e-292], N[(b * N[(x * N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.05e+77], N[(y4 * N[(j * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(N[(y2 * y5), $MachinePrecision] * (-y0)), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y2 < -9.6e9

   1. Initial program 20.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Simplified 49.1%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(x \cdot y1\right) + t \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(x \cdot y1\right) + t \cdot y5\right)\right)} \]

      2. associate-*r* N/A

         \[\leadsto a \cdot \left(y2 \cdot \left(\color{blue}{\left(-1 \cdot x\right) \cdot y1} + t \cdot y5\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot x, y1, t \cdot y5\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y1, t \cdot y5\right)\right) \]

      5. lower-neg.f64 N/A

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y1, t \cdot y5\right)\right) \]

      6. lower-*.f64 40.6

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(-x, y1, \color{blue}{t \cdot y5}\right)\right) \]

   8. Simplified 40.6%

      \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \mathsf{fma}\left(-x, y1, t \cdot y5\right)\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(x \cdot \left(y1 \cdot y2\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(a \cdot \left(x \cdot \left(y1 \cdot y2\right)\right)\right)} \]

       2. distribute-rgt-neg-in N/A

          \[\leadsto \color{blue}{a \cdot \left(\mathsf{neg}\left(x \cdot \left(y1 \cdot y2\right)\right)\right)} \]

       3. mul-1-neg N/A

          \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(x \cdot \left(y1 \cdot y2\right)\right)\right)} \]

       4. lower-*.f64 N/A

          \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(x \cdot \left(y1 \cdot y2\right)\right)\right)} \]

       5. mul-1-neg N/A

          \[\leadsto a \cdot \color{blue}{\left(\mathsf{neg}\left(x \cdot \left(y1 \cdot y2\right)\right)\right)} \]

       6. *-commutative N/A

          \[\leadsto a \cdot \left(\mathsf{neg}\left(x \cdot \color{blue}{\left(y2 \cdot y1\right)}\right)\right) \]

       7. associate-*r* N/A

          \[\leadsto a \cdot \left(\mathsf{neg}\left(\color{blue}{\left(x \cdot y2\right) \cdot y1}\right)\right) \]

       8. distribute-lft-neg-out N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(\mathsf{neg}\left(x \cdot y2\right)\right) \cdot y1\right)} \]

       9. *-commutative N/A

          \[\leadsto a \cdot \left(\left(\mathsf{neg}\left(\color{blue}{y2 \cdot x}\right)\right) \cdot y1\right) \]

       10. distribute-rgt-neg-in N/A

           \[\leadsto a \cdot \left(\color{blue}{\left(y2 \cdot \left(\mathsf{neg}\left(x\right)\right)\right)} \cdot y1\right) \]

       11. mul-1-neg N/A

           \[\leadsto a \cdot \left(\left(y2 \cdot \color{blue}{\left(-1 \cdot x\right)}\right) \cdot y1\right) \]

       12. associate-*r* N/A

           \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(\left(-1 \cdot x\right) \cdot y1\right)\right)} \]

       13. associate-*r* N/A

           \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\left(-1 \cdot \left(x \cdot y1\right)\right)}\right) \]

       14. lower-*.f64 N/A

           \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(x \cdot y1\right)\right)\right)} \]

       15. associate-*r* N/A

           \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\left(\left(-1 \cdot x\right) \cdot y1\right)}\right) \]

       16. lower-*.f64 N/A

           \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\left(\left(-1 \cdot x\right) \cdot y1\right)}\right) \]

       17. mul-1-neg N/A

           \[\leadsto a \cdot \left(y2 \cdot \left(\color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot y1\right)\right) \]

       18. lower-neg.f64 33.6

           \[\leadsto a \cdot \left(y2 \cdot \left(\color{blue}{\left(-x\right)} \cdot y1\right)\right) \]

   11. Simplified 33.6%

       \[\leadsto \color{blue}{a \cdot \left(y2 \cdot \left(\left(-x\right) \cdot y1\right)\right)} \]

   if -9.6e9 < y2 < -4.8000000000000002e-292

   1. Initial program 28.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. lower--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{x \cdot y - t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. lower-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - \color{blue}{t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, \color{blue}{y4 \cdot \left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. lower--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - \color{blue}{k \cdot y}\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      13. lower-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

      14. lower--.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \color{blue}{\left(j \cdot x - k \cdot z\right)}\right) \]

      15. lower-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(\color{blue}{j \cdot x} - k \cdot z\right)\right) \]

      16. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

      17. lower-*.f64 34.6

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 34.6%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto b \cdot \color{blue}{\left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]
   7. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y + \left(\mathsf{neg}\left(j \cdot y0\right)\right)\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y + \color{blue}{-1 \cdot \left(j \cdot y0\right)}\right)\right) \]

      3. +-commutative N/A

         \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y0\right) + a \cdot y\right)}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(x \cdot \left(-1 \cdot \left(j \cdot y0\right) + a \cdot y\right)\right)} \]

      5. +-commutative N/A

         \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y + -1 \cdot \left(j \cdot y0\right)\right)}\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \color{blue}{\mathsf{fma}\left(a, y, -1 \cdot \left(j \cdot y0\right)\right)}\right) \]

      7. associate-*r* N/A

         \[\leadsto b \cdot \left(x \cdot \mathsf{fma}\left(a, y, \color{blue}{\left(-1 \cdot j\right) \cdot y0}\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \mathsf{fma}\left(a, y, \color{blue}{\left(-1 \cdot j\right) \cdot y0}\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto b \cdot \left(x \cdot \mathsf{fma}\left(a, y, \color{blue}{\left(\mathsf{neg}\left(j\right)\right)} \cdot y0\right)\right) \]

      10. lower-neg.f64 47.1

          \[\leadsto b \cdot \left(x \cdot \mathsf{fma}\left(a, y, \color{blue}{\left(-j\right)} \cdot y0\right)\right) \]

   8. Simplified 47.1%

      \[\leadsto b \cdot \color{blue}{\left(x \cdot \mathsf{fma}\left(a, y, \left(-j\right) \cdot y0\right)\right)} \]

   9. Taylor expanded in a around inf

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y\right)}\right) \]
   10. Step-by-step derivation

       1. lower-*.f64 33.5

          \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y\right)}\right) \]

   11. Simplified 33.5%

       \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y\right)}\right) \]

   if -4.8000000000000002e-292 < y2 < 2.05e77

   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. Add Preprocessing

   3. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Simplified 45.0%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right)\right) - c \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto y4 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto y4 \cdot \left(j \cdot \left(b \cdot t + \color{blue}{\left(\mathsf{neg}\left(y1 \cdot y3\right)\right)}\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t - y1 \cdot y3\right)}\right) \]

      5. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t - y1 \cdot y3\right)}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(j \cdot \left(\color{blue}{b \cdot t} - y1 \cdot y3\right)\right) \]

      7. lower-*.f64 45.5

         \[\leadsto y4 \cdot \left(j \cdot \left(b \cdot t - \color{blue}{y1 \cdot y3}\right)\right) \]

   8. Simplified 45.5%

      \[\leadsto y4 \cdot \color{blue}{\left(j \cdot \left(b \cdot t - y1 \cdot y3\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t\right)}\right) \]
   10. Step-by-step derivation

       1. lower-*.f64 33.5

          \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t\right)}\right) \]

   11. Simplified 33.5%

       \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t\right)}\right) \]

   if 2.05e77 < y2

   1. Initial program 24.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(\left(-1 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(y0 \cdot \left(\left(-1 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y0}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot \left(\mathsf{neg}\left(y0\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot y0\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot \left(-1 \cdot y0\right)} \]

   5. Simplified 36.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(y5, \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right), b \cdot \left(j \cdot x - z \cdot k\right)\right)\right) \cdot \left(-y0\right)} \]

   6. Taylor expanded in k around -inf

      \[\leadsto \color{blue}{k \cdot \left(y0 \cdot \left(-1 \cdot \left(y2 \cdot y5\right) + b \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(k \cdot y0\right) \cdot \left(-1 \cdot \left(y2 \cdot y5\right) + b \cdot z\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(k \cdot y0\right) \cdot \left(-1 \cdot \left(y2 \cdot y5\right) + b \cdot z\right)} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(y0 \cdot k\right)} \cdot \left(-1 \cdot \left(y2 \cdot y5\right) + b \cdot z\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(y0 \cdot k\right)} \cdot \left(-1 \cdot \left(y2 \cdot y5\right) + b \cdot z\right) \]

      5. +-commutative N/A

         \[\leadsto \left(y0 \cdot k\right) \cdot \color{blue}{\left(b \cdot z + -1 \cdot \left(y2 \cdot y5\right)\right)} \]

      6. lower-fma.f64 N/A

         \[\leadsto \left(y0 \cdot k\right) \cdot \color{blue}{\mathsf{fma}\left(b, z, -1 \cdot \left(y2 \cdot y5\right)\right)} \]

      7. mul-1-neg N/A

         \[\leadsto \left(y0 \cdot k\right) \cdot \mathsf{fma}\left(b, z, \color{blue}{\mathsf{neg}\left(y2 \cdot y5\right)}\right) \]

      8. *-commutative N/A

         \[\leadsto \left(y0 \cdot k\right) \cdot \mathsf{fma}\left(b, z, \mathsf{neg}\left(\color{blue}{y5 \cdot y2}\right)\right) \]

      9. distribute-rgt-neg-in N/A

         \[\leadsto \left(y0 \cdot k\right) \cdot \mathsf{fma}\left(b, z, \color{blue}{y5 \cdot \left(\mathsf{neg}\left(y2\right)\right)}\right) \]

      10. mul-1-neg N/A

          \[\leadsto \left(y0 \cdot k\right) \cdot \mathsf{fma}\left(b, z, y5 \cdot \color{blue}{\left(-1 \cdot y2\right)}\right) \]

      11. lower-*.f64 N/A

          \[\leadsto \left(y0 \cdot k\right) \cdot \mathsf{fma}\left(b, z, \color{blue}{y5 \cdot \left(-1 \cdot y2\right)}\right) \]

      12. mul-1-neg N/A

          \[\leadsto \left(y0 \cdot k\right) \cdot \mathsf{fma}\left(b, z, y5 \cdot \color{blue}{\left(\mathsf{neg}\left(y2\right)\right)}\right) \]

      13. lower-neg.f64 40.7

          \[\leadsto \left(y0 \cdot k\right) \cdot \mathsf{fma}\left(b, z, y5 \cdot \color{blue}{\left(-y2\right)}\right) \]

   8. Simplified 40.7%

      \[\leadsto \color{blue}{\left(y0 \cdot k\right) \cdot \mathsf{fma}\left(b, z, y5 \cdot \left(-y2\right)\right)} \]

   9. Taylor expanded in b around 0

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)\right)} \]

       2. lower-neg.f64 N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)\right)} \]

       3. lower-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)}\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{neg}\left(k \cdot \color{blue}{\left(\left(y2 \cdot y5\right) \cdot y0\right)}\right) \]

       5. lower-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(k \cdot \color{blue}{\left(\left(y2 \cdot y5\right) \cdot y0\right)}\right) \]

       6. lower-*.f64 40.7

          \[\leadsto -k \cdot \left(\color{blue}{\left(y2 \cdot y5\right)} \cdot y0\right) \]

   11. Simplified 40.7%

       \[\leadsto \color{blue}{-k \cdot \left(\left(y2 \cdot y5\right) \cdot y0\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 35.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -9600000000:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(x \cdot \left(-y1\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -4.8 \cdot 10^{-292}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a\right)\right)\\ \mathbf{elif}\;y2 \leq 2.05 \cdot 10^{+77}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(t \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot y5\right) \cdot \left(-y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 31.2% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, x \cdot b\right)\right)\\ \mathbf{if}\;y \leq -1.45 \cdot 10^{-190}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+79}:\\ \;\;\;\;a \cdot \left(z \cdot \mathsf{fma}\left(y1, y3, t \cdot \left(-b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y (fma (- y3) y5 (* x b))))))
   (if (<= y -1.45e-190)
     t_1
     (if (<= y 2.3e+79) (* a (* z (fma y1 y3 (* t (- b))))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y * fma(-y3, y5, (x * b)));
	double tmp;
	if (y <= -1.45e-190) {
		tmp = t_1;
	} else if (y <= 2.3e+79) {
		tmp = a * (z * fma(y1, y3, (t * -b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y * fma(Float64(-y3), y5, Float64(x * b))))
	tmp = 0.0
	if (y <= -1.45e-190)
		tmp = t_1;
	elseif (y <= 2.3e+79)
		tmp = Float64(a * Float64(z * fma(y1, y3, Float64(t * Float64(-b)))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y * N[((-y3) * y5 + N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.45e-190], t$95$1, If[LessEqual[y, 2.3e+79], N[(a * N[(z * N[(y1 * y3 + N[(t * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4500000000000001e-190 or 2.3e79 < y

   1. Initial program 21.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Simplified 44.5%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto a \cdot \left(y \cdot \left(\color{blue}{\left(-1 \cdot y3\right) \cdot y5} + b \cdot x\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot y3, y5, b \cdot x\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y3\right)}, y5, b \cdot x\right)\right) \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y3\right)}, y5, b \cdot x\right)\right) \]

      7. lower-*.f64 49.3

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, \color{blue}{b \cdot x}\right)\right) \]

   8. Simplified 49.3%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, b \cdot x\right)\right)} \]

   if -1.4500000000000001e-190 < y < 2.3e79

   1. Initial program 33.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Simplified 44.9%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in z around inf

      \[\leadsto a \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto a \cdot \left(z \cdot \color{blue}{\left(y1 \cdot y3 + -1 \cdot \left(b \cdot t\right)\right)}\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(z \cdot \color{blue}{\mathsf{fma}\left(y1, y3, -1 \cdot \left(b \cdot t\right)\right)}\right) \]

      4. associate-*r* N/A

         \[\leadsto a \cdot \left(z \cdot \mathsf{fma}\left(y1, y3, \color{blue}{\left(-1 \cdot b\right) \cdot t}\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto a \cdot \left(z \cdot \mathsf{fma}\left(y1, y3, \color{blue}{\left(-1 \cdot b\right) \cdot t}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto a \cdot \left(z \cdot \mathsf{fma}\left(y1, y3, \color{blue}{\left(\mathsf{neg}\left(b\right)\right)} \cdot t\right)\right) \]

      7. lower-neg.f64 35.6

         \[\leadsto a \cdot \left(z \cdot \mathsf{fma}\left(y1, y3, \color{blue}{\left(-b\right)} \cdot t\right)\right) \]

   8. Simplified 35.6%

      \[\leadsto a \cdot \color{blue}{\left(z \cdot \mathsf{fma}\left(y1, y3, \left(-b\right) \cdot t\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-190}:\\ \;\;\;\;a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, x \cdot b\right)\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+79}:\\ \;\;\;\;a \cdot \left(z \cdot \mathsf{fma}\left(y1, y3, t \cdot \left(-b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, x \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 31.0% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, x \cdot b\right)\right)\\ \mathbf{if}\;y \leq -3.65 \cdot 10^{-174}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{+81}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y (fma (- y3) y5 (* x b))))))
   (if (<= y -3.65e-174)
     t_1
     (if (<= y 6.1e+81) (* a (* y1 (- (* z y3) (* x 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 = a * (y * fma(-y3, y5, (x * b)));
	double tmp;
	if (y <= -3.65e-174) {
		tmp = t_1;
	} else if (y <= 6.1e+81) {
		tmp = a * (y1 * ((z * y3) - (x * 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(a * Float64(y * fma(Float64(-y3), y5, Float64(x * b))))
	tmp = 0.0
	if (y <= -3.65e-174)
		tmp = t_1;
	elseif (y <= 6.1e+81)
		tmp = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y * N[((-y3) * y5 + N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.65e-174], t$95$1, If[LessEqual[y, 6.1e+81], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.65e-174 or 6.10000000000000038e81 < y

   1. Initial program 21.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Simplified 46.4%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto a \cdot \left(y \cdot \left(\color{blue}{\left(-1 \cdot y3\right) \cdot y5} + b \cdot x\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot y3, y5, b \cdot x\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y3\right)}, y5, b \cdot x\right)\right) \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y3\right)}, y5, b \cdot x\right)\right) \]

      7. lower-*.f64 51.5

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, \color{blue}{b \cdot x}\right)\right) \]

   8. Simplified 51.5%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, b \cdot x\right)\right)} \]

   if -3.65e-174 < y < 6.10000000000000038e81

   1. Initial program 32.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Simplified 42.1%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y1 around inf

      \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(y3 \cdot z - x \cdot y2\right)}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y1 \cdot \left(\color{blue}{y3 \cdot z} - x \cdot y2\right)\right) \]

      4. lower-*.f64 33.0

         \[\leadsto a \cdot \left(y1 \cdot \left(y3 \cdot z - \color{blue}{x \cdot y2}\right)\right) \]

   8. Simplified 33.0%

      \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.65 \cdot 10^{-174}:\\ \;\;\;\;a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, x \cdot b\right)\right)\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{+81}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, x \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 22.6% accurate, 5.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+19}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(t \cdot b\right)\right)\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{-71}:\\ \;\;\;\;\left(-a\right) \cdot \left(y5 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+79}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= t -2.05e+19)
   (* y4 (* j (* t b)))
   (if (<= t 5.3e-71)
     (* (- a) (* y5 (* y y3)))
     (if (<= t 4.2e+79) (* b (* k (* z y0))) (* a (* y2 (* t 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 (t <= -2.05e+19) {
		tmp = y4 * (j * (t * b));
	} else if (t <= 5.3e-71) {
		tmp = -a * (y5 * (y * y3));
	} else if (t <= 4.2e+79) {
		tmp = b * (k * (z * y0));
	} else {
		tmp = a * (y2 * (t * 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 (t <= (-2.05d+19)) then
        tmp = y4 * (j * (t * b))
    else if (t <= 5.3d-71) then
        tmp = -a * (y5 * (y * y3))
    else if (t <= 4.2d+79) then
        tmp = b * (k * (z * y0))
    else
        tmp = a * (y2 * (t * 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 (t <= -2.05e+19) {
		tmp = y4 * (j * (t * b));
	} else if (t <= 5.3e-71) {
		tmp = -a * (y5 * (y * y3));
	} else if (t <= 4.2e+79) {
		tmp = b * (k * (z * y0));
	} else {
		tmp = a * (y2 * (t * 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 t <= -2.05e+19:
		tmp = y4 * (j * (t * b))
	elif t <= 5.3e-71:
		tmp = -a * (y5 * (y * y3))
	elif t <= 4.2e+79:
		tmp = b * (k * (z * y0))
	else:
		tmp = a * (y2 * (t * 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 (t <= -2.05e+19)
		tmp = Float64(y4 * Float64(j * Float64(t * b)));
	elseif (t <= 5.3e-71)
		tmp = Float64(Float64(-a) * Float64(y5 * Float64(y * y3)));
	elseif (t <= 4.2e+79)
		tmp = Float64(b * Float64(k * Float64(z * y0)));
	else
		tmp = Float64(a * Float64(y2 * Float64(t * 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 (t <= -2.05e+19)
		tmp = y4 * (j * (t * b));
	elseif (t <= 5.3e-71)
		tmp = -a * (y5 * (y * y3));
	elseif (t <= 4.2e+79)
		tmp = b * (k * (z * y0));
	else
		tmp = a * (y2 * (t * 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[t, -2.05e+19], N[(y4 * N[(j * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.3e-71], N[((-a) * N[(y5 * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.2e+79], N[(b * N[(k * N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y2 * N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.05e19

   1. Initial program 29.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Simplified 51.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right)\right) - c \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto y4 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto y4 \cdot \left(j \cdot \left(b \cdot t + \color{blue}{\left(\mathsf{neg}\left(y1 \cdot y3\right)\right)}\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t - y1 \cdot y3\right)}\right) \]

      5. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t - y1 \cdot y3\right)}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(j \cdot \left(\color{blue}{b \cdot t} - y1 \cdot y3\right)\right) \]

      7. lower-*.f64 46.0

         \[\leadsto y4 \cdot \left(j \cdot \left(b \cdot t - \color{blue}{y1 \cdot y3}\right)\right) \]

   8. Simplified 46.0%

      \[\leadsto y4 \cdot \color{blue}{\left(j \cdot \left(b \cdot t - y1 \cdot y3\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t\right)}\right) \]
   10. Step-by-step derivation

       1. lower-*.f64 46.2

          \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t\right)}\right) \]

   11. Simplified 46.2%

       \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t\right)}\right) \]

   if -2.05e19 < t < 5.29999999999999999e-71

   1. Initial program 28.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Simplified 45.7%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto a \cdot \left(y \cdot \left(\color{blue}{\left(-1 \cdot y3\right) \cdot y5} + b \cdot x\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot y3, y5, b \cdot x\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y3\right)}, y5, b \cdot x\right)\right) \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y3\right)}, y5, b \cdot x\right)\right) \]

      7. lower-*.f64 38.0

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, \color{blue}{b \cdot x}\right)\right) \]

   8. Simplified 38.0%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, b \cdot x\right)\right)} \]

   9. Taylor expanded in y3 around inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(a \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]

       2. distribute-rgt-neg-in N/A

          \[\leadsto \color{blue}{a \cdot \left(\mathsf{neg}\left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]

       3. mul-1-neg N/A

          \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]

       4. lower-*.f64 N/A

          \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]

       5. mul-1-neg N/A

          \[\leadsto a \cdot \color{blue}{\left(\mathsf{neg}\left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]

       6. *-commutative N/A

          \[\leadsto a \cdot \left(\mathsf{neg}\left(\color{blue}{\left(y3 \cdot y5\right) \cdot y}\right)\right) \]

       7. distribute-lft-neg-in N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(\mathsf{neg}\left(y3 \cdot y5\right)\right) \cdot y\right)} \]

       8. mul-1-neg N/A

          \[\leadsto a \cdot \left(\color{blue}{\left(-1 \cdot \left(y3 \cdot y5\right)\right)} \cdot y\right) \]

       9. lower-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot y5\right)\right) \cdot y\right)} \]

       10. mul-1-neg N/A

           \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y3 \cdot y5\right)\right)} \cdot y\right) \]

       11. *-commutative N/A

           \[\leadsto a \cdot \left(\left(\mathsf{neg}\left(\color{blue}{y5 \cdot y3}\right)\right) \cdot y\right) \]

       12. distribute-rgt-neg-in N/A

           \[\leadsto a \cdot \left(\color{blue}{\left(y5 \cdot \left(\mathsf{neg}\left(y3\right)\right)\right)} \cdot y\right) \]

       13. mul-1-neg N/A

           \[\leadsto a \cdot \left(\left(y5 \cdot \color{blue}{\left(-1 \cdot y3\right)}\right) \cdot y\right) \]

       14. lower-*.f64 N/A

           \[\leadsto a \cdot \left(\color{blue}{\left(y5 \cdot \left(-1 \cdot y3\right)\right)} \cdot y\right) \]

       15. mul-1-neg N/A

           \[\leadsto a \cdot \left(\left(y5 \cdot \color{blue}{\left(\mathsf{neg}\left(y3\right)\right)}\right) \cdot y\right) \]

       16. lower-neg.f64 28.3

           \[\leadsto a \cdot \left(\left(y5 \cdot \color{blue}{\left(-y3\right)}\right) \cdot y\right) \]

   11. Simplified 28.3%

       \[\leadsto \color{blue}{a \cdot \left(\left(y5 \cdot \left(-y3\right)\right) \cdot y\right)} \]
   12. Step-by-step derivation

       1. lift-neg.f64 N/A

          \[\leadsto a \cdot \left(\left(y5 \cdot \color{blue}{\left(\mathsf{neg}\left(y3\right)\right)}\right) \cdot y\right) \]

       2. associate-*l* N/A

          \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(\left(\mathsf{neg}\left(y3\right)\right) \cdot y\right)\right)} \]

       3. *-commutative N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(\left(\mathsf{neg}\left(y3\right)\right) \cdot y\right) \cdot y5\right)} \]

       4. lower-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(\left(\mathsf{neg}\left(y3\right)\right) \cdot y\right) \cdot y5\right)} \]

       5. *-commutative N/A

          \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot \left(\mathsf{neg}\left(y3\right)\right)\right)} \cdot y5\right) \]

       6. lower-*.f64 29.2

          \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot \left(-y3\right)\right)} \cdot y5\right) \]

   13. Applied egg-rr 29.2%

       \[\leadsto a \cdot \color{blue}{\left(\left(y \cdot \left(-y3\right)\right) \cdot y5\right)} \]

   if 5.29999999999999999e-71 < t < 4.20000000000000016e79

   1. Initial program 11.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. lower--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{x \cdot y - t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. lower-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - \color{blue}{t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, \color{blue}{y4 \cdot \left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. lower--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - \color{blue}{k \cdot y}\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      13. lower-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

      14. lower--.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \color{blue}{\left(j \cdot x - k \cdot z\right)}\right) \]

      15. lower-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(\color{blue}{j \cdot x} - k \cdot z\right)\right) \]

      16. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

      17. lower-*.f64 54.1

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 54.1%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(z \cdot \left(a \cdot t - k \cdot y0\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(z \cdot \left(a \cdot t - k \cdot y0\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(z \cdot \left(a \cdot t - k \cdot y0\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(b\right)\right)} \cdot \left(z \cdot \left(a \cdot t - k \cdot y0\right)\right) \]

      4. lower-neg.f64 N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(b\right)\right)} \cdot \left(z \cdot \left(a \cdot t - k \cdot y0\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(b\right)\right) \cdot \color{blue}{\left(z \cdot \left(a \cdot t - k \cdot y0\right)\right)} \]

      6. sub-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(b\right)\right) \cdot \left(z \cdot \color{blue}{\left(a \cdot t + \left(\mathsf{neg}\left(k \cdot y0\right)\right)\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(b\right)\right) \cdot \left(z \cdot \left(a \cdot t + \color{blue}{-1 \cdot \left(k \cdot y0\right)}\right)\right) \]

      8. +-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(b\right)\right) \cdot \left(z \cdot \color{blue}{\left(-1 \cdot \left(k \cdot y0\right) + a \cdot t\right)}\right) \]

      9. associate-*r* N/A

         \[\leadsto \left(\mathsf{neg}\left(b\right)\right) \cdot \left(z \cdot \left(\color{blue}{\left(-1 \cdot k\right) \cdot y0} + a \cdot t\right)\right) \]

      10. lower-fma.f64 N/A

          \[\leadsto \left(\mathsf{neg}\left(b\right)\right) \cdot \left(z \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot k, y0, a \cdot t\right)}\right) \]

      11. mul-1-neg N/A

          \[\leadsto \left(\mathsf{neg}\left(b\right)\right) \cdot \left(z \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(k\right)}, y0, a \cdot t\right)\right) \]

      12. lower-neg.f64 N/A

          \[\leadsto \left(\mathsf{neg}\left(b\right)\right) \cdot \left(z \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(k\right)}, y0, a \cdot t\right)\right) \]

      13. lower-*.f64 50.6

          \[\leadsto \left(-b\right) \cdot \left(z \cdot \mathsf{fma}\left(-k, y0, \color{blue}{a \cdot t}\right)\right) \]

   8. Simplified 50.6%

      \[\leadsto \color{blue}{\left(-b\right) \cdot \left(z \cdot \mathsf{fma}\left(-k, y0, a \cdot t\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto \color{blue}{b \cdot \left(k \cdot \left(y0 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \color{blue}{b \cdot \left(k \cdot \left(y0 \cdot z\right)\right)} \]

       2. lower-*.f64 N/A

          \[\leadsto b \cdot \color{blue}{\left(k \cdot \left(y0 \cdot z\right)\right)} \]

       3. lower-*.f64 47.1

          \[\leadsto b \cdot \left(k \cdot \color{blue}{\left(y0 \cdot z\right)}\right) \]

   11. Simplified 47.1%

       \[\leadsto \color{blue}{b \cdot \left(k \cdot \left(y0 \cdot z\right)\right)} \]

   if 4.20000000000000016e79 < t

   1. Initial program 19.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Simplified 40.9%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(x \cdot y1\right) + t \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(x \cdot y1\right) + t \cdot y5\right)\right)} \]

      2. associate-*r* N/A

         \[\leadsto a \cdot \left(y2 \cdot \left(\color{blue}{\left(-1 \cdot x\right) \cdot y1} + t \cdot y5\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot x, y1, t \cdot y5\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y1, t \cdot y5\right)\right) \]

      5. lower-neg.f64 N/A

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y1, t \cdot y5\right)\right) \]

      6. lower-*.f64 31.9

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(-x, y1, \color{blue}{t \cdot y5}\right)\right) \]

   8. Simplified 31.9%

      \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \mathsf{fma}\left(-x, y1, t \cdot y5\right)\right)} \]

   9. Taylor expanded in x around 0

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} \]

       2. *-commutative N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(y2 \cdot y5\right) \cdot t\right)} \]

       3. associate-*r* N/A

          \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(y5 \cdot t\right)\right)} \]

       4. *-commutative N/A

          \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\left(t \cdot y5\right)}\right) \]

       5. lower-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(t \cdot y5\right)\right)} \]

       6. *-commutative N/A

          \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\left(y5 \cdot t\right)}\right) \]

       7. lower-*.f64 29.6

          \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\left(y5 \cdot t\right)}\right) \]

   11. Simplified 29.6%

       \[\leadsto \color{blue}{a \cdot \left(y2 \cdot \left(y5 \cdot t\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 36.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+19}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(t \cdot b\right)\right)\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{-71}:\\ \;\;\;\;\left(-a\right) \cdot \left(y5 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+79}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 21.7% accurate, 5.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-35}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-240}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+52}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y -7e-35)
   (* a (* x (* y b)))
   (if (<= y 9.5e-240)
     (* b (* k (* z y0)))
     (if (<= y 3e+52) (* a (* y2 (* t y5))) (* b (* (* x y) a))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -7e-35) {
		tmp = a * (x * (y * b));
	} else if (y <= 9.5e-240) {
		tmp = b * (k * (z * y0));
	} else if (y <= 3e+52) {
		tmp = a * (y2 * (t * y5));
	} else {
		tmp = b * ((x * y) * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y <= (-7d-35)) then
        tmp = a * (x * (y * b))
    else if (y <= 9.5d-240) then
        tmp = b * (k * (z * y0))
    else if (y <= 3d+52) then
        tmp = a * (y2 * (t * y5))
    else
        tmp = b * ((x * y) * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -7e-35) {
		tmp = a * (x * (y * b));
	} else if (y <= 9.5e-240) {
		tmp = b * (k * (z * y0));
	} else if (y <= 3e+52) {
		tmp = a * (y2 * (t * y5));
	} else {
		tmp = b * ((x * y) * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y <= -7e-35:
		tmp = a * (x * (y * b))
	elif y <= 9.5e-240:
		tmp = b * (k * (z * y0))
	elif y <= 3e+52:
		tmp = a * (y2 * (t * y5))
	else:
		tmp = b * ((x * y) * a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y <= -7e-35)
		tmp = Float64(a * Float64(x * Float64(y * b)));
	elseif (y <= 9.5e-240)
		tmp = Float64(b * Float64(k * Float64(z * y0)));
	elseif (y <= 3e+52)
		tmp = Float64(a * Float64(y2 * Float64(t * y5)));
	else
		tmp = Float64(b * Float64(Float64(x * y) * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y <= -7e-35)
		tmp = a * (x * (y * b));
	elseif (y <= 9.5e-240)
		tmp = b * (k * (z * y0));
	elseif (y <= 3e+52)
		tmp = a * (y2 * (t * y5));
	else
		tmp = b * ((x * y) * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y, -7e-35], N[(a * N[(x * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5e-240], N[(b * N[(k * N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3e+52], N[(a * N[(y2 * N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(x * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.99999999999999992e-35

   1. Initial program 14.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Simplified 47.0%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto a \cdot \left(y \cdot \left(\color{blue}{\left(-1 \cdot y3\right) \cdot y5} + b \cdot x\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot y3, y5, b \cdot x\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y3\right)}, y5, b \cdot x\right)\right) \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y3\right)}, y5, b \cdot x\right)\right) \]

      7. lower-*.f64 51.5

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, \color{blue}{b \cdot x}\right)\right) \]

   8. Simplified 51.5%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, b \cdot x\right)\right)} \]

   9. Taylor expanded in y3 around 0

      \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x\right)}\right) \]
   10. Step-by-step derivation

       1. lower-*.f64 28.8

          \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x\right)}\right) \]

   11. Simplified 28.8%

       \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x\right)}\right) \]
   12. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(y \cdot b\right) \cdot x\right)} \]

       2. lower-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(y \cdot b\right) \cdot x\right)} \]

       3. lower-*.f64 32.8

          \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot b\right)} \cdot x\right) \]

   13. Applied egg-rr 32.8%

       \[\leadsto a \cdot \color{blue}{\left(\left(y \cdot b\right) \cdot x\right)} \]

   if -6.99999999999999992e-35 < y < 9.5000000000000005e-240

   1. Initial program 40.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. lower--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{x \cdot y - t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. lower-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - \color{blue}{t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, \color{blue}{y4 \cdot \left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. lower--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - \color{blue}{k \cdot y}\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      13. lower-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

      14. lower--.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \color{blue}{\left(j \cdot x - k \cdot z\right)}\right) \]

      15. lower-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(\color{blue}{j \cdot x} - k \cdot z\right)\right) \]

      16. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

      17. lower-*.f64 30.8

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 30.8%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(z \cdot \left(a \cdot t - k \cdot y0\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(z \cdot \left(a \cdot t - k \cdot y0\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(z \cdot \left(a \cdot t - k \cdot y0\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(b\right)\right)} \cdot \left(z \cdot \left(a \cdot t - k \cdot y0\right)\right) \]

      4. lower-neg.f64 N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(b\right)\right)} \cdot \left(z \cdot \left(a \cdot t - k \cdot y0\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(b\right)\right) \cdot \color{blue}{\left(z \cdot \left(a \cdot t - k \cdot y0\right)\right)} \]

      6. sub-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(b\right)\right) \cdot \left(z \cdot \color{blue}{\left(a \cdot t + \left(\mathsf{neg}\left(k \cdot y0\right)\right)\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(b\right)\right) \cdot \left(z \cdot \left(a \cdot t + \color{blue}{-1 \cdot \left(k \cdot y0\right)}\right)\right) \]

      8. +-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(b\right)\right) \cdot \left(z \cdot \color{blue}{\left(-1 \cdot \left(k \cdot y0\right) + a \cdot t\right)}\right) \]

      9. associate-*r* N/A

         \[\leadsto \left(\mathsf{neg}\left(b\right)\right) \cdot \left(z \cdot \left(\color{blue}{\left(-1 \cdot k\right) \cdot y0} + a \cdot t\right)\right) \]

      10. lower-fma.f64 N/A

          \[\leadsto \left(\mathsf{neg}\left(b\right)\right) \cdot \left(z \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot k, y0, a \cdot t\right)}\right) \]

      11. mul-1-neg N/A

          \[\leadsto \left(\mathsf{neg}\left(b\right)\right) \cdot \left(z \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(k\right)}, y0, a \cdot t\right)\right) \]

      12. lower-neg.f64 N/A

          \[\leadsto \left(\mathsf{neg}\left(b\right)\right) \cdot \left(z \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(k\right)}, y0, a \cdot t\right)\right) \]

      13. lower-*.f64 24.1

          \[\leadsto \left(-b\right) \cdot \left(z \cdot \mathsf{fma}\left(-k, y0, \color{blue}{a \cdot t}\right)\right) \]

   8. Simplified 24.1%

      \[\leadsto \color{blue}{\left(-b\right) \cdot \left(z \cdot \mathsf{fma}\left(-k, y0, a \cdot t\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto \color{blue}{b \cdot \left(k \cdot \left(y0 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \color{blue}{b \cdot \left(k \cdot \left(y0 \cdot z\right)\right)} \]

       2. lower-*.f64 N/A

          \[\leadsto b \cdot \color{blue}{\left(k \cdot \left(y0 \cdot z\right)\right)} \]

       3. lower-*.f64 15.5

          \[\leadsto b \cdot \left(k \cdot \color{blue}{\left(y0 \cdot z\right)}\right) \]

   11. Simplified 15.5%

       \[\leadsto \color{blue}{b \cdot \left(k \cdot \left(y0 \cdot z\right)\right)} \]

   if 9.5000000000000005e-240 < y < 3e52

   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. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Simplified 53.2%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(x \cdot y1\right) + t \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(x \cdot y1\right) + t \cdot y5\right)\right)} \]

      2. associate-*r* N/A

         \[\leadsto a \cdot \left(y2 \cdot \left(\color{blue}{\left(-1 \cdot x\right) \cdot y1} + t \cdot y5\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot x, y1, t \cdot y5\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y1, t \cdot y5\right)\right) \]

      5. lower-neg.f64 N/A

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y1, t \cdot y5\right)\right) \]

      6. lower-*.f64 34.3

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(-x, y1, \color{blue}{t \cdot y5}\right)\right) \]

   8. Simplified 34.3%

      \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \mathsf{fma}\left(-x, y1, t \cdot y5\right)\right)} \]

   9. Taylor expanded in x around 0

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} \]

       2. *-commutative N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(y2 \cdot y5\right) \cdot t\right)} \]

       3. associate-*r* N/A

          \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(y5 \cdot t\right)\right)} \]

       4. *-commutative N/A

          \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\left(t \cdot y5\right)}\right) \]

       5. lower-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(t \cdot y5\right)\right)} \]

       6. *-commutative N/A

          \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\left(y5 \cdot t\right)}\right) \]

       7. lower-*.f64 31.2

          \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\left(y5 \cdot t\right)}\right) \]

   11. Simplified 31.2%

       \[\leadsto \color{blue}{a \cdot \left(y2 \cdot \left(y5 \cdot t\right)\right)} \]

   if 3e52 < y

   1. Initial program 24.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. lower--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{x \cdot y - t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. lower-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - \color{blue}{t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, \color{blue}{y4 \cdot \left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. lower--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - \color{blue}{k \cdot y}\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      13. lower-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

      14. lower--.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \color{blue}{\left(j \cdot x - k \cdot z\right)}\right) \]

      15. lower-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(\color{blue}{j \cdot x} - k \cdot z\right)\right) \]

      16. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

      17. lower-*.f64 42.4

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 42.4%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto b \cdot \color{blue}{\left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]
   7. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y + \left(\mathsf{neg}\left(j \cdot y0\right)\right)\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y + \color{blue}{-1 \cdot \left(j \cdot y0\right)}\right)\right) \]

      3. +-commutative N/A

         \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y0\right) + a \cdot y\right)}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(x \cdot \left(-1 \cdot \left(j \cdot y0\right) + a \cdot y\right)\right)} \]

      5. +-commutative N/A

         \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y + -1 \cdot \left(j \cdot y0\right)\right)}\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \color{blue}{\mathsf{fma}\left(a, y, -1 \cdot \left(j \cdot y0\right)\right)}\right) \]

      7. associate-*r* N/A

         \[\leadsto b \cdot \left(x \cdot \mathsf{fma}\left(a, y, \color{blue}{\left(-1 \cdot j\right) \cdot y0}\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \mathsf{fma}\left(a, y, \color{blue}{\left(-1 \cdot j\right) \cdot y0}\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto b \cdot \left(x \cdot \mathsf{fma}\left(a, y, \color{blue}{\left(\mathsf{neg}\left(j\right)\right)} \cdot y0\right)\right) \]

      10. lower-neg.f64 52.6

          \[\leadsto b \cdot \left(x \cdot \mathsf{fma}\left(a, y, \color{blue}{\left(-j\right)} \cdot y0\right)\right) \]

   8. Simplified 52.6%

      \[\leadsto b \cdot \color{blue}{\left(x \cdot \mathsf{fma}\left(a, y, \left(-j\right) \cdot y0\right)\right)} \]

   9. Taylor expanded in a around inf

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y\right)\right)} \]

       2. lower-*.f64 37.0

          \[\leadsto b \cdot \left(a \cdot \color{blue}{\left(x \cdot y\right)}\right) \]

   11. Simplified 37.0%

       \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 29.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-35}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-240}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+52}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 20.0% accurate, 6.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -27000000000000:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(t \cdot b\right)\right)\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-230}:\\ \;\;\;\;\left(y3 \cdot \left(j \cdot y1\right)\right) \cdot \left(-y4\right)\\ \mathbf{else}:\\ \;\;\;\;-a \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= t -27000000000000.0)
   (* y4 (* j (* t b)))
   (if (<= t 4.1e-230) (* (* y3 (* j y1)) (- y4)) (- (* 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 (t <= -27000000000000.0) {
		tmp = y4 * (j * (t * b));
	} else if (t <= 4.1e-230) {
		tmp = (y3 * (j * y1)) * -y4;
	} 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 (t <= (-27000000000000.0d0)) then
        tmp = y4 * (j * (t * b))
    else if (t <= 4.1d-230) then
        tmp = (y3 * (j * y1)) * -y4
    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 (t <= -27000000000000.0) {
		tmp = y4 * (j * (t * b));
	} else if (t <= 4.1e-230) {
		tmp = (y3 * (j * y1)) * -y4;
	} 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 t <= -27000000000000.0:
		tmp = y4 * (j * (t * b))
	elif t <= 4.1e-230:
		tmp = (y3 * (j * y1)) * -y4
	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 (t <= -27000000000000.0)
		tmp = Float64(y4 * Float64(j * Float64(t * b)));
	elseif (t <= 4.1e-230)
		tmp = Float64(Float64(y3 * Float64(j * y1)) * Float64(-y4));
	else
		tmp = Float64(-Float64(a * Float64(y * Float64(y3 * y5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (t <= -27000000000000.0)
		tmp = y4 * (j * (t * b));
	elseif (t <= 4.1e-230)
		tmp = (y3 * (j * y1)) * -y4;
	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[t, -27000000000000.0], N[(y4 * N[(j * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.1e-230], N[(N[(y3 * N[(j * y1), $MachinePrecision]), $MachinePrecision] * (-y4)), $MachinePrecision], (-N[(a * N[(y * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision])]]

Derivation

1. Split input into 3 regimes

2. if t < -2.7e13

   1. Initial program 29.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Simplified 50.5%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right)\right) - c \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto y4 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto y4 \cdot \left(j \cdot \left(b \cdot t + \color{blue}{\left(\mathsf{neg}\left(y1 \cdot y3\right)\right)}\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t - y1 \cdot y3\right)}\right) \]

      5. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t - y1 \cdot y3\right)}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(j \cdot \left(\color{blue}{b \cdot t} - y1 \cdot y3\right)\right) \]

      7. lower-*.f64 45.4

         \[\leadsto y4 \cdot \left(j \cdot \left(b \cdot t - \color{blue}{y1 \cdot y3}\right)\right) \]

   8. Simplified 45.4%

      \[\leadsto y4 \cdot \color{blue}{\left(j \cdot \left(b \cdot t - y1 \cdot y3\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t\right)}\right) \]
   10. Step-by-step derivation

       1. lower-*.f64 45.6

          \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t\right)}\right) \]

   11. Simplified 45.6%

       \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t\right)}\right) \]

   if -2.7e13 < t < 4.1000000000000002e-230

   1. Initial program 25.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Simplified 45.9%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right)\right) - c \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto y4 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto y4 \cdot \left(j \cdot \left(b \cdot t + \color{blue}{\left(\mathsf{neg}\left(y1 \cdot y3\right)\right)}\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t - y1 \cdot y3\right)}\right) \]

      5. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t - y1 \cdot y3\right)}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(j \cdot \left(\color{blue}{b \cdot t} - y1 \cdot y3\right)\right) \]

      7. lower-*.f64 32.3

         \[\leadsto y4 \cdot \left(j \cdot \left(b \cdot t - \color{blue}{y1 \cdot y3}\right)\right) \]

   8. Simplified 32.3%

      \[\leadsto y4 \cdot \color{blue}{\left(j \cdot \left(b \cdot t - y1 \cdot y3\right)\right)} \]

   9. Taylor expanded in b around 0

      \[\leadsto y4 \cdot \color{blue}{\left(-1 \cdot \left(j \cdot \left(y1 \cdot y3\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto y4 \cdot \color{blue}{\left(\mathsf{neg}\left(j \cdot \left(y1 \cdot y3\right)\right)\right)} \]

       2. lower-neg.f64 N/A

          \[\leadsto y4 \cdot \color{blue}{\left(\mathsf{neg}\left(j \cdot \left(y1 \cdot y3\right)\right)\right)} \]

       3. associate-*r* N/A

          \[\leadsto y4 \cdot \left(\mathsf{neg}\left(\color{blue}{\left(j \cdot y1\right) \cdot y3}\right)\right) \]

       4. lower-*.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{neg}\left(\color{blue}{\left(j \cdot y1\right) \cdot y3}\right)\right) \]

       5. lower-*.f64 33.4

          \[\leadsto y4 \cdot \left(-\color{blue}{\left(j \cdot y1\right)} \cdot y3\right) \]

   11. Simplified 33.4%

       \[\leadsto y4 \cdot \color{blue}{\left(-\left(j \cdot y1\right) \cdot y3\right)} \]

   if 4.1000000000000002e-230 < t

   1. Initial program 22.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Simplified 48.0%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto a \cdot \left(y \cdot \left(\color{blue}{\left(-1 \cdot y3\right) \cdot y5} + b \cdot x\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot y3, y5, b \cdot x\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y3\right)}, y5, b \cdot x\right)\right) \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y3\right)}, y5, b \cdot x\right)\right) \]

      7. lower-*.f64 41.8

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, \color{blue}{b \cdot x}\right)\right) \]

   8. Simplified 41.8%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, b \cdot x\right)\right)} \]

   9. Taylor expanded in y3 around inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(a \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]

       2. distribute-rgt-neg-in N/A

          \[\leadsto \color{blue}{a \cdot \left(\mathsf{neg}\left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]

       3. mul-1-neg N/A

          \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]

       4. lower-*.f64 N/A

          \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]

       5. mul-1-neg N/A

          \[\leadsto a \cdot \color{blue}{\left(\mathsf{neg}\left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]

       6. *-commutative N/A

          \[\leadsto a \cdot \left(\mathsf{neg}\left(\color{blue}{\left(y3 \cdot y5\right) \cdot y}\right)\right) \]

       7. distribute-lft-neg-in N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(\mathsf{neg}\left(y3 \cdot y5\right)\right) \cdot y\right)} \]

       8. mul-1-neg N/A

          \[\leadsto a \cdot \left(\color{blue}{\left(-1 \cdot \left(y3 \cdot y5\right)\right)} \cdot y\right) \]

       9. lower-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot y5\right)\right) \cdot y\right)} \]

       10. mul-1-neg N/A

           \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y3 \cdot y5\right)\right)} \cdot y\right) \]

       11. *-commutative N/A

           \[\leadsto a \cdot \left(\left(\mathsf{neg}\left(\color{blue}{y5 \cdot y3}\right)\right) \cdot y\right) \]

       12. distribute-rgt-neg-in N/A

           \[\leadsto a \cdot \left(\color{blue}{\left(y5 \cdot \left(\mathsf{neg}\left(y3\right)\right)\right)} \cdot y\right) \]

       13. mul-1-neg N/A

           \[\leadsto a \cdot \left(\left(y5 \cdot \color{blue}{\left(-1 \cdot y3\right)}\right) \cdot y\right) \]

       14. lower-*.f64 N/A

           \[\leadsto a \cdot \left(\color{blue}{\left(y5 \cdot \left(-1 \cdot y3\right)\right)} \cdot y\right) \]

       15. mul-1-neg N/A

           \[\leadsto a \cdot \left(\left(y5 \cdot \color{blue}{\left(\mathsf{neg}\left(y3\right)\right)}\right) \cdot y\right) \]

       16. lower-neg.f64 29.3

           \[\leadsto a \cdot \left(\left(y5 \cdot \color{blue}{\left(-y3\right)}\right) \cdot y\right) \]

   11. Simplified 29.3%

       \[\leadsto \color{blue}{a \cdot \left(\left(y5 \cdot \left(-y3\right)\right) \cdot y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 35.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -27000000000000:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(t \cdot b\right)\right)\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-230}:\\ \;\;\;\;\left(y3 \cdot \left(j \cdot y1\right)\right) \cdot \left(-y4\right)\\ \mathbf{else}:\\ \;\;\;\;-a \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 27.6% accurate, 6.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.35 \cdot 10^{+86}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(t \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, x \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= t -2.35e+86)
   (* y4 (* j (* t b)))
   (* a (* y (fma (- y3) y5 (* x b))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (t <= -2.35e+86) {
		tmp = y4 * (j * (t * b));
	} else {
		tmp = a * (y * fma(-y3, y5, (x * b)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (t <= -2.35e+86)
		tmp = Float64(y4 * Float64(j * Float64(t * b)));
	else
		tmp = Float64(a * Float64(y * fma(Float64(-y3), y5, Float64(x * b))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[t, -2.35e+86], N[(y4 * N[(j * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y * N[((-y3) * y5 + N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.3500000000000001e86

   1. Initial program 29.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Simplified 53.4%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right)\right) - c \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto y4 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto y4 \cdot \left(j \cdot \left(b \cdot t + \color{blue}{\left(\mathsf{neg}\left(y1 \cdot y3\right)\right)}\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t - y1 \cdot y3\right)}\right) \]

      5. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t - y1 \cdot y3\right)}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(j \cdot \left(\color{blue}{b \cdot t} - y1 \cdot y3\right)\right) \]

      7. lower-*.f64 48.8

         \[\leadsto y4 \cdot \left(j \cdot \left(b \cdot t - \color{blue}{y1 \cdot y3}\right)\right) \]

   8. Simplified 48.8%

      \[\leadsto y4 \cdot \color{blue}{\left(j \cdot \left(b \cdot t - y1 \cdot y3\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t\right)}\right) \]
   10. Step-by-step derivation

       1. lower-*.f64 47.3

          \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t\right)}\right) \]

   11. Simplified 47.3%

       \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t\right)}\right) \]

   if -2.3500000000000001e86 < t

   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. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Simplified 46.9%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto a \cdot \left(y \cdot \left(\color{blue}{\left(-1 \cdot y3\right) \cdot y5} + b \cdot x\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot y3, y5, b \cdot x\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y3\right)}, y5, b \cdot x\right)\right) \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y3\right)}, y5, b \cdot x\right)\right) \]

      7. lower-*.f64 38.6

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, \color{blue}{b \cdot x}\right)\right) \]

   8. Simplified 38.6%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, b \cdot x\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.35 \cdot 10^{+86}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(t \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, x \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 22.4% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+19}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(t \cdot b\right)\right)\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{+73}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= t -2.1e+19)
   (* y4 (* j (* t b)))
   (if (<= t 2.65e+73) (* b (* x (* y a))) (* a (* y2 (* t 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 (t <= -2.1e+19) {
		tmp = y4 * (j * (t * b));
	} else if (t <= 2.65e+73) {
		tmp = b * (x * (y * a));
	} else {
		tmp = a * (y2 * (t * 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 (t <= (-2.1d+19)) then
        tmp = y4 * (j * (t * b))
    else if (t <= 2.65d+73) then
        tmp = b * (x * (y * a))
    else
        tmp = a * (y2 * (t * 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 (t <= -2.1e+19) {
		tmp = y4 * (j * (t * b));
	} else if (t <= 2.65e+73) {
		tmp = b * (x * (y * a));
	} else {
		tmp = a * (y2 * (t * 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 t <= -2.1e+19:
		tmp = y4 * (j * (t * b))
	elif t <= 2.65e+73:
		tmp = b * (x * (y * a))
	else:
		tmp = a * (y2 * (t * 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 (t <= -2.1e+19)
		tmp = Float64(y4 * Float64(j * Float64(t * b)));
	elseif (t <= 2.65e+73)
		tmp = Float64(b * Float64(x * Float64(y * a)));
	else
		tmp = Float64(a * Float64(y2 * Float64(t * 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 (t <= -2.1e+19)
		tmp = y4 * (j * (t * b));
	elseif (t <= 2.65e+73)
		tmp = b * (x * (y * a));
	else
		tmp = a * (y2 * (t * 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[t, -2.1e+19], N[(y4 * N[(j * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.65e+73], N[(b * N[(x * N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y2 * N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.1e19

   1. Initial program 29.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Simplified 51.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right)\right) - c \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto y4 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto y4 \cdot \left(j \cdot \left(b \cdot t + \color{blue}{\left(\mathsf{neg}\left(y1 \cdot y3\right)\right)}\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t - y1 \cdot y3\right)}\right) \]

      5. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t - y1 \cdot y3\right)}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(j \cdot \left(\color{blue}{b \cdot t} - y1 \cdot y3\right)\right) \]

      7. lower-*.f64 46.0

         \[\leadsto y4 \cdot \left(j \cdot \left(b \cdot t - \color{blue}{y1 \cdot y3}\right)\right) \]

   8. Simplified 46.0%

      \[\leadsto y4 \cdot \color{blue}{\left(j \cdot \left(b \cdot t - y1 \cdot y3\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t\right)}\right) \]
   10. Step-by-step derivation

       1. lower-*.f64 46.2

          \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t\right)}\right) \]

   11. Simplified 46.2%

       \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t\right)}\right) \]

   if -2.1e19 < t < 2.64999999999999998e73

   1. Initial program 25.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. lower--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{x \cdot y - t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. lower-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - \color{blue}{t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, \color{blue}{y4 \cdot \left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. lower--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - \color{blue}{k \cdot y}\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      13. lower-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

      14. lower--.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \color{blue}{\left(j \cdot x - k \cdot z\right)}\right) \]

      15. lower-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(\color{blue}{j \cdot x} - k \cdot z\right)\right) \]

      16. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

      17. lower-*.f64 36.9

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 36.9%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto b \cdot \color{blue}{\left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]
   7. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y + \left(\mathsf{neg}\left(j \cdot y0\right)\right)\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y + \color{blue}{-1 \cdot \left(j \cdot y0\right)}\right)\right) \]

      3. +-commutative N/A

         \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y0\right) + a \cdot y\right)}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(x \cdot \left(-1 \cdot \left(j \cdot y0\right) + a \cdot y\right)\right)} \]

      5. +-commutative N/A

         \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y + -1 \cdot \left(j \cdot y0\right)\right)}\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \color{blue}{\mathsf{fma}\left(a, y, -1 \cdot \left(j \cdot y0\right)\right)}\right) \]

      7. associate-*r* N/A

         \[\leadsto b \cdot \left(x \cdot \mathsf{fma}\left(a, y, \color{blue}{\left(-1 \cdot j\right) \cdot y0}\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \mathsf{fma}\left(a, y, \color{blue}{\left(-1 \cdot j\right) \cdot y0}\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto b \cdot \left(x \cdot \mathsf{fma}\left(a, y, \color{blue}{\left(\mathsf{neg}\left(j\right)\right)} \cdot y0\right)\right) \]

      10. lower-neg.f64 38.0

          \[\leadsto b \cdot \left(x \cdot \mathsf{fma}\left(a, y, \color{blue}{\left(-j\right)} \cdot y0\right)\right) \]

   8. Simplified 38.0%

      \[\leadsto b \cdot \color{blue}{\left(x \cdot \mathsf{fma}\left(a, y, \left(-j\right) \cdot y0\right)\right)} \]

   9. Taylor expanded in a around inf

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y\right)}\right) \]
   10. Step-by-step derivation

       1. lower-*.f64 27.2

          \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y\right)}\right) \]

   11. Simplified 27.2%

       \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y\right)}\right) \]

   if 2.64999999999999998e73 < t

   1. Initial program 18.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Simplified 39.0%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(x \cdot y1\right) + t \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(x \cdot y1\right) + t \cdot y5\right)\right)} \]

      2. associate-*r* N/A

         \[\leadsto a \cdot \left(y2 \cdot \left(\color{blue}{\left(-1 \cdot x\right) \cdot y1} + t \cdot y5\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot x, y1, t \cdot y5\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y1, t \cdot y5\right)\right) \]

      5. lower-neg.f64 N/A

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y1, t \cdot y5\right)\right) \]

      6. lower-*.f64 30.5

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(-x, y1, \color{blue}{t \cdot y5}\right)\right) \]

   8. Simplified 30.5%

      \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \mathsf{fma}\left(-x, y1, t \cdot y5\right)\right)} \]

   9. Taylor expanded in x around 0

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} \]

       2. *-commutative N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(y2 \cdot y5\right) \cdot t\right)} \]

       3. associate-*r* N/A

          \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(y5 \cdot t\right)\right)} \]

       4. *-commutative N/A

          \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\left(t \cdot y5\right)}\right) \]

       5. lower-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(t \cdot y5\right)\right)} \]

       6. *-commutative N/A

          \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\left(y5 \cdot t\right)}\right) \]

       7. lower-*.f64 28.3

          \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\left(y5 \cdot t\right)}\right) \]

   11. Simplified 28.3%

       \[\leadsto \color{blue}{a \cdot \left(y2 \cdot \left(y5 \cdot t\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 33.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+19}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(t \cdot b\right)\right)\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{+73}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 22.4% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+19}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j\right)\right)\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{+73}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= t -2.1e+19)
   (* y4 (* b (* t j)))
   (if (<= t 2.65e+73) (* b (* x (* y a))) (* a (* y2 (* t 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 (t <= -2.1e+19) {
		tmp = y4 * (b * (t * j));
	} else if (t <= 2.65e+73) {
		tmp = b * (x * (y * a));
	} else {
		tmp = a * (y2 * (t * 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 (t <= (-2.1d+19)) then
        tmp = y4 * (b * (t * j))
    else if (t <= 2.65d+73) then
        tmp = b * (x * (y * a))
    else
        tmp = a * (y2 * (t * 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 (t <= -2.1e+19) {
		tmp = y4 * (b * (t * j));
	} else if (t <= 2.65e+73) {
		tmp = b * (x * (y * a));
	} else {
		tmp = a * (y2 * (t * 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 t <= -2.1e+19:
		tmp = y4 * (b * (t * j))
	elif t <= 2.65e+73:
		tmp = b * (x * (y * a))
	else:
		tmp = a * (y2 * (t * 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 (t <= -2.1e+19)
		tmp = Float64(y4 * Float64(b * Float64(t * j)));
	elseif (t <= 2.65e+73)
		tmp = Float64(b * Float64(x * Float64(y * a)));
	else
		tmp = Float64(a * Float64(y2 * Float64(t * 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 (t <= -2.1e+19)
		tmp = y4 * (b * (t * j));
	elseif (t <= 2.65e+73)
		tmp = b * (x * (y * a));
	else
		tmp = a * (y2 * (t * 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[t, -2.1e+19], N[(y4 * N[(b * N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.65e+73], N[(b * N[(x * N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y2 * N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.1e19

   1. Initial program 29.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Simplified 51.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right)\right) - c \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto y4 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto y4 \cdot \left(j \cdot \left(b \cdot t + \color{blue}{\left(\mathsf{neg}\left(y1 \cdot y3\right)\right)}\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t - y1 \cdot y3\right)}\right) \]

      5. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t - y1 \cdot y3\right)}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(j \cdot \left(\color{blue}{b \cdot t} - y1 \cdot y3\right)\right) \]

      7. lower-*.f64 46.0

         \[\leadsto y4 \cdot \left(j \cdot \left(b \cdot t - \color{blue}{y1 \cdot y3}\right)\right) \]

   8. Simplified 46.0%

      \[\leadsto y4 \cdot \color{blue}{\left(j \cdot \left(b \cdot t - y1 \cdot y3\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto y4 \cdot \color{blue}{\left(b \cdot \left(j \cdot t\right)\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto y4 \cdot \color{blue}{\left(b \cdot \left(j \cdot t\right)\right)} \]

       2. lower-*.f64 41.5

          \[\leadsto y4 \cdot \left(b \cdot \color{blue}{\left(j \cdot t\right)}\right) \]

   11. Simplified 41.5%

       \[\leadsto y4 \cdot \color{blue}{\left(b \cdot \left(j \cdot t\right)\right)} \]

   if -2.1e19 < t < 2.64999999999999998e73

   1. Initial program 25.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. lower--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{x \cdot y - t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. lower-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - \color{blue}{t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, \color{blue}{y4 \cdot \left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. lower--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - \color{blue}{k \cdot y}\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      13. lower-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

      14. lower--.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \color{blue}{\left(j \cdot x - k \cdot z\right)}\right) \]

      15. lower-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(\color{blue}{j \cdot x} - k \cdot z\right)\right) \]

      16. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

      17. lower-*.f64 36.9

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 36.9%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto b \cdot \color{blue}{\left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]
   7. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y + \left(\mathsf{neg}\left(j \cdot y0\right)\right)\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y + \color{blue}{-1 \cdot \left(j \cdot y0\right)}\right)\right) \]

      3. +-commutative N/A

         \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y0\right) + a \cdot y\right)}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(x \cdot \left(-1 \cdot \left(j \cdot y0\right) + a \cdot y\right)\right)} \]

      5. +-commutative N/A

         \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y + -1 \cdot \left(j \cdot y0\right)\right)}\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \color{blue}{\mathsf{fma}\left(a, y, -1 \cdot \left(j \cdot y0\right)\right)}\right) \]

      7. associate-*r* N/A

         \[\leadsto b \cdot \left(x \cdot \mathsf{fma}\left(a, y, \color{blue}{\left(-1 \cdot j\right) \cdot y0}\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \mathsf{fma}\left(a, y, \color{blue}{\left(-1 \cdot j\right) \cdot y0}\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto b \cdot \left(x \cdot \mathsf{fma}\left(a, y, \color{blue}{\left(\mathsf{neg}\left(j\right)\right)} \cdot y0\right)\right) \]

      10. lower-neg.f64 38.0

          \[\leadsto b \cdot \left(x \cdot \mathsf{fma}\left(a, y, \color{blue}{\left(-j\right)} \cdot y0\right)\right) \]

   8. Simplified 38.0%

      \[\leadsto b \cdot \color{blue}{\left(x \cdot \mathsf{fma}\left(a, y, \left(-j\right) \cdot y0\right)\right)} \]

   9. Taylor expanded in a around inf

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y\right)}\right) \]
   10. Step-by-step derivation

       1. lower-*.f64 27.2

          \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y\right)}\right) \]

   11. Simplified 27.2%

       \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y\right)}\right) \]

   if 2.64999999999999998e73 < t

   1. Initial program 18.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Simplified 39.0%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(x \cdot y1\right) + t \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(x \cdot y1\right) + t \cdot y5\right)\right)} \]

      2. associate-*r* N/A

         \[\leadsto a \cdot \left(y2 \cdot \left(\color{blue}{\left(-1 \cdot x\right) \cdot y1} + t \cdot y5\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot x, y1, t \cdot y5\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y1, t \cdot y5\right)\right) \]

      5. lower-neg.f64 N/A

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y1, t \cdot y5\right)\right) \]

      6. lower-*.f64 30.5

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(-x, y1, \color{blue}{t \cdot y5}\right)\right) \]

   8. Simplified 30.5%

      \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \mathsf{fma}\left(-x, y1, t \cdot y5\right)\right)} \]

   9. Taylor expanded in x around 0

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} \]

       2. *-commutative N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(y2 \cdot y5\right) \cdot t\right)} \]

       3. associate-*r* N/A

          \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(y5 \cdot t\right)\right)} \]

       4. *-commutative N/A

          \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\left(t \cdot y5\right)}\right) \]

       5. lower-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(t \cdot y5\right)\right)} \]

       6. *-commutative N/A

          \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\left(y5 \cdot t\right)}\right) \]

       7. lower-*.f64 28.3

          \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\left(y5 \cdot t\right)}\right) \]

   11. Simplified 28.3%

       \[\leadsto \color{blue}{a \cdot \left(y2 \cdot \left(y5 \cdot t\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 31.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+19}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j\right)\right)\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{+73}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 22.5% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{+38}:\\ \;\;\;\;b \cdot \left(\left(t \cdot j\right) \cdot y4\right)\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{+73}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= t -2.25e+38)
   (* b (* (* t j) y4))
   (if (<= t 2.65e+73) (* b (* x (* y a))) (* a (* y2 (* t 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 (t <= -2.25e+38) {
		tmp = b * ((t * j) * y4);
	} else if (t <= 2.65e+73) {
		tmp = b * (x * (y * a));
	} else {
		tmp = a * (y2 * (t * 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 (t <= (-2.25d+38)) then
        tmp = b * ((t * j) * y4)
    else if (t <= 2.65d+73) then
        tmp = b * (x * (y * a))
    else
        tmp = a * (y2 * (t * 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 (t <= -2.25e+38) {
		tmp = b * ((t * j) * y4);
	} else if (t <= 2.65e+73) {
		tmp = b * (x * (y * a));
	} else {
		tmp = a * (y2 * (t * 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 t <= -2.25e+38:
		tmp = b * ((t * j) * y4)
	elif t <= 2.65e+73:
		tmp = b * (x * (y * a))
	else:
		tmp = a * (y2 * (t * 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 (t <= -2.25e+38)
		tmp = Float64(b * Float64(Float64(t * j) * y4));
	elseif (t <= 2.65e+73)
		tmp = Float64(b * Float64(x * Float64(y * a)));
	else
		tmp = Float64(a * Float64(y2 * Float64(t * 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 (t <= -2.25e+38)
		tmp = b * ((t * j) * y4);
	elseif (t <= 2.65e+73)
		tmp = b * (x * (y * a));
	else
		tmp = a * (y2 * (t * 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[t, -2.25e+38], N[(b * N[(N[(t * j), $MachinePrecision] * y4), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.65e+73], N[(b * N[(x * N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y2 * N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.2499999999999999e38

   1. Initial program 28.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Simplified 51.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right)\right) - c \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto y4 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto y4 \cdot \left(j \cdot \left(b \cdot t + \color{blue}{\left(\mathsf{neg}\left(y1 \cdot y3\right)\right)}\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t - y1 \cdot y3\right)}\right) \]

      5. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(b \cdot t - y1 \cdot y3\right)}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(j \cdot \left(\color{blue}{b \cdot t} - y1 \cdot y3\right)\right) \]

      7. lower-*.f64 45.6

         \[\leadsto y4 \cdot \left(j \cdot \left(b \cdot t - \color{blue}{y1 \cdot y3}\right)\right) \]

   8. Simplified 45.6%

      \[\leadsto y4 \cdot \color{blue}{\left(j \cdot \left(b \cdot t - y1 \cdot y3\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]

       2. associate-*r* N/A

          \[\leadsto b \cdot \color{blue}{\left(\left(j \cdot t\right) \cdot y4\right)} \]

       3. lower-*.f64 N/A

          \[\leadsto b \cdot \color{blue}{\left(\left(j \cdot t\right) \cdot y4\right)} \]

       4. lower-*.f64 42.0

          \[\leadsto b \cdot \left(\color{blue}{\left(j \cdot t\right)} \cdot y4\right) \]

   11. Simplified 42.0%

       \[\leadsto \color{blue}{b \cdot \left(\left(j \cdot t\right) \cdot y4\right)} \]

   if -2.2499999999999999e38 < t < 2.64999999999999998e73

   1. Initial program 26.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. lower--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{x \cdot y - t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. lower-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - \color{blue}{t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, \color{blue}{y4 \cdot \left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. lower--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - \color{blue}{k \cdot y}\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      13. lower-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

      14. lower--.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \color{blue}{\left(j \cdot x - k \cdot z\right)}\right) \]

      15. lower-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(\color{blue}{j \cdot x} - k \cdot z\right)\right) \]

      16. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

      17. lower-*.f64 38.2

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 38.2%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto b \cdot \color{blue}{\left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]
   7. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y + \left(\mathsf{neg}\left(j \cdot y0\right)\right)\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y + \color{blue}{-1 \cdot \left(j \cdot y0\right)}\right)\right) \]

      3. +-commutative N/A

         \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y0\right) + a \cdot y\right)}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(x \cdot \left(-1 \cdot \left(j \cdot y0\right) + a \cdot y\right)\right)} \]

      5. +-commutative N/A

         \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y + -1 \cdot \left(j \cdot y0\right)\right)}\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \color{blue}{\mathsf{fma}\left(a, y, -1 \cdot \left(j \cdot y0\right)\right)}\right) \]

      7. associate-*r* N/A

         \[\leadsto b \cdot \left(x \cdot \mathsf{fma}\left(a, y, \color{blue}{\left(-1 \cdot j\right) \cdot y0}\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \mathsf{fma}\left(a, y, \color{blue}{\left(-1 \cdot j\right) \cdot y0}\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto b \cdot \left(x \cdot \mathsf{fma}\left(a, y, \color{blue}{\left(\mathsf{neg}\left(j\right)\right)} \cdot y0\right)\right) \]

      10. lower-neg.f64 37.9

          \[\leadsto b \cdot \left(x \cdot \mathsf{fma}\left(a, y, \color{blue}{\left(-j\right)} \cdot y0\right)\right) \]

   8. Simplified 37.9%

      \[\leadsto b \cdot \color{blue}{\left(x \cdot \mathsf{fma}\left(a, y, \left(-j\right) \cdot y0\right)\right)} \]

   9. Taylor expanded in a around inf

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y\right)}\right) \]
   10. Step-by-step derivation

       1. lower-*.f64 27.5

          \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y\right)}\right) \]

   11. Simplified 27.5%

       \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y\right)}\right) \]

   if 2.64999999999999998e73 < t

   1. Initial program 18.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Simplified 39.0%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(x \cdot y1\right) + t \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(x \cdot y1\right) + t \cdot y5\right)\right)} \]

      2. associate-*r* N/A

         \[\leadsto a \cdot \left(y2 \cdot \left(\color{blue}{\left(-1 \cdot x\right) \cdot y1} + t \cdot y5\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot x, y1, t \cdot y5\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y1, t \cdot y5\right)\right) \]

      5. lower-neg.f64 N/A

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y1, t \cdot y5\right)\right) \]

      6. lower-*.f64 30.5

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(-x, y1, \color{blue}{t \cdot y5}\right)\right) \]

   8. Simplified 30.5%

      \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \mathsf{fma}\left(-x, y1, t \cdot y5\right)\right)} \]

   9. Taylor expanded in x around 0

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} \]

       2. *-commutative N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(y2 \cdot y5\right) \cdot t\right)} \]

       3. associate-*r* N/A

          \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(y5 \cdot t\right)\right)} \]

       4. *-commutative N/A

          \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\left(t \cdot y5\right)}\right) \]

       5. lower-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(t \cdot y5\right)\right)} \]

       6. *-commutative N/A

          \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\left(y5 \cdot t\right)}\right) \]

       7. lower-*.f64 28.3

          \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\left(y5 \cdot t\right)}\right) \]

   11. Simplified 28.3%

       \[\leadsto \color{blue}{a \cdot \left(y2 \cdot \left(y5 \cdot t\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 31.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{+38}:\\ \;\;\;\;b \cdot \left(\left(t \cdot j\right) \cdot y4\right)\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{+73}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 21.7% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{if}\;b \leq -6.8 \cdot 10^{-43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-73}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* x (* y b)))))
   (if (<= b -6.8e-43) t_1 (if (<= b 1.3e-73) (* a (* y2 (* t y5))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (x * (y * b));
	double tmp;
	if (b <= -6.8e-43) {
		tmp = t_1;
	} else if (b <= 1.3e-73) {
		tmp = a * (y2 * (t * y5));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (x * (y * b))
    if (b <= (-6.8d-43)) then
        tmp = t_1
    else if (b <= 1.3d-73) then
        tmp = a * (y2 * (t * y5))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (x * (y * b));
	double tmp;
	if (b <= -6.8e-43) {
		tmp = t_1;
	} else if (b <= 1.3e-73) {
		tmp = a * (y2 * (t * y5));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (x * (y * b))
	tmp = 0
	if b <= -6.8e-43:
		tmp = t_1
	elif b <= 1.3e-73:
		tmp = a * (y2 * (t * y5))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(x * Float64(y * b)))
	tmp = 0.0
	if (b <= -6.8e-43)
		tmp = t_1;
	elseif (b <= 1.3e-73)
		tmp = Float64(a * Float64(y2 * Float64(t * y5)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (x * (y * b));
	tmp = 0.0;
	if (b <= -6.8e-43)
		tmp = t_1;
	elseif (b <= 1.3e-73)
		tmp = a * (y2 * (t * y5));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(x * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.8e-43], t$95$1, If[LessEqual[b, 1.3e-73], N[(a * N[(y2 * N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -6.8000000000000001e-43 or 1.3e-73 < b

   1. Initial program 19.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Simplified 46.3%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto a \cdot \left(y \cdot \left(\color{blue}{\left(-1 \cdot y3\right) \cdot y5} + b \cdot x\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot y3, y5, b \cdot x\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y3\right)}, y5, b \cdot x\right)\right) \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y3\right)}, y5, b \cdot x\right)\right) \]

      7. lower-*.f64 41.4

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, \color{blue}{b \cdot x}\right)\right) \]

   8. Simplified 41.4%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, b \cdot x\right)\right)} \]

   9. Taylor expanded in y3 around 0

      \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x\right)}\right) \]
   10. Step-by-step derivation

       1. lower-*.f64 29.5

          \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x\right)}\right) \]

   11. Simplified 29.5%

       \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x\right)}\right) \]
   12. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(y \cdot b\right) \cdot x\right)} \]

       2. lower-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(y \cdot b\right) \cdot x\right)} \]

       3. lower-*.f64 32.1

          \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot b\right)} \cdot x\right) \]

   13. Applied egg-rr 32.1%

       \[\leadsto a \cdot \color{blue}{\left(\left(y \cdot b\right) \cdot x\right)} \]

   if -6.8000000000000001e-43 < b < 1.3e-73

   1. Initial program 34.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Simplified 42.4%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(x \cdot y1\right) + t \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(x \cdot y1\right) + t \cdot y5\right)\right)} \]

      2. associate-*r* N/A

         \[\leadsto a \cdot \left(y2 \cdot \left(\color{blue}{\left(-1 \cdot x\right) \cdot y1} + t \cdot y5\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot x, y1, t \cdot y5\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y1, t \cdot y5\right)\right) \]

      5. lower-neg.f64 N/A

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y1, t \cdot y5\right)\right) \]

      6. lower-*.f64 30.8

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(-x, y1, \color{blue}{t \cdot y5}\right)\right) \]

   8. Simplified 30.8%

      \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \mathsf{fma}\left(-x, y1, t \cdot y5\right)\right)} \]

   9. Taylor expanded in x around 0

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} \]

       2. *-commutative N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(y2 \cdot y5\right) \cdot t\right)} \]

       3. associate-*r* N/A

          \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(y5 \cdot t\right)\right)} \]

       4. *-commutative N/A

          \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\left(t \cdot y5\right)}\right) \]

       5. lower-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(t \cdot y5\right)\right)} \]

       6. *-commutative N/A

          \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\left(y5 \cdot t\right)}\right) \]

       7. lower-*.f64 22.0

          \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\left(y5 \cdot t\right)}\right) \]

   11. Simplified 22.0%

       \[\leadsto \color{blue}{a \cdot \left(y2 \cdot \left(y5 \cdot t\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 27.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{-43}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-73}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 21.7% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{if}\;b \leq -6.8 \cdot 10^{-43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-73}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y (* x b)))))
   (if (<= b -6.8e-43) t_1 (if (<= b 1.3e-73) (* a (* y2 (* t y5))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y * (x * b));
	double tmp;
	if (b <= -6.8e-43) {
		tmp = t_1;
	} else if (b <= 1.3e-73) {
		tmp = a * (y2 * (t * y5));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (y * (x * b))
    if (b <= (-6.8d-43)) then
        tmp = t_1
    else if (b <= 1.3d-73) then
        tmp = a * (y2 * (t * y5))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y * (x * b));
	double tmp;
	if (b <= -6.8e-43) {
		tmp = t_1;
	} else if (b <= 1.3e-73) {
		tmp = a * (y2 * (t * y5));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y * (x * b))
	tmp = 0
	if b <= -6.8e-43:
		tmp = t_1
	elif b <= 1.3e-73:
		tmp = a * (y2 * (t * y5))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y * Float64(x * b)))
	tmp = 0.0
	if (b <= -6.8e-43)
		tmp = t_1;
	elseif (b <= 1.3e-73)
		tmp = Float64(a * Float64(y2 * Float64(t * y5)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y * (x * b));
	tmp = 0.0;
	if (b <= -6.8e-43)
		tmp = t_1;
	elseif (b <= 1.3e-73)
		tmp = a * (y2 * (t * y5));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.8e-43], t$95$1, If[LessEqual[b, 1.3e-73], N[(a * N[(y2 * N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -6.8000000000000001e-43 or 1.3e-73 < b

   1. Initial program 19.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Simplified 46.3%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto a \cdot \left(y \cdot \left(\color{blue}{\left(-1 \cdot y3\right) \cdot y5} + b \cdot x\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot y3, y5, b \cdot x\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y3\right)}, y5, b \cdot x\right)\right) \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y3\right)}, y5, b \cdot x\right)\right) \]

      7. lower-*.f64 41.4

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, \color{blue}{b \cdot x}\right)\right) \]

   8. Simplified 41.4%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, b \cdot x\right)\right)} \]

   9. Taylor expanded in y3 around 0

      \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x\right)}\right) \]
   10. Step-by-step derivation

       1. lower-*.f64 29.5

          \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x\right)}\right) \]

   11. Simplified 29.5%

       \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x\right)}\right) \]

   if -6.8000000000000001e-43 < b < 1.3e-73

   1. Initial program 34.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Simplified 42.4%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(x \cdot y1\right) + t \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(x \cdot y1\right) + t \cdot y5\right)\right)} \]

      2. associate-*r* N/A

         \[\leadsto a \cdot \left(y2 \cdot \left(\color{blue}{\left(-1 \cdot x\right) \cdot y1} + t \cdot y5\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot x, y1, t \cdot y5\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y1, t \cdot y5\right)\right) \]

      5. lower-neg.f64 N/A

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y1, t \cdot y5\right)\right) \]

      6. lower-*.f64 30.8

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(-x, y1, \color{blue}{t \cdot y5}\right)\right) \]

   8. Simplified 30.8%

      \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \mathsf{fma}\left(-x, y1, t \cdot y5\right)\right)} \]

   9. Taylor expanded in x around 0

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} \]

       2. *-commutative N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(y2 \cdot y5\right) \cdot t\right)} \]

       3. associate-*r* N/A

          \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(y5 \cdot t\right)\right)} \]

       4. *-commutative N/A

          \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\left(t \cdot y5\right)}\right) \]

       5. lower-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(t \cdot y5\right)\right)} \]

       6. *-commutative N/A

          \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\left(y5 \cdot t\right)}\right) \]

       7. lower-*.f64 22.0

          \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\left(y5 \cdot t\right)}\right) \]

   11. Simplified 22.0%

       \[\leadsto \color{blue}{a \cdot \left(y2 \cdot \left(y5 \cdot t\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 26.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{-43}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-73}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 16.6% accurate, 12.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(y \cdot \left(x \cdot b\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* y (* x b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (y * (x * b));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = a * (y * (x * b))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (y * (x * b));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * (y * (x * b))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(y * Float64(x * b)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * (y * (x * b));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 25.7%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
2. Add Preprocessing

3. Taylor expanded in a around inf

   \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
4. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   2. associate--l+ N/A

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

   3. mul-1-neg N/A

      \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

   4. distribute-rgt-neg-in N/A

      \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

   5. lower-fma.f64 N/A

      \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. lower-neg.f64 N/A

      \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   7. lower--.f64 N/A

      \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   8. *-commutative N/A

      \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   9. lower-*.f64 N/A

      \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   10. *-commutative N/A

       \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   11. lower-*.f64 N/A

       \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   12. sub-neg N/A

       \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

5. Simplified 44.7%

   \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

6. Taylor expanded in y around inf

   \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
7. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

   2. lower-*.f64 N/A

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

   3. associate-*r* N/A

      \[\leadsto a \cdot \left(y \cdot \left(\color{blue}{\left(-1 \cdot y3\right) \cdot y5} + b \cdot x\right)\right) \]

   4. lower-fma.f64 N/A

      \[\leadsto a \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot y3, y5, b \cdot x\right)}\right) \]

   5. mul-1-neg N/A

      \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y3\right)}, y5, b \cdot x\right)\right) \]

   6. lower-neg.f64 N/A

      \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y3\right)}, y5, b \cdot x\right)\right) \]

   7. lower-*.f64 35.8

      \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, \color{blue}{b \cdot x}\right)\right) \]

8. Simplified 35.8%

   \[\leadsto \color{blue}{a \cdot \left(y \cdot \mathsf{fma}\left(-y3, y5, b \cdot x\right)\right)} \]

9. Taylor expanded in y3 around 0

   \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x\right)}\right) \]
10. Step-by-step derivation

    1. lower-*.f64 19.8

       \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x\right)}\right) \]

11. Simplified 19.8%

    \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x\right)}\right) \]

12. Final simplification 19.8%

    \[\leadsto a \cdot \left(y \cdot \left(x \cdot b\right)\right) \]
13. Add Preprocessing

Developer Target 1: 27.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot c - y5 \cdot a\\ t_2 := x \cdot y2 - z \cdot y3\\ t_3 := y2 \cdot t - y3 \cdot y\\ t_4 := k \cdot y2 - j \cdot y3\\ t_5 := y4 \cdot b - y5 \cdot i\\ t_6 := \left(j \cdot t - k \cdot y\right) \cdot t\_5\\ t_7 := b \cdot a - i \cdot c\\ t_8 := t\_7 \cdot \left(y \cdot x - t \cdot z\right)\\ t_9 := j \cdot x - k \cdot z\\ t_10 := \left(b \cdot y0 - i \cdot y1\right) \cdot t\_9\\ t_11 := t\_9 \cdot \left(y0 \cdot b - i \cdot y1\right)\\ t_12 := y4 \cdot y1 - y5 \cdot y0\\ t_13 := t\_4 \cdot t\_12\\ t_14 := \left(y2 \cdot k - y3 \cdot j\right) \cdot t\_12\\ t_15 := \left(\left(\left(\left(k \cdot y\right) \cdot \left(y5 \cdot i\right) - \left(y \cdot b\right) \cdot \left(y4 \cdot k\right)\right) - \left(y5 \cdot t\right) \cdot \left(i \cdot j\right)\right) - \left(t\_3 \cdot t\_1 - t\_14\right)\right) + \left(t\_8 - \left(t\_11 - \left(y2 \cdot x - y3 \cdot z\right) \cdot \left(c \cdot y0 - y1 \cdot a\right)\right)\right)\\ t_16 := \left(\left(t\_6 - \left(y3 \cdot y\right) \cdot \left(y5 \cdot a - y4 \cdot c\right)\right) + \left(\left(y5 \cdot a\right) \cdot \left(t \cdot y2\right) + t\_13\right)\right) + \left(t\_2 \cdot \left(c \cdot y0 - a \cdot y1\right) - \left(t\_10 - \left(y \cdot x - z \cdot t\right) \cdot t\_7\right)\right)\\ t_17 := t \cdot y2 - y \cdot y3\\ \mathbf{if}\;y4 < -7.206256231996481 \cdot 10^{+60}:\\ \;\;\;\;\left(t\_8 - \left(t\_11 - t\_6\right)\right) - \left(\frac{t\_3}{\frac{1}{t\_1}} - t\_14\right)\\ \mathbf{elif}\;y4 < -3.364603505246317 \cdot 10^{-66}:\\ \;\;\;\;\left(\left(\left(\left(t \cdot c\right) \cdot \left(i \cdot z\right) - \left(a \cdot t\right) \cdot \left(b \cdot z\right)\right) - \left(y \cdot c\right) \cdot \left(i \cdot x\right)\right) - t\_10\right) + \left(\left(y0 \cdot c - a \cdot y1\right) \cdot t\_2 - \left(t\_17 \cdot \left(y4 \cdot c - a \cdot y5\right) - \left(y1 \cdot y4 - y5 \cdot y0\right) \cdot t\_4\right)\right)\\ \mathbf{elif}\;y4 < -1.2000065055686116 \cdot 10^{-105}:\\ \;\;\;\;t\_16\\ \mathbf{elif}\;y4 < 6.718963124057495 \cdot 10^{-279}:\\ \;\;\;\;t\_15\\ \mathbf{elif}\;y4 < 4.77962681403792 \cdot 10^{-222}:\\ \;\;\;\;t\_16\\ \mathbf{elif}\;y4 < 2.2852241541266835 \cdot 10^{-175}:\\ \;\;\;\;t\_15\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(k \cdot \left(i \cdot \left(z \cdot y1\right)\right) - \left(j \cdot \left(i \cdot \left(x \cdot y1\right)\right) + y0 \cdot \left(k \cdot \left(z \cdot b\right)\right)\right)\right)\right) + \left(z \cdot \left(y3 \cdot \left(a \cdot y1\right)\right) - \left(y2 \cdot \left(x \cdot \left(a \cdot y1\right)\right) + y0 \cdot \left(z \cdot \left(c \cdot y3\right)\right)\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot t\_5\right) - t\_17 \cdot t\_1\right) + t\_13\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y4 c) (* y5 a)))
        (t_2 (- (* x y2) (* z y3)))
        (t_3 (- (* y2 t) (* y3 y)))
        (t_4 (- (* k y2) (* j y3)))
        (t_5 (- (* y4 b) (* y5 i)))
        (t_6 (* (- (* j t) (* k y)) t_5))
        (t_7 (- (* b a) (* i c)))
        (t_8 (* t_7 (- (* y x) (* t z))))
        (t_9 (- (* j x) (* k z)))
        (t_10 (* (- (* b y0) (* i y1)) t_9))
        (t_11 (* t_9 (- (* y0 b) (* i y1))))
        (t_12 (- (* y4 y1) (* y5 y0)))
        (t_13 (* t_4 t_12))
        (t_14 (* (- (* y2 k) (* y3 j)) t_12))
        (t_15
         (+
          (-
           (-
            (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k)))
            (* (* y5 t) (* i j)))
           (- (* t_3 t_1) t_14))
          (- t_8 (- t_11 (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))))
        (t_16
         (+
          (+
           (- t_6 (* (* y3 y) (- (* y5 a) (* y4 c))))
           (+ (* (* y5 a) (* t y2)) t_13))
          (-
           (* t_2 (- (* c y0) (* a y1)))
           (- t_10 (* (- (* y x) (* z t)) t_7)))))
        (t_17 (- (* t y2) (* y y3))))
   (if (< y4 -7.206256231996481e+60)
     (- (- t_8 (- t_11 t_6)) (- (/ t_3 (/ 1.0 t_1)) t_14))
     (if (< y4 -3.364603505246317e-66)
       (+
        (-
         (- (- (* (* t c) (* i z)) (* (* a t) (* b z))) (* (* y c) (* i x)))
         t_10)
        (-
         (* (- (* y0 c) (* a y1)) t_2)
         (- (* t_17 (- (* y4 c) (* a y5))) (* (- (* y1 y4) (* y5 y0)) t_4))))
       (if (< y4 -1.2000065055686116e-105)
         t_16
         (if (< y4 6.718963124057495e-279)
           t_15
           (if (< y4 4.77962681403792e-222)
             t_16
             (if (< y4 2.2852241541266835e-175)
               t_15
               (+
                (-
                 (+
                  (+
                   (-
                    (* (- (* x y) (* z t)) (- (* a b) (* c i)))
                    (-
                     (* k (* i (* z y1)))
                     (+ (* j (* i (* x y1))) (* y0 (* k (* z b))))))
                   (-
                    (* z (* y3 (* a y1)))
                    (+ (* y2 (* x (* a y1))) (* y0 (* z (* c y3))))))
                  (* (- (* t j) (* y k)) t_5))
                 (* t_17 t_1))
                t_13)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y4 * c) - (y5 * a);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (y2 * t) - (y3 * y);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = (y4 * b) - (y5 * i);
	double t_6 = ((j * t) - (k * y)) * t_5;
	double t_7 = (b * a) - (i * c);
	double t_8 = t_7 * ((y * x) - (t * z));
	double t_9 = (j * x) - (k * z);
	double t_10 = ((b * y0) - (i * y1)) * t_9;
	double t_11 = t_9 * ((y0 * b) - (i * y1));
	double t_12 = (y4 * y1) - (y5 * y0);
	double t_13 = t_4 * t_12;
	double t_14 = ((y2 * k) - (y3 * j)) * t_12;
	double t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	double t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	double t_17 = (t * y2) - (y * y3);
	double tmp;
	if (y4 < -7.206256231996481e+60) {
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	} else if (y4 < -3.364603505246317e-66) {
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	} else if (y4 < -1.2000065055686116e-105) {
		tmp = t_16;
	} else if (y4 < 6.718963124057495e-279) {
		tmp = t_15;
	} else if (y4 < 4.77962681403792e-222) {
		tmp = t_16;
	} else if (y4 < 2.2852241541266835e-175) {
		tmp = t_15;
	} else {
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_10
    real(8) :: t_11
    real(8) :: t_12
    real(8) :: t_13
    real(8) :: t_14
    real(8) :: t_15
    real(8) :: t_16
    real(8) :: t_17
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = (y4 * c) - (y5 * a)
    t_2 = (x * y2) - (z * y3)
    t_3 = (y2 * t) - (y3 * y)
    t_4 = (k * y2) - (j * y3)
    t_5 = (y4 * b) - (y5 * i)
    t_6 = ((j * t) - (k * y)) * t_5
    t_7 = (b * a) - (i * c)
    t_8 = t_7 * ((y * x) - (t * z))
    t_9 = (j * x) - (k * z)
    t_10 = ((b * y0) - (i * y1)) * t_9
    t_11 = t_9 * ((y0 * b) - (i * y1))
    t_12 = (y4 * y1) - (y5 * y0)
    t_13 = t_4 * t_12
    t_14 = ((y2 * k) - (y3 * j)) * t_12
    t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))))
    t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)))
    t_17 = (t * y2) - (y * y3)
    if (y4 < (-7.206256231996481d+60)) then
        tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0d0 / t_1)) - t_14)
    else if (y4 < (-3.364603505246317d-66)) then
        tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)))
    else if (y4 < (-1.2000065055686116d-105)) then
        tmp = t_16
    else if (y4 < 6.718963124057495d-279) then
        tmp = t_15
    else if (y4 < 4.77962681403792d-222) then
        tmp = t_16
    else if (y4 < 2.2852241541266835d-175) then
        tmp = t_15
    else
        tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y4 * c) - (y5 * a);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (y2 * t) - (y3 * y);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = (y4 * b) - (y5 * i);
	double t_6 = ((j * t) - (k * y)) * t_5;
	double t_7 = (b * a) - (i * c);
	double t_8 = t_7 * ((y * x) - (t * z));
	double t_9 = (j * x) - (k * z);
	double t_10 = ((b * y0) - (i * y1)) * t_9;
	double t_11 = t_9 * ((y0 * b) - (i * y1));
	double t_12 = (y4 * y1) - (y5 * y0);
	double t_13 = t_4 * t_12;
	double t_14 = ((y2 * k) - (y3 * j)) * t_12;
	double t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	double t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	double t_17 = (t * y2) - (y * y3);
	double tmp;
	if (y4 < -7.206256231996481e+60) {
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	} else if (y4 < -3.364603505246317e-66) {
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	} else if (y4 < -1.2000065055686116e-105) {
		tmp = t_16;
	} else if (y4 < 6.718963124057495e-279) {
		tmp = t_15;
	} else if (y4 < 4.77962681403792e-222) {
		tmp = t_16;
	} else if (y4 < 2.2852241541266835e-175) {
		tmp = t_15;
	} else {
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y4 * c) - (y5 * a)
	t_2 = (x * y2) - (z * y3)
	t_3 = (y2 * t) - (y3 * y)
	t_4 = (k * y2) - (j * y3)
	t_5 = (y4 * b) - (y5 * i)
	t_6 = ((j * t) - (k * y)) * t_5
	t_7 = (b * a) - (i * c)
	t_8 = t_7 * ((y * x) - (t * z))
	t_9 = (j * x) - (k * z)
	t_10 = ((b * y0) - (i * y1)) * t_9
	t_11 = t_9 * ((y0 * b) - (i * y1))
	t_12 = (y4 * y1) - (y5 * y0)
	t_13 = t_4 * t_12
	t_14 = ((y2 * k) - (y3 * j)) * t_12
	t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))))
	t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)))
	t_17 = (t * y2) - (y * y3)
	tmp = 0
	if y4 < -7.206256231996481e+60:
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14)
	elif y4 < -3.364603505246317e-66:
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)))
	elif y4 < -1.2000065055686116e-105:
		tmp = t_16
	elif y4 < 6.718963124057495e-279:
		tmp = t_15
	elif y4 < 4.77962681403792e-222:
		tmp = t_16
	elif y4 < 2.2852241541266835e-175:
		tmp = t_15
	else:
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y4 * c) - Float64(y5 * a))
	t_2 = Float64(Float64(x * y2) - Float64(z * y3))
	t_3 = Float64(Float64(y2 * t) - Float64(y3 * y))
	t_4 = Float64(Float64(k * y2) - Float64(j * y3))
	t_5 = Float64(Float64(y4 * b) - Float64(y5 * i))
	t_6 = Float64(Float64(Float64(j * t) - Float64(k * y)) * t_5)
	t_7 = Float64(Float64(b * a) - Float64(i * c))
	t_8 = Float64(t_7 * Float64(Float64(y * x) - Float64(t * z)))
	t_9 = Float64(Float64(j * x) - Float64(k * z))
	t_10 = Float64(Float64(Float64(b * y0) - Float64(i * y1)) * t_9)
	t_11 = Float64(t_9 * Float64(Float64(y0 * b) - Float64(i * y1)))
	t_12 = Float64(Float64(y4 * y1) - Float64(y5 * y0))
	t_13 = Float64(t_4 * t_12)
	t_14 = Float64(Float64(Float64(y2 * k) - Float64(y3 * j)) * t_12)
	t_15 = Float64(Float64(Float64(Float64(Float64(Float64(k * y) * Float64(y5 * i)) - Float64(Float64(y * b) * Float64(y4 * k))) - Float64(Float64(y5 * t) * Float64(i * j))) - Float64(Float64(t_3 * t_1) - t_14)) + Float64(t_8 - Float64(t_11 - Float64(Float64(Float64(y2 * x) - Float64(y3 * z)) * Float64(Float64(c * y0) - Float64(y1 * a))))))
	t_16 = Float64(Float64(Float64(t_6 - Float64(Float64(y3 * y) * Float64(Float64(y5 * a) - Float64(y4 * c)))) + Float64(Float64(Float64(y5 * a) * Float64(t * y2)) + t_13)) + Float64(Float64(t_2 * Float64(Float64(c * y0) - Float64(a * y1))) - Float64(t_10 - Float64(Float64(Float64(y * x) - Float64(z * t)) * t_7))))
	t_17 = Float64(Float64(t * y2) - Float64(y * y3))
	tmp = 0.0
	if (y4 < -7.206256231996481e+60)
		tmp = Float64(Float64(t_8 - Float64(t_11 - t_6)) - Float64(Float64(t_3 / Float64(1.0 / t_1)) - t_14));
	elseif (y4 < -3.364603505246317e-66)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(t * c) * Float64(i * z)) - Float64(Float64(a * t) * Float64(b * z))) - Float64(Float64(y * c) * Float64(i * x))) - t_10) + Float64(Float64(Float64(Float64(y0 * c) - Float64(a * y1)) * t_2) - Float64(Float64(t_17 * Float64(Float64(y4 * c) - Float64(a * y5))) - Float64(Float64(Float64(y1 * y4) - Float64(y5 * y0)) * t_4))));
	elseif (y4 < -1.2000065055686116e-105)
		tmp = t_16;
	elseif (y4 < 6.718963124057495e-279)
		tmp = t_15;
	elseif (y4 < 4.77962681403792e-222)
		tmp = t_16;
	elseif (y4 < 2.2852241541266835e-175)
		tmp = t_15;
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) - Float64(z * t)) * Float64(Float64(a * b) - Float64(c * i))) - Float64(Float64(k * Float64(i * Float64(z * y1))) - Float64(Float64(j * Float64(i * Float64(x * y1))) + Float64(y0 * Float64(k * Float64(z * b)))))) + Float64(Float64(z * Float64(y3 * Float64(a * y1))) - Float64(Float64(y2 * Float64(x * Float64(a * y1))) + Float64(y0 * Float64(z * Float64(c * y3)))))) + Float64(Float64(Float64(t * j) - Float64(y * k)) * t_5)) - Float64(t_17 * t_1)) + t_13);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y4 * c) - (y5 * a);
	t_2 = (x * y2) - (z * y3);
	t_3 = (y2 * t) - (y3 * y);
	t_4 = (k * y2) - (j * y3);
	t_5 = (y4 * b) - (y5 * i);
	t_6 = ((j * t) - (k * y)) * t_5;
	t_7 = (b * a) - (i * c);
	t_8 = t_7 * ((y * x) - (t * z));
	t_9 = (j * x) - (k * z);
	t_10 = ((b * y0) - (i * y1)) * t_9;
	t_11 = t_9 * ((y0 * b) - (i * y1));
	t_12 = (y4 * y1) - (y5 * y0);
	t_13 = t_4 * t_12;
	t_14 = ((y2 * k) - (y3 * j)) * t_12;
	t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	t_17 = (t * y2) - (y * y3);
	tmp = 0.0;
	if (y4 < -7.206256231996481e+60)
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	elseif (y4 < -3.364603505246317e-66)
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	elseif (y4 < -1.2000065055686116e-105)
		tmp = t_16;
	elseif (y4 < 6.718963124057495e-279)
		tmp = t_15;
	elseif (y4 < 4.77962681403792e-222)
		tmp = t_16;
	elseif (y4 < 2.2852241541266835e-175)
		tmp = t_15;
	else
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y4 * c), $MachinePrecision] - N[(y5 * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y2 * t), $MachinePrecision] - N[(y3 * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(y4 * b), $MachinePrecision] - N[(y5 * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision] * t$95$5), $MachinePrecision]}, Block[{t$95$7 = N[(N[(b * a), $MachinePrecision] - N[(i * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(t$95$7 * N[(N[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$10 = N[(N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision] * t$95$9), $MachinePrecision]}, Block[{t$95$11 = N[(t$95$9 * N[(N[(y0 * b), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$12 = N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$13 = N[(t$95$4 * t$95$12), $MachinePrecision]}, Block[{t$95$14 = N[(N[(N[(y2 * k), $MachinePrecision] - N[(y3 * j), $MachinePrecision]), $MachinePrecision] * t$95$12), $MachinePrecision]}, Block[{t$95$15 = N[(N[(N[(N[(N[(N[(k * y), $MachinePrecision] * N[(y5 * i), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] * N[(y4 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y5 * t), $MachinePrecision] * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$3 * t$95$1), $MachinePrecision] - t$95$14), $MachinePrecision]), $MachinePrecision] + N[(t$95$8 - N[(t$95$11 - N[(N[(N[(y2 * x), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision] * N[(N[(c * y0), $MachinePrecision] - N[(y1 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$16 = N[(N[(N[(t$95$6 - N[(N[(y3 * y), $MachinePrecision] * N[(N[(y5 * a), $MachinePrecision] - N[(y4 * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y5 * a), $MachinePrecision] * N[(t * y2), $MachinePrecision]), $MachinePrecision] + t$95$13), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$10 - N[(N[(N[(y * x), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$17 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, If[Less[y4, -7.206256231996481e+60], N[(N[(t$95$8 - N[(t$95$11 - t$95$6), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$3 / N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision] - t$95$14), $MachinePrecision]), $MachinePrecision], If[Less[y4, -3.364603505246317e-66], N[(N[(N[(N[(N[(N[(t * c), $MachinePrecision] * N[(i * z), $MachinePrecision]), $MachinePrecision] - N[(N[(a * t), $MachinePrecision] * N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * c), $MachinePrecision] * N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$10), $MachinePrecision] + N[(N[(N[(N[(y0 * c), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision] - N[(N[(t$95$17 * N[(N[(y4 * c), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(y1 * y4), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision] * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[y4, -1.2000065055686116e-105], t$95$16, If[Less[y4, 6.718963124057495e-279], t$95$15, If[Less[y4, 4.77962681403792e-222], t$95$16, If[Less[y4, 2.2852241541266835e-175], t$95$15, N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(k * N[(i * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * N[(i * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(k * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(y3 * N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y2 * N[(x * N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(z * N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * t$95$5), $MachinePrecision]), $MachinePrecision] - N[(t$95$17 * t$95$1), $MachinePrecision]), $MachinePrecision] + t$95$13), $MachinePrecision]]]]]]]]]]]]]]]]]]]]]]]]

Reproduce

herbie shell --seed 2024207 
(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :name "Linear.Matrix:det44 from linear-1.19.1.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y4 -7206256231996481000000000000000000000000000000000000000000000) (- (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))))) (- (/ (- (* y2 t) (* y3 y)) (/ 1 (- (* y4 c) (* y5 a)))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (if (< y4 -3364603505246317/1000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (- (- (* (* t c) (* i z)) (* (* a t) (* b z))) (* (* y c) (* i x))) (* (- (* b y0) (* i y1)) (- (* j x) (* k z)))) (- (* (- (* y0 c) (* a y1)) (- (* x y2) (* z y3))) (- (* (- (* t y2) (* y y3)) (- (* y4 c) (* a y5))) (* (- (* y1 y4) (* y5 y0)) (- (* k y2) (* j y3)))))) (if (< y4 -3000016263921529/2500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (+ (- (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))) (* (* y3 y) (- (* y5 a) (* y4 c)))) (+ (* (* y5 a) (* t y2)) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* x y2) (* z y3)) (- (* c y0) (* a y1))) (- (* (- (* b y0) (* i y1)) (- (* j x) (* k z))) (* (- (* y x) (* z t)) (- (* b a) (* i c)))))) (if (< y4 1343792624811499/200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (- (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k))) (* (* y5 t) (* i j))) (- (* (- (* y2 t) (* y3 y)) (- (* y4 c) (* y5 a))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))) (if (< y4 29872667587737/6250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (+ (- (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))) (* (* y3 y) (- (* y5 a) (* y4 c)))) (+ (* (* y5 a) (* t y2)) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* x y2) (* z y3)) (- (* c y0) (* a y1))) (- (* (- (* b y0) (* i y1)) (- (* j x) (* k z))) (* (- (* y x) (* z t)) (- (* b a) (* i c)))))) (if (< y4 4570448308253367/20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (- (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k))) (* (* y5 t) (* i j))) (- (* (- (* y2 t) (* y3 y)) (- (* y4 c) (* y5 a))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))) (+ (- (+ (+ (- (* (- (* x y) (* z t)) (- (* a b) (* c i))) (- (* k (* i (* z y1))) (+ (* j (* i (* x y1))) (* y0 (* k (* z b)))))) (- (* z (* y3 (* a y1))) (+ (* y2 (* x (* a y1))) (* y0 (* z (* c y3)))))) (* (- (* t j) (* y k)) (- (* y4 b) (* y5 i)))) (* (- (* t y2) (* y y3)) (- (* y4 c) (* y5 a)))) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0)))))))))))

  (+ (- (+ (+ (- (* (- (* x y) (* z t)) (- (* a b) (* c i))) (* (- (* x j) (* z k)) (- (* y0 b) (* y1 i)))) (* (- (* x y2) (* z y3)) (- (* y0 c) (* y1 a)))) (* (- (* t j) (* y k)) (- (* y4 b) (* y5 i)))) (* (- (* t y2) (* y y3)) (- (* y4 c) (* y5 a)))) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0)))))